diff --git a/RELEASE_NOTES b/RELEASE_NOTES index 67aa3d810..a2b526550 100644 --- a/RELEASE_NOTES +++ b/RELEASE_NOTES @@ -35,7 +35,7 @@ Version 4.7.1 ============= - New requirements: - - uses stdbool and stdint as part of z3.h + - uses stdbool and stdint as part of z3. - New features: - none diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt index d8a773747..9020c9e4b 100644 --- a/src/CMakeLists.txt +++ b/src/CMakeLists.txt @@ -12,7 +12,6 @@ set(Z3_API_HEADER_FILES_TO_SCAN z3_rcf.h z3_fixedpoint.h z3_optimization.h - z3_interp.h z3_fpa.h z3_spacer.h ) @@ -63,7 +62,6 @@ add_subdirectory(sat/tactic) add_subdirectory(tactic/arith) add_subdirectory(nlsat/tactic) add_subdirectory(ackermannization) -add_subdirectory(interp) add_subdirectory(cmd_context) add_subdirectory(cmd_context/extra_cmds) add_subdirectory(parsers/smt2) @@ -79,7 +77,6 @@ add_subdirectory(tactic/bv) add_subdirectory(smt/tactic) add_subdirectory(tactic/sls) add_subdirectory(qe) -add_subdirectory(duality) add_subdirectory(muz/base) add_subdirectory(muz/dataflow) add_subdirectory(muz/transforms) @@ -89,7 +86,6 @@ add_subdirectory(muz/clp) add_subdirectory(muz/tab) add_subdirectory(muz/bmc) add_subdirectory(muz/ddnf) -add_subdirectory(muz/duality) add_subdirectory(muz/spacer) add_subdirectory(muz/fp) add_subdirectory(tactic/ufbv) @@ -159,7 +155,6 @@ set (libz3_public_headers z3_fpa.h z3.h c++/z3++.h - z3_interp.h z3_macros.h z3_optimization.h z3_polynomial.h diff --git a/src/api/CMakeLists.txt b/src/api/CMakeLists.txt index fcdbb1651..4a5514a7b 100644 --- a/src/api/CMakeLists.txt +++ b/src/api/CMakeLists.txt @@ -48,7 +48,6 @@ z3_add_component(api api_datatype.cpp api_fpa.cpp api_goal.cpp - api_interp.cpp api_log.cpp api_model.cpp api_numeral.cpp @@ -67,7 +66,6 @@ z3_add_component(api z3_replayer.cpp ${full_path_generated_files} COMPONENT_DEPENDENCIES - interp opt portfolio realclosure diff --git a/src/api/api_ast.cpp b/src/api/api_ast.cpp index 1f4a86903..536b94fb2 100644 --- a/src/api/api_ast.cpp +++ b/src/api/api_ast.cpp @@ -195,7 +195,6 @@ extern "C" { MK_BINARY(Z3_mk_xor, mk_c(c)->get_basic_fid(), OP_XOR, SKIP); MK_NARY(Z3_mk_and, mk_c(c)->get_basic_fid(), OP_AND, SKIP); MK_NARY(Z3_mk_or, mk_c(c)->get_basic_fid(), OP_OR, SKIP); - MK_UNARY(Z3_mk_interpolant, mk_c(c)->get_basic_fid(), OP_INTERP, SKIP); Z3_ast mk_ite_core(Z3_context c, Z3_ast t1, Z3_ast t2, Z3_ast t3) { expr * result = mk_c(c)->m().mk_ite(to_expr(t1), to_expr(t2), to_expr(t3)); @@ -900,7 +899,6 @@ extern "C" { case OP_NOT: return Z3_OP_NOT; case OP_IMPLIES: return Z3_OP_IMPLIES; case OP_OEQ: return Z3_OP_OEQ; - case OP_INTERP: return Z3_OP_INTERP; case PR_UNDEF: return Z3_OP_PR_UNDEF; case PR_TRUE: return Z3_OP_PR_TRUE; diff --git a/src/api/dotnet/CMakeLists.txt b/src/api/dotnet/CMakeLists.txt index add1b0ded..76516bf39 100644 --- a/src/api/dotnet/CMakeLists.txt +++ b/src/api/dotnet/CMakeLists.txt @@ -80,7 +80,6 @@ set(Z3_DOTNET_ASSEMBLY_SOURCES_IN_SRC_TREE Global.cs Goal.cs IDecRefQueue.cs - InterpolationContext.cs IntExpr.cs IntNum.cs IntSort.cs diff --git a/src/api/dotnet/InterpolationContext.cs b/src/api/dotnet/InterpolationContext.cs deleted file mode 100644 index e2b814983..000000000 --- a/src/api/dotnet/InterpolationContext.cs +++ /dev/null @@ -1,161 +0,0 @@ - -/*++ -Copyright (c) 2015 Microsoft Corporation - ---*/ - -using System; -using System.Collections.Generic; -using System.Linq; -using System.Text; -using System.Diagnostics.Contracts; -using System.Runtime.InteropServices; - -namespace Microsoft.Z3 -{ - /// - /// The InterpolationContext is suitable for generation of interpolants. - /// - /// For more information on interpolation please refer - /// too the C/C++ API, which is well documented. - [ContractVerification(true)] - public class InterpolationContext : Context - { - - /// - /// Constructor. - /// - public InterpolationContext() : base() { } - - /// - /// Constructor. - /// - /// - public InterpolationContext(Dictionary settings) : base(settings) { } - - #region Terms - /// - /// Create an expression that marks a formula position for interpolation. - /// - public BoolExpr MkInterpolant(BoolExpr a) - { - Contract.Requires(a != null); - Contract.Ensures(Contract.Result() != null); - - CheckContextMatch(a); - return new BoolExpr(this, Native.Z3_mk_interpolant(nCtx, a.NativeObject)); - } - #endregion - - /// - /// Computes an interpolant. - /// - /// For more information on interpolation please refer - /// too the function Z3_get_interpolant in the C/C++ API, which is - /// well documented. - public BoolExpr[] GetInterpolant(Expr pf, Expr pat, Params p) - { - Contract.Requires(pf != null); - Contract.Requires(pat != null); - Contract.Requires(p != null); - Contract.Ensures(Contract.Result() != null); - - CheckContextMatch(pf); - CheckContextMatch(pat); - CheckContextMatch(p); - - ASTVector seq = new ASTVector(this, Native.Z3_get_interpolant(nCtx, pf.NativeObject, pat.NativeObject, p.NativeObject)); - return seq.ToBoolExprArray(); - } - - /// - /// Computes an interpolant. - /// - /// For more information on interpolation please refer - /// too the function Z3_compute_interpolant in the C/C++ API, which is - /// well documented. - public Z3_lbool ComputeInterpolant(Expr pat, Params p, out BoolExpr[] interp, out Model model) - { - Contract.Requires(pat != null); - Contract.Requires(p != null); - Contract.Ensures(Contract.ValueAtReturn(out interp) != null); - Contract.Ensures(Contract.ValueAtReturn(out model) != null); - - CheckContextMatch(pat); - CheckContextMatch(p); - - IntPtr i = IntPtr.Zero, m = IntPtr.Zero; - int r = Native.Z3_compute_interpolant(nCtx, pat.NativeObject, p.NativeObject, ref i, ref m); - interp = new ASTVector(this, i).ToBoolExprArray(); - model = new Model(this, m); - return (Z3_lbool)r; - } - - /// - /// Return a string summarizing cumulative time used for interpolation. - /// - /// For more information on interpolation please refer - /// too the function Z3_interpolation_profile in the C/C++ API, which is - /// well documented. - public string InterpolationProfile() - { - return Native.Z3_interpolation_profile(nCtx); - } - - /// - /// Checks the correctness of an interpolant. - /// - /// For more information on interpolation please refer - /// too the function Z3_check_interpolant in the C/C++ API, which is - /// well documented. - public int CheckInterpolant(Expr[] cnsts, uint[] parents, BoolExpr[] interps, out string error, Expr[] theory) - { - Contract.Requires(cnsts.Length == parents.Length); - Contract.Requires(cnsts.Length == interps.Length + 1); - IntPtr n_err_str; - int r = Native.Z3_check_interpolant(nCtx, - (uint)cnsts.Length, - Expr.ArrayToNative(cnsts), - parents, - Expr.ArrayToNative(interps), - out n_err_str, - (uint)theory.Length, - Expr.ArrayToNative(theory)); - error = Marshal.PtrToStringAnsi(n_err_str); - return r; - } - - /// - /// Reads an interpolation problem from a file. - /// - /// For more information on interpolation please refer - /// too the function Z3_read_interpolation_problem in the C/C++ API, which is - /// well documented. - public int ReadInterpolationProblem(string filename, out Expr[] cnsts, out uint[] parents, out string error, out Expr[] theory) - { - uint num = 0; - IntPtr n_err_str; - ASTVector _cnsts = new ASTVector(this); - ASTVector _theory = new ASTVector(this); - - int r = Native.Z3_read_interpolation_problem(nCtx, _cnsts.NativeObject, ref num, out parents, filename, out n_err_str, _theory.NativeObject); - error = Marshal.PtrToStringAnsi(n_err_str); - cnsts = _cnsts.ToExprArray(); - parents = new uint[num]; - theory = _theory.ToExprArray(); - return r; - } - - /// - /// Writes an interpolation problem to a file. - /// - /// For more information on interpolation please refer - /// too the function Z3_write_interpolation_problem in the C/C++ API, which is - /// well documented. - public void WriteInterpolationProblem(string filename, Expr[] cnsts, uint[] parents, Expr[] theory) - { - Contract.Requires(cnsts.Length == parents.Length); - Native.Z3_write_interpolation_problem(nCtx, (uint)cnsts.Length, Expr.ArrayToNative(cnsts), parents, filename, (uint)theory.Length, Expr.ArrayToNative(theory)); - } - } -} diff --git a/src/api/java/CMakeLists.txt b/src/api/java/CMakeLists.txt index dce2bc4ea..7f0774955 100644 --- a/src/api/java/CMakeLists.txt +++ b/src/api/java/CMakeLists.txt @@ -137,7 +137,6 @@ set(Z3_JAVA_JAR_SOURCE_FILES GoalDecRefQueue.java Goal.java IDecRefQueue.java - InterpolationContext.java IntExpr.java IntNum.java IntSort.java diff --git a/src/api/java/InterpolationContext.java b/src/api/java/InterpolationContext.java deleted file mode 100644 index bce789807..000000000 --- a/src/api/java/InterpolationContext.java +++ /dev/null @@ -1,210 +0,0 @@ -/** -Copyright (c) 2012-2014 Microsoft Corporation - -Module Name: - - InterpolationContext.java - -Abstract: - -Author: - - @author Christoph Wintersteiger (cwinter) 2012-03-15 - -Notes: - -**/ - -package com.microsoft.z3; - -import com.microsoft.z3.enumerations.Z3_lbool; - -import java.util.Map; - -/** - * The InterpolationContext is suitable for generation of interpolants. - * - * Remarks: For more information on interpolation please refer - * too the C/C++ API, which is well documented. - **/ -public class InterpolationContext extends Context -{ - /** - * Constructor. - **/ - public static InterpolationContext mkContext() - { - long m_ctx; - synchronized(creation_lock) { - m_ctx = Native.mkInterpolationContext(0); - } - return new InterpolationContext(m_ctx); - } - - /** - * Constructor. - * - * - * Remarks: - * @see Context#Context - **/ - public static InterpolationContext mkContext(Map settings) - { - long m_ctx; - synchronized(creation_lock) { - long cfg = Native.mkConfig(); - for (Map.Entry kv : settings.entrySet()) - Native.setParamValue(cfg, kv.getKey(), kv.getValue()); - m_ctx = Native.mkInterpolationContext(cfg); - Native.delConfig(cfg); - } - return new InterpolationContext(m_ctx); - } - - private InterpolationContext(long m_ctx) { - super(m_ctx); - } - - /** - * Create an expression that marks a formula position for interpolation. - * @throws Z3Exception - **/ - public BoolExpr MkInterpolant(BoolExpr a) - { - checkContextMatch(a); - return new BoolExpr(this, Native.mkInterpolant(nCtx(), a.getNativeObject())); - } - - /** - * Computes an interpolant. - * Remarks: For more information on interpolation please refer - * too the function Z3_get_interpolant in the C/C++ API, which is - * well documented. - * @throws Z3Exception - **/ - public BoolExpr[] GetInterpolant(Expr pf, Expr pat, Params p) - { - checkContextMatch(pf); - checkContextMatch(pat); - checkContextMatch(p); - - ASTVector seq = new ASTVector(this, Native.getInterpolant(nCtx(), pf.getNativeObject(), pat.getNativeObject(), p.getNativeObject())); - return seq.ToBoolExprArray(); - } - - public class ComputeInterpolantResult - { - public Z3_lbool status = Z3_lbool.Z3_L_UNDEF; - public BoolExpr[] interp = null; - public Model model = null; - }; - - /** - * Computes an interpolant. - * Remarks: For more information on interpolation please refer - * too the function Z3_compute_interpolant in the C/C++ API, which is - * well documented. - * @throws Z3Exception - **/ - public ComputeInterpolantResult ComputeInterpolant(Expr pat, Params p) - { - checkContextMatch(pat); - checkContextMatch(p); - - ComputeInterpolantResult res = new ComputeInterpolantResult(); - Native.LongPtr n_i = new Native.LongPtr(); - Native.LongPtr n_m = new Native.LongPtr(); - res.status = Z3_lbool.fromInt(Native.computeInterpolant(nCtx(), pat.getNativeObject(), p.getNativeObject(), n_i, n_m)); - if (res.status == Z3_lbool.Z3_L_FALSE) - res.interp = (new ASTVector(this, n_i.value)).ToBoolExprArray(); - if (res.status == Z3_lbool.Z3_L_TRUE) - res.model = new Model(this, n_m.value); - return res; - } - - /// - /// Return a string summarizing cumulative time used for interpolation. - /// - /// Remarks: For more information on interpolation please refer - /// too the function Z3_interpolation_profile in the C/C++ API, which is - /// well documented. - public String InterpolationProfile() - { - return Native.interpolationProfile(nCtx()); - } - - public class CheckInterpolantResult - { - public int return_value = 0; - public String error = null; - } - - /// - /// Checks the correctness of an interpolant. - /// - /// Remarks: For more information on interpolation please refer - /// too the function Z3_check_interpolant in the C/C++ API, which is - /// well documented. - public CheckInterpolantResult CheckInterpolant(Expr[] cnsts, int[] parents, BoolExpr[] interps, String error, Expr[] theory) - { - CheckInterpolantResult res = new CheckInterpolantResult(); - Native.StringPtr n_err_str = new Native.StringPtr(); - res.return_value = Native.checkInterpolant(nCtx(), - cnsts.length, - Expr.arrayToNative(cnsts), - parents, - Expr.arrayToNative(interps), - n_err_str, - theory.length, - Expr.arrayToNative(theory)); - res.error = n_err_str.value; - return res; - } - - public class ReadInterpolationProblemResult - { - public int return_value = 0; - public Expr[] cnsts; - public int[] parents; - public String error; - public Expr[] theory; - }; - - /// - /// Reads an interpolation problem from a file. - /// - /// Remarks: For more information on interpolation please refer - /// too the function Z3_read_interpolation_problem in the C/C++ API, which is - /// well documented. - public ReadInterpolationProblemResult ReadInterpolationProblem(String filename) - { - ReadInterpolationProblemResult res = new ReadInterpolationProblemResult(); - Native.UIntArrayPtr n_parents = new Native.UIntArrayPtr(); - ASTVector _cnsts = new ASTVector(this); - ASTVector _theory = new ASTVector(this); - Native.StringPtr n_err_str = new Native.StringPtr(); - Native.IntPtr n_num = new Native.IntPtr(); - res.return_value = Native.readInterpolationProblem(nCtx(), _cnsts.getNativeObject(), n_num, - n_parents, filename, n_err_str, _theory.getNativeObject()); - res.error = n_err_str.value; - res.theory = _theory.ToExprArray(); - res.cnsts = _cnsts.ToExprArray(); - int num = n_num.value; - res.parents = new int[num]; - for (int i = 0; i < num; i++) { - res.parents[i] = n_parents.value[i]; - } - return res; - } - - /// - /// Writes an interpolation problem to a file. - /// - /// Remarks: For more information on interpolation please refer - /// too the function Z3_write_interpolation_problem in the C/C++ API, which is - /// well documented. - public void WriteInterpolationProblem(String filename, Expr[] cnsts, int[] parents, String error, Expr[] theory) - { - Native.writeInterpolationProblem(nCtx(), cnsts.length, Expr.arrayToNative(cnsts), parents, filename, theory.length, Expr.arrayToNative(theory)); - } -} diff --git a/src/api/z3.h b/src/api/z3.h index 37ea68f84..382bc4b07 100644 --- a/src/api/z3.h +++ b/src/api/z3.h @@ -32,7 +32,6 @@ Notes: #include "z3_rcf.h" #include "z3_fixedpoint.h" #include "z3_optimization.h" -#include "z3_interp.h" #include "z3_fpa.h" #include "z3_spacer.h" #endif diff --git a/src/api/z3_api.h b/src/api/z3_api.h index d5c279d63..3e47833b4 100644 --- a/src/api/z3_api.h +++ b/src/api/z3_api.h @@ -212,8 +212,6 @@ typedef enum - Z3_OP_OEQ Binary equivalence modulo namings. This binary predicate is used in proof terms. It captures equisatisfiability and equivalence modulo renamings. - - Z3_OP_INTERP Marks a sub-formula for interpolation. - - Z3_OP_ANUM Arithmetic numeral. - Z3_OP_AGNUM Arithmetic algebraic numeral. Algebraic numbers are used to represent irrational numbers in Z3. @@ -991,7 +989,6 @@ typedef enum { Z3_OP_NOT, Z3_OP_IMPLIES, Z3_OP_OEQ, - Z3_OP_INTERP, // Arithmetic Z3_OP_ANUM = 0x200, diff --git a/src/api/z3_interp.h b/src/api/z3_interp.h deleted file mode 100644 index 765870bd5..000000000 --- a/src/api/z3_interp.h +++ /dev/null @@ -1,283 +0,0 @@ -/*++ -Copyright (c) 2014 Microsoft Corporation - -Module Name: - - z3_interp.h - -Abstract: - - API for interpolation - -Author: - - Kenneth McMillan (kenmcmil) - -Notes: - ---*/ -#ifndef Z3_INTERPOLATION_H_ -#define Z3_INTERPOLATION_H_ - -#ifdef __cplusplus -extern "C" { -#endif // __cplusplus - - /** \defgroup capi C API */ - /*@{*/ - - /** @name Interpolation facilities */ - /*@{*/ - /** - \brief Create an AST node marking a formula position for interpolation. - - The node \c a must have Boolean sort. - - def_API('Z3_mk_interpolant', AST, (_in(CONTEXT), _in(AST))) - */ - Z3_ast Z3_API Z3_mk_interpolant(Z3_context c, Z3_ast a); - - - /** \brief This function generates a Z3 context suitable for generation of - interpolants. Formulas can be generated as abstract syntax trees in - this context using the Z3 C API. - - Interpolants are also generated as AST's in this context. - - If cfg is non-null, it will be used as the base configuration - for the Z3 context. This makes it possible to set Z3 options - to be used during interpolation. This feature should be used - with some caution however, as it may be that certain Z3 options - are incompatible with interpolation. - - def_API('Z3_mk_interpolation_context', CONTEXT, (_in(CONFIG),)) - - */ - - Z3_context Z3_API Z3_mk_interpolation_context(Z3_config cfg); - - /** Compute an interpolant from a refutation. This takes a proof of - "false" from a set of formulas C, and an interpolation - pattern. The pattern pat is a formula combining the formulas in C - using logical conjunction and the "interp" operator (see - #Z3_mk_interpolant). This interp operator is logically the identity - operator. It marks the sub-formulas of the pattern for which interpolants should - be computed. The interpolant is a map sigma from marked subformulas to - formulas, such that, for each marked subformula phi of pat (where phi sigma - is phi with sigma(psi) substituted for each subformula psi of phi such that - psi in dom(sigma)): - - 1) phi sigma implies sigma(phi), and - - 2) sigma(phi) is in the common uninterpreted vocabulary between - the formulas of C occurring in phi and those not occurring in - phi - - and moreover pat sigma implies false. In the simplest case - an interpolant for the pattern "(and (interp A) B)" maps A - to an interpolant for A /\ B. - - The return value is a vector of formulas representing sigma. The - vector contains sigma(phi) for each marked subformula of pat, in - pre-order traversal. This means that subformulas of phi occur before phi - in the vector. Also, subformulas that occur multiply in pat will - occur multiply in the result vector. - - In particular, calling Z3_get_interpolant on a pattern of the - form (interp ... (interp (and (interp A_1) A_2)) ... A_N) will - result in a sequence interpolant for A_1, A_2,... A_N. - - Neglecting interp markers, the pattern must be a conjunction of - formulas in C, the set of premises of the proof. Otherwise an - error is flagged. - - Any premises of the proof not present in the pattern are - treated as "background theory". Predicate and function symbols - occurring in the background theory are treated as interpreted and - thus always allowed in the interpolant. - - Interpolant may not necessarily be computable from all - proofs. To be sure an interpolant can be computed, the proof - must be generated by an SMT solver for which interpolation is - supported, and the premises must be expressed using only - theories and operators for which interpolation is supported. - - Currently, the only SMT solver that is supported is the legacy - SMT solver. Such a solver is available as the default solver in - \c Z3_context objects produced by #Z3_mk_interpolation_context. - Currently, the theories supported are equality with - uninterpreted functions, linear integer arithmetic, and the - theory of arrays (in SMT-LIB terms, this is AUFLIA). - Quantifiers are allowed. Use of any other operators (including - "labels") may result in failure to compute an interpolant from a - proof. - - Parameters: - - \param c logical context. - \param pf a refutation from premises (assertions) C - \param pat an interpolation pattern over C - \param p parameters - - def_API('Z3_get_interpolant', AST_VECTOR, (_in(CONTEXT), _in(AST), _in(AST), _in(PARAMS))) - */ - - Z3_ast_vector Z3_API Z3_get_interpolant(Z3_context c, Z3_ast pf, Z3_ast pat, Z3_params p); - - /* Compute an interpolant for an unsatisfiable conjunction of formulas. - - This takes as an argument an interpolation pattern as in - #Z3_get_interpolant. This is a conjunction, some subformulas of - which are marked with the "interp" operator (see #Z3_mk_interpolant). - - The conjunction is first checked for unsatisfiability. The result - of this check is returned in the out parameter "status". If the result - is unsat, an interpolant is computed from the refutation as in #Z3_get_interpolant - and returned as a vector of formulas. Otherwise the return value is - an empty formula. - - See #Z3_get_interpolant for a discussion of supported theories. - - The advantage of this function over #Z3_get_interpolant is that - it is not necessary to create a suitable SMT solver and generate - a proof. The disadvantage is that it is not possible to use the - solver incrementally. - - Parameters: - - \param c logical context. - \param pat an interpolation pattern - \param p parameters for solver creation - \param status returns the status of the sat check - \param model returns model if satisfiable - - Return value: status of SAT check - - def_API('Z3_compute_interpolant', INT, (_in(CONTEXT), _in(AST), _in(PARAMS), _out(AST_VECTOR), _out(MODEL))) - */ - - Z3_lbool Z3_API Z3_compute_interpolant(Z3_context c, - Z3_ast pat, - Z3_params p, - Z3_ast_vector *interp, - Z3_model *model); - - /** Return a string summarizing cumulative time used for - interpolation. This string is purely for entertainment purposes - and has no semantics. - - \param ctx The context (currently ignored) - - - def_API('Z3_interpolation_profile', STRING, (_in(CONTEXT),)) - */ - - Z3_string Z3_API Z3_interpolation_profile(Z3_context ctx); - - /** - \brief Read an interpolation problem from file. - - \param ctx The Z3 context. This resets the error handler of ctx. - \param filename The file name to read. - \param num Returns length of sequence. - \param cnsts Returns sequence of formulas (do not free) - \param parents Returns the parents vector (or NULL for sequence) - \param error Returns an error message in case of failure (do not free the string) - \param num_theory Number of theory terms - \param theory Theory terms - - Returns true on success. - - File formats: Currently two formats are supported, based on - SMT-LIB2. For sequence interpolants, the sequence of constraints is - represented by the sequence of "assert" commands in the file. - - For tree interpolants, one symbol of type bool is associated to - each vertex of the tree. For each vertex v there is an "assert" - of the form: - - (implies (and c1 ... cn f) v) - - where c1 .. cn are the children of v (which must precede v in the file) - and f is the formula associated to node v. The last formula in the - file is the root vertex, and is represented by the predicate "false". - - A solution to a tree interpolation problem can be thought of as a - valuation of the vertices that makes all the implications true - where each value is represented using the common symbols between - the formulas in the subtree and the remainder of the formulas. - - def_API('Z3_read_interpolation_problem', INT, (_in(CONTEXT), _in(AST_VECTOR), _out(UINT), _out_managed_array(2, UINT), _in(STRING), _out(STRING), _in(AST_VECTOR))) - - */ - - int Z3_API Z3_read_interpolation_problem(Z3_context ctx, - Z3_ast_vector cnsts, - unsigned* num, - unsigned* parents[], - Z3_string filename, - Z3_string_ptr error, - Z3_ast_vector theory); - - - - /** Check the correctness of an interpolant. The Z3 context must - have no constraints asserted when this call is made. That means - that after interpolating, you must first fully pop the Z3 - context before calling this. See Z3_interpolate for meaning of parameters. - - \param ctx The Z3 context. Must be generated by Z3_mk_interpolation_context - \param num The number of constraints in the sequence - \param cnsts Array of constraints (AST's in context ctx) - \param parents The parents vector (or NULL for sequence) - \param interps The interpolant to check - \param error Returns an error message if interpolant incorrect (do not free the string) - \param num_theory Number of theory terms - \param theory Theory terms - - Return value is Z3_L_TRUE if interpolant is verified, Z3_L_FALSE if - incorrect, and Z3_L_UNDEF if unknown. - - def_API('Z3_check_interpolant', INT, (_in(CONTEXT), _in(UINT), _in_array(1, AST), _in_array(1, UINT), _in_array(1, AST), _out(STRING), _in(UINT), _in_array(6, AST))) - */ - - int Z3_API Z3_check_interpolant(Z3_context ctx, - unsigned num, - Z3_ast cnsts[], - unsigned parents[], - Z3_ast *interps, - Z3_string_ptr error, - unsigned num_theory, - Z3_ast theory[]); - - /** Write an interpolation problem to file suitable for reading with - Z3_read_interpolation_problem. The output file is a sequence - of SMT-LIB2 format commands, suitable for reading with command-line Z3 - or other interpolating solvers. - - \param ctx The Z3 context. Must be generated by z3_mk_interpolation_context - \param num The number of constraints in the sequence - \param cnsts Array of constraints - \param parents The parents vector (or NULL for sequence) - \param filename The file name to write - \param num_theory Number of theory terms - \param theory Theory terms - - def_API('Z3_write_interpolation_problem', VOID, (_in(CONTEXT), _in(UINT), _in_array(1, AST), _in_array(1, UINT), _in(STRING), _in(UINT), _in_array(5, AST))) - */ - - void Z3_API Z3_write_interpolation_problem(Z3_context ctx, - unsigned num, - Z3_ast cnsts[], - unsigned parents[], - Z3_string filename, - unsigned num_theory, - Z3_ast theory[]); - /*@}*/ - /*@}*/ - -#ifdef __cplusplus -} -#endif // __cplusplus - -#endif diff --git a/src/ast/ast.cpp b/src/ast/ast.cpp index a07be0b22..cae1618c0 100644 --- a/src/ast/ast.cpp +++ b/src/ast/ast.cpp @@ -646,7 +646,6 @@ basic_decl_plugin::basic_decl_plugin(): m_iff_decl(nullptr), m_xor_decl(nullptr), m_not_decl(nullptr), - m_interp_decl(nullptr), m_implies_decl(nullptr), m_proof_sort(nullptr), @@ -865,7 +864,6 @@ void basic_decl_plugin::set_manager(ast_manager * m, family_id id) { m_iff_decl = mk_bool_op_decl("iff", OP_IFF, 2, false, true, false, false, true); m_xor_decl = mk_bool_op_decl("xor", OP_XOR, 2, true, true); m_not_decl = mk_bool_op_decl("not", OP_NOT, 1); - m_interp_decl = mk_bool_op_decl("interp", OP_INTERP, 1); m_implies_decl = mk_implies_decl(); m_proof_sort = m->mk_sort(symbol("Proof"), sort_info(id, PROOF_SORT)); @@ -890,7 +888,6 @@ void basic_decl_plugin::get_op_names(svector & op_names, symbol co op_names.push_back(builtin_name("or", OP_OR)); op_names.push_back(builtin_name("xor", OP_XOR)); op_names.push_back(builtin_name("not", OP_NOT)); - op_names.push_back(builtin_name("interp", OP_INTERP)); op_names.push_back(builtin_name("=>", OP_IMPLIES)); if (logic == symbol::null) { // user friendly aliases @@ -902,7 +899,6 @@ void basic_decl_plugin::get_op_names(svector & op_names, symbol co op_names.push_back(builtin_name("||", OP_OR)); op_names.push_back(builtin_name("equals", OP_EQ)); op_names.push_back(builtin_name("equiv", OP_IFF)); - op_names.push_back(builtin_name("@@", OP_INTERP)); } } @@ -923,7 +919,6 @@ void basic_decl_plugin::finalize() { DEC_REF(m_and_decl); DEC_REF(m_or_decl); DEC_REF(m_not_decl); - DEC_REF(m_interp_decl); DEC_REF(m_iff_decl); DEC_REF(m_xor_decl); DEC_REF(m_implies_decl); @@ -1056,7 +1051,6 @@ func_decl * basic_decl_plugin::mk_func_decl(decl_kind k, unsigned num_parameters case OP_AND: return m_and_decl; case OP_OR: return m_or_decl; case OP_NOT: return m_not_decl; - case OP_INTERP: return m_interp_decl; case OP_IFF: return m_iff_decl; case OP_IMPLIES: return m_implies_decl; case OP_XOR: return m_xor_decl; @@ -1099,7 +1093,6 @@ func_decl * basic_decl_plugin::mk_func_decl(decl_kind k, unsigned num_parameters case OP_AND: return m_and_decl; case OP_OR: return m_or_decl; case OP_NOT: return m_not_decl; - case OP_INTERP: return m_interp_decl; case OP_IFF: return m_iff_decl; case OP_IMPLIES: return m_implies_decl; case OP_XOR: return m_xor_decl; diff --git a/src/ast/ast.h b/src/ast/ast.h index 2db0fde04..e85f164e1 100644 --- a/src/ast/ast.h +++ b/src/ast/ast.h @@ -1041,7 +1041,7 @@ enum basic_sort_kind { }; enum basic_op_kind { - OP_TRUE, OP_FALSE, OP_EQ, OP_DISTINCT, OP_ITE, OP_AND, OP_OR, OP_IFF, OP_XOR, OP_NOT, OP_IMPLIES, OP_OEQ, OP_INTERP, LAST_BASIC_OP, + OP_TRUE, OP_FALSE, OP_EQ, OP_DISTINCT, OP_ITE, OP_AND, OP_OR, OP_IFF, OP_XOR, OP_NOT, OP_IMPLIES, OP_OEQ, LAST_BASIC_OP, PR_UNDEF, PR_TRUE, PR_ASSERTED, PR_GOAL, PR_MODUS_PONENS, PR_REFLEXIVITY, PR_SYMMETRY, PR_TRANSITIVITY, PR_TRANSITIVITY_STAR, PR_MONOTONICITY, PR_QUANT_INTRO, PR_DISTRIBUTIVITY, PR_AND_ELIM, PR_NOT_OR_ELIM, PR_REWRITE, PR_REWRITE_STAR, PR_PULL_QUANT, @@ -1063,7 +1063,6 @@ protected: func_decl * m_iff_decl; func_decl * m_xor_decl; func_decl * m_not_decl; - func_decl * m_interp_decl; func_decl * m_implies_decl; ptr_vector m_eq_decls; // cached eqs ptr_vector m_ite_decls; // cached ites @@ -2054,7 +2053,6 @@ public: app * mk_true() const { return m_true; } app * mk_false() const { return m_false; } app * mk_bool_val(bool b) { return b?m_true:m_false; } - app * mk_interp(expr * arg) { return mk_app(m_basic_family_id, OP_INTERP, arg); } func_decl* mk_and_decl() { diff --git a/src/cmd_context/CMakeLists.txt b/src/cmd_context/CMakeLists.txt index f7b888343..8da871f9a 100644 --- a/src/cmd_context/CMakeLists.txt +++ b/src/cmd_context/CMakeLists.txt @@ -8,14 +8,12 @@ z3_add_component(cmd_context context_params.cpp echo_tactic.cpp eval_cmd.cpp - interpolant_cmds.cpp parametric_cmd.cpp pdecl.cpp simplify_cmd.cpp tactic_cmds.cpp tactic_manager.cpp COMPONENT_DEPENDENCIES - interp rewriter solver EXTRA_REGISTER_MODULE_HEADERS diff --git a/src/cmd_context/cmd_context.cpp b/src/cmd_context/cmd_context.cpp index e42f884d6..7d2b2f17a 100644 --- a/src/cmd_context/cmd_context.cpp +++ b/src/cmd_context/cmd_context.cpp @@ -46,7 +46,6 @@ Notes: #include "tactic/generic_model_converter.h" #include "solver/smt_logics.h" #include "cmd_context/basic_cmds.h" -#include "cmd_context/interpolant_cmds.h" #include "cmd_context/cmd_context.h" func_decls::func_decls(ast_manager & m, func_decl * f): @@ -484,7 +483,6 @@ cmd_context::cmd_context(bool main_ctx, ast_manager * m, symbol const & l): install_basic_cmds(*this); install_ext_basic_cmds(*this); install_core_tactic_cmds(*this); - install_interpolant_cmds(*this); SASSERT(m != 0 || !has_manager()); if (m_main_ctx) { set_verbose_stream(diagnostic_stream()); diff --git a/src/cmd_context/interpolant_cmds.cpp b/src/cmd_context/interpolant_cmds.cpp deleted file mode 100644 index dd1d0acec..000000000 --- a/src/cmd_context/interpolant_cmds.cpp +++ /dev/null @@ -1,263 +0,0 @@ -/*++ - Copyright (c) 2013 Microsoft Corporation - - Module Name: - - interpolant_cmds.cpp - - Abstract: - Commands for interpolation. - - Author: - - Leonardo (leonardo) 2011-12-23 - - Notes: - - --*/ -#include -#include "cmd_context/cmd_context.h" -#include "cmd_context/cmd_util.h" -#include "util/scoped_timer.h" -#include "util/scoped_ctrl_c.h" -#include "util/cancel_eh.h" -#include "ast/ast_pp.h" -#include "ast/ast_smt_pp.h" -#include "ast/ast_smt2_pp.h" -#include "cmd_context/parametric_cmd.h" -#include "util/mpq.h" -#include "ast/expr2var.h" -#include "ast/pp.h" -#include "interp/iz3interp.h" -#include "interp/iz3checker.h" -#include "interp/iz3profiling.h" -#include "interp/interp_params.hpp" -#include "ast/scoped_proof.h" - -static void show_interpolant_and_maybe_check(cmd_context & ctx, - ptr_vector &cnsts, - expr *t, - ptr_vector &interps, - params_ref &m_params, - bool check) -{ - - if (m_params.get_bool("som", false)) - m_params.set_bool("flat", true); - th_rewriter s(ctx.m(), m_params); - - ctx.regular_stream() << "(interpolants"; - for(unsigned i = 0; i < interps.size(); i++){ - expr_ref r(ctx.m()); - proof_ref pr(ctx.m()); - s(to_expr(interps[i]),r,pr); - ctx.regular_stream() << "\n " << r; - } - ctx.regular_stream() << ")\n"; - - s.cleanup(); - - // verify, for the paranoid... - if(check || interp_params(m_params).check()){ - std::ostringstream err; - ast_manager &_m = ctx.m(); - - // need a solver -- make one here FIXME is this right? - bool proofs_enabled, models_enabled, unsat_core_enabled; - params_ref p; - ctx.params().get_solver_params(_m, p, proofs_enabled, models_enabled, unsat_core_enabled); - scoped_ptr sp = (ctx.get_solver_factory())(_m, p, false, true, false, ctx.get_logic()); - - if(iz3check(_m,sp.get(),err,cnsts,t,interps)) - ctx.regular_stream() << "correct\n"; - else - ctx.regular_stream() << "incorrect: " << err.str().c_str() << "\n"; - } - - for(unsigned i = 0; i < interps.size(); i++){ - ctx.m().dec_ref(interps[i]); - } - - interp_params itp_params(m_params); - if(itp_params.profile()) - profiling::print(ctx.regular_stream()); - -} - -static void check_can_interpolate(cmd_context & ctx){ - if (!ctx.produce_interpolants()) - throw cmd_exception("interpolation is not enabled, use command (set-option :produce-interpolants true)"); -} - - -static void get_interpolant_and_maybe_check(cmd_context & ctx, expr * t, params_ref &m_params, bool check) { - - check_can_interpolate(ctx); - - // get the proof, if there is one - - if (!ctx.has_manager() || - ctx.cs_state() != cmd_context::css_unsat) - throw cmd_exception("proof is not available"); - expr_ref pr(ctx.m()); - pr = ctx.get_check_sat_result()->get_proof(); - if (pr == 0) - throw cmd_exception("proof is not available"); - - // get the assertions from the context - - ptr_vector::const_iterator it = ctx.begin_assertions(); - ptr_vector::const_iterator end = ctx.end_assertions(); - ptr_vector cnsts((unsigned)(end - it)); - for (int i = 0; it != end; ++it, ++i) - cnsts[i] = *it; - - // compute an interpolant - - ptr_vector interps; - - try { - iz3interpolate(ctx.m(),pr.get(),cnsts,t,interps,nullptr); - } - catch (iz3_bad_tree &) { - throw cmd_exception("interpolation pattern contains non-asserted formula"); - } - catch (iz3_incompleteness &) { - throw cmd_exception("incompleteness in interpolator"); - } - - show_interpolant_and_maybe_check(ctx, cnsts, t, interps, m_params, check); -} - -static void get_interpolant(cmd_context & ctx, expr * t, params_ref &m_params) { - get_interpolant_and_maybe_check(ctx,t,m_params,false); -} - -#if 0 -static void get_and_check_interpolant(cmd_context & ctx, params_ref &m_params, expr * t) { - get_interpolant_and_maybe_check(ctx,t,m_params,true); -} -#endif - -static void compute_interpolant_and_maybe_check(cmd_context & ctx, expr * t, params_ref &m_params, bool check){ - - // create a fresh solver suitable for interpolation - bool proofs_enabled, models_enabled, unsat_core_enabled; - params_ref p; - ast_manager &_m = ctx.m(); - // TODO: the following is a HACK to enable proofs in the old smt solver - // When we stop using that solver, this hack can be removed - scoped_proof_mode spm(_m,PGM_ENABLED); - ctx.params().get_solver_params(_m, p, proofs_enabled, models_enabled, unsat_core_enabled); - p.set_bool("proof", true); - scoped_ptr sp = (ctx.get_interpolating_solver_factory())(_m, p, true, models_enabled, false, ctx.get_logic()); - - ptr_vector cnsts; - ptr_vector interps; - model_ref m; - - // compute an interpolant - - lbool res; - try { - res = iz3interpolate(_m, *sp.get(), t, cnsts, interps, m, nullptr); - } - catch (iz3_incompleteness &) { - throw cmd_exception("incompleteness in interpolator"); - } - - switch(res){ - case l_false: - ctx.regular_stream() << "unsat\n"; - show_interpolant_and_maybe_check(ctx, cnsts, t, interps, m_params, check); - break; - - case l_true: - ctx.regular_stream() << "sat\n"; - // TODO: how to return the model to the context, if it exists? - break; - - case l_undef: - ctx.regular_stream() << "unknown\n"; - // TODO: how to return the model to the context, if it exists? - break; - } - - for(unsigned i = 0; i < cnsts.size(); i++) - ctx.m().dec_ref(cnsts[i]); - -} - -static expr *make_tree(cmd_context & ctx, const ptr_vector &exprs){ - if(exprs.size() == 0) - throw cmd_exception("not enough arguments"); - expr *foo = exprs[0]; - for(unsigned i = 1; i < exprs.size(); i++){ - foo = ctx.m().mk_and(ctx.m().mk_interp(foo),exprs[i]); - } - return foo; -} - -static void get_interpolant(cmd_context & ctx, const ptr_vector &exprs, params_ref &m_params) { - expr_ref foo(make_tree(ctx, exprs),ctx.m()); - get_interpolant(ctx,foo.get(),m_params); -} - -static void compute_interpolant(cmd_context & ctx, const ptr_vector &exprs, params_ref &m_params) { - expr_ref foo(make_tree(ctx, exprs),ctx.m()); - compute_interpolant_and_maybe_check(ctx,foo.get(),m_params,false); -} - - -// UNARY_CMD(get_interpolant_cmd, "get-interpolant", "", "get interpolant for marked positions in fmla", CPK_EXPR, expr *, get_interpolant(ctx, arg);); - -// UNARY_CMD(get_and_check_interpolant_cmd, "get-and-check-interpolant", "", "get and check interpolant for marked positions in fmla", CPK_EXPR, expr *, get_and_check_interpolant(ctx, arg);); - -class get_interpolant_cmd : public parametric_cmd { -protected: - ptr_vector m_targets; -public: - get_interpolant_cmd(char const * name = "get-interpolant"):parametric_cmd(name) {} - - char const * get_usage() const override { return "+"; } - - char const * get_main_descr() const override { - return "get interpolant for formulas"; - } - - void init_pdescrs(cmd_context & ctx, param_descrs & p) override { - } - - void prepare(cmd_context & ctx) override { - parametric_cmd::prepare(ctx); - m_targets.resize(0); - } - - cmd_arg_kind next_arg_kind(cmd_context & ctx) const override { - return CPK_EXPR; - } - - void set_next_arg(cmd_context & ctx, expr * arg) override { - m_targets.push_back(arg); - } - - void execute(cmd_context & ctx) override { - get_interpolant(ctx,m_targets,m_params); - } -}; - -class compute_interpolant_cmd : public get_interpolant_cmd { -public: - compute_interpolant_cmd(char const * name = "compute-interpolant"):get_interpolant_cmd(name) {} - - void execute(cmd_context & ctx) override { - compute_interpolant(ctx,m_targets,m_params); - } - -}; - -void install_interpolant_cmds(cmd_context & ctx) { - ctx.insert(alloc(get_interpolant_cmd)); - ctx.insert(alloc(compute_interpolant_cmd)); - // ctx.insert(alloc(get_and_check_interpolant_cmd)); -} diff --git a/src/cmd_context/interpolant_cmds.h b/src/cmd_context/interpolant_cmds.h deleted file mode 100644 index daef70926..000000000 --- a/src/cmd_context/interpolant_cmds.h +++ /dev/null @@ -1,24 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - interpolant_cmds.h - - Abstract: - Commands for interpolation. - - Author: - - Leonardo (leonardo) 2011-12-23 - - Notes: - - --*/ -#ifndef INTERPOLANT_CMDS_H_ -#define INTERPOLANT_CMDS_H_ - -class cmd_context; -void install_interpolant_cmds(cmd_context & ctx); - -#endif diff --git a/src/duality/CMakeLists.txt b/src/duality/CMakeLists.txt deleted file mode 100644 index eb2d5c4f2..000000000 --- a/src/duality/CMakeLists.txt +++ /dev/null @@ -1,11 +0,0 @@ -z3_add_component(duality - SOURCES - duality_profiling.cpp - duality_rpfp.cpp - duality_solver.cpp - duality_wrapper.cpp - COMPONENT_DEPENDENCIES - interp - qe - smt -) diff --git a/src/duality/duality.h b/src/duality/duality.h deleted file mode 100644 index 9bf323d8b..000000000 --- a/src/duality/duality.h +++ /dev/null @@ -1,1365 +0,0 @@ -/*++ - Copyright (c) 2012 Microsoft Corporation - - Module Name: - - duality.h - - Abstract: - - main header for duality - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - - --*/ - -#pragma once - -#include "duality/duality_wrapper.h" -#include -#include -#include - -// make hash_map and hash_set available -using namespace stl_ext; - -namespace Duality { - - struct implicant_solver; - - /* Generic operations on Z3 formulas */ - - struct Z3User { - - context &ctx; - - typedef func_decl FuncDecl; - typedef expr Term; - - Z3User(context &_ctx) : ctx(_ctx){} - - const char *string_of_int(int n); - - Term conjoin(const std::vector &args); - - Term sum(const std::vector &args); - - Term CloneQuantifier(const Term &t, const Term &new_body); - - Term SubstRec(hash_map &memo, const Term &t); - - Term SubstRec(hash_map &memo, hash_map &map, const Term &t); - - void Strengthen(Term &x, const Term &y); - - // return the func_del of an app if it is uninterpreted - - bool get_relation(const Term &t, func_decl &R); - - // return true if term is an individual variable - // TODO: have to check that it is not a background symbol - - bool is_variable(const Term &t); - - FuncDecl SuffixFuncDecl(const Term &t, int n); - - - Term SubstRecHide(hash_map &memo, const Term &t, int number); - - void CollectConjuncts(const Term &f, std::vector &lits, bool pos = true); - - void SortTerms(std::vector &terms); - - Term SortSum(const Term &t); - - void Summarize(const Term &t); - - int CountOperators(const Term &t); - - Term SubstAtom(hash_map &memo, const expr &t, const expr &atom, const expr &val); - - Term CloneQuantAndSimp(const expr &t, const expr &body); - - Term RemoveRedundancy(const Term &t); - - Term IneqToEq(const Term &t); - - bool IsLiteral(const expr &lit, expr &atom, expr &val); - - expr Negate(const expr &f); - - expr SimplifyAndOr(const std::vector &args, bool is_and); - - expr ReallySimplifyAndOr(const std::vector &args, bool is_and); - - int MaxIndex(hash_map &memo, const Term &t); - - bool IsClosedFormula(const Term &t); - - Term AdjustQuantifiers(const Term &t); - - FuncDecl RenumberPred(const FuncDecl &f, int n); - - FuncDecl NumberPred(const FuncDecl &f, int n); - - Term ExtractStores(hash_map &memo, const Term &t, std::vector &cnstrs, hash_map &renaming); - - - protected: - - void SummarizeRec(hash_set &memo, std::vector &lits, int &ops, const Term &t); - int CountOperatorsRec(hash_set &memo, const Term &t); - void RemoveRedundancyOp(bool pol, std::vector &args, hash_map &smemo); - Term RemoveRedundancyRec(hash_map &memo, hash_map &smemo, const Term &t); - Term SubstAtomTriv(const expr &foo, const expr &atom, const expr &val); - expr ReduceAndOr(const std::vector &args, bool is_and, std::vector &res); - expr FinishAndOr(const std::vector &args, bool is_and); - expr PullCommonFactors(std::vector &args, bool is_and); - Term IneqToEqRec(hash_map &memo, const Term &t); - Term CloneQuantAndSimp(const expr &t, const expr &body, bool is_forall); - Term PushQuantifier(const expr &t, const expr &body, bool is_forall); - void CollectJuncts(const Term &f, std::vector &lits, decl_kind op, bool negate); - Term DeleteBoundRec(hash_map > &memo, int level, int num, const Term &t); - Term DeleteBound(int level, int num, const Term &t); - - }; - - /** This class represents a relation post-fixed point (RPFP) problem as - * a "problem graph". The graph consists of Nodes and hyper-edges. - * - * A node consists of - * - Annotation, a symbolic relation - * - Bound, a symbolic relation giving an upper bound on Annotation - * - * - * A hyper-edge consists of: - * - Children, a sequence of children Nodes, - * - F, a symbolic relational transformer, - * - Parent, a single parent Node. - * - * The graph is "solved" when: - * - For every Node n, n.Annotation subseteq n.Bound - * - For every hyperedge e, e.F(e.Children.Annotation) subseteq e.Parent.Annotation - * - * where, if x is a sequence of Nodes, x.Annotation is the sequences - * of Annotations of the nodes in the sequence. - * - * A symbolic Transformer consists of - * - RelParams, a sequence of relational symbols - * - IndParams, a sequence of individual symbols - * - Formula, a formula over RelParams and IndParams - * - * A Transformer t represents a function that takes sequence R of relations - * and yields the relation lambda (t.Indparams). Formula(R/RelParams). - * - * As a special case, a nullary Transformer (where RelParams is the empty sequence) - * represents a fixed relation. - * - * An RPFP consists of - * - Nodes, a set of Nodes - * - Edges, a set of hyper-edges - * - Context, a prover context that contains formula AST's - * - * Multiple RPFP's can use the same Context, but you should be careful - * that only one RPFP asserts constraints in the context at any time. - * - * */ - class RPFP : public Z3User - { - public: - - class Edge; - class Node; - bool HornClauses; - - - /** Interface class for interpolating solver. */ - - class LogicSolver { - public: - - context *ctx; /** Z3 context for formulas */ - solver *slvr; /** Z3 solver */ - bool need_goals; /** Can the solver use the goal tree to optimize interpolants? */ - solver aux_solver; /** For temporary use -- don't leave assertions here. */ - - /** Tree interpolation. This method assumes the formulas in TermTree - "assumptions" are currently asserted in the solver. The return - value indicates whether the assertions are satisfiable. In the - UNSAT case, a tree interpolant is returned in "interpolants". - In the SAT case, a model is returned. - */ - - virtual - lbool interpolate_tree(TermTree *assumptions, - TermTree *&interpolants, - model &_model, - TermTree *goals = nullptr, - bool weak = false - ) = 0; - - /** Declare a constant in the background theory. */ - virtual void declare_constant(const func_decl &f) = 0; - - /** Is this a background constant? */ - virtual bool is_constant(const func_decl &f) = 0; - - /** Get the constants in the background vocabulary */ - virtual hash_set &get_constants() = 0; - - /** Assert a background axiom. */ - virtual void assert_axiom(const expr &axiom) = 0; - - /** Get the background axioms. */ - virtual const std::vector &get_axioms() = 0; - - /** Return a string describing performance. */ - virtual std::string profile() = 0; - - virtual void write_interpolation_problem(const std::string &file_name, - const std::vector &assumptions, - const std::vector &theory - ){} - - /** Cancel, throw Canceled object if possible. */ - virtual void cancel(){ } - - /* Note: aux solver uses extensional array theory, since it - needs to be able to produce counter-models for - interpolants the have array equalities in them. - */ - LogicSolver(context &c) : aux_solver(c,true){} - - virtual ~LogicSolver(){} - }; - - /** This solver uses iZ3. */ - class iZ3LogicSolver : public LogicSolver { - public: - interpolating_context *ictx; /** iZ3 context for formulas */ - interpolating_solver *islvr; /** iZ3 solver */ - - lbool interpolate_tree(TermTree *assumptions, - TermTree *&interpolants, - model &_model, - TermTree *goals = nullptr, - bool weak = false) override - { - literals _labels; - islvr->SetWeakInterpolants(weak); - return islvr->interpolate_tree(assumptions,interpolants,_model,_labels,true); - } - - void assert_axiom(const expr &axiom) override { -#if 1 - // HACK: large "distict" predicates can kill the legacy SMT solver. - // encode them with a UIF - if(axiom.is_app() && axiom.decl().get_decl_kind() == Distinct) - if(axiom.num_args() > 10){ - sort s = axiom.arg(0).get_sort(); - std::vector sv; - sv.push_back(s); - int nargs = axiom.num_args(); - std::vector args(nargs); - func_decl f = ctx->fresh_func_decl("@distinct",sv,ctx->int_sort()); - for(int i = 0; i < nargs; i++){ - expr a = axiom.arg(i); - expr new_cnstr = f(a) == ctx->int_val(i); - args[i] = new_cnstr; - } - expr cnstr = ctx->make(And,args); - islvr->AssertInterpolationAxiom(cnstr); - return; - } -#endif - islvr->AssertInterpolationAxiom(axiom); - } - - const std::vector &get_axioms() override { - return islvr->GetInterpolationAxioms(); - } - - std::string profile() override { - return islvr->profile(); - } - -#if 0 - iZ3LogicSolver(config &_config){ - ctx = ictx = new interpolating_context(_config); - slvr = islvr = new interpolating_solver(*ictx); - need_goals = false; - islvr->SetWeakInterpolants(true); - } -#endif - - iZ3LogicSolver(context &c, bool models = true) : LogicSolver(c) { - ctx = ictx = &c; - slvr = islvr = new interpolating_solver(*ictx, models); - need_goals = false; - islvr->SetWeakInterpolants(true); - } - - void write_interpolation_problem(const std::string &file_name, - const std::vector &assumptions, - const std::vector &theory - ) override { -#if 0 - islvr->write_interpolation_problem(file_name,assumptions,theory); -#endif - - } - - void cancel() override {islvr->cancel();} - - /** Declare a constant in the background theory. */ - void declare_constant(const func_decl &f) override { - bckg.insert(f); - } - - /** Is this a background constant? */ - bool is_constant(const func_decl &f) override { - return bckg.find(f) != bckg.end(); - } - - /** Get the constants in the background vocabulary */ - hash_set &get_constants() override { - return bckg; - } - - ~iZ3LogicSolver() override { - // delete ictx; - delete islvr; - } - private: - hash_set bckg; - - }; - -#if 0 - /** Create a logic solver from a Z3 configuration. */ - static iZ3LogicSolver *CreateLogicSolver(config &_config){ - return new iZ3LogicSolver(_config); - } -#endif - - /** Create a logic solver from a low-level Z3 context. - Only use this if you know what you're doing. */ - static iZ3LogicSolver *CreateLogicSolver(context c){ - return new iZ3LogicSolver(c); - } - - LogicSolver *ls; - - protected: - int nodeCount; - int edgeCount; - - class stack_entry - { - public: - std::list edges; - std::list nodes; - std::list > constraints; - }; - - - public: - model dualModel; - protected: - literals dualLabels; - std::list stack; - std::vector axioms; // only saved here for printing purposes - solver &aux_solver; - hash_set *proof_core; - - public: - - /** Construct an RPFP graph with a given interpolating prover context. It is allowed to - have multiple RPFP's use the same context, but you should never have teo RPFP's - with the same conext asserting nodes or edges at the same time. Note, if you create - axioms in one RPFP, them create a second RPFP with the same context, the second will - inherit the axioms. - */ - - RPFP(LogicSolver *_ls) : Z3User(*(_ls->ctx)), dualModel(*(_ls->ctx)), aux_solver(_ls->aux_solver) - { - ls = _ls; - nodeCount = 0; - edgeCount = 0; - stack.push_back(stack_entry()); - HornClauses = false; - proof_core = nullptr; - } - - virtual ~RPFP(); - - /** Symbolic representation of a relational transformer */ - class Transformer - { - public: - std::vector RelParams; - std::vector IndParams; - Term Formula; - RPFP *owner; - hash_map labels; - - Transformer *Clone() - { - return new Transformer(*this); - } - - void SetEmpty(){ - Formula = owner->ctx.bool_val(false); - } - - void SetFull(){ - Formula = owner->ctx.bool_val(true); - } - - bool IsEmpty(){ - return eq(Formula,owner->ctx.bool_val(false)); - } - - bool IsFull(){ - return eq(Formula,owner->ctx.bool_val(true)); - } - - void UnionWith(const Transformer &other){ - Term t = owner->SubstParams(other.IndParams,IndParams,other.Formula); - Formula = Formula || t; - } - - void IntersectWith(const Transformer &other){ - Term t = owner->SubstParams(other.IndParams,IndParams,other.Formula); - Formula = Formula && t; - } - - bool SubsetEq(const Transformer &other){ - Term t = owner->SubstParams(other.IndParams,IndParams,other.Formula); - expr test = Formula && !t; - owner->aux_solver.push(); - owner->aux_solver.add(test); - check_result res = owner->aux_solver.check(); - owner->aux_solver.pop(1); - return res == unsat; - } - - void Complement(){ - Formula = !Formula; - } - - void Simplify(){ - Formula = Formula.simplify(); - } - - Transformer(const std::vector &_RelParams, const std::vector &_IndParams, const Term &_Formula, RPFP *_owner) - : RelParams(_RelParams), IndParams(_IndParams), Formula(_Formula) {owner = _owner;} - }; - - /** Create a symbolic transformer. */ - Transformer CreateTransformer(const std::vector &_RelParams, const std::vector &_IndParams, const Term &_Formula) - { - // var ops = new Util.ContextOps(ctx); - // var foo = ops.simplify_lhs(_Formula); - // t.Formula = foo.Item1; - // t.labels = foo.Item2; - return Transformer(_RelParams,_IndParams,_Formula,this); - } - - /** Create a relation (nullary relational transformer) */ - Transformer CreateRelation(const std::vector &_IndParams, const Term &_Formula) - { - return CreateTransformer(std::vector(), _IndParams, _Formula); - } - - /** A node in the RPFP graph */ - class Node - { - public: - FuncDecl Name; - Transformer Annotation; - Transformer Bound; - Transformer Underapprox; - RPFP *owner; - int number; - Edge *Outgoing; - std::vector Incoming; - Term dual; - Node *map; - unsigned recursion_bound; - - Node(const FuncDecl &_Name, const Transformer &_Annotation, const Transformer &_Bound, const Transformer &_Underapprox, const Term &_dual, RPFP *_owner, int _number) - : Name(_Name), Annotation(_Annotation), Bound(_Bound), Underapprox(_Underapprox), dual(_dual) {owner = _owner; number = _number; Outgoing = nullptr; recursion_bound = UINT_MAX;} - }; - - /** Create a node in the graph. The input is a term R(v_1...v_n) - * where R is an arbitrary relational symbol and v_1...v_n are - * arbitary distinct variables. The names are only of mnemonic value, - * however, the number and type of arguments determine the type - * of the relation at this node. */ - - Node *CreateNode(const Term &t) - { - std::vector _IndParams; - int nargs = t.num_args(); - _IndParams.reserve(nargs); - for(int i = 0; i < nargs; i++) - _IndParams.push_back(t.arg(i)); - Node *n = new Node(t.decl(), - CreateRelation(_IndParams,ctx.bool_val(true)), - CreateRelation(_IndParams,ctx.bool_val(true)), - CreateRelation(_IndParams,ctx.bool_val(false)), - expr(ctx), this, ++nodeCount - ); - nodes.push_back(n); - return n; - } - - /** Clone a node (can be from another graph). */ - - Node *CloneNode(Node *old) - { - Node *n = new Node(old->Name, - old->Annotation, - old->Bound, - old->Underapprox, - expr(ctx), - this, - ++nodeCount - ); - nodes.push_back(n); - n->map = old; - return n; - } - - /** Delete a node. You can only do this if not connected to any edges.*/ - void DeleteNode(Node *node){ - if(node->Outgoing || !node->Incoming.empty()) - throw "cannot delete RPFP node"; - for(std::vector::iterator it = nodes.end(), en = nodes.begin(); it != en;){ - if(*(--it) == node){ - nodes.erase(it); - break; - } - } - delete node; - } - - /** This class represents a hyper-edge in the RPFP graph */ - - class Edge - { - public: - Transformer F; - Node *Parent; - std::vector Children; - RPFP *owner; - int number; - // these should be internal... - Term dual; - hash_map relMap; - hash_map varMap; - Edge *map; - Term labeled; - std::vector constraints; - - Edge(Node *_Parent, const Transformer &_F, const std::vector &_Children, RPFP *_owner, int _number) - : F(_F), Parent(_Parent), Children(_Children), dual(expr(_owner->ctx)) { - owner = _owner; - number = _number; - } - }; - - - /** Create a hyper-edge. */ - Edge *CreateEdge(Node *_Parent, const Transformer &_F, const std::vector &_Children) - { - Edge *e = new Edge(_Parent,_F,_Children,this,++edgeCount); - _Parent->Outgoing = e; - for(unsigned i = 0; i < _Children.size(); i++) - _Children[i]->Incoming.push_back(e); - edges.push_back(e); - return e; - } - - - /** Delete a hyper-edge and unlink it from any nodes. */ - void DeleteEdge(Edge *edge){ - if(edge->Parent) - edge->Parent->Outgoing = nullptr; - for(unsigned int i = 0; i < edge->Children.size(); i++){ - std::vector &ic = edge->Children[i]->Incoming; - for(std::vector::iterator it = ic.begin(), en = ic.end(); it != en; ++it){ - if(*it == edge){ - ic.erase(it); - break; - } - } - } - for(std::vector::iterator it = edges.end(), en = edges.begin(); it != en;){ - if(*(--it) == edge){ - edges.erase(it); - break; - } - } - delete edge; - } - - /** Create an edge that lower-bounds its parent. */ - Edge *CreateLowerBoundEdge(Node *_Parent) - { - return CreateEdge(_Parent, _Parent->Annotation, std::vector()); - } - - - /** For incremental solving, asserts the constraint associated - * with this edge in the SMT context. If this edge is removed, - * you must pop the context accordingly. The second argument is - * the number of pushes we are inside. */ - - virtual void AssertEdge(Edge *e, int persist = 0, bool with_children = false, bool underapprox = false); - - /* Constrain an edge by the annotation of one of its children. */ - - void ConstrainParent(Edge *parent, Node *child); - - /** For incremental solving, asserts the negation of the upper bound associated - * with a node. - * */ - - void AssertNode(Node *n); - - /** Assert a constraint on an edge in the SMT context. - */ - void ConstrainEdge(Edge *e, const Term &t); - - /** Fix the truth values of atomic propositions in the given - edge to their values in the current assignment. */ - void FixCurrentState(Edge *root); - - void FixCurrentStateFull(Edge *edge, const expr &extra); - - void FixCurrentStateFull(Edge *edge, const std::vector &assumps, const hash_map &renaming); - - /** Declare a constant in the background theory. */ - - void DeclareConstant(const FuncDecl &f); - - /** Assert a background axiom. Background axioms can be used to provide the - * theory of auxilliary functions or relations. All symbols appearing in - * background axioms are considered global, and may appear in both transformer - * and relational solutions. Semantically, a solution to the RPFP gives - * an interpretation of the unknown relations for each interpretation of the - * auxilliary symbols that is consistent with the axioms. Axioms should be - * asserted before any calls to Push. They cannot be de-asserted by Pop. */ - - void AssertAxiom(const Term &t); - -#if 0 - /** Do not call this. */ - - void RemoveAxiom(const Term &t); -#endif - - /** Solve an RPFP graph. This means either strengthen the annotation - * so that the bound at the given root node is satisfied, or - * show that this cannot be done by giving a dual solution - * (i.e., a counterexample). - * - * In the current implementation, this only works for graphs that - * are: - * - tree-like - * - * - closed. - * - * In a tree-like graph, every nod has out most one incoming and one out-going edge, - * and there are no cycles. In a closed graph, every node has exactly one out-going - * edge. This means that the leaves of the tree are all hyper-edges with no - * children. Such an edge represents a relation (nullary transformer) and thus - * a lower bound on its parent. The parameter root must be the root of this tree. - * - * If Solve returns LBool.False, this indicates success. The annotation of the tree - * has been updated to satisfy the upper bound at the root. - * - * If Solve returns LBool.True, this indicates a counterexample. For each edge, - * you can then call Eval to determine the values of symbols in the transformer formula. - * You can also call Empty on a node to determine if its value in the counterexample - * is the empty relation. - * - * \param root The root of the tree - * \param persist Number of context pops through which result should persist - * - * - */ - - lbool Solve(Node *root, int persist); - - /** Same as Solve, but annotates only a single node. */ - - lbool SolveSingleNode(Node *root, Node *node); - - /** Get the constraint tree (but don't solve it) */ - - TermTree *GetConstraintTree(Node *root, Node *skip_descendant = nullptr); - - /** Dispose of the dual model (counterexample) if there is one. */ - - void DisposeDualModel(); - - /** Check satisfiability of asserted edges and nodes. Same functionality as - * Solve, except no primal solution (interpolant) is generated in the unsat case. */ - - check_result Check(Node *root, std::vector underapproxes = std::vector(), - std::vector *underapprox_core = nullptr); - - /** Update the model, attempting to make the propositional literals in assumps true. If possible, - return sat, else return unsat and keep the old model. */ - - check_result CheckUpdateModel(Node *root, std::vector assumps); - - /** Determines the value in the counterexample of a symbol occurring in the transformer formula of - * a given edge. */ - - Term Eval(Edge *e, const Term& t); - - /** Return the fact derived at node p in a counterexample. */ - - Term EvalNode(Node *p); - - /** Returns true if the given node is empty in the primal solution. For procedure summaries, - this means that the procedure is not called in the current counter-model. */ - - bool Empty(Node *p); - - /** Compute an underapproximation of every node in a tree rooted at "root", - based on a previously computed counterexample. */ - - Term ComputeUnderapprox(Node *root, int persist); - - /** Try to strengthen the annotation of a node by removing disjuncts. */ - void Generalize(Node *root, Node *node); - - - /** Compute disjunctive interpolant for node by case splitting */ - void InterpolateByCases(Node *root, Node *node); - - /** Push a scope. Assertions made after Push can be undone by Pop. */ - - void Push(); - - /** Exception thrown when bad clause is encountered */ - - struct bad_clause { - std::string msg; - int i; - bad_clause(const std::string &_msg, int _i){ - msg = _msg; - i = _i; - } - }; - - struct parse_error { - std::string msg; - parse_error(const std::string &_msg){ - msg = _msg; - } - }; - - struct file_not_found { - }; - - struct bad_format { - }; - - // thrown on internal error - struct Bad { - }; - - // thrown on more serious internal error - struct ReallyBad { - }; - - // throw when greedy reduction fails - struct greedy_reduce_failed {}; - - /** Pop a scope (see Push). Note, you cannot pop axioms. */ - - void Pop(int num_scopes); - - /** Erase the proof by performing a Pop, Push and re-assertion of - all the popped constraints */ - void PopPush(); - - /** Return true if the given edge is used in the proof of unsat. - Can be called only after Solve or Check returns an unsat result. */ - - bool EdgeUsedInProof(Edge *edge); - - - /** Convert a collection of clauses to Nodes and Edges in the RPFP. - - Predicate unknowns are uninterpreted predicates not - occurring in the background theory. - - Clauses are of the form - - B => P(t_1,...,t_k) - - where P is a predicate unknown and predicate unknowns - occur only positivey in H and only under existential - quantifiers in prenex form. - - Each predicate unknown maps to a node. Each clause maps to - an edge. Let C be a clause B => P(t_1,...,t_k) where the - sequence of predicate unknowns occurring in B (in order - of occurrence) is P_1..P_n. The clause maps to a transformer - T where: - - T.Relparams = P_1..P_n - T.Indparams = x_1...x+k - T.Formula = B /\ t_1 = x_1 /\ ... /\ t_k = x_k - - Throws exception bad_clause(msg,i) if a clause i is - in the wrong form. - - */ - - struct label_struct { - symbol name; - expr value; - bool pos; - label_struct(const symbol &s, const expr &e, bool b) - : name(s), value(e), pos(b) {} - }; - - -#ifdef _WINDOWS - __declspec(dllexport) -#endif - void FromClauses(const std::vector &clauses, const std::vector *bounds = nullptr); - - void FromFixpointContext(fixedpoint fp, std::vector &queries); - - void WriteSolution(std::ostream &s); - - void WriteCounterexample(std::ostream &s, Node *node); - - enum FileFormat {DualityFormat, SMT2Format, HornFormat}; - - /** Write the RPFP to a file (currently in SMTLIB 1.2 format) */ - void WriteProblemToFile(std::string filename, FileFormat format = DualityFormat); - - /** Read the RPFP from a file (in specified format) */ - void ReadProblemFromFile(std::string filename, FileFormat format = DualityFormat); - - /** Translate problem to Horn clause form */ - void ToClauses(std::vector &cnsts, FileFormat format = DualityFormat); - - /** Translate the RPFP to a fixed point context, with queries */ - fixedpoint ToFixedPointProblem(std::vector &queries); - - /** Nodes of the graph. */ - std::vector nodes; - - /** Edges of the graph. */ - std::vector edges; - - /** Fuse a vector of transformers. If the total number of inputs of the transformers - is N, then the result is an N-ary transformer whose output is the union of - the outputs of the given transformers. The is, suppose we have a vector of transformers - {T_i(r_i1,...,r_iN(i) : i=1..M}. The result is a transformer - - F(r_11,...,r_iN(1),...,r_M1,...,r_MN(M)) = - T_1(r_11,...,r_iN(1)) U ... U T_M(r_M1,...,r_MN(M)) - */ - - Transformer Fuse(const std::vector &trs); - - /** Fuse edges so that each node is the output of at most one edge. This - transformation is solution-preserving, but changes the numbering of edges in - counterexamples. - */ - void FuseEdges(); - - void RemoveDeadNodes(); - - Term SubstParams(const std::vector &from, - const std::vector &to, const Term &t); - - Term SubstParamsNoCapture(const std::vector &from, - const std::vector &to, const Term &t); - - Term Localize(Edge *e, const Term &t); - - void EvalNodeAsConstraint(Node *p, Transformer &res); - - TermTree *GetGoalTree(Node *root); - - int EvalTruth(hash_map &memo, Edge *e, const Term &f); - - void GetLabels(Edge *e, std::vector &labels); - - // int GetLabelsRec(hash_map *memo, const Term &f, std::vector &labels, bool labpos); - - /** Compute and save the proof core for future calls to - EdgeUsedInProof. You only need to call this if you will pop - the solver before calling EdgeUsedInProof. - */ - void ComputeProofCore(); - - int CumulativeDecisions(); - - void GreedyReduceNodes(std::vector &nodes); - - check_result CheckWithConstrainedNodes(std::vector &posnodes,std::vector &negnodes); - - solver &slvr(){ - return *ls->slvr; - } - - protected: - - void ClearProofCore(){ - if(proof_core) - delete proof_core; - proof_core = nullptr; - } - - Term SuffixVariable(const Term &t, int n); - - Term HideVariable(const Term &t, int n); - - void RedVars(Node *node, Term &b, std::vector &v); - - Term RedDualRela(Edge *e, std::vector &args, int idx); - - Term LocalizeRec(Edge *e, hash_map &memo, const Term &t); - - void SetEdgeMaps(Edge *e); - - Term ReducedDualEdge(Edge *e); - - TermTree *ToTermTree(Node *root, Node *skip_descendant = nullptr); - - TermTree *ToGoalTree(Node *root); - - void CollapseTermTreeRec(TermTree *root, TermTree *node); - - TermTree *CollapseTermTree(TermTree *node); - - void DecodeTree(Node *root, TermTree *interp, int persist); - - Term GetUpperBound(Node *n); - - TermTree *AddUpperBound(Node *root, TermTree *t); - -#if 0 - void WriteInterps(System.IO.StreamWriter f, TermTree t); -#endif - - void WriteEdgeVars(Edge *e, hash_map &memo, const Term &t, std::ostream &s); - - void WriteEdgeAssignment(std::ostream &s, Edge *e); - - - // Scan the clause body for occurrences of the predicate unknowns - - Term ScanBody(hash_map &memo, - const Term &t, - hash_map &pmap, - std::vector &res, - std::vector &nodes); - - Term RemoveLabelsRec(hash_map &memo, const Term &t, std::vector &lbls); - - Term RemoveLabels(const Term &t, std::vector &lbls); - - Term GetAnnotation(Node *n); - - - Term GetUnderapprox(Node *n); - - Term UnderapproxFlag(Node *n); - - hash_map underapprox_flag_rev; - - Node *UnderapproxFlagRev(const Term &flag); - - Term ProjectFormula(std::vector &keep_vec, const Term &f); - - int SubtermTruth(hash_map &memo, const Term &); - - void ImplicantRed(hash_map &memo, const Term &f, std::vector &lits, - hash_set *done, bool truth, hash_set &dont_cares); - - void Implicant(hash_map &memo, const Term &f, std::vector &lits, hash_set &dont_cares); - - Term UnderapproxFormula(const Term &f, hash_set &dont_cares); - - void ImplicantFullRed(hash_map &memo, const Term &f, std::vector &lits, - hash_set &done, hash_set &dont_cares, bool extensional = true); - - public: - Term UnderapproxFullFormula(const Term &f, bool extensional = true); - - protected: - Term ToRuleRec(Edge *e, hash_map &memo, const Term &t, std::vector &quants); - - hash_map resolve_ite_memo; - - Term ResolveIte(hash_map &memo, const Term &t, std::vector &lits, - hash_set *done, hash_set &dont_cares); - - struct ArrayValue { - bool defined; - std::map entries; - expr def_val; - }; - - void EvalArrayTerm(const Term &t, ArrayValue &res); - - Term EvalArrayEquality(const Term &f); - - Term ModelValueAsConstraint(const Term &t); - - void GetLabelsRec(hash_map &memo, const Term &f, std::vector &labels, - hash_set *done, bool truth); - - Term SubstBoundRec(hash_map > &memo, hash_map &subst, int level, const Term &t); - - Term SubstBound(hash_map &subst, const Term &t); - - void ConstrainEdgeLocalized(Edge *e, const Term &t); - - void GreedyReduce(solver &s, std::vector &conjuncts); - - void NegateLits(std::vector &lits); - - expr SimplifyOr(std::vector &lits); - - expr SimplifyAnd(std::vector &lits); - - void SetAnnotation(Node *root, const expr &t); - - void AddEdgeToSolver(Edge *edge); - - void AddEdgeToSolver(implicant_solver &aux_solver, Edge *edge); - - void AddToProofCore(hash_set &core); - - void GetGroundLitsUnderQuants(hash_set *memo, const Term &f, std::vector &res, int under); - - Term StrengthenFormulaByCaseSplitting(const Term &f, std::vector &case_lits); - - expr NegateLit(const expr &f); - - expr GetEdgeFormula(Edge *e, int persist, bool with_children, bool underapprox); - - bool IsVar(const expr &t); - - void GetVarsRec(hash_set &memo, const expr &cnst, std::vector &vars); - - expr UnhoistPullRec(hash_map & memo, const expr &w, hash_map & init_defs, hash_map & const_params, hash_map &const_params_inv, std::vector &new_params); - - void AddParamsToTransformer(Transformer &trans, const std::vector ¶ms); - - expr AddParamsToApp(const expr &app, const func_decl &new_decl, const std::vector ¶ms); - - expr GetRelRec(hash_set &memo, const expr &t, const func_decl &rel); - - expr GetRel(Edge *edge, int child_idx); - - void GetDefs(const expr &cnst, hash_map &defs); - - void GetDefsRec(const expr &cnst, hash_map &defs); - - void AddParamsToNode(Node *node, const std::vector ¶ms); - - void UnhoistLoop(Edge *loop_edge, Edge *init_edge); - - void Unhoist(); - - Term ElimIteRec(hash_map &memo, const Term &t, std::vector &cnsts); - - Term ElimIte(const Term &t); - - void MarkLiveNodes(hash_map > &outgoing, hash_set &live_nodes, Node *node); - - virtual void slvr_add(const expr &e); - - virtual void slvr_pop(int i); - - virtual void slvr_push(); - - virtual check_result slvr_check(unsigned n = 0, expr * const assumptions = nullptr, unsigned *core_size = nullptr, expr *core = nullptr); - - virtual lbool ls_interpolate_tree(TermTree *assumptions, - TermTree *&interpolants, - model &_model, - TermTree *goals = nullptr, - bool weak = false); - - virtual bool proof_core_contains(const expr &e); - - }; - - - /** RPFP solver base class. */ - - class Solver { - - public: - - class Counterexample { - private: - RPFP *tree; - RPFP::Node *root; - public: - Counterexample(){ - tree = nullptr; - root = nullptr; - } - Counterexample(RPFP *_tree, RPFP::Node *_root){ - tree = _tree; - root = _root; - } - ~Counterexample(){ - if(tree) delete tree; - } - void swap(Counterexample &other){ - std::swap(tree,other.tree); - std::swap(root,other.root); - } - void set(RPFP *_tree, RPFP::Node *_root){ - if(tree) delete tree; - tree = _tree; - root = _root; - } - void clear(){ - if(tree) delete tree; - tree = nullptr; - } - RPFP *get_tree() const {return tree;} - RPFP::Node *get_root() const {return root;} - private: - Counterexample &operator=(const Counterexample &); - Counterexample(const Counterexample &); - }; - - /** Solve the problem. You can optionally give an old - counterexample to use as a guide. This is chiefly useful for - abstraction refinement metholdologies, and is only used as a - heuristic. */ - - virtual bool Solve() = 0; - - virtual Counterexample &GetCounterexample() = 0; - - virtual bool SetOption(const std::string &option, const std::string &value) = 0; - - /** Learn heuristic information from another solver. This - is chiefly useful for abstraction refinement, when we want to - solve a series of similar problems. */ - - virtual void LearnFrom(Solver *old_solver) = 0; - - /** Return true if the solution be incorrect due to recursion bounding. - That is, the returned "solution" might contain all derivable facts up to the - given recursion bound, but not be actually a fixed point. - */ - - virtual bool IsResultRecursionBounded() = 0; - - virtual ~Solver(){} - - static Solver *Create(const std::string &solver_class, RPFP *rpfp); - - /** This can be called asynchrnously to cause Solve to throw a - Canceled exception at some time in the future. - */ - virtual void Cancel() = 0; - - /** Object thrown on cancellation */ - struct Canceled {}; - - /** Object thrown on incompleteness */ - struct Incompleteness {}; - }; -} - - -// Allow to hash on nodes and edges in deterministic way - -namespace hash_space { - template <> - class hash { - public: - size_t operator()(const Duality::RPFP::Node *p) const { - return p->number; - } - }; -} - -namespace hash_space { - template <> - class hash { - public: - size_t operator()(const Duality::RPFP::Edge *p) const { - return p->number; - } - }; -} - -// allow to walk sets of nodes without address dependency - -namespace std { - template <> - class less { - public: - bool operator()(Duality::RPFP::Node * const &s, Duality::RPFP::Node * const &t) const { - return s->number < t->number; // s.raw()->get_id() < t.raw()->get_id(); - } - }; -} - -// #define LIMIT_STACK_WEIGHT 5 - - -namespace Duality { - /** Caching version of RPFP. Instead of asserting constraints, returns assumption literals */ - - class RPFP_caching : public RPFP { - public: - - /** appends assumption literals for edge to lits. if with_children is true, - includes that annotation of the edge's children. - */ - void AssertEdgeCache(Edge *e, std::vector &lits, bool with_children = false); - - /** appends assumption literals for node to lits */ - void AssertNodeCache(Node *, std::vector lits); - - /** check assumption lits, and return core */ - check_result CheckCore(const std::vector &assumps, std::vector &core); - - /** Clone another RPFP into this one, keeping a map */ - void Clone(RPFP *other); - - /** Get the clone of a node */ - Node *GetNodeClone(Node *other_node); - - /** Get the clone of an edge */ - Edge *GetEdgeClone(Edge *other_edge); - - /** Try to strengthen the parent of an edge */ - void GeneralizeCache(Edge *edge); - - /** Try to propagate some facts from children to parents of edge. - Return true if success. */ - bool PropagateCache(Edge *edge); - - /** Construct a caching RPFP using a LogicSolver */ - RPFP_caching(LogicSolver *_ls) : RPFP(_ls) {} - - /** Constraint an edge by its child's annotation. Return - assumption lits. */ - void ConstrainParentCache(Edge *parent, Node *child, std::vector &lits); - -#ifdef LIMIT_STACK_WEIGHT - virtual void AssertEdge(Edge *e, int persist = 0, bool with_children = false, bool underapprox = false); -#endif - - ~RPFP_caching() override {} - - protected: - hash_map AssumptionLits; - hash_map NodeCloneMap; - hash_map EdgeCloneMap; - std::vector alit_stack; - std::vector alit_stack_sizes; - - // to let us use one solver per edge - struct edge_solver { - hash_map AssumptionLits; - uptr slvr; - }; - hash_map edge_solvers; - -#ifdef LIMIT_STACK_WEIGHT - struct weight_counter { - int val; - weight_counter(){val = 0;} - void swap(weight_counter &other){ - std::swap(val,other.val); - } - }; - - struct big_stack_entry { - weight_counter weight_added; - std::vector new_alits; - std::vector alit_stack; - std::vector alit_stack_sizes; - }; - - std::vector new_alits; - weight_counter weight_added; - std::vector big_stack; -#endif - - - - void GetAssumptionLits(const expr &fmla, std::vector &lits, hash_map *opt_map = nullptr); - - void GreedyReduceCache(std::vector &assumps, std::vector &core); - - void FilterCore(std::vector &core, std::vector &full_core); - void ConstrainEdgeLocalizedCache(Edge *e, const Term &tl, std::vector &lits); - - void slvr_add(const expr &e) override; - - void slvr_pop(int i) override; - - void slvr_push() override; - - check_result slvr_check(unsigned n = 0, expr * const assumptions = nullptr, unsigned *core_size = nullptr, expr *core = nullptr) override; - - lbool ls_interpolate_tree(TermTree *assumptions, - TermTree *&interpolants, - model &_model, - TermTree *goals = nullptr, - bool weak = false) override; - - bool proof_core_contains(const expr &e) override; - - void GetTermTreeAssertionLiterals(TermTree *assumptions); - - void GetTermTreeAssertionLiteralsRec(TermTree *assumptions); - - edge_solver &SolverForEdge(Edge *edge, bool models, bool axioms); - - public: - struct scoped_solver_for_edge { - solver *orig_slvr; - RPFP_caching *rpfp; - edge_solver *es; - scoped_solver_for_edge(RPFP_caching *_rpfp, Edge *edge, bool models = false, bool axioms = false){ - rpfp = _rpfp; - orig_slvr = rpfp->ls->slvr; - es = &(rpfp->SolverForEdge(edge,models,axioms)); - rpfp->ls->slvr = es->slvr.get(); - rpfp->AssumptionLits.swap(es->AssumptionLits); - } - ~scoped_solver_for_edge(){ - rpfp->ls->slvr = orig_slvr; - rpfp->AssumptionLits.swap(es->AssumptionLits); - } - }; - - }; - -} diff --git a/src/duality/duality_profiling.cpp b/src/duality/duality_profiling.cpp deleted file mode 100644 index 6bb995e2d..000000000 --- a/src/duality/duality_profiling.cpp +++ /dev/null @@ -1,144 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - duality_profiling.cpp - - Abstract: - - collection performance information for duality - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - - --*/ - - -#include -#include -#include -#include -#include - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#endif - -#include "duality/duality_wrapper.h" -#include "interp/iz3profiling.h" - -namespace Duality { - - void show_time(){ - output_time(std::cout,current_time()); - std::cout << "\n"; - } - - typedef std::map nmap; - - struct node { - std::string name; - clock_t time; - clock_t start_time; - nmap sub; - struct node *parent; - - node(); - } top; - - node::node(){ - time = 0; - parent = nullptr; - } - - struct node *current; - - struct init { - init(){ - top.name = "TOTAL"; - current = ⊤ - } - } initializer; - - struct time_entry { - clock_t t; - time_entry(){t = 0;}; - void add(clock_t incr){t += incr;} - }; - - struct ltstr - { - bool operator()(const char* s1, const char* s2) const - { - return strcmp(s1, s2) < 0; - } - }; - - typedef std::map tmap; - - static std::ostream *pfs; - - void print_node(node &top, int indent, tmap &totals){ - for(int i = 0; i < indent; i++) (*pfs) << " "; - (*pfs) << top.name; - int dots = 70 - 2 * indent - top.name.size(); - for(int i = 0; i second,indent+1,totals); - } - - void print_profile(std::ostream &os) { - pfs = &os; - top.time = 0; - for(nmap::iterator it = top.sub.begin(); it != top.sub.end(); it++) - top.time += it->second.time; - tmap totals; - print_node(top,0,totals); - (*pfs) << "TOTALS:" << std::endl; - for(tmap::iterator it = totals.begin(); it != totals.end(); it++){ - (*pfs) << (it->first) << " "; - output_time(*pfs, it->second.t); - (*pfs) << std::endl; - } - profiling::print(os); // print the interpolation stats - } - - void timer_start(const char *name){ - node &child = current->sub[name]; - if(child.name.empty()){ // a new node - child.parent = current; - child.name = name; - } - child.start_time = current_time(); - current = &child; - } - - void timer_stop(const char *name){ - if (current->name != name || !current->parent) { -#if 0 - std::cerr << "imbalanced timer_start and timer_stop"; - exit(1); -#endif - // in case we lost a timer stop due to an exception - while (current->name != name && current->parent) - current = current->parent; - if (current->parent) { - current->time += (current_time() - current->start_time); - current = current->parent; - } - return; - } - current->time += (current_time() - current->start_time); - current = current->parent; - } -} diff --git a/src/duality/duality_profiling.h b/src/duality/duality_profiling.h deleted file mode 100755 index 5f0e5120c..000000000 --- a/src/duality/duality_profiling.h +++ /dev/null @@ -1,38 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - duality_profiling.h - - Abstract: - - collection performance information for duality - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - - --*/ - -#ifndef DUALITYPROFILING_H -#define DUALITYPROFILING_H - -#include - -namespace Duality { - /** Start a timer with given name */ - void timer_start(const char *); - /** Stop a timer with given name */ - void timer_stop(const char *); - /** Print out timings */ - void print_profile(std::ostream &s); - /** Show the current time. */ - void show_time(); -} - -#endif - diff --git a/src/duality/duality_rpfp.cpp b/src/duality/duality_rpfp.cpp deleted file mode 100644 index 3358eb45e..000000000 --- a/src/duality/duality_rpfp.cpp +++ /dev/null @@ -1,4250 +0,0 @@ -/*++ - Copyright (c) 2012 Microsoft Corporation - - Module Name: - - duality_rpfp.h - - Abstract: - - implements relational post-fixedpoint problem - (RPFP) data structure. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - - --*/ - - - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#endif - -#include -#include -#include -#include - - -#include "duality/duality.h" -#include "duality/duality_profiling.h" - -// TODO: do we need these? -#ifdef Z3OPS - -class Z3_subterm_truth { -public: - virtual bool eval(Z3_ast f) = 0; - ~Z3_subterm_truth(){} -}; - -Z3_subterm_truth *Z3_mk_subterm_truth(Z3_context ctx, Z3_model model); - -#endif - -#include - -// TODO: use something official for this -int debug_gauss = 0; - -namespace Duality { - - static char string_of_int_buffer[20]; - - const char *Z3User::string_of_int(int n){ - sprintf(string_of_int_buffer,"%d",n); - return string_of_int_buffer; - } - - RPFP::Term RPFP::SuffixVariable(const Term &t, int n) - { - std::string name = t.decl().name().str() + "_" + string_of_int(n); - return ctx.constant(name.c_str(), t.get_sort()); - } - - RPFP::Term RPFP::HideVariable(const Term &t, int n) - { - std::string name = std::string("@p_") + t.decl().name().str() + "_" + string_of_int(n); - return ctx.constant(name.c_str(), t.get_sort()); - } - - void RPFP::RedVars(Node *node, Term &b, std::vector &v) - { - int idx = node->number; - if(HornClauses) - b = ctx.bool_val(true); - else { - std::string name = std::string("@b_") + string_of_int(idx); - symbol sym = ctx.str_symbol(name.c_str()); - b = ctx.constant(sym,ctx.bool_sort()); - } - // ctx.constant(name.c_str(), ctx.bool_sort()); - v = node->Annotation.IndParams; - for(unsigned i = 0; i < v.size(); i++) - v[i] = SuffixVariable(v[i],idx); - } - - void Z3User::SummarizeRec(hash_set &memo, std::vector &lits, int &ops, const Term &t){ - if(memo.find(t) != memo.end()) - return; - memo.insert(t); - if(t.is_app()){ - decl_kind k = t.decl().get_decl_kind(); - if (k == And || k == Or || k == Not || k == Implies || k == Iff) { - ops++; - int nargs = t.num_args(); - for (int i = 0; i < nargs; i++) - SummarizeRec(memo, lits, ops, t.arg(i)); - return; - } - } - lits.push_back(t); - } - - int RPFP::CumulativeDecisions(){ -#if 0 - std::string stats = Z3_statistics_to_string(ctx); - int pos = stats.find("decisions:"); - pos += 10; - int end = stats.find('\n',pos); - std::string val = stats.substr(pos,end-pos); - return atoi(val.c_str()); -#endif - return slvr().get_num_decisions(); - } - - - void Z3User::Summarize(const Term &t){ - hash_set memo; std::vector lits; int ops = 0; - SummarizeRec(memo, lits, ops, t); - std::cout << ops << ": "; - for(unsigned i = 0; i < lits.size(); i++){ - if(i > 0) std::cout << ", "; - std::cout << lits[i]; - } - } - - int Z3User::CountOperatorsRec(hash_set &memo, const Term &t){ - if(memo.find(t) != memo.end()) - return 0; - memo.insert(t); - if(t.is_app()){ - decl_kind k = t.decl().get_decl_kind(); - if (k == And || k == Or) { - int count = 1; - int nargs = t.num_args(); - for (int i = 0; i < nargs; i++) - count += CountOperatorsRec(memo, t.arg(i)); - return count; - } - return 0; - } - if(t.is_quantifier()){ - int nbv = t.get_quantifier_num_bound(); - return CountOperatorsRec(memo,t.body()) + 2 * nbv; // count 2 for each quantifier - } - return 0; - } - - int Z3User::CountOperators(const Term &t){ - hash_set memo; - return CountOperatorsRec(memo,t); - } - - - Z3User::Term Z3User::conjoin(const std::vector &args){ - return ctx.make(And,args); - } - - Z3User::Term Z3User::sum(const std::vector &args){ - return ctx.make(Plus,args); - } - - RPFP::Term RPFP::RedDualRela(Edge *e, std::vector &args, int idx){ - Node *child = e->Children[idx]; - Term b(ctx); - std::vector v; - RedVars(child, b, v); - for (unsigned i = 0; i < args.size(); i++) { - if (eq(args[i].get_sort(), ctx.bool_sort())) - args[i] = ctx.make(Iff, args[i], v[i]); - else - args[i] = args[i] == v[i]; - } - return args.size() > 0 ? (b && conjoin(args)) : b; - } - - Z3User::Term Z3User::CloneQuantifier(const Term &t, const Term &new_body){ -#if 0 - Z3_context c = ctx; - Z3_ast a = t; - std::vector pats; - int num_pats = Z3_get_quantifier_num_patterns(c,a); - for(int i = 0; i < num_pats; i++) - pats.push_back(Z3_get_quantifier_pattern_ast(c,a,i)); - std::vector no_pats; - int num_no_pats = Z3_get_quantifier_num_patterns(c,a); - for(int i = 0; i < num_no_pats; i++) - no_pats.push_back(Z3_get_quantifier_no_pattern_ast(c,a,i)); - int bound = Z3_get_quantifier_num_bound(c,a); - std::vector sorts; - std::vector names; - for(int i = 0; i < bound; i++){ - sorts.push_back(Z3_get_quantifier_bound_sort(c,a,i)); - names.push_back(Z3_get_quantifier_bound_name(c,a,i)); - } - Z3_ast foo = Z3_mk_quantifier_ex(c, - Z3_is_quantifier_forall(c,a), - Z3_get_quantifier_weight(c,a), - 0, - 0, - num_pats, - VEC2PTR(pats), - num_no_pats, - VEC2PTR(no_pats), - bound, - VEC2PTR(sorts), - VEC2PTR(names), - new_body); - return expr(ctx,foo); -#endif - return clone_quantifier(t,new_body); - } - - - RPFP::Term RPFP::LocalizeRec(Edge *e, hash_map &memo, const Term &t) - { - std::pair foo(t,expr(ctx)); - std::pair::iterator, bool> bar = memo.insert(foo); - Term &res = bar.first->second; - if(!bar.second) return res; - hash_map::iterator it = e->varMap.find(t); - if (it != e->varMap.end()){ - res = it->second; - return res; - } - if (t.is_app()) { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - args.reserve(nargs); - for (int i = 0; i < nargs; i++) - args.push_back(LocalizeRec(e, memo, t.arg(i))); - hash_map::iterator rit = e->relMap.find(f); - if (rit != e->relMap.end()) - res = RedDualRela(e, args, (rit->second)); - else { - if (args.size() == 0 && f.get_decl_kind() == Uninterpreted && !ls->is_constant(f)) { - res = HideVariable(t, e->number); - } - else { - res = f(args.size(), VEC2PTR(args)); - } - } - } - else if (t.is_quantifier()) { - std::vector pats; - t.get_patterns(pats); - for (unsigned i = 0; i < pats.size(); i++) - pats[i] = LocalizeRec(e, memo, pats[i]); - Term body = LocalizeRec(e, memo, t.body()); - res = clone_quantifier(t, body, pats); - } - else res = t; - return res; - } - - void RPFP::SetEdgeMaps(Edge *e){ - timer_start("SetEdgeMaps"); - e->relMap.clear(); - e->varMap.clear(); - for(unsigned i = 0; i < e->F.RelParams.size(); i++){ - e->relMap[e->F.RelParams[i]] = i; - } - Term b(ctx); - std::vector v; - RedVars(e->Parent, b, v); - for(unsigned i = 0; i < e->F.IndParams.size(); i++){ - // func_decl parentParam = e->Parent.Annotation.IndParams[i]; - expr oldname = e->F.IndParams[i]; - expr newname = v[i]; - e->varMap[oldname] = newname; - } - timer_stop("SetEdgeMaps"); - - } - - - RPFP::Term RPFP::Localize(Edge *e, const Term &t){ - timer_start("Localize"); - hash_map memo; - if(e->F.IndParams.size() > 0 && e->varMap.empty()) - SetEdgeMaps(e); // TODO: why is this needed? - Term res = LocalizeRec(e,memo,t); - timer_stop("Localize"); - return res; - } - - - RPFP::Term RPFP::ReducedDualEdge(Edge *e) - { - SetEdgeMaps(e); - timer_start("RedVars"); - Term b(ctx); - std::vector v; - RedVars(e->Parent, b, v); - timer_stop("RedVars"); - // ast_to_track = (ast)b; - return implies(b, Localize(e, e->F.Formula)); - } - - TermTree *RPFP::ToTermTree(Node *root, Node *skip_descendant) - { - if(skip_descendant && root == skip_descendant) - return new TermTree(ctx.bool_val(true)); - Edge *e = root->Outgoing; - if(!e) return new TermTree(ctx.bool_val(true), std::vector()); - std::vector children(e->Children.size()); - for(unsigned i = 0; i < children.size(); i++) - children[i] = ToTermTree(e->Children[i],skip_descendant); - // Term top = ReducedDualEdge(e); - Term top = e->dual.null() ? ctx.bool_val(true) : e->dual; - TermTree *res = new TermTree(top, children); - for(unsigned i = 0; i < e->constraints.size(); i++) - res->addTerm(e->constraints[i]); - return res; - } - - TermTree *RPFP::GetGoalTree(Node *root){ - std::vector children(1); - children[0] = ToGoalTree(root); - return new TermTree(ctx.bool_val(false),children); - } - - TermTree *RPFP::ToGoalTree(Node *root) - { - Term b(ctx); - std::vector v; - RedVars(root, b, v); - Term goal = root->Name(v); - Edge *e = root->Outgoing; - if(!e) return new TermTree(goal, std::vector()); - std::vector children(e->Children.size()); - for(unsigned i = 0; i < children.size(); i++) - children[i] = ToGoalTree(e->Children[i]); - // Term top = ReducedDualEdge(e); - return new TermTree(goal, children); - } - - Z3User::Term Z3User::SubstRec(hash_map &memo, const Term &t) - { - std::pair foo(t,expr(ctx)); - std::pair::iterator, bool> bar = memo.insert(foo); - Term &res = bar.first->second; - if(!bar.second) return res; - if (t.is_app()) { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - args.reserve(nargs); - for (int i = 0; i < nargs; i++) - args.push_back(SubstRec(memo, t.arg(i))); - res = f(args.size(), VEC2PTR(args)); - } - else if (t.is_quantifier()) { - std::vector pats; - t.get_patterns(pats); - for (unsigned i = 0; i < pats.size(); i++) - pats[i] = SubstRec(memo, pats[i]); - Term body = SubstRec(memo, t.body()); - res = clone_quantifier(t, body, pats); - } - // res = CloneQuantifier(t,SubstRec(memo, t.body())); - else res = t; - return res; - } - - Z3User::Term Z3User::SubstRec(hash_map &memo, hash_map &map, const Term &t) - { - std::pair foo(t,expr(ctx)); - std::pair::iterator, bool> bar = memo.insert(foo); - Term &res = bar.first->second; - if(!bar.second) return res; - if (t.is_app()) { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - args.reserve(nargs); - for (int i = 0; i < nargs; i++) - args.push_back(SubstRec(memo, map, t.arg(i))); - hash_map::iterator it = map.find(f); - if (it != map.end()) - f = it->second; - res = f(args.size(), VEC2PTR(args)); - } - else if (t.is_quantifier()) { - std::vector pats; - t.get_patterns(pats); - for (unsigned i = 0; i < pats.size(); i++) - pats[i] = SubstRec(memo, map, pats[i]); - Term body = SubstRec(memo, map, t.body()); - res = clone_quantifier(t, body, pats); - } - // res = CloneQuantifier(t,SubstRec(memo, t.body())); - else res = t; - return res; - } - - Z3User::Term Z3User::ExtractStores(hash_map &memo, const Term &t, std::vector &cnstrs, hash_map &renaming) - { - std::pair foo(t,expr(ctx)); - std::pair::iterator, bool> bar = memo.insert(foo); - Term &res = bar.first->second; - if(!bar.second) return res; - if (t.is_app()) { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - args.reserve(nargs); - for (int i = 0; i < nargs; i++) - args.push_back(ExtractStores(memo, t.arg(i), cnstrs, renaming)); - res = f(args.size(), VEC2PTR(args)); - if (f.get_decl_kind() == Store) { - func_decl fresh = ctx.fresh_func_decl("@arr", res.get_sort()); - expr y = fresh(); - expr equ = ctx.make(Equal, y, res); - cnstrs.push_back(equ); - renaming[y] = res; - res = y; - } - } - else res = t; - return res; - } - - - bool Z3User::IsLiteral(const expr &lit, expr &atom, expr &val){ - if (!(lit.is_quantifier() && IsClosedFormula(lit))) { - if (!lit.is_app()) - return false; - decl_kind k = lit.decl().get_decl_kind(); - if (k == Not) { - if (IsLiteral(lit.arg(0), atom, val)) { - val = eq(val, ctx.bool_val(true)) ? ctx.bool_val(false) : ctx.bool_val(true); - return true; - } - return false; - } - if (k == And || k == Or || k == Iff || k == Implies) - return false; - } - atom = lit; - val = ctx.bool_val(true); - return true; - } - - expr Z3User::Negate(const expr &f){ - if(f.is_app() && f.decl().get_decl_kind() == Not) - return f.arg(0); - else if(eq(f,ctx.bool_val(true))) - return ctx.bool_val(false); - else if(eq(f,ctx.bool_val(false))) - return ctx.bool_val(true); - return !f; - } - - expr Z3User::ReduceAndOr(const std::vector &args, bool is_and, std::vector &res){ - for(unsigned i = 0; i < args.size(); i++) - if (!eq(args[i], ctx.bool_val(is_and))) { - if (eq(args[i], ctx.bool_val(!is_and))) - return ctx.bool_val(!is_and); - res.push_back(args[i]); - } - return expr(); - } - - expr Z3User::FinishAndOr(const std::vector &args, bool is_and){ - if(args.size() == 0) - return ctx.bool_val(is_and); - if(args.size() == 1) - return args[0]; - return ctx.make(is_and ? And : Or,args); - } - - expr Z3User::SimplifyAndOr(const std::vector &args, bool is_and){ - std::vector sargs; - expr res = ReduceAndOr(args,is_and,sargs); - if(!res.null()) return res; - return FinishAndOr(sargs,is_and); - } - - expr Z3User::PullCommonFactors(std::vector &args, bool is_and){ - - // first check if there's anything to do... - if(args.size() < 2) - return FinishAndOr(args,is_and); - for (unsigned i = 0; i < args.size(); i++) { - const expr &a = args[i]; - if (!(a.is_app() && a.decl().get_decl_kind() == (is_and ? Or : And))) - return FinishAndOr(args, is_and); - } - std::vector common; - for (unsigned i = 0; i < args.size(); i++) { - unsigned n = args[i].num_args(); - std::vector v(n), w; - for (unsigned j = 0; j < n; j++) - v[j] = args[i].arg(j); - std::less comp; - std::sort(v.begin(), v.end(), comp); - if (i == 0) - common.swap(v); - else { - std::set_intersection(common.begin(), common.end(), v.begin(), v.end(), std::inserter(w, w.begin()), comp); - common.swap(w); - } - } - if(common.empty()) - return FinishAndOr(args,is_and); - std::set common_set(common.begin(),common.end()); - for(unsigned i = 0; i < args.size(); i++){ - unsigned n = args[i].num_args(); - std::vector lits; - for (unsigned j = 0; j < n; j++) { - const expr b = args[i].arg(j); - if (common_set.find(b) == common_set.end()) - lits.push_back(b); - } - args[i] = SimplifyAndOr(lits,!is_and); - } - common.push_back(SimplifyAndOr(args,is_and)); - return SimplifyAndOr(common,!is_and); - } - - expr Z3User::ReallySimplifyAndOr(const std::vector &args, bool is_and){ - std::vector sargs; - expr res = ReduceAndOr(args,is_and,sargs); - if(!res.null()) return res; - return PullCommonFactors(sargs,is_and); - } - - Z3User::Term Z3User::SubstAtomTriv(const expr &foo, const expr &atom, const expr &val){ - if(eq(foo,atom)) - return val; - else if(foo.is_app() && foo.decl().get_decl_kind() == Not && eq(foo.arg(0),atom)) - return Negate(val); - else - return foo; - } - - Z3User::Term Z3User::PushQuantifier(const expr &t, const expr &body, bool is_forall){ - if (t.get_quantifier_num_bound() == 1) { - std::vector fmlas, free, not_free; - CollectJuncts(body, fmlas, is_forall ? Or : And, false); - for (unsigned i = 0; i < fmlas.size(); i++) { - const expr &fmla = fmlas[i]; - if (fmla.has_free(0)) - free.push_back(fmla); - else - not_free.push_back(fmla); - } - decl_kind op = is_forall ? Or : And; - if (free.empty()) - return DeleteBound(0, 1, SimplifyAndOr(not_free, op == And)); - expr q = clone_quantifier(is_forall ? Forall : Exists, t, SimplifyAndOr(free, op == And)); - if (!not_free.empty()) - q = ctx.make(op, q, DeleteBound(0, 1, SimplifyAndOr(not_free, op == And))); - return q; - } - return clone_quantifier(is_forall ? Forall : Exists,t,body); - } - - Z3User::Term Z3User::CloneQuantAndSimp(const expr &t, const expr &body, bool is_forall) { - if (body.is_app()) { - if (body.decl().get_decl_kind() == (is_forall ? And : Or)) { // quantifier distributes - int nargs = body.num_args(); - std::vector args(nargs); - for (int i = 0; i < nargs; i++) - args[i] = CloneQuantAndSimp(t, body.arg(i), is_forall); - return SimplifyAndOr(args, body.decl().get_decl_kind() == And); - } - else if (body.decl().get_decl_kind() == (is_forall ? Or : And)) { // quantifier distributes - return PushQuantifier(t, body, is_forall); // may distribute partially - } - else if (body.decl().get_decl_kind() == Not) { - return ctx.make(Not, CloneQuantAndSimp(t, body.arg(0), !is_forall)); - } - } - if (t.get_quantifier_num_bound() == 1 && !body.has_free(0)) - return DeleteBound(0, 1, body); // drop the quantifier - return clone_quantifier(is_forall ? Forall : Exists, t, body); - } - - Z3User::Term Z3User::CloneQuantAndSimp(const expr &t, const expr &body){ - return CloneQuantAndSimp(t,body,t.is_quantifier_forall()); - } - - Z3User::Term Z3User::SubstAtom(hash_map &memo, const expr &t, const expr &atom, const expr &val) { - std::pair foo(t, expr(ctx)); - std::pair::iterator, bool> bar = memo.insert(foo); - Term &res = bar.first->second; - if (!bar.second) return res; - if (t.is_app()) { - func_decl f = t.decl(); - decl_kind k = f.get_decl_kind(); - - // TODO: recur here, but how much? We don't want to be quadractic in formula size - - if (k == And || k == Or) { - int nargs = t.num_args(); - std::vector args(nargs); - for (int i = 0; i < nargs; i++) - args[i] = SubstAtom(memo, t.arg(i), atom, val); - res = ReallySimplifyAndOr(args, k == And); - return res; - } - } - else if (t.is_quantifier() && atom.is_quantifier()) { - if (eq(t, atom)) - res = val; - else - res = clone_quantifier(t, SubstAtom(memo, t.body(), atom, val)); - return res; - } - res = SubstAtomTriv(t, atom, val); - return res; - } - - void Z3User::RemoveRedundancyOp(bool pol, std::vector &args, hash_map &smemo) { - for (unsigned i = 0; i < args.size(); i++) { - const expr &lit = args[i]; - expr atom, val; - if (IsLiteral(lit, atom, val)) { - if (atom.is_app() && atom.decl().get_decl_kind() == Equal) - if (pol ? eq(val, ctx.bool_val(true)) : eq(val, ctx.bool_val(false))) { - expr lhs = atom.arg(0), rhs = atom.arg(1); - if (lhs.is_numeral()) - std::swap(lhs, rhs); - if (rhs.is_numeral() && lhs.is_app()) { - for (unsigned j = 0; j < args.size(); j++) - if (j != i) { - smemo.clear(); - smemo[lhs] = rhs; - args[j] = SubstRec(smemo, args[j]); - } - } - } - for (unsigned j = 0; j < args.size(); j++) - if (j != i) { - smemo.clear(); - args[j] = SubstAtom(smemo, args[j], atom, pol ? val : !val); - } - } - } - } - - - Z3User::Term Z3User::RemoveRedundancyRec(hash_map &memo, hash_map &smemo, const Term &t) { - std::pair foo(t, expr(ctx)); - std::pair::iterator, bool> bar = memo.insert(foo); - Term &res = bar.first->second; - if (!bar.second) return res; - if (t.is_app()) { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - args.reserve(nargs); - for (int i = 0; i < nargs; i++) - args.push_back(RemoveRedundancyRec(memo, smemo, t.arg(i))); - - decl_kind k = f.get_decl_kind(); - if (k == And) { - RemoveRedundancyOp(true, args, smemo); - res = ReallySimplifyAndOr(args, true); - } - else if (k == Or) { - RemoveRedundancyOp(false, args, smemo); - res = ReallySimplifyAndOr(args, false); - } - else { - if (k == Equal && args[0].get_id() > args[1].get_id()) - std::swap(args[0], args[1]); - res = f(args.size(), VEC2PTR(args)); - } - } - else if (t.is_quantifier()) { - Term body = RemoveRedundancyRec(memo, smemo, t.body()); - res = CloneQuantAndSimp(t, body); - } - else res = t; - return res; - } - - Z3User::Term Z3User::RemoveRedundancy(const Term &t){ - hash_map memo; - hash_map smemo; - return RemoveRedundancyRec(memo,smemo,t); - } - - Z3User::Term Z3User::AdjustQuantifiers(const Term &t) - { - if(t.is_quantifier() || (t.is_app() && t.has_quantifiers())) - return t.qe_lite(); - return t; - } - - Z3User::Term Z3User::IneqToEqRec(hash_map &memo, const Term &t) { - std::pair foo(t, expr(ctx)); - std::pair::iterator, bool> bar = memo.insert(foo); - Term &res = bar.first->second; - if (!bar.second) return res; - if (t.is_app()) { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - args.reserve(nargs); - for (int i = 0; i < nargs; i++) - args.push_back(IneqToEqRec(memo, t.arg(i))); - - decl_kind k = f.get_decl_kind(); - if (k == And) { - for (int i = 0; i < nargs - 1; i++) { - if ((args[i].is_app() && args[i].decl().get_decl_kind() == Geq && - args[i + 1].is_app() && args[i + 1].decl().get_decl_kind() == Leq) - || - (args[i].is_app() && args[i].decl().get_decl_kind() == Leq && - args[i + 1].is_app() && args[i + 1].decl().get_decl_kind() == Geq)) - if (eq(args[i].arg(0), args[i + 1].arg(0)) && eq(args[i].arg(1), args[i + 1].arg(1))) { - args[i] = ctx.make(Equal, args[i].arg(0), args[i].arg(1)); - args[i + 1] = ctx.bool_val(true); - } - } - } - res = f(args.size(), VEC2PTR(args)); - } - else if (t.is_quantifier()) { - Term body = IneqToEqRec(memo, t.body()); - res = clone_quantifier(t, body); - } - else res = t; - return res; - } - - Z3User::Term Z3User::IneqToEq(const Term &t){ - hash_map memo; - return IneqToEqRec(memo,t); - } - - Z3User::Term Z3User::SubstRecHide(hash_map &memo, const Term &t, int number) { - std::pair foo(t, expr(ctx)); - std::pair::iterator, bool> bar = memo.insert(foo); - Term &res = bar.first->second; - if (!bar.second) return res; - if (t.is_app()) { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - if (nargs == 0 && f.get_decl_kind() == Uninterpreted) { - std::string name = std::string("@q_") + t.decl().name().str() + "_" + string_of_int(number); - res = ctx.constant(name.c_str(), t.get_sort()); - return res; - } - args.reserve(nargs); - for (int i = 0; i < nargs; i++) - args.push_back(SubstRec(memo, t.arg(i))); - res = f(args.size(), VEC2PTR(args)); - } - else if (t.is_quantifier()) - res = CloneQuantifier(t, SubstRec(memo, t.body())); - else res = t; - return res; - } - - RPFP::Term RPFP::SubstParams(const std::vector &from, - const std::vector &to, const Term &t) { - hash_map memo; - bool some_diff = false; - for (unsigned i = 0; i < from.size(); i++) - if (i < to.size() && !eq(from[i], to[i])) { - memo[from[i]] = to[i]; - some_diff = true; - } - return some_diff ? SubstRec(memo, t) : t; - } - - RPFP::Term RPFP::SubstParamsNoCapture(const std::vector &from, - const std::vector &to, const Term &t) { - hash_map memo; - bool some_diff = false; - for (unsigned i = 0; i < from.size(); i++) - if (i < to.size() && !eq(from[i], to[i])) { - memo[from[i]] = to[i]; - // if the new param is not being mapped to anything else, we need to rename it to prevent capture - // note, if the new param *is* mapped later in the list, it will override this substitution - const expr &w = to[i]; - if (memo.find(w) == memo.end()) { - std::string old_name = w.decl().name().str(); - func_decl fresh = ctx.fresh_func_decl(old_name.c_str(), w.get_sort()); - expr y = fresh(); - memo[w] = y; - } - some_diff = true; - } - return some_diff ? SubstRec(memo, t) : t; - } - - - - RPFP::Transformer RPFP::Fuse(const std::vector &trs) { - assert(!trs.empty()); - const std::vector ¶ms = trs[0]->IndParams; - std::vector fmlas(trs.size()); - fmlas[0] = trs[0]->Formula; - for (unsigned i = 1; i < trs.size(); i++) - fmlas[i] = SubstParamsNoCapture(trs[i]->IndParams, params, trs[i]->Formula); - std::vector rel_params = trs[0]->RelParams; - for (unsigned i = 1; i < trs.size(); i++) { - const std::vector ¶ms2 = trs[i]->RelParams; - hash_map map; - for (unsigned j = 0; j < params2.size(); j++) { - func_decl rel = RenumberPred(params2[j], rel_params.size()); - rel_params.push_back(rel); - map[params2[j]] = rel; - } - hash_map memo; - fmlas[i] = SubstRec(memo, map, fmlas[i]); - } - return Transformer(rel_params, params, ctx.make(Or, fmlas), trs[0]->owner); - } - - - void Z3User::Strengthen(Term &x, const Term &y) - { - if (eq(x,ctx.bool_val(true))) - x = y; - else - x = x && y; - } - - void RPFP::SetAnnotation(Node *root, const expr &t){ - hash_map memo; - Term b; - std::vector v; - RedVars(root, b, v); - memo[b] = ctx.bool_val(true); - for (unsigned i = 0; i < v.size(); i++) - memo[v[i]] = root->Annotation.IndParams[i]; - Term annot = SubstRec(memo, t); - // Strengthen(ref root.Annotation.Formula, annot); - root->Annotation.Formula = annot; - } - - void RPFP::DecodeTree(Node *root, TermTree *interp, int persist) { - std::vector &ic = interp->getChildren(); - if (ic.size() > 0) { - std::vector &nc = root->Outgoing->Children; - for (unsigned i = 0; i < nc.size(); i++) - DecodeTree(nc[i], ic[i], persist); - } - SetAnnotation(root, interp->getTerm()); -#if 0 - if(persist != 0) - Z3_persist_ast(ctx,root->Annotation.Formula,persist); -#endif - } - - RPFP::Term RPFP::GetUpperBound(Node *n) - { - // TODO: cache this - Term b(ctx); std::vector v; - RedVars(n, b, v); - hash_map memo; - for (unsigned int i = 0; i < v.size(); i++) - memo[n->Bound.IndParams[i]] = v[i]; - Term cnst = SubstRec(memo, n->Bound.Formula); - return b && !cnst; - } - - RPFP::Term RPFP::GetAnnotation(Node *n) - { - if(eq(n->Annotation.Formula,ctx.bool_val(true))) - return n->Annotation.Formula; - // TODO: cache this - Term b(ctx); std::vector v; - RedVars(n, b, v); - hash_map memo; - for (unsigned i = 0; i < v.size(); i++) - memo[n->Annotation.IndParams[i]] = v[i]; - Term cnst = SubstRec(memo, n->Annotation.Formula); - return !b || cnst; - } - - RPFP::Term RPFP::GetUnderapprox(Node *n) - { - // TODO: cache this - Term b(ctx); std::vector v; - RedVars(n, b, v); - hash_map memo; - for (unsigned i = 0; i < v.size(); i++) - memo[n->Underapprox.IndParams[i]] = v[i]; - Term cnst = SubstRecHide(memo, n->Underapprox.Formula, n->number); - return !b || cnst; - } - - TermTree *RPFP::AddUpperBound(Node *root, TermTree *t) - { - Term f = !((ast)(root->dual)) ? ctx.bool_val(true) : root->dual; - std::vector c(1); c[0] = t; - return new TermTree(f, c); - } - -#if 0 - void RPFP::WriteInterps(System.IO.StreamWriter f, TermTree t) - { - foreach (var c in t.getChildren()) - WriteInterps(f, c); - f.WriteLine(t.getTerm()); - } -#endif - - - expr RPFP::GetEdgeFormula(Edge *e, int persist, bool with_children, bool underapprox) { - if (e->dual.null()) { - timer_start("ReducedDualEdge"); - e->dual = ReducedDualEdge(e); - timer_stop("ReducedDualEdge"); - timer_start("getting children"); - if (underapprox) { - std::vector cus(e->Children.size()); - for (unsigned i = 0; i < e->Children.size(); i++) - cus[i] = !UnderapproxFlag(e->Children[i]) || GetUnderapprox(e->Children[i]); - expr cnst = conjoin(cus); - e->dual = e->dual && cnst; - } - timer_stop("getting children"); - timer_start("Persisting"); - std::list::reverse_iterator it = stack.rbegin(); - for (int i = 0; i < persist && it != stack.rend(); i++) - it++; - if (it != stack.rend()) - it->edges.push_back(e); - timer_stop("Persisting"); - //Console.WriteLine("{0}", cnst); - } - return e->dual; - } - - /** For incremental solving, asserts the constraint associated - * with this edge in the SMT context. If this edge is removed, - * you must pop the context accordingly. The second argument is - * the number of pushes we are inside. The constraint formula - * will survive "persist" pops of the context. If you plan - * to reassert the edge after popping the context once, - * you can save time re-constructing the formula by setting - * "persist" to one. If you set "persist" too high, however, - * you could have a memory leak. - * - * The flag "with children" causes the annotations of the children - * to be asserted. The flag underapprox causes the underapproximations - * of the children to be asserted *conditionally*. See Check() on - * how to actually enforce these constraints. - * - */ - - void RPFP::AssertEdge(Edge *e, int persist, bool with_children, bool underapprox) { - if (eq(e->F.Formula, ctx.bool_val(true)) && (!with_children || e->Children.empty())) - return; - expr fmla = GetEdgeFormula(e, persist, with_children, underapprox); - timer_start("solver add"); - slvr_add(e->dual); - timer_stop("solver add"); - if (with_children) - for (unsigned i = 0; i < e->Children.size(); i++) - ConstrainParent(e, e->Children[i]); - } - - -#ifdef LIMIT_STACK_WEIGHT - void RPFP_caching::AssertEdge(Edge *e, int persist, bool with_children, bool underapprox) - { - unsigned old_new_alits = new_alits.size(); - if(eq(e->F.Formula,ctx.bool_val(true)) && (!with_children || e->Children.empty())) - return; - expr fmla = GetEdgeFormula(e, persist, with_children, underapprox); - timer_start("solver add"); - slvr_add(e->dual); - timer_stop("solver add"); - if(old_new_alits < new_alits.size()) - weight_added.val++; - if(with_children) - for(unsigned i = 0; i < e->Children.size(); i++) - ConstrainParent(e,e->Children[i]); - } -#endif - - // caching verion of above - void RPFP_caching::AssertEdgeCache(Edge *e, std::vector &lits, bool with_children) { - if (eq(e->F.Formula, ctx.bool_val(true)) && (!with_children || e->Children.empty())) - return; - expr fmla = GetEdgeFormula(e, 0, with_children, false); - GetAssumptionLits(fmla, lits); - if (with_children) - for (unsigned i = 0; i < e->Children.size(); i++) - ConstrainParentCache(e, e->Children[i], lits); - } - - void RPFP::slvr_add(const expr &e){ - slvr().add(e); - } - - void RPFP_caching::slvr_add(const expr &e){ - GetAssumptionLits(e,alit_stack); - } - - void RPFP::slvr_pop(int i){ - slvr().pop(i); - } - - void RPFP::slvr_push(){ - slvr().push(); - } - - void RPFP_caching::slvr_pop(int i){ - for(int j = 0; j < i; j++){ -#ifdef LIMIT_STACK_WEIGHT - if(alit_stack_sizes.empty()){ - if(big_stack.empty()) - throw "stack underflow"; - for(unsigned k = 0; k < new_alits.size(); k++){ - if(AssumptionLits.find(new_alits[k]) == AssumptionLits.end()) - throw "foo!"; - AssumptionLits.erase(new_alits[k]); - } - big_stack_entry &bsb = big_stack.back(); - bsb.alit_stack_sizes.swap(alit_stack_sizes); - bsb.alit_stack.swap(alit_stack); - bsb.new_alits.swap(new_alits); - bsb.weight_added.swap(weight_added); - big_stack.pop_back(); - slvr().pop(1); - continue; - } -#endif - alit_stack.resize(alit_stack_sizes.back()); - alit_stack_sizes.pop_back(); - } - } - - void RPFP_caching::slvr_push(){ -#ifdef LIMIT_STACK_WEIGHT - if(weight_added.val > LIMIT_STACK_WEIGHT){ - big_stack.resize(big_stack.size()+1); - big_stack_entry &bsb = big_stack.back(); - bsb.alit_stack_sizes.swap(alit_stack_sizes); - bsb.alit_stack.swap(alit_stack); - bsb.new_alits.swap(new_alits); - bsb.weight_added.swap(weight_added); - slvr().push(); - for(unsigned i = 0; i < bsb.alit_stack.size(); i++) - slvr().add(bsb.alit_stack[i]); - return; - } -#endif - alit_stack_sizes.push_back(alit_stack.size()); - } - - check_result RPFP::slvr_check(unsigned n, expr * const assumptions, unsigned *core_size, expr *core){ - return slvr().check(n, assumptions, core_size, core); - } - - check_result RPFP_caching::slvr_check(unsigned n, expr * const assumptions, unsigned *core_size, expr *core){ - unsigned oldsiz = alit_stack.size(); - if(n && assumptions) - std::copy(assumptions,assumptions+n,std::inserter(alit_stack,alit_stack.end())); - check_result res; - if (core_size && core) { - std::vector full_core(alit_stack.size()), core1(n); - std::copy(assumptions, assumptions + n, core1.begin()); - res = slvr().check(alit_stack.size(), VEC2PTR(alit_stack), core_size, VEC2PTR(full_core)); - full_core.resize(*core_size); - if (res == unsat) { - FilterCore(core1, full_core); - *core_size = core1.size(); - std::copy(core1.begin(), core1.end(), core); - } - } - else - res = slvr().check(alit_stack.size(), VEC2PTR(alit_stack)); - alit_stack.resize(oldsiz); - return res; - } - - lbool RPFP::ls_interpolate_tree(TermTree *assumptions, - TermTree *&interpolants, - model &_model, - TermTree *goals, - bool weak) { - return ls->interpolate_tree(assumptions, interpolants, _model, goals, weak); - } - - lbool RPFP_caching::ls_interpolate_tree(TermTree *assumptions, - TermTree *&interpolants, - model &_model, - TermTree *goals, - bool weak) { - GetTermTreeAssertionLiterals(assumptions); - return ls->interpolate_tree(assumptions, interpolants, _model, goals, weak); - } - - void RPFP_caching::GetTermTreeAssertionLiteralsRec(TermTree *assumptions){ - std::vector alits; - hash_map map; - GetAssumptionLits(assumptions->getTerm(),alits,&map); - std::vector &ts = assumptions->getTerms(); - for(unsigned i = 0; i < ts.size(); i++) - GetAssumptionLits(ts[i],alits,&map); - assumptions->setTerm(ctx.bool_val(true)); - ts = alits; - for(unsigned i = 0; i < alits.size(); i++) - ts.push_back(ctx.make(Implies,alits[i],map[alits[i]])); - for(unsigned i = 0; i < assumptions->getChildren().size(); i++) - GetTermTreeAssertionLiterals(assumptions->getChildren()[i]); - return; - } - - void RPFP_caching::GetTermTreeAssertionLiterals(TermTree *assumptions) { - // optimize binary case - if (assumptions->getChildren().size() == 1 - && assumptions->getChildren()[0]->getChildren().size() == 0) { - hash_map map; - TermTree *child = assumptions->getChildren()[0]; - std::vector dummy; - GetAssumptionLits(child->getTerm(), dummy, &map); - std::vector &ts = child->getTerms(); - for (unsigned i = 0; i < ts.size(); i++) - GetAssumptionLits(ts[i], dummy, &map); - std::vector assumps; - slvr().get_proof().get_assumptions(assumps); - if (!proof_core) { // save the proof core for later use - proof_core = new hash_set < ast > ; - for (unsigned i = 0; i < assumps.size(); i++) - proof_core->insert(assumps[i]); - } - std::vector *cnsts[2] = { &child->getTerms(), &assumptions->getTerms() }; - for (unsigned i = 0; i < assumps.size(); i++) { - expr &as = assumps[i]; - expr alit = (as.is_app() && as.decl().get_decl_kind() == Implies) ? as.arg(0) : as; - bool isA = map.find(alit) != map.end(); - cnsts[isA ? 0 : 1]->push_back(as); - } - } - else - GetTermTreeAssertionLiteralsRec(assumptions); - } - - void RPFP::AddToProofCore(hash_set &core){ - std::vector assumps; - slvr().get_proof().get_assumptions(assumps); - for(unsigned i = 0; i < assumps.size(); i++) - core.insert(assumps[i]); - } - - void RPFP::ComputeProofCore(){ - if(!proof_core){ - proof_core = new hash_set; - AddToProofCore(*proof_core); - } - } - - - void RPFP_caching::GetAssumptionLits(const expr &fmla, std::vector &lits, hash_map *opt_map) { - std::vector conjs; - CollectConjuncts(fmla, conjs); - for (unsigned i = 0; i < conjs.size(); i++) { - const expr &conj = conjs[i]; - std::pair foo(conj, expr(ctx)); - std::pair::iterator, bool> bar = AssumptionLits.insert(foo); - Term &res = bar.first->second; - if (bar.second) { - func_decl pred = ctx.fresh_func_decl("@alit", ctx.bool_sort()); - res = pred(); -#ifdef LIMIT_STACK_WEIGHT - new_alits.push_back(conj); -#endif - slvr().add(ctx.make(Implies, res, conj)); - // std::cout << res << ": " << conj << "\n"; - } - if (opt_map) - (*opt_map)[res] = conj; - lits.push_back(res); - } - } - - void RPFP::ConstrainParent(Edge *parent, Node *child){ - ConstrainEdgeLocalized(parent,GetAnnotation(child)); - } - - void RPFP_caching::ConstrainParentCache(Edge *parent, Node *child, std::vector &lits){ - ConstrainEdgeLocalizedCache(parent,GetAnnotation(child),lits); - } - - - /** For incremental solving, asserts the negation of the upper bound associated - * with a node. - * */ - - void RPFP::AssertNode(Node *n) - { - if (n->dual.null()) { - n->dual = GetUpperBound(n); - stack.back().nodes.push_back(n); - slvr_add(n->dual); - } - } - - // caching version of above - void RPFP_caching::AssertNodeCache(Node *n, std::vector lits){ - if (n->dual.null()) { - n->dual = GetUpperBound(n); - stack.back().nodes.push_back(n); - GetAssumptionLits(n->dual, lits); - } - } - - /** Clone another RPFP into this one, keeping a map */ - void RPFP_caching::Clone(RPFP *other) { -#if 0 - for(unsigned i = 0; i < other->nodes.size(); i++) - NodeCloneMap[other->nodes[i]] = CloneNode(other->nodes[i]); -#endif - for (unsigned i = 0; i < other->edges.size(); i++) { - Edge *edge = other->edges[i]; - Node *parent = CloneNode(edge->Parent); - std::vector cs; - for (unsigned j = 0; j < edge->Children.size(); j++) - // cs.push_back(NodeCloneMap[edge->Children[j]]); - cs.push_back(CloneNode(edge->Children[j])); - EdgeCloneMap[edge] = CreateEdge(parent, edge->F, cs); - } - } - - /** Get the clone of a node */ - RPFP::Node *RPFP_caching::GetNodeClone(Node *other_node){ - return NodeCloneMap[other_node]; - } - - /** Get the clone of an edge */ - RPFP::Edge *RPFP_caching::GetEdgeClone(Edge *other_edge){ - return EdgeCloneMap[other_edge]; - } - - /** check assumption lits, and return core */ - check_result RPFP_caching::CheckCore(const std::vector &assumps, std::vector &core){ - core.resize(assumps.size()); - unsigned core_size; - check_result res = slvr().check(assumps.size(),(expr *)VEC2PTR(assumps),&core_size, VEC2PTR(core)); - if(res == unsat) - core.resize(core_size); - else - core.clear(); - return res; - } - - - /** Assert a constraint on an edge in the SMT context. - */ - - void RPFP::ConstrainEdge(Edge *e, const Term &t) - { - Term tl = Localize(e, t); - ConstrainEdgeLocalized(e,tl); - } - - void RPFP::ConstrainEdgeLocalized(Edge *e, const Term &tl) - { - e->constraints.push_back(tl); - stack.back().constraints.push_back(std::pair(e,tl)); - slvr_add(tl); - } - - void RPFP_caching::ConstrainEdgeLocalizedCache(Edge *e, const Term &tl, std::vector &lits) - { - e->constraints.push_back(tl); - stack.back().constraints.push_back(std::pair(e,tl)); - GetAssumptionLits(tl,lits); - } - - - /** Declare a constant in the background theory. */ - - void RPFP::DeclareConstant(const FuncDecl &f){ - ls->declare_constant(f); - } - - /** Assert a background axiom. Background axioms can be used to provide the - * theory of auxilliary functions or relations. All symbols appearing in - * background axioms are considered global, and may appear in both transformer - * and relational solutions. Semantically, a solution to the RPFP gives - * an interpretation of the unknown relations for each interpretation of the - * auxilliary symbols that is consistent with the axioms. Axioms should be - * asserted before any calls to Push. They cannot be de-asserted by Pop. */ - - void RPFP::AssertAxiom(const Term &t) - { - ls->assert_axiom(t); - axioms.push_back(t); // for printing only - } - -#if 0 - /** Do not call this. */ - - void RPFP::RemoveAxiom(const Term &t) - { - slvr().RemoveInterpolationAxiom(t); - } -#endif - - /** Solve an RPFP graph. This means either strengthen the annotation - * so that the bound at the given root node is satisfied, or - * show that this cannot be done by giving a dual solution - * (i.e., a counterexample). - * - * In the current implementation, this only works for graphs that - * are: - * - tree-like - * - * - closed. - * - * In a tree-like graph, every nod has out most one incoming and one out-going edge, - * and there are no cycles. In a closed graph, every node has exactly one out-going - * edge. This means that the leaves of the tree are all hyper-edges with no - * children. Such an edge represents a relation (nullary transformer) and thus - * a lower bound on its parent. The parameter root must be the root of this tree. - * - * If Solve returns LBool.False, this indicates success. The annotation of the tree - * has been updated to satisfy the upper bound at the root. - * - * If Solve returns LBool.True, this indicates a counterexample. For each edge, - * you can then call Eval to determine the values of symbols in the transformer formula. - * You can also call Empty on a node to determine if its value in the counterexample - * is the empty relation. - * - * \param root The root of the tree - * \param persist Number of context pops through which result should persist - * - * - */ - - lbool RPFP::Solve(Node *root, int persist) - { - timer_start("Solve"); - TermTree *tree = GetConstraintTree(root); - TermTree *interpolant = nullptr; - TermTree *goals = nullptr; - if(ls->need_goals) - goals = GetGoalTree(root); - ClearProofCore(); - - // if (dualModel != null) dualModel.Dispose(); - // if (dualLabels != null) dualLabels.Dispose(); - - timer_start("interpolate_tree"); - lbool res = ls_interpolate_tree(tree, interpolant, dualModel,goals,true); - timer_stop("interpolate_tree"); - if (res == l_false) { - DecodeTree(root, interpolant->getChildren()[0], persist); - delete interpolant; - } - - delete tree; - if(goals) - delete goals; - - timer_stop("Solve"); - return res; - } - - void RPFP::CollapseTermTreeRec(TermTree *root, TermTree *node){ - root->addTerm(node->getTerm()); - std::vector &cnsts = node->getTerms(); - for(unsigned i = 0; i < cnsts.size(); i++) - root->addTerm(cnsts[i]); - std::vector &chs = node->getChildren(); - for(unsigned i = 0; i < chs.size(); i++){ - CollapseTermTreeRec(root,chs[i]); - } - } - - TermTree *RPFP::CollapseTermTree(TermTree *node){ - std::vector &chs = node->getChildren(); - for(unsigned i = 0; i < chs.size(); i++) - CollapseTermTreeRec(node,chs[i]); - for(unsigned i = 0; i < chs.size(); i++) - delete chs[i]; - chs.clear(); - return node; - } - - lbool RPFP::SolveSingleNode(Node *root, Node *node) - { - timer_start("Solve"); - TermTree *tree = CollapseTermTree(GetConstraintTree(root,node)); - tree->getChildren().push_back(CollapseTermTree(ToTermTree(node))); - TermTree *interpolant = nullptr; - ClearProofCore(); - - timer_start("interpolate_tree"); - lbool res = ls_interpolate_tree(tree, interpolant, dualModel,nullptr,true); - timer_stop("interpolate_tree"); - if (res == l_false) { - DecodeTree(node, interpolant->getChildren()[0], 0); - delete interpolant; - } - - delete tree; - timer_stop("Solve"); - return res; - } - - /** Get the constraint tree (but don't solve it) */ - - TermTree *RPFP::GetConstraintTree(Node *root, Node *skip_descendant) - { - return AddUpperBound(root, ToTermTree(root,skip_descendant)); - } - - /** Dispose of the dual model (counterexample) if there is one. */ - - void RPFP::DisposeDualModel() - { - dualModel = model(ctx,nullptr); - } - - RPFP::Term RPFP::UnderapproxFlag(Node *n){ - expr flag = ctx.constant((std::string("@under") + string_of_int(n->number)).c_str(), ctx.bool_sort()); - underapprox_flag_rev[flag] = n; - return flag; - } - - RPFP::Node *RPFP::UnderapproxFlagRev(const Term &flag){ - return underapprox_flag_rev[flag]; - } - - /** Check satisfiability of asserted edges and nodes. Same functionality as - * Solve, except no primal solution (interpolant) is generated in the unsat case. - * The vector underapproxes gives the set of node underapproximations to be enforced - * (assuming these were conditionally asserted by AssertEdge). - * - */ - - check_result RPFP::Check(Node *root, std::vector underapproxes, std::vector *underapprox_core) { - timer_start("Check"); - ClearProofCore(); - // if (dualModel != null) dualModel.Dispose(); - check_result res; - if (!underapproxes.size()) - res = slvr_check(); - else { - std::vector us(underapproxes.size()); - for (unsigned i = 0; i < underapproxes.size(); i++) - us[i] = UnderapproxFlag(underapproxes[i]); - slvr_check(); // TODO: no idea why I need to do this - if (underapprox_core) { - std::vector unsat_core(us.size()); - unsigned core_size = 0; - res = slvr_check(us.size(), VEC2PTR(us), &core_size, VEC2PTR(unsat_core)); - underapprox_core->resize(core_size); - for (unsigned i = 0; i < core_size; i++) - (*underapprox_core)[i] = UnderapproxFlagRev(unsat_core[i]); - } - else { - res = slvr_check(us.size(), VEC2PTR(us)); - bool dump = false; - if (dump) { - std::vector cnsts; - // cnsts.push_back(axioms[0]); - cnsts.push_back(root->dual); - cnsts.push_back(root->Outgoing->dual); - ls->write_interpolation_problem("temp.smt", cnsts, std::vector()); - } - } - // check_result temp = slvr_check(); - } - dualModel = slvr().get_model(); - timer_stop("Check"); - return res; - } - - check_result RPFP::CheckUpdateModel(Node *root, std::vector assumps){ - // check_result temp1 = slvr_check(); // no idea why I need to do this - ClearProofCore(); - check_result res = slvr_check(assumps.size(), VEC2PTR(assumps)); - model mod = slvr().get_model(); - if(!mod.null()) - dualModel = mod;; - return res; - } - - /** Determines the value in the counterexample of a symbol occurring in the transformer formula of - * a given edge. */ - - RPFP::Term RPFP::Eval(Edge *e, const Term& t) - { - Term tl = Localize(e, t); - return dualModel.eval(tl); - } - - /** Returns true if the given node is empty in the primal solution. For proceudure summaries, - this means that the procedure is not called in the current counter-model. */ - - bool RPFP::Empty(Node *p) - { - Term b; std::vector v; - RedVars(p, b, v); - // dualModel.show_internals(); - // std::cout << "b: " << b << std::endl; - expr bv = dualModel.eval(b); - // std::cout << "bv: " << bv << std::endl; - bool res = !eq(bv,ctx.bool_val(true)); - return res; - } - - RPFP::Term RPFP::EvalNode(Node *p) - { - Term b; std::vector v; - RedVars(p, b, v); - std::vector args; - for(unsigned i = 0; i < v.size(); i++) - args.push_back(dualModel.eval(v[i])); - return (p->Name)(args); - } - - void RPFP::EvalArrayTerm(const RPFP::Term &t, ArrayValue &res){ - if (t.is_app()) { - decl_kind k = t.decl().get_decl_kind(); - if (k == AsArray) { - func_decl fd = t.decl().get_func_decl_parameter(0); - func_interp r = dualModel.get_func_interp(fd); - int num = r.num_entries(); - res.defined = true; - for (int i = 0; i < num; i++) { - expr arg = r.get_arg(i, 0); - expr value = r.get_value(i); - res.entries[arg] = value; - } - res.def_val = r.else_value(); - return; - } - else if (k == Store) { - EvalArrayTerm(t.arg(0), res); - if (!res.defined)return; - expr addr = t.arg(1); - expr val = t.arg(2); - if (addr.is_numeral() && val.is_numeral()) { - if (eq(val, res.def_val)) - res.entries.erase(addr); - else - res.entries[addr] = val; - } - else - res.defined = false; - return; - } - } - res.defined = false; - } - - int eae_count = 0; - - RPFP::Term RPFP::EvalArrayEquality(const RPFP::Term &f) { - ArrayValue lhs, rhs; - eae_count++; - EvalArrayTerm(f.arg(0), lhs); - EvalArrayTerm(f.arg(1), rhs); - if (lhs.defined && rhs.defined) { - if (eq(lhs.def_val, rhs.def_val)) - if (lhs.entries == rhs.entries) - return ctx.bool_val(true); - return ctx.bool_val(false); - } - return f; - } - - /** Compute truth values of all boolean subterms in current model. - Assumes formulas has been simplified by Z3, so only boolean ops - ands and, or, not. Returns result in memo. - */ - - int RPFP::SubtermTruth(hash_map &memo, const Term &f) { - TRACE("duality", tout << f << "\n";); - if (memo.find(f) != memo.end()) { - return memo[f]; - } - int res; - if (f.is_app()) { - int nargs = f.num_args(); - decl_kind k = f.decl().get_decl_kind(); - if (k == Implies) { - res = SubtermTruth(memo, !f.arg(0) || f.arg(1)); - goto done; - } - if (k == And) { - res = 1; - for (int i = 0; i < nargs; i++) { - int ar = SubtermTruth(memo, f.arg(i)); - if (ar == 0) { - res = 0; - goto done; - } - if (ar == 2)res = 2; - } - goto done; - } - else if (k == Or) { - res = 0; - for (int i = 0; i < nargs; i++) { - int ar = SubtermTruth(memo, f.arg(i)); - if (ar == 1) { - res = 1; - goto done; - } - if (ar == 2)res = 2; - } - goto done; - } - else if (k == Not) { - int ar = SubtermTruth(memo, f.arg(0)); - res = (ar == 0) ? 1 : ((ar == 1) ? 0 : 2); - goto done; - } - } - { - bool pos; std::vector names; - if (f.is_label(pos, names)) { - res = SubtermTruth(memo, f.arg(0)); - goto done; - } - } - { - expr bv = dualModel.eval(f); - if (bv.is_app() && bv.decl().get_decl_kind() == Equal && - bv.arg(0).is_array()) { - bv = EvalArrayEquality(bv); - } - // Hack!!!! array equalities can occur negatively! - if (bv.is_app() && bv.decl().get_decl_kind() == Not && - bv.arg(0).decl().get_decl_kind() == Equal && - bv.arg(0).arg(0).is_array()) { - bv = dualModel.eval(!EvalArrayEquality(bv.arg(0))); - } - if (eq(bv, ctx.bool_val(true))) - res = 1; - else if (eq(bv, ctx.bool_val(false))) - res = 0; - else - res = 2; - } - done: - memo[f] = res; - return res; - } - - int RPFP::EvalTruth(hash_map &memo, Edge *e, const Term &f){ - Term tl = Localize(e, f); - return SubtermTruth(memo,tl); - } - - /** Compute truth values of all boolean subterms in current model. - Assumes formulas has been simplified by Z3, so only boolean ops - ands and, or, not. Returns result in memo. - */ - - - void RPFP::GetLabelsRec(hash_map &memo, const Term &f, std::vector &labels, - hash_set *done, bool truth) { - if (done[truth].find(f) != done[truth].end()) - return; /* already processed */ - if (f.is_app()) { - int nargs = f.num_args(); - decl_kind k = f.decl().get_decl_kind(); - if (k == Implies) { - GetLabelsRec(memo, f.arg(1) || !f.arg(0), labels, done, truth); - goto done; - } - if (k == Iff) { - int b = SubtermTruth(memo, f.arg(0)); - if (b == 2) { - goto done; - // bypass error - std::ostringstream os; - os << "disaster in SubtermTruth processing " << f; - throw default_exception(os.str()); - } - GetLabelsRec(memo, f.arg(1), labels, done, truth ? b : !b); - goto done; - } - if (truth ? k == And : k == Or) { - for (int i = 0; i < nargs; i++) - GetLabelsRec(memo, f.arg(i), labels, done, truth); - goto done; - } - if (truth ? k == Or : k == And) { - for (int i = 0; i < nargs; i++) { - Term a = f.arg(i); - timer_start("SubtermTruth"); - int b = SubtermTruth(memo, a); - timer_stop("SubtermTruth"); - if (truth ? (b == 1) : (b == 0)) { - GetLabelsRec(memo, a, labels, done, truth); - goto done; - } - } - /* Unreachable! */ - // throw "error in RPFP::GetLabelsRec"; - goto done; - } - else if (k == Not) { - GetLabelsRec(memo, f.arg(0), labels, done, !truth); - goto done; - } - else { - bool pos; std::vector names; - if (f.is_label(pos, names)) { - GetLabelsRec(memo, f.arg(0), labels, done, truth); - if (pos == truth) - for (unsigned i = 0; i < names.size(); i++) - labels.push_back(names[i]); - goto done; - } - } - } - done: - done[truth].insert(f); - } - - void RPFP::GetLabels(Edge *e, std::vector &labels){ - if(!e->map || e->map->labeled.null()) - return; - Term tl = Localize(e, e->map->labeled); - hash_map memo; - hash_set done[2]; - GetLabelsRec(memo,tl,labels,done,true); - } - -#ifdef Z3OPS - static Z3_subterm_truth *stt; -#endif - - int ir_count = 0; - - void RPFP::ImplicantRed(hash_map &memo, const Term &f, std::vector &lits, - hash_set *done, bool truth, hash_set &dont_cares) { - if (done[truth].find(f) != done[truth].end()) - return; /* already processed */ -#if 0 - int this_count = ir_count++; - if(this_count == 50092) - std::cout << "foo!\n"; -#endif - if (f.is_app()) { - int nargs = f.num_args(); - decl_kind k = f.decl().get_decl_kind(); - if (k == Implies) { - ImplicantRed(memo, f.arg(1) || !f.arg(0), lits, done, truth, dont_cares); - goto done; - } - if (k == Iff) { - int b = SubtermTruth(memo, f.arg(0)); - if (b == 2) { - std::ostringstream os; - os << "disaster in SubtermTruth processing " << f; - throw default_exception(os.str()); - } - ImplicantRed(memo, f.arg(1), lits, done, truth ? b : !b, dont_cares); - goto done; - } - if (truth ? k == And : k == Or) { - for (int i = 0; i < nargs; i++) - ImplicantRed(memo, f.arg(i), lits, done, truth, dont_cares); - goto done; - } - if (truth ? k == Or : k == And) { - for (int i = 0; i < nargs; i++) { - Term a = f.arg(i); -#if 0 - if(i == nargs - 1){ // last chance! - ImplicantRed(memo,a,lits,done,truth,dont_cares); - goto done; - } -#endif - timer_start("SubtermTruth"); -#ifdef Z3OPS - bool b = stt->eval(a); -#else - int b = SubtermTruth(memo, a); -#endif - timer_stop("SubtermTruth"); - if (truth ? (b == 1) : (b == 0)) { - ImplicantRed(memo, a, lits, done, truth, dont_cares); - goto done; - } - } - /* Unreachable! */ - // TODO: need to indicate this failure to caller - // std::cerr << "error in RPFP::ImplicantRed"; - goto done; - } - else if (k == Not) { - ImplicantRed(memo, f.arg(0), lits, done, !truth, dont_cares); - goto done; - } - } - { - if (dont_cares.find(f) == dont_cares.end()) { - expr rf = ResolveIte(memo, f, lits, done, dont_cares); - expr bv = truth ? rf : !rf; - lits.push_back(bv); - } - } - done: - done[truth].insert(f); - } - - void RPFP::ImplicantFullRed(hash_map &memo, const Term &f, std::vector &lits, - hash_set &done, hash_set &dont_cares, bool extensional) { - if (done.find(f) != done.end()) - return; /* already processed */ - if (f.is_app()) { - int nargs = f.num_args(); - decl_kind k = f.decl().get_decl_kind(); - if (k == Implies || k == Iff || k == And || k == Or || k == Not) { - for (int i = 0; i < nargs; i++) - ImplicantFullRed(memo, f.arg(i), lits, done, dont_cares, extensional); - goto done; - } - } - { - if (dont_cares.find(f) == dont_cares.end()) { - int b = SubtermTruth(memo, f); - if (b != 0 && b != 1) goto done; - if (f.is_app() && f.decl().get_decl_kind() == Equal && f.arg(0).is_array()) { - if (b == 1 && !extensional) { - expr x = dualModel.eval(f.arg(0)); expr y = dualModel.eval(f.arg(1)); - if (!eq(x, y)) - b = 0; - } - if (b == 0) - goto done; - } - expr bv = (b == 1) ? f : !f; - lits.push_back(bv); - } - } - done: - done.insert(f); - } - - RPFP::Term RPFP::ResolveIte(hash_map &memo, const Term &t, std::vector &lits, - hash_set *done, hash_set &dont_cares) { - if (resolve_ite_memo.find(t) != resolve_ite_memo.end()) - return resolve_ite_memo[t]; - Term res; - if (t.is_app()) { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - if (f.get_decl_kind() == Ite) { - timer_start("SubtermTruth"); -#ifdef Z3OPS - bool sel = stt->eval(t.arg(0)); -#else - int xval = SubtermTruth(memo, t.arg(0)); - bool sel; - if (xval == 0)sel = false; - else if (xval == 1)sel = true; - else - throw "unresolved ite in model"; -#endif - timer_stop("SubtermTruth"); - ImplicantRed(memo, t.arg(0), lits, done, sel, dont_cares); - res = ResolveIte(memo, t.arg(sel ? 1 : 2), lits, done, dont_cares); - } - else { - for (int i = 0; i < nargs; i++) - args.push_back(ResolveIte(memo, t.arg(i), lits, done, dont_cares)); - res = f(args.size(), VEC2PTR(args)); - } - } - else res = t; - resolve_ite_memo[t] = res; - return res; - } - - RPFP::Term RPFP::ElimIteRec(hash_map &memo, const Term &t, std::vector &cnsts) { - std::pair foo(t, expr(ctx)); - std::pair::iterator, bool> bar = memo.insert(foo); - Term &res = bar.first->second; - if (bar.second) { - if (t.is_app()) { - int nargs = t.num_args(); - std::vector args; - if (t.decl().get_decl_kind() == Equal) { - expr lhs = t.arg(0); - expr rhs = t.arg(1); - if (rhs.decl().get_decl_kind() == Ite) { - expr rhs_args[3]; - lhs = ElimIteRec(memo, lhs, cnsts); - for (int i = 0; i < 3; i++) - rhs_args[i] = ElimIteRec(memo, rhs.arg(i), cnsts); - res = (rhs_args[0] && (lhs == rhs_args[1])) || ((!rhs_args[0]) && (lhs == rhs_args[2])); - goto done; - } - } - if (t.decl().get_decl_kind() == Ite) { - func_decl sym = ctx.fresh_func_decl("@ite", t.get_sort()); - res = sym(); - cnsts.push_back(ElimIteRec(memo, ctx.make(Equal, res, t), cnsts)); - } - else { - for (int i = 0; i < nargs; i++) - args.push_back(ElimIteRec(memo, t.arg(i), cnsts)); - res = t.decl()(args.size(), VEC2PTR(args)); - } - } - else if (t.is_quantifier()) - res = clone_quantifier(t, ElimIteRec(memo, t.body(), cnsts)); - else - res = t; - } - done: - return res; - } - - RPFP::Term RPFP::ElimIte(const Term &t){ - hash_map memo; - std::vector cnsts; - expr res = ElimIteRec(memo,t,cnsts); - if(!cnsts.empty()){ - cnsts.push_back(res); - res = ctx.make(And,cnsts); - } - return res; - } - - void RPFP::Implicant(hash_map &memo, const Term &f, std::vector &lits, hash_set &dont_cares){ - hash_set done[2]; - ImplicantRed(memo,f,lits,done,true, dont_cares); - } - - - /** Underapproximate a formula using current counterexample. */ - - RPFP::Term RPFP::UnderapproxFormula(const Term &f, hash_set &dont_cares){ - /* first compute truth values of subterms */ - hash_map memo; -#ifdef Z3OPS - stt = Z3_mk_subterm_truth(ctx,dualModel); -#endif - // SubtermTruth(memo,f); - /* now compute an implicant */ - std::vector lits; - Implicant(memo,f,lits, dont_cares); -#ifdef Z3OPS - delete stt; stt = 0; -#endif - /* return conjunction of literals */ - return conjoin(lits); - } - - RPFP::Term RPFP::UnderapproxFullFormula(const Term &f, bool extensional){ - hash_set dont_cares; - resolve_ite_memo.clear(); - timer_start("UnderapproxFormula"); - /* first compute truth values of subterms */ - hash_map memo; - hash_set done; - std::vector lits; - ImplicantFullRed(memo,f,lits,done,dont_cares, extensional); - timer_stop("UnderapproxFormula"); - /* return conjunction of literals */ - return conjoin(lits); - } - - struct VariableProjector : Z3User { - - struct elim_cand { - Term var; - int sup; - Term val; - }; - - typedef expr Term; - - hash_set keep; - hash_map var_ord; - int num_vars; - std::vector elim_cands; - hash_map > sup_map; - hash_map elim_map; - std::vector ready_cands; - hash_map cand_map; - params simp_params; - - VariableProjector(Z3User &_user, std::vector &keep_vec) : - Z3User(_user), simp_params() { - num_vars = 0; - for (unsigned i = 0; i < keep_vec.size(); i++) { - keep.insert(keep_vec[i]); - var_ord[keep_vec[i]] = num_vars++; - } - } - int VarNum(const Term &v) { - if (var_ord.find(v) == var_ord.end()) - var_ord[v] = num_vars++; - return var_ord[v]; - } - - bool IsVar(const Term &t){ - return t.is_app() && t.num_args() == 0 && t.decl().get_decl_kind() == Uninterpreted; - } - - bool IsPropLit(const Term &t, Term &a) { - if (IsVar(t)) { - a = t; - return true; - } - else if (t.is_app() && t.decl().get_decl_kind() == Not) - return IsPropLit(t.arg(0), a); - return false; - } - - void CountOtherVarsRec(hash_map &memo, - const Term &t, - int id, - int &count) { - std::pair foo(t, 0); - std::pair::iterator, bool> bar = memo.insert(foo); - // int &res = bar.first->second; - if (!bar.second) return; - if (t.is_app()) { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - if (nargs == 0 && f.get_decl_kind() == Uninterpreted) { - if (cand_map.find(t) != cand_map.end()) { - count++; - sup_map[t].push_back(id); - } - } - for (int i = 0; i < nargs; i++) - CountOtherVarsRec(memo, t.arg(i), id, count); - } - else if (t.is_quantifier()) - CountOtherVarsRec(memo, t.body(), id, count); - } - - void NewElimCand(const Term &lhs, const Term &rhs) { - if (debug_gauss) { - std::cout << "mapping " << lhs << " to " << rhs << std::endl; - } - elim_cand cand; - cand.var = lhs; - cand.sup = 0; - cand.val = rhs; - elim_cands.push_back(cand); - cand_map[lhs] = elim_cands.size() - 1; - } - - void MakeElimCand(const Term &lhs, const Term &rhs) { - if (eq(lhs, rhs)) - return; - if (!IsVar(lhs)) { - if (IsVar(rhs)) { - MakeElimCand(rhs, lhs); - return; - } - else { - std::cout << "would have mapped a non-var\n"; - return; - } - } - if (IsVar(rhs) && VarNum(rhs) > VarNum(lhs)) { - MakeElimCand(rhs, lhs); - return; - } - if (keep.find(lhs) != keep.end()) - return; - if (cand_map.find(lhs) == cand_map.end()) - NewElimCand(lhs, rhs); - else { - int cand_idx = cand_map[lhs]; - if (IsVar(rhs) && cand_map.find(rhs) == cand_map.end() - && keep.find(rhs) == keep.end()) - NewElimCand(rhs, elim_cands[cand_idx].val); - elim_cands[cand_idx].val = rhs; - } - } - - Term FindRep(const Term &t) { - if (cand_map.find(t) == cand_map.end()) - return t; - Term &res = elim_cands[cand_map[t]].val; - if (IsVar(res)) { - assert(VarNum(res) < VarNum(t)); - res = FindRep(res); - return res; - } - return t; - } - - void GaussElimCheap(const std::vector &lits_in, - std::vector &lits_out) { - for (unsigned i = 0; i < lits_in.size(); i++) { - Term lit = lits_in[i]; - if (lit.is_app()) { - decl_kind k = lit.decl().get_decl_kind(); - if (k == Equal || k == Iff) - MakeElimCand(FindRep(lit.arg(0)), FindRep(lit.arg(1))); - } - } - - for (unsigned i = 0; i < elim_cands.size(); i++) { - elim_cand &cand = elim_cands[i]; - hash_map memo; - CountOtherVarsRec(memo, cand.val, i, cand.sup); - if (cand.sup == 0) - ready_cands.push_back(i); - } - - while (!ready_cands.empty()) { - elim_cand &cand = elim_cands[ready_cands.back()]; - ready_cands.pop_back(); - Term rep = FindRep(cand.var); - if (!eq(rep, cand.var)) - if (cand_map.find(rep) != cand_map.end()) { - int rep_pos = cand_map[rep]; - cand.val = elim_cands[rep_pos].val; - } - Term val = SubstRec(elim_map, cand.val); - if (debug_gauss) { - std::cout << "subbing " << cand.var << " --> " << val << std::endl; - } - elim_map[cand.var] = val; - std::vector &sup = sup_map[cand.var]; - for (unsigned i = 0; i < sup.size(); i++) { - int c = sup[i]; - if ((--elim_cands[c].sup) == 0) - ready_cands.push_back(c); - } - } - - for (unsigned i = 0; i < lits_in.size(); i++) { - Term lit = lits_in[i]; - lit = SubstRec(elim_map, lit); - lit = lit.simplify(); - if (eq(lit, ctx.bool_val(true))) - continue; - Term a; - if (IsPropLit(lit, a)) - if (keep.find(lit) == keep.end()) - continue; - lits_out.push_back(lit); - } - } - - // maps variables to constrains in which the occur pos, neg - hash_map la_index[2]; - hash_map la_coeffs[2]; - std::vector la_pos_vars; - bool fixing; - - void IndexLAcoeff(const Term &coeff1, const Term &coeff2, const Term &t, int id) { - Term coeff = coeff1 * coeff2; - coeff = coeff.simplify(); - Term is_pos = (coeff >= ctx.int_val(0)); - is_pos = is_pos.simplify(); - if (eq(is_pos, ctx.bool_val(true))) - IndexLA(true, coeff, t, id); - else - IndexLA(false, coeff, t, id); - } - - void IndexLAremove(const Term &t) { - if (IsVar(t)) { - la_index[0][t] = -1; // means ineligible to be eliminated - la_index[1][t] = -1; // (more that one occurrence, or occurs not in linear comb) - } - else if (t.is_app()) { - int nargs = t.num_args(); - for (int i = 0; i < nargs; i++) - IndexLAremove(t.arg(i)); - } - // TODO: quantifiers? - } - - - void IndexLA(bool pos, const Term &coeff, const Term &t, int id) { - if (t.is_numeral()) - return; - if (t.is_app()) { - int nargs = t.num_args(); - switch (t.decl().get_decl_kind()) { - case Plus: - for (int i = 0; i < nargs; i++) - IndexLA(pos, coeff, t.arg(i), id); - break; - case Sub: - IndexLA(pos, coeff, t.arg(0), id); - IndexLA(!pos, coeff, t.arg(1), id); - break; - case Times: - if (t.arg(0).is_numeral()) - IndexLAcoeff(coeff, t.arg(0), t.arg(1), id); - else if (t.arg(1).is_numeral()) - IndexLAcoeff(coeff, t.arg(1), t.arg(0), id); - break; - default: - if (IsVar(t) && (fixing || la_index[pos].find(t) == la_index[pos].end())) { - la_index[pos][t] = id; - la_coeffs[pos][t] = coeff; - if (pos && !fixing) - la_pos_vars.push_back(t); // this means we only add a var once - } - else - IndexLAremove(t); - } - } - } - - void IndexLAstart(bool pos, const Term &t, int id){ - IndexLA(pos,(pos ? ctx.int_val(1) : ctx.int_val(-1)), t, id); - } - - void IndexLApred(bool pos, const Term &p, int id) { - if (p.is_app()) { - switch (p.decl().get_decl_kind()) { - case Not: - IndexLApred(!pos, p.arg(0), id); - break; - case Leq: - case Lt: - IndexLAstart(!pos, p.arg(0), id); - IndexLAstart(pos, p.arg(1), id); - break; - case Geq: - case Gt: - IndexLAstart(pos, p.arg(0), id); - IndexLAstart(!pos, p.arg(1), id); - break; - default: - IndexLAremove(p); - } - } - } - - void IndexLAfix(const Term &p, int id){ - fixing = true; - IndexLApred(true,p,id); - fixing = false; - } - - bool IsCanonIneq(const Term &lit, Term &term, Term &bound) { - // std::cout << Z3_simplify_get_help(ctx) << std::endl; - bool pos = lit.decl().get_decl_kind() != Not; - Term atom = pos ? lit : lit.arg(0); - if (atom.decl().get_decl_kind() == Leq) { - if (pos) { - bound = atom.arg(0); - term = atom.arg(1).simplify(simp_params); -#if Z3_MAJOR_VERSION < 4 - term = SortSum(term); -#endif - } - else { - bound = (atom.arg(1) + ctx.int_val(1)); - term = atom.arg(0); - // std::cout << "simplifying bound: " << bound << std::endl; - bound = bound.simplify(); - term = term.simplify(simp_params); -#if Z3_MAJOR_VERSION < 4 - term = SortSum(term); -#endif - } - return true; - } - else if (atom.decl().get_decl_kind() == Geq) { - if (pos) { - bound = atom.arg(1); // integer axiom - term = atom.arg(0).simplify(simp_params); -#if Z3_MAJOR_VERSION < 4 - term = SortSum(term); -#endif - return true; - } - else { - bound = -(atom.arg(1) - ctx.int_val(1)); // integer axiom - term = -atom.arg(0); - bound = bound.simplify(); - term = term.simplify(simp_params); -#if Z3_MAJOR_VERSION < 4 - term = SortSum(term); -#endif - } - return true; - } - return false; - } - - Term CanonIneqTerm(const Term &p){ - Term term,bound; - Term ps = p.simplify(); - VERIFY(IsCanonIneq(ps,term,bound)); - return term - bound; - } - - void ElimRedundantBounds(std::vector &lits) { - hash_map best_bound; - for (unsigned i = 0; i < lits.size(); i++) { - lits[i] = lits[i].simplify(simp_params); - Term term, bound; - if (IsCanonIneq(lits[i], term, bound)) { - if (best_bound.find(term) == best_bound.end()) - best_bound[term] = i; - else { - int best = best_bound[term]; - Term bterm, bbound; - IsCanonIneq(lits[best], bterm, bbound); - Term comp = bound > bbound; - comp = comp.simplify(); - if (eq(comp, ctx.bool_val(true))) { - lits[best] = ctx.bool_val(true); - best_bound[term] = i; - } - else { - lits[i] = ctx.bool_val(true); - } - } - } - } - } - - void FourierMotzkinCheap(const std::vector &lits_in, - std::vector &lits_out) { - simp_params.set(":som", true); - simp_params.set(":sort-sums", true); - fixing = false; lits_out = lits_in; - ElimRedundantBounds(lits_out); - for (unsigned i = 0; i < lits_out.size(); i++) - IndexLApred(true, lits_out[i], i); - - for (unsigned i = 0; i < la_pos_vars.size(); i++) { - Term var = la_pos_vars[i]; - if (la_index[false].find(var) != la_index[false].end()) { - int pos_idx = la_index[true][var]; - int neg_idx = la_index[false][var]; - if (pos_idx >= 0 && neg_idx >= 0) { - if (keep.find(var) != keep.end()) { - std::cout << "would have eliminated keep var\n"; - continue; - } - Term tpos = CanonIneqTerm(lits_out[pos_idx]); - Term tneg = CanonIneqTerm(lits_out[neg_idx]); - Term pos_coeff = la_coeffs[true][var]; - Term neg_coeff = -la_coeffs[false][var]; - Term comb = neg_coeff * tpos + pos_coeff * tneg; - Term ineq = ctx.int_val(0) <= comb; - ineq = ineq.simplify(); - lits_out[pos_idx] = ineq; - lits_out[neg_idx] = ctx.bool_val(true); - IndexLAfix(ineq, pos_idx); - } - } - } - } - - Term ProjectFormula(const Term &f){ - std::vector lits, new_lits1, new_lits2; - CollectConjuncts(f,lits); - timer_start("GaussElimCheap"); - GaussElimCheap(lits,new_lits1); - timer_stop("GaussElimCheap"); - timer_start("FourierMotzkinCheap"); - FourierMotzkinCheap(new_lits1,new_lits2); - timer_stop("FourierMotzkinCheap"); - return conjoin(new_lits2); - } - }; - - void Z3User::CollectConjuncts(const Term &f, std::vector &lits, bool pos) { - if (f.is_app() && f.decl().get_decl_kind() == Not) - CollectConjuncts(f.arg(0), lits, !pos); - else if (pos && f.is_app() && f.decl().get_decl_kind() == And) { - int num_args = f.num_args(); - for (int i = 0; i < num_args; i++) - CollectConjuncts(f.arg(i), lits, true); - } - else if (!pos && f.is_app() && f.decl().get_decl_kind() == Or) { - int num_args = f.num_args(); - for (int i = 0; i < num_args; i++) - CollectConjuncts(f.arg(i), lits, false); - } - else if (pos) { - if (!eq(f, ctx.bool_val(true))) - lits.push_back(f); - } - else { - if (!eq(f, ctx.bool_val(false))) - lits.push_back(!f); - } - } - - void Z3User::CollectJuncts(const Term &f, std::vector &lits, decl_kind op, bool negate) { - if (f.is_app() && f.decl().get_decl_kind() == Not) - CollectJuncts(f.arg(0), lits, (op == And) ? Or : And, !negate); - else if (f.is_app() && f.decl().get_decl_kind() == op) { - int num_args = f.num_args(); - for (int i = 0; i < num_args; i++) - CollectJuncts(f.arg(i), lits, op, negate); - } - else { - expr junct = negate ? Negate(f) : f; - lits.push_back(junct); - } - } - - struct TermLt { - bool operator()(const expr &x, const expr &y){ - unsigned xid = x.get_id(); - unsigned yid = y.get_id(); - return xid < yid; - } - }; - - void Z3User::SortTerms(std::vector &terms){ - TermLt foo; - std::sort(terms.begin(),terms.end(),foo); - } - - Z3User::Term Z3User::SortSum(const Term &t){ - if(!(t.is_app() && t.decl().get_decl_kind() == Plus)) - return t; - int nargs = t.num_args(); - if(nargs < 2) return t; - std::vector args(nargs); - for(int i = 0; i < nargs; i++) - args[i] = t.arg(i); - SortTerms(args); - if(nargs == 2) - return args[0] + args[1]; - return sum(args); - } - - - RPFP::Term RPFP::ProjectFormula(std::vector &keep_vec, const Term &f){ - VariableProjector vp(*this,keep_vec); - return vp.ProjectFormula(f); - } - - /** Compute an underapproximation of every node in a tree rooted at "root", - based on a previously computed counterexample. The underapproximation - may contain free variables that are implicitly existentially quantified. - */ - - RPFP::Term RPFP::ComputeUnderapprox(Node *root, int persist){ - /* if terminated underapprox is empty set (false) */ - bool show_model = false; - if(show_model) - std::cout << dualModel << std::endl; - if(!root->Outgoing){ - root->Underapprox.SetEmpty(); - return ctx.bool_val(true); - } - /* if not used in cex, underapprox is empty set (false) */ - if(Empty(root)){ - root->Underapprox.SetEmpty(); - return ctx.bool_val(true); - } - /* compute underapprox of children first */ - std::vector &chs = root->Outgoing->Children; - std::vector chu(chs.size()); - for(unsigned i = 0; i < chs.size(); i++) - chu[i] = ComputeUnderapprox(chs[i],persist); - - Term b; std::vector v; - RedVars(root, b, v); - /* underapproximate the edge formula */ - hash_set dont_cares; - dont_cares.insert(b); - resolve_ite_memo.clear(); - timer_start("UnderapproxFormula"); - Term dual = root->Outgoing->dual.null() ? ctx.bool_val(true) : root->Outgoing->dual; - Term eu = UnderapproxFormula(dual,dont_cares); - timer_stop("UnderapproxFormula"); - /* combine with children */ - chu.push_back(eu); - eu = conjoin(chu); - /* project onto appropriate variables */ - eu = ProjectFormula(v,eu); - eu = eu.simplify(); - -#if 0 - /* check the result is consistent */ - { - hash_map memo; - int res = SubtermTruth(memo, eu); - if(res != 1) - throw "inconsistent projection"; - } -#endif - - /* rename to appropriate variable names */ - hash_map memo; - for (unsigned i = 0; i < v.size(); i++) - memo[v[i]] = root->Annotation.IndParams[i]; /* copy names from annotation */ - Term funder = SubstRec(memo, eu); - root->Underapprox = CreateRelation(root->Annotation.IndParams,funder); -#if 0 - if(persist) - Z3_persist_ast(ctx,root->Underapprox.Formula,persist); -#endif - return eu; - } - - void RPFP::FixCurrentState(Edge *edge){ - hash_set dont_cares; - resolve_ite_memo.clear(); - timer_start("UnderapproxFormula"); - Term dual = edge->dual.null() ? ctx.bool_val(true) : edge->dual; - Term eu = UnderapproxFormula(dual,dont_cares); - timer_stop("UnderapproxFormula"); - ConstrainEdgeLocalized(edge,eu); - } - - void RPFP::GetGroundLitsUnderQuants(hash_set *memo, const Term &f, std::vector &res, int under){ - if(memo[under].find(f) != memo[under].end()) - return; - memo[under].insert(f); - if (f.is_app()) { - if (!under && !f.has_quantifiers()) - return; - decl_kind k = f.decl().get_decl_kind(); - if (k == And || k == Or || k == Implies || k == Iff) { - int num_args = f.num_args(); - for (int i = 0; i < num_args; i++) - GetGroundLitsUnderQuants(memo, f.arg(i), res, under); - return; - } - } - else if (f.is_quantifier()){ -#if 0 - // treat closed quantified formula as a literal 'cause we hate nested quantifiers - if(under && IsClosedFormula(f)) - res.push_back(f); - else -#endif - GetGroundLitsUnderQuants(memo,f.body(),res,1); - return; - } - if(f.is_var()){ - // std::cout << "foo!\n"; - return; - } - if(under && f.is_ground()) - res.push_back(f); - } - - RPFP::Term RPFP::StrengthenFormulaByCaseSplitting(const Term &f, std::vector &case_lits){ - hash_set memo[2]; - std::vector lits; - GetGroundLitsUnderQuants(memo, f, lits, 0); - hash_set lits_hash; - for(unsigned i = 0; i < lits.size(); i++) - lits_hash.insert(lits[i]); - hash_map subst; - hash_map stt_memo; - std::vector conjuncts; - for(unsigned i = 0; i < lits.size(); i++){ - const expr &lit = lits[i]; - if(lits_hash.find(NegateLit(lit)) == lits_hash.end()){ - case_lits.push_back(lit); - bool tval = false; - expr atom = lit; - if(lit.is_app() && lit.decl().get_decl_kind() == Not){ - tval = true; - atom = lit.arg(0); - } - expr etval = ctx.bool_val(tval); - if(atom.is_quantifier()) - subst[atom] = etval; // this is a bit desperate, since we can't eval quants - else { - int b = SubtermTruth(stt_memo,atom); - if(b == (tval ? 1 : 0)) - subst[atom] = etval; - else { - if(b == 0 || b == 1){ - etval = ctx.bool_val(b ? true : false); - subst[atom] = etval; - conjuncts.push_back(b ? atom : !atom); - } - } - } - } - } - expr g = f; - if(!subst.empty()){ - g = SubstRec(subst,f); - if(conjuncts.size()) - g = g && ctx.make(And,conjuncts); - g = g.simplify(); - } -#if 1 - expr g_old = g; - g = RemoveRedundancy(g); - bool changed = !eq(g,g_old); - g = g.simplify(); - if(changed) { // a second pass can get some more simplification - g = RemoveRedundancy(g); - g = g.simplify(); - } -#else - g = RemoveRedundancy(g); - g = g.simplify(); -#endif - g = AdjustQuantifiers(g); - return g; - } - - RPFP::Term RPFP::ModelValueAsConstraint(const Term &t) { - if (t.is_array()) { - ArrayValue arr; - Term e = dualModel.eval(t); - EvalArrayTerm(e, arr); - if (arr.defined) { - std::vector cs; - for (std::map::iterator it = arr.entries.begin(), en = arr.entries.end(); it != en; ++it) { - expr foo = select(t, expr(ctx, it->first)) == expr(ctx, it->second); - cs.push_back(foo); - } - return conjoin(cs); - } - } - else { - expr r = dualModel.get_const_interp(t.decl()); - if (!r.null()) { - expr res = t == expr(ctx, r); - return res; - } - } - return ctx.bool_val(true); - } - - void RPFP::EvalNodeAsConstraint(Node *p, Transformer &res) - { - Term b; std::vector v; - RedVars(p, b, v); - std::vector args; - for(unsigned i = 0; i < v.size(); i++){ - expr val = ModelValueAsConstraint(v[i]); - if(!eq(val,ctx.bool_val(true))) - args.push_back(val); - } - expr cnst = conjoin(args); - hash_map memo; - for (unsigned i = 0; i < v.size(); i++) - memo[v[i]] = p->Annotation.IndParams[i]; /* copy names from annotation */ - Term funder = SubstRec(memo, cnst); - res = CreateRelation(p->Annotation.IndParams,funder); - } - -#if 0 - void RPFP::GreedyReduce(solver &s, std::vector &conjuncts){ - // verify - s.push(); - expr conj = ctx.make(And,conjuncts); - s.add(conj); - check_result res = s.check(); - if(res != unsat) - throw "should be unsat"; - s.pop(1); - - for(unsigned i = 0; i < conjuncts.size(); ){ - std::swap(conjuncts[i],conjuncts.back()); - expr save = conjuncts.back(); - conjuncts.pop_back(); - s.push(); - expr conj = ctx.make(And,conjuncts); - s.add(conj); - check_result res = s.check(); - s.pop(1); - if(res != unsat){ - conjuncts.push_back(save); - std::swap(conjuncts[i],conjuncts.back()); - i++; - } - } - } -#endif - - void RPFP::GreedyReduce(solver &s, std::vector &conjuncts){ - std::vector lits(conjuncts.size()); - for(unsigned i = 0; i < lits.size(); i++){ - func_decl pred = ctx.fresh_func_decl("@alit", ctx.bool_sort()); - lits[i] = pred(); - s.add(ctx.make(Implies,lits[i],conjuncts[i])); - } - - // verify - check_result res = s.check(lits.size(), VEC2PTR(lits)); - if(res != unsat){ - // add the axioms in the off chance they are useful - const std::vector &theory = ls->get_axioms(); - for(unsigned i = 0; i < theory.size(); i++) - s.add(theory[i]); - for(int k = 0; k < 100; k++) // keep trying, maybe MBQI will do something! - if(s.check(lits.size(), VEC2PTR(lits)) == unsat) - goto is_unsat; - throw "should be unsat"; - } - is_unsat: - for(unsigned i = 0; i < conjuncts.size(); ){ - std::swap(conjuncts[i],conjuncts.back()); - std::swap(lits[i],lits.back()); - check_result res = s.check(lits.size()-1, VEC2PTR(lits)); - if(res != unsat){ - std::swap(conjuncts[i],conjuncts.back()); - std::swap(lits[i],lits.back()); - i++; - } - else { - conjuncts.pop_back(); - lits.pop_back(); - } - } - } - - void foobar(){ - } - - void RPFP::GreedyReduceNodes(std::vector &nodes){ - std::vector lits; - for(unsigned i = 0; i < nodes.size(); i++){ - Term b; std::vector v; - RedVars(nodes[i], b, v); - lits.push_back(!b); - expr bv = dualModel.eval(b); - if(eq(bv,ctx.bool_val(true))){ - check_result res = slvr_check(lits.size(), VEC2PTR(lits)); - if(res == unsat) - lits.pop_back(); - else - foobar(); - } - } - } - - check_result RPFP::CheckWithConstrainedNodes(std::vector &posnodes,std::vector &negnodes){ - timer_start("Check"); - std::vector lits; - for(unsigned i = 0; i < posnodes.size(); i++){ - Term b; std::vector v; - RedVars(posnodes[i], b, v); - lits.push_back(b); - } - for(unsigned i = 0; i < negnodes.size(); i++){ - Term b; std::vector v; - RedVars(negnodes[i], b, v); - lits.push_back(!b); - } - check_result res = slvr_check(lits.size(), VEC2PTR(lits)); - if(res == unsat && posnodes.size()){ - lits.resize(posnodes.size()); - res = slvr_check(lits.size(), VEC2PTR(lits)); - } - dualModel = slvr().get_model(); -#if 0 - if(!dualModel.null()){ - std::cout << "posnodes called:\n"; - for(unsigned i = 0; i < posnodes.size(); i++) - if(!Empty(posnodes[i])) - std::cout << posnodes[i]->Name.name() << "\n"; - std::cout << "negnodes called:\n"; - for(unsigned i = 0; i < negnodes.size(); i++) - if(!Empty(negnodes[i])) - std::cout << negnodes[i]->Name.name() << "\n"; - } -#endif - timer_stop("Check"); - return res; - } - - - void RPFP_caching::FilterCore(std::vector &core, std::vector &full_core){ - hash_set core_set; - std::copy(full_core.begin(),full_core.end(),std::inserter(core_set,core_set.begin())); - std::vector new_core; - for(unsigned i = 0; i < core.size(); i++) - if(core_set.find(core[i]) != core_set.end()) - new_core.push_back(core[i]); - core.swap(new_core); - } - - void RPFP_caching::GreedyReduceCache(std::vector &assumps, std::vector &core){ - std::vector lits = assumps, full_core; - std::copy(core.begin(),core.end(),std::inserter(lits,lits.end())); - - // verify - check_result res = CheckCore(lits,full_core); - if(res != unsat){ - // add the axioms in the off chance they are useful - const std::vector &theory = ls->get_axioms(); - for(unsigned i = 0; i < theory.size(); i++) - GetAssumptionLits(theory[i],assumps); - lits = assumps; - std::copy(core.begin(),core.end(),std::inserter(lits,lits.end())); - - for(int k = 0; k < 4; k++) // keep trying, maybe MBQI will do something! - if((res = CheckCore(lits,full_core)) == unsat) - goto is_unsat; - throw greedy_reduce_failed(); - } - is_unsat: - FilterCore(core,full_core); - - std::vector dummy; - if(CheckCore(full_core,dummy) != unsat) - throw "should be unsat"; - - for(unsigned i = 0; i < core.size(); ){ - expr temp = core[i]; - std::swap(core[i],core.back()); - core.pop_back(); - lits.resize(assumps.size()); - std::copy(core.begin(),core.end(),std::inserter(lits,lits.end())); - res = CheckCore(lits,full_core); - if(res != unsat){ - core.push_back(temp); - std::swap(core[i],core.back()); - i++; - } - } - } - - expr RPFP::NegateLit(const expr &f){ - if(f.is_app() && f.decl().get_decl_kind() == Not) - return f.arg(0); - else - return !f; - } - - void RPFP::NegateLits(std::vector &lits){ - for(unsigned i = 0; i < lits.size(); i++){ - expr &f = lits[i]; - if(f.is_app() && f.decl().get_decl_kind() == Not) - f = f.arg(0); - else - f = !f; - } - } - - expr RPFP::SimplifyOr(std::vector &lits){ - if(lits.size() == 0) - return ctx.bool_val(false); - if(lits.size() == 1) - return lits[0]; - return ctx.make(Or,lits); - } - - expr RPFP::SimplifyAnd(std::vector &lits){ - if(lits.size() == 0) - return ctx.bool_val(true); - if(lits.size() == 1) - return lits[0]; - return ctx.make(And,lits); - } - - - /* This is a wrapper for a solver that is intended to compute - implicants from models. It works around a problem in Z3 with - models in the non-extensional array theory. It does this by - naming all of the store terms in a formula. That is, (store ...) - is replaced by "name" with an added constraint name = (store - ...). This allows us to determine from the model whether an array - equality is true or false (it is false if the two sides are - mapped to different function symbols, even if they have the same - contents). - */ - - struct implicant_solver { - RPFP *owner; - solver &aux_solver; - std::vector assumps, namings; - std::vector assump_stack, naming_stack; - hash_map renaming, renaming_memo; - - void add(const expr &e){ - expr t = e; - if(!aux_solver.extensional_array_theory()){ - unsigned i = namings.size(); - t = owner->ExtractStores(renaming_memo,t,namings,renaming); - for(; i < namings.size(); i++) - aux_solver.add(namings[i]); - } - assumps.push_back(t); - aux_solver.add(t); - } - - void push() { - assump_stack.push_back(assumps.size()); - naming_stack.push_back(namings.size()); - aux_solver.push(); - } - - // When we pop the solver, we have to re-add any namings that were lost - - void pop(int n) { - aux_solver.pop(n); - int new_assumps = assump_stack[assump_stack.size()-n]; - int new_namings = naming_stack[naming_stack.size()-n]; - for(unsigned i = new_namings; i < namings.size(); i++) - aux_solver.add(namings[i]); - assumps.resize(new_assumps); - namings.resize(new_namings); - assump_stack.resize(assump_stack.size()-1); - naming_stack.resize(naming_stack.size()-1); - } - - check_result check() { - return aux_solver.check(); - } - - model get_model() { - return aux_solver.get_model(); - } - - expr get_implicant() { - owner->dualModel = aux_solver.get_model(); - expr dual = owner->ctx.make(And,assumps); - bool ext = aux_solver.extensional_array_theory(); - expr eu = owner->UnderapproxFullFormula(dual,ext); - // if we renamed store terms, we have to undo - if(!ext) - eu = owner->SubstRec(renaming,eu); - return eu; - } - - implicant_solver(RPFP *_owner, solver &_aux_solver) - : owner(_owner), aux_solver(_aux_solver) - {} - }; - - // set up edge constraint in aux solver - void RPFP::AddEdgeToSolver(implicant_solver &aux_solver, Edge *edge){ - if(!edge->dual.null()) - aux_solver.add(edge->dual); - for(unsigned i = 0; i < edge->constraints.size(); i++){ - expr tl = edge->constraints[i]; - aux_solver.add(tl); - } - } - - void RPFP::AddEdgeToSolver(Edge *edge){ - if(!edge->dual.null()) - aux_solver.add(edge->dual); - for(unsigned i = 0; i < edge->constraints.size(); i++){ - expr tl = edge->constraints[i]; - aux_solver.add(tl); - } - } - - static int by_case_counter = 0; - - void RPFP::InterpolateByCases(Node *root, Node *node){ - timer_start("InterpolateByCases"); - bool axioms_added = false; - hash_set axioms_needed; - const std::vector &theory = ls->get_axioms(); - for(unsigned i = 0; i < theory.size(); i++) - axioms_needed.insert(theory[i]); - implicant_solver is(this,aux_solver); - is.push(); - AddEdgeToSolver(is,node->Outgoing); - node->Annotation.SetEmpty(); - hash_set *core = new hash_set; - core->insert(node->Outgoing->dual); - expr prev_annot = ctx.bool_val(false); - expr prev_impl = ctx.bool_val(false); - int repeated_case_count = 0; - while(1){ - by_case_counter++; - is.push(); - expr annot = !GetAnnotation(node); - Transformer old_annot = node->Annotation; - is.add(annot); - if(is.check() == unsat){ - is.pop(1); - break; - } - is.pop(1); - Push(); - expr the_impl = is.get_implicant(); - if(eq(the_impl,prev_impl)){ - // std::cout << "got old implicant\n"; - repeated_case_count++; - } - prev_impl = the_impl; - ConstrainEdgeLocalized(node->Outgoing,the_impl); - ConstrainEdgeLocalized(node->Outgoing,!GetAnnotation(node)); //TODO: need this? - - { - check_result foo = Check(root); - if(foo != unsat){ - Pop(1); - is.pop(1); - delete core; - timer_stop("InterpolateByCases"); - throw ReallyBad(); - // slvr().print("should_be_unsat.smt2"); - // throw "should be unsat"; - } - std::vector assumps, axioms_to_add; - slvr().get_proof().get_assumptions(assumps); - for(unsigned i = 0; i < assumps.size(); i++){ - (*core).insert(assumps[i]); - if(axioms_needed.find(assumps[i]) != axioms_needed.end()){ - axioms_to_add.push_back(assumps[i]); - axioms_needed.erase(assumps[i]); - } - } - // AddToProofCore(*core); - - try { - SolveSingleNode(root,node); - } - catch (char const *msg){ - // This happens if interpolation fails - Pop(1); - is.pop(1); - delete core; - timer_stop("InterpolateByCases"); - throw msg; - } - { - expr itp = GetAnnotation(node); - dualModel = is.get_model(); // TODO: what does this mean? - std::vector case_lits; - itp = StrengthenFormulaByCaseSplitting(itp, case_lits); - SetAnnotation(node,itp); - node->Annotation.Formula = node->Annotation.Formula.simplify(); - } - - for(unsigned i = 0; i < axioms_to_add.size(); i++) - is.add(axioms_to_add[i]); - -#define TEST_BAD -#ifdef TEST_BAD - { - static int bad_count = 0, num_bads = 1; - if(bad_count >= num_bads){ - bad_count = 0; - num_bads = num_bads * 2; - Pop(1); - is.pop(1); - delete core; - timer_stop("InterpolateByCases"); - throw Bad(); - } - bad_count++; - } -#endif - } - - if(node->Annotation.IsEmpty() || eq(node->Annotation.Formula,prev_annot) || (repeated_case_count > 0 && !axioms_added) || (repeated_case_count >= 10)){ - //looks_bad: - if(!axioms_added){ - // add the axioms in the off chance they are useful - const std::vector &theory = ls->get_axioms(); - for(unsigned i = 0; i < theory.size(); i++) - is.add(theory[i]); - axioms_added = true; - } - else { - //#define KILL_ON_BAD_INTERPOLANT -#ifdef KILL_ON_BAD_INTERPOLANT - std::cout << "bad in InterpolateByCase -- core:\n"; -#if 0 - std::vector assumps; - slvr().get_proof().get_assumptions(assumps); - for(unsigned i = 0; i < assumps.size(); i++) - assumps[i].show(); -#endif - std::cout << "checking for inconsistency\n"; - std::cout << "model:\n"; - is.get_model().show(); - expr impl = is.get_implicant(); - std::vector conjuncts; - CollectConjuncts(impl,conjuncts,true); - std::cout << "impl:\n"; - for(unsigned i = 0; i < conjuncts.size(); i++) - conjuncts[i].show(); - std::cout << "annot:\n"; - annot.show(); - is.add(annot); - for(unsigned i = 0; i < conjuncts.size(); i++) - is.add(conjuncts[i]); - if(is.check() == unsat){ - std::cout << "inconsistent!\n"; - std::vector is_assumps; - is.aux_solver.get_proof().get_assumptions(is_assumps); - std::cout << "core:\n"; - for(unsigned i = 0; i < is_assumps.size(); i++) - is_assumps[i].show(); - } - else { - std::cout << "consistent!\n"; - is.aux_solver.print("should_be_inconsistent.smt2"); - } - std::cout << "by_case_counter = " << by_case_counter << "\n"; - throw "ack!"; -#endif - Pop(1); - is.pop(1); - delete core; - timer_stop("InterpolateByCases"); - throw ReallyBad(); - } - } - Pop(1); - prev_annot = node->Annotation.Formula; - node->Annotation.UnionWith(old_annot); - } - if(proof_core) - delete proof_core; // shouldn't happen - proof_core = core; - is.pop(1); - timer_stop("InterpolateByCases"); - } - - void RPFP::Generalize(Node *root, Node *node){ - timer_start("Generalize"); - aux_solver.push(); - AddEdgeToSolver(node->Outgoing); - expr fmla = GetAnnotation(node); - std::vector conjuncts; - CollectConjuncts(fmla,conjuncts,false); - GreedyReduce(aux_solver,conjuncts); // try to remove conjuncts one at a tme - aux_solver.pop(1); - NegateLits(conjuncts); - SetAnnotation(node,SimplifyOr(conjuncts)); - timer_stop("Generalize"); - } - - RPFP_caching::edge_solver &RPFP_caching::SolverForEdge(Edge *edge, bool models, bool axioms){ - edge_solver &es = edge_solvers[edge]; - uptr &p = es.slvr; - if(!p.get()){ - scoped_no_proof no_proofs_please(ctx.m()); // no proofs - p.set(new solver(ctx,true,models)); // no models - if(axioms){ - RPFP::LogicSolver *ls = edge->owner->ls; - const std::vector &axs = ls->get_axioms(); - for(unsigned i = 0; i < axs.size(); i++) - p.get()->add(axs[i]); - } - } - return es; - } - - - // caching version of above - void RPFP_caching::GeneralizeCache(Edge *edge){ - timer_start("Generalize"); - scoped_solver_for_edge ssfe(this,edge); - Node *node = edge->Parent; - std::vector assumps, core, conjuncts; - AssertEdgeCache(edge,assumps); - for(unsigned i = 0; i < edge->Children.size(); i++){ - expr as = GetAnnotation(edge->Children[i]); - std::vector clauses; - if(!as.is_true()){ - CollectConjuncts(as.arg(1),clauses); - for(unsigned j = 0; j < clauses.size(); j++) - GetAssumptionLits(as.arg(0) || clauses[j],assumps); - } - } - expr fmla = GetAnnotation(node); - std::vector lits; - if(fmla.is_true()){ - timer_stop("Generalize"); - return; - } - assumps.push_back(fmla.arg(0).arg(0)); - CollectConjuncts(!fmla.arg(1),lits); -#if 0 - for(unsigned i = 0; i < lits.size(); i++){ - const expr &lit = lits[i]; - if(lit.is_app() && lit.decl().get_decl_kind() == Equal){ - lits[i] = ctx.make(Leq,lit.arg(0),lit.arg(1)); - lits.push_back(ctx.make(Leq,lit.arg(1),lit.arg(0))); - } - } -#endif - hash_map lit_map; - for(unsigned i = 0; i < lits.size(); i++) - GetAssumptionLits(lits[i],core,&lit_map); - GreedyReduceCache(assumps,core); - for(unsigned i = 0; i < core.size(); i++) - conjuncts.push_back(lit_map[core[i]]); - NegateLits(conjuncts); - SetAnnotation(node,SimplifyOr(conjuncts)); - timer_stop("Generalize"); - } - - // caching version of above - bool RPFP_caching::PropagateCache(Edge *edge){ - timer_start("PropagateCache"); - scoped_solver_for_edge ssfe(this,edge); - bool some = false; - { - std::vector candidates, skip; - Node *node = edge->Parent; - CollectConjuncts(node->Annotation.Formula,skip); - for(unsigned i = 0; i < edge->Children.size(); i++){ - Node *child = edge->Children[i]; - if(child->map == node->map){ - CollectConjuncts(child->Annotation.Formula,candidates); - break; - } - } - if(candidates.empty()) goto done; - hash_set skip_set; - std::copy(skip.begin(),skip.end(),std::inserter(skip_set,skip_set.begin())); - std::vector new_candidates; - for(unsigned i = 0; i < candidates.size(); i++) - if(skip_set.find(candidates[i]) == skip_set.end()) - new_candidates.push_back(candidates[i]); - candidates.swap(new_candidates); - if(candidates.empty()) goto done; - std::vector assumps, core, conjuncts; - AssertEdgeCache(edge,assumps); - for(unsigned i = 0; i < edge->Children.size(); i++){ - expr ass = GetAnnotation(edge->Children[i]); - if(eq(ass,ctx.bool_val(true))) - continue; - std::vector clauses; - CollectConjuncts(ass.arg(1),clauses); - for(unsigned j = 0; j < clauses.size(); j++) - GetAssumptionLits(ass.arg(0) || clauses[j],assumps); - } - for(unsigned i = 0; i < candidates.size(); i++){ - unsigned old_size = assumps.size(); - node->Annotation.Formula = candidates[i]; - expr fmla = GetAnnotation(node); - assumps.push_back(fmla.arg(0).arg(0)); - GetAssumptionLits(!fmla.arg(1),assumps); - std::vector full_core; - check_result res = CheckCore(assumps,full_core); - if(res == unsat) - conjuncts.push_back(candidates[i]); - assumps.resize(old_size); - } - if(conjuncts.empty()) - goto done; - SetAnnotation(node,SimplifyAnd(conjuncts)); - some = true; - } - done: - timer_stop("PropagateCache"); - return some; - } - - - /** Push a scope. Assertions made after Push can be undone by Pop. */ - - void RPFP::Push() - { - stack.push_back(stack_entry()); - slvr_push(); - } - - /** Pop a scope (see Push). Note, you cannot pop axioms. */ - - void RPFP::Pop(int num_scopes) - { - slvr_pop(num_scopes); - for (int i = 0; i < num_scopes; i++) - { - stack_entry &back = stack.back(); - for(std::list::iterator it = back.edges.begin(), en = back.edges.end(); it != en; ++it) - (*it)->dual = expr(ctx,nullptr); - for(std::list::iterator it = back.nodes.begin(), en = back.nodes.end(); it != en; ++it) - (*it)->dual = expr(ctx,nullptr); - for(std::list >::iterator it = back.constraints.begin(), en = back.constraints.end(); it != en; ++it) - (*it).first->constraints.pop_back(); - stack.pop_back(); - } - } - - /** Erase the proof by performing a Pop, Push and re-assertion of - all the popped constraints */ - - void RPFP::PopPush(){ - slvr_pop(1); - slvr_push(); - stack_entry &back = stack.back(); - for(std::list::iterator it = back.edges.begin(), en = back.edges.end(); it != en; ++it) - slvr_add((*it)->dual); - for(std::list::iterator it = back.nodes.begin(), en = back.nodes.end(); it != en; ++it) - slvr_add((*it)->dual); - for(std::list >::iterator it = back.constraints.begin(), en = back.constraints.end(); it != en; ++it) - slvr_add((*it).second); - } - - - - // This returns a new FuncDel with same sort as top-level function - // of term t, but with numeric suffix appended to name. - - Z3User::FuncDecl Z3User::SuffixFuncDecl(const Term &t, int n) - { - std::string name = t.decl().name().str() + "_" + string_of_int(n); - std::vector sorts; - int nargs = t.num_args(); - sorts.reserve(nargs); - for(int i = 0; i < nargs; i++) - sorts.push_back(t.arg(i).get_sort()); - return ctx.function(name.c_str(), nargs, VEC2PTR(sorts), t.get_sort()); - } - - Z3User::FuncDecl Z3User::RenumberPred(const FuncDecl &f, int n) - { - std::string name = f.name().str(); - name = name.substr(0,name.rfind('_')) + "_" + string_of_int(n); - int arity = f.arity(); - std::vector domain; - domain.reserve(arity); - for(int i = 0; i < arity; i++) - domain.push_back(f.domain(i)); - return ctx.function(name.c_str(), arity, VEC2PTR(domain), f.range()); - } - - Z3User::FuncDecl Z3User::NumberPred(const FuncDecl &f, int n) - { - std::string name = f.name().str(); - name = name + "_" + string_of_int(n); - int arity = f.arity(); - std::vector domain; - domain.reserve(arity); - for(int i = 0; i < arity; i++) - domain.push_back(f.domain(i)); - return ctx.function(name.c_str(), arity, VEC2PTR(domain), f.range()); - } - - // Scan the clause body for occurrences of the predicate unknowns - - RPFP::Term RPFP::ScanBody(hash_map &memo, - const Term &t, - hash_map &pmap, - std::vector &parms, - std::vector &nodes) - { - if(memo.find(t) != memo.end()) - return memo[t]; - Term res(ctx); - if (t.is_app()) { - func_decl f = t.decl(); - if(pmap.find(f) != pmap.end()){ - nodes.push_back(pmap[f]); - f = SuffixFuncDecl(t,parms.size()); - parms.push_back(f); - } - int nargs = t.num_args(); - std::vector args; - args.reserve(nargs); - for(int i = 0; i < nargs; i++) - args.push_back(ScanBody(memo,t.arg(i),pmap,parms,nodes)); - res = f(nargs, VEC2PTR(args)); - } - else if (t.is_quantifier()) - res = CloneQuantifier(t,ScanBody(memo,t.body(),pmap,parms,nodes)); - else - res = t; - memo[t] = res; - return res; - } - - // return the func_del of an app if it is uninterpreted - - bool Z3User::get_relation(const Term &t, func_decl &R){ - if(!t.is_app()) - return false; - R = t.decl(); - return R.get_decl_kind() == Uninterpreted; - } - - // return true if term is an individual variable - // TODO: have to check that it is not a background symbol - - bool Z3User::is_variable(const Term &t){ - if(!t.is_app()) - return t.is_var(); - return t.decl().get_decl_kind() == Uninterpreted - && t.num_args() == 0; - } - - RPFP::Term RPFP::RemoveLabelsRec(hash_map &memo, const Term &t, - std::vector &lbls){ - if(memo.find(t) != memo.end()) - return memo[t]; - Term res(ctx); - if (t.is_app()){ - func_decl f = t.decl(); - std::vector names; - bool pos; - if(t.is_label(pos,names)){ - res = RemoveLabelsRec(memo,t.arg(0),lbls); - for(unsigned i = 0; i < names.size(); i++) - lbls.push_back(label_struct(names[i],res,pos)); - } - else { - int nargs = t.num_args(); - std::vector args; - args.reserve(nargs); - for(int i = 0; i < nargs; i++) - args.push_back(RemoveLabelsRec(memo,t.arg(i),lbls)); - res = f(nargs, VEC2PTR(args)); - } - } - else if (t.is_quantifier()) - res = CloneQuantifier(t,RemoveLabelsRec(memo,t.body(),lbls)); - else - res = t; - memo[t] = res; - return res; - } - - RPFP::Term RPFP::RemoveLabels(const Term &t, std::vector &lbls){ - hash_map memo ; - return RemoveLabelsRec(memo,t,lbls); - } - - RPFP::Term RPFP::SubstBoundRec(hash_map > &memo, hash_map &subst, int level, const Term &t) - { - std::pair foo(t,expr(ctx)); - std::pair::iterator, bool> bar = memo[level].insert(foo); - Term &res = bar.first->second; - if(!bar.second) return res; - if (t.is_app()) - { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - args.reserve(nargs); - if(nargs == 0 && f.get_decl_kind() == Uninterpreted) - ls->declare_constant(f); // keep track of background constants - for(int i = 0; i < nargs; i++) - args.push_back(SubstBoundRec(memo, subst, level, t.arg(i))); - res = f(args.size(), VEC2PTR(args)); - } - else if (t.is_quantifier()){ - int bound = t.get_quantifier_num_bound(); - std::vector pats; - t.get_patterns(pats); - for(unsigned i = 0; i < pats.size(); i++) - pats[i] = SubstBoundRec(memo, subst, level + bound, pats[i]); - res = clone_quantifier(t, SubstBoundRec(memo, subst, level + bound, t.body()), pats); - } - else if (t.is_var()) { - int idx = t.get_index_value(); - if(idx >= level && subst.find(idx-level) != subst.end()){ - res = subst[idx-level]; - } - else res = t; - } - else res = t; - return res; - } - - RPFP::Term RPFP::SubstBound(hash_map &subst, const Term &t){ - hash_map > memo; - return SubstBoundRec(memo, subst, 0, t); - } - - // Eliminate the deBruijn indices from level to level+num-1 - Z3User::Term Z3User::DeleteBoundRec(hash_map > &memo, int level, int num, const Term &t) - { - std::pair foo(t,expr(ctx)); - std::pair::iterator, bool> bar = memo[level].insert(foo); - Term &res = bar.first->second; - if(!bar.second) return res; - if (t.is_app()) - { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - args.reserve(nargs); - for(int i = 0; i < nargs; i++) - args.push_back(DeleteBoundRec(memo, level, num, t.arg(i))); - res = f(args.size(), VEC2PTR(args)); - } - else if (t.is_quantifier()){ - int bound = t.get_quantifier_num_bound(); - std::vector pats; - t.get_patterns(pats); - for(unsigned i = 0; i < pats.size(); i++) - pats[i] = DeleteBoundRec(memo, level + bound, num, pats[i]); - res = clone_quantifier(t, DeleteBoundRec(memo, level + bound, num, t.body()), pats); - } - else if (t.is_var()) { - int idx = t.get_index_value(); - if(idx >= level){ - res = ctx.make_var(idx-num,t.get_sort()); - } - else res = t; - } - else res = t; - return res; - } - - Z3User::Term Z3User::DeleteBound(int level, int num, const Term &t){ - hash_map > memo; - return DeleteBoundRec(memo, level, num, t); - } - - int Z3User::MaxIndex(hash_map &memo, const Term &t) - { - std::pair foo(t,-1); - std::pair::iterator, bool> bar = memo.insert(foo); - int &res = bar.first->second; - if(!bar.second) return res; - if (t.is_app()){ - func_decl f = t.decl(); - int nargs = t.num_args(); - for(int i = 0; i < nargs; i++){ - int m = MaxIndex(memo, t.arg(i)); - if(m > res) - res = m; - } - } - else if (t.is_quantifier()){ - int bound = t.get_quantifier_num_bound(); - res = MaxIndex(memo,t.body()) - bound; - } - else if (t.is_var()) { - res = t.get_index_value(); - } - return res; - } - - bool Z3User::IsClosedFormula(const Term &t){ - hash_map memo; - return MaxIndex(memo,t) < 0; - } - - - /** Convert a collection of clauses to Nodes and Edges in the RPFP. - - Predicate unknowns are uninterpreted predicates not - occurring in the background theory. - - Clauses are of the form - - B => P(t_1,...,t_k) - - where P is a predicate unknown and predicate unknowns - occur only positivey in H and only under existential - quantifiers in prenex form. - - Each predicate unknown maps to a node. Each clause maps to - an edge. Let C be a clause B => P(t_1,...,t_k) where the - sequence of predicate unknowns occurring in B (in order - of occurrence) is P_1..P_n. The clause maps to a transformer - T where: - - T.Relparams = P_1..P_n - T.Indparams = x_1...x+k - T.Formula = B /\ t_1 = x_1 /\ ... /\ t_k = x_k - - Throws exception bad_clause(msg,i) if a clause i is - in the wrong form. - - */ - - - static bool canonical_clause(const expr &clause){ - if(clause.decl().get_decl_kind() != Implies) - return false; - expr arg = clause.arg(1); - return arg.is_app() && (arg.decl().get_decl_kind() == False || - arg.decl().get_decl_kind() == Uninterpreted); - } - -#define USE_QE_LITE - - void RPFP::FromClauses(const std::vector &unskolemized_clauses, const std::vector *bounds){ - hash_map pmap; - func_decl fail_pred = ctx.fresh_func_decl("@Fail", ctx.bool_sort()); - - std::vector clauses(unskolemized_clauses); - // first, skolemize the clauses - -#ifndef USE_QE_LITE - for(unsigned i = 0; i < clauses.size(); i++){ - expr &t = clauses[i]; - if (t.is_quantifier() && t.is_quantifier_forall()) { - int bound = t.get_quantifier_num_bound(); - std::vector sorts; - std::vector names; - hash_map subst; - for(int j = 0; j < bound; j++){ - sort the_sort = t.get_quantifier_bound_sort(j); - symbol name = t.get_quantifier_bound_name(j); - expr skolem = ctx.constant(symbol(ctx,name),sort(ctx,the_sort)); - subst[bound-1-j] = skolem; - } - t = SubstBound(subst,t.body()); - } - } -#else - std::vector > substs(clauses.size()); -#endif - - // create the nodes from the heads of the clauses - - for(unsigned i = 0; i < clauses.size(); i++){ - Term &clause = clauses[i]; - -#ifdef USE_QE_LITE - Term &t = clause; - if (t.is_quantifier() && t.is_quantifier_forall()) { - int bound = t.get_quantifier_num_bound(); - std::vector sorts; - std::vector names; - for(int j = 0; j < bound; j++){ - sort the_sort = t.get_quantifier_bound_sort(j); - symbol name = t.get_quantifier_bound_name(j); - expr skolem = ctx.constant(symbol(ctx,name),sort(ctx,the_sort)); - substs[i][bound-1-j] = skolem; - } - clause = t.body(); - } - -#endif - - if(clause.is_app() && clause.decl().get_decl_kind() == Uninterpreted) - clause = implies(ctx.bool_val(true),clause); - if(!canonical_clause(clause)) - clause = implies((!clause).simplify(),ctx.bool_val(false)); - Term head = clause.arg(1); - func_decl R(ctx); - bool is_query = false; - if (eq(head,ctx.bool_val(false))){ - R = fail_pred; - // R = ctx.constant("@Fail", ctx.bool_sort()).decl(); - is_query = true; - } - else if(!get_relation(head,R)) - throw bad_clause("rhs must be a predicate application",i); - if(pmap.find(R) == pmap.end()){ - - // If the node doesn't exitst, create it. The Indparams - // are arbitrary, but we use the rhs arguments if they - // are variables for mnomonic value. - - hash_set seen; - std::vector Indparams; - for(unsigned j = 0; j < head.num_args(); j++){ - Term arg = head.arg(j); - if(!is_variable(arg) || seen.find(arg) != seen.end()){ - std::string name = std::string("@a_") + string_of_int(j); - arg = ctx.constant(name.c_str(),arg.get_sort()); - } - seen.insert(arg); - Indparams.push_back(arg); - } -#ifdef USE_QE_LITE - { - hash_map > sb_memo; - for(unsigned j = 0; j < Indparams.size(); j++) - Indparams[j] = SubstBoundRec(sb_memo, substs[i], 0, Indparams[j]); - } -#endif - Node *node = CreateNode(R(Indparams.size(),VEC2PTR(Indparams))); - //nodes.push_back(node); - pmap[R] = node; - if (is_query) - node->Bound = CreateRelation(std::vector(), ctx.bool_val(false)); - node->recursion_bound = bounds ? 0 : UINT_MAX; - } - } - - bool some_labels = false; - - // create the edges - - for(unsigned i = 0; i < clauses.size(); i++){ - Term clause = clauses[i]; - Term body = clause.arg(0); - Term head = clause.arg(1); - func_decl R(ctx); - if (eq(head,ctx.bool_val(false))) - R = fail_pred; - //R = ctx.constant("@Fail", ctx.bool_sort()).decl(); - else get_relation(head,R); - Node *Parent = pmap[R]; - std::vector Indparams; - hash_set seen; - for(unsigned j = 0; j < head.num_args(); j++){ - Term arg = head.arg(j); - if(!is_variable(arg) || seen.find(arg) != seen.end()){ - std::string name = std::string("@a_") + string_of_int(j); - Term var = ctx.constant(name.c_str(),arg.get_sort()); - body = body && (arg == var); - arg = var; - } - seen.insert(arg); - Indparams.push_back(arg); - } - - // We extract the relparams positionally - - std::vector Relparams; - hash_map scan_memo; - std::vector Children; - body = ScanBody(scan_memo,body,pmap,Relparams,Children); - Term labeled = body; - std::vector lbls; // TODO: throw this away for now - body = RemoveLabels(body,lbls); - if(!eq(labeled,body)) - some_labels = true; // remember if there are labels, as we then can't do qe_lite - // body = IneqToEq(body); // UFO converts x=y to (x<=y & x >= y). Undo this. - body = body.simplify(); - -#ifdef USE_QE_LITE - std::set idxs; - if(!some_labels){ // can't do qe_lite if we have to reconstruct labels - for(unsigned j = 0; j < Indparams.size(); j++) - if(Indparams[j].is_var()) - idxs.insert(Indparams[j].get_index_value()); - body = body.qe_lite(idxs,false); - } - hash_map > sb_memo; - body = SubstBoundRec(sb_memo,substs[i],0,body); - if(some_labels) - labeled = SubstBoundRec(sb_memo,substs[i],0,labeled); - for(unsigned j = 0; j < Indparams.size(); j++) - Indparams[j] = SubstBoundRec(sb_memo, substs[i], 0, Indparams[j]); -#endif - - // Create the edge - Transformer T = CreateTransformer(Relparams,Indparams,body); - Edge *edge = CreateEdge(Parent,T,Children); - edge->labeled = labeled;; // remember for label extraction - if(bounds) - Parent->recursion_bound = std::max(Parent->recursion_bound,(*bounds)[i]); - // edges.push_back(edge); - } - - // undo hoisting of expressions out of loops - RemoveDeadNodes(); - Unhoist(); - // FuseEdges(); - } - - - // The following mess is used to undo hoisting of expressions outside loops by compilers - - expr RPFP::UnhoistPullRec(hash_map & memo, const expr &w, hash_map & init_defs, hash_map & const_params, hash_map &const_params_inv, std::vector &new_params){ - if(memo.find(w) != memo.end()) - return memo[w]; - expr res; - if(init_defs.find(w) != init_defs.end()){ - expr d = init_defs[w]; - std::vector vars; - hash_set get_vars_memo; - GetVarsRec(get_vars_memo,d,vars); - hash_map map; - for(unsigned j = 0; j < vars.size(); j++){ - expr x = vars[j]; - map[x] = UnhoistPullRec(memo,x,init_defs,const_params,const_params_inv,new_params); - } - expr defn = SubstRec(map,d); - res = defn; - } - else if(const_params_inv.find(w) == const_params_inv.end()){ - std::string old_name = w.decl().name().str(); - func_decl fresh = ctx.fresh_func_decl(old_name.c_str(), w.get_sort()); - expr y = fresh(); - const_params[y] = w; - const_params_inv[w] = y; - new_params.push_back(y); - res = y; - } - else - res = const_params_inv[w]; - memo[w] = res; - return res; - } - - void RPFP::AddParamsToTransformer(Transformer &trans, const std::vector ¶ms){ - std::copy(params.begin(),params.end(),std::inserter(trans.IndParams,trans.IndParams.end())); - } - - expr RPFP::AddParamsToApp(const expr &app, const func_decl &new_decl, const std::vector ¶ms){ - int n = app.num_args(); - std::vector args(n); - for (int i = 0; i < n; i++) - args[i] = app.arg(i); - std::copy(params.begin(),params.end(),std::inserter(args,args.end())); - return new_decl(args); - } - - expr RPFP::GetRelRec(hash_set &memo, const expr &t, const func_decl &rel){ - if(memo.find(t) != memo.end()) - return expr(); - memo.insert(t); - if (t.is_app()) - { - func_decl f = t.decl(); - if(f == rel) - return t; - int nargs = t.num_args(); - for(int i = 0; i < nargs; i++){ - expr res = GetRelRec(memo,t.arg(i),rel); - if(!res.null()) - return res; - } - } - else if (t.is_quantifier()) - return GetRelRec(memo,t.body(),rel); - return expr(); - } - - expr RPFP::GetRel(Edge *edge, int child_idx){ - func_decl &rel = edge->F.RelParams[child_idx]; - hash_set memo; - return GetRelRec(memo,edge->F.Formula,rel); - } - - void RPFP::GetDefsRec(const expr &cnst, hash_map &defs){ - if(cnst.is_app()){ - switch(cnst.decl().get_decl_kind()){ - case And: { - int n = cnst.num_args(); - for(int i = 0; i < n; i++) - GetDefsRec(cnst.arg(i),defs); - break; - } - case Equal: { - expr lhs = cnst.arg(0); - expr rhs = cnst.arg(1); - if(IsVar(lhs)) - defs[lhs] = rhs; - break; - } - default: - break; - } - } - } - - void RPFP::GetDefs(const expr &cnst, hash_map &defs){ - // GetDefsRec(IneqToEq(cnst),defs); - GetDefsRec(cnst,defs); - } - - bool RPFP::IsVar(const expr &t){ - return t.is_app() && t.num_args() == 0 && t.decl().get_decl_kind() == Uninterpreted; - } - - void RPFP::GetVarsRec(hash_set &memo, const expr &t, std::vector &vars){ - if(memo.find(t) != memo.end()) - return; - memo.insert(t); - if (t.is_app()) - { - if(IsVar(t)){ - vars.push_back(t); - return; - } - int nargs = t.num_args(); - for(int i = 0; i < nargs; i++){ - GetVarsRec(memo,t.arg(i),vars); - } - } - else if (t.is_quantifier()) - GetVarsRec(memo,t.body(),vars); - } - - void RPFP::AddParamsToNode(Node *node, const std::vector ¶ms){ - int arity = node->Annotation.IndParams.size(); - std::vector domain; - domain.reserve(arity + params.size()); - for(int i = 0; i < arity; i++) - domain.push_back(node->Annotation.IndParams[i].get_sort()); - for(unsigned i = 0; i < params.size(); i++) - domain.push_back(params[i].get_sort()); - std::string old_name = node->Name.name().str(); - func_decl fresh = ctx.fresh_func_decl(old_name.c_str(), domain, ctx.bool_sort()); - node->Name = fresh; - AddParamsToTransformer(node->Annotation,params); - AddParamsToTransformer(node->Bound,params); - AddParamsToTransformer(node->Underapprox,params); - } - - void RPFP::UnhoistLoop(Edge *loop_edge, Edge *init_edge){ - loop_edge->F.Formula = IneqToEq(loop_edge->F.Formula); - init_edge->F.Formula = IneqToEq(init_edge->F.Formula); - expr pre = GetRel(loop_edge,0); - if(pre.null()) - return; // this means the loop got simplified away - int nparams = loop_edge->F.IndParams.size(); - hash_map const_params, const_params_inv; - std::vector work_list; - // find the parameters that are constant in the loop - for(int i = 0; i < nparams; i++){ - if(eq(pre.arg(i),loop_edge->F.IndParams[i])){ - const_params[pre.arg(i)] = init_edge->F.IndParams[i]; - const_params_inv[init_edge->F.IndParams[i]] = pre.arg(i); - work_list.push_back(pre.arg(i)); - } - } - // get the definitions in the initialization - hash_map defs,memo,subst; - GetDefs(init_edge->F.Formula,defs); - // try to pull them inside the loop - std::vector new_params; - for(unsigned i = 0; i < work_list.size(); i++){ - expr v = work_list[i]; - expr w = const_params[v]; - expr def = UnhoistPullRec(memo,w,defs,const_params,const_params_inv,new_params); - if(!eq(def,v)) - subst[v] = def; - } - // do the substitutions - if(subst.empty()) - return; - subst[pre] = pre; // don't substitute inside the precondition itself - loop_edge->F.Formula = SubstRec(subst,loop_edge->F.Formula); - loop_edge->F.Formula = ElimIte(loop_edge->F.Formula); - init_edge->F.Formula = ElimIte(init_edge->F.Formula); - // add the new parameters - if(new_params.empty()) - return; - Node *parent = loop_edge->Parent; - AddParamsToNode(parent,new_params); - AddParamsToTransformer(loop_edge->F,new_params); - AddParamsToTransformer(init_edge->F,new_params); - std::vector &incoming = parent->Incoming; - for(unsigned i = 0; i < incoming.size(); i++){ - Edge *in_edge = incoming[i]; - std::vector &chs = in_edge->Children; - for(unsigned j = 0; j < chs.size(); j++) - if(chs[j] == parent){ - expr lit = GetRel(in_edge,j); - expr new_lit = AddParamsToApp(lit,parent->Name,new_params); - func_decl fd = SuffixFuncDecl(new_lit,j); - int nargs = new_lit.num_args(); - std::vector args; - args.reserve(nargs); - for(int k = 0; k < nargs; k++) - args.push_back(new_lit.arg(k)); - new_lit = fd(nargs, VEC2PTR(args)); - in_edge->F.RelParams[j] = fd; - hash_map map; - map[lit] = new_lit; - in_edge->F.Formula = SubstRec(map,in_edge->F.Formula); - } - } - } - - void RPFP::Unhoist(){ - hash_map > outgoing; - for(unsigned i = 0; i < edges.size(); i++) - outgoing[edges[i]->Parent].push_back(edges[i]); - for(unsigned i = 0; i < nodes.size(); i++){ - Node *node = nodes[i]; - std::vector &outs = outgoing[node]; - // if we're not a simple loop with one entry, give up - if(outs.size() == 2){ - for(int j = 0; j < 2; j++){ - Edge *loop_edge = outs[j]; - Edge *init_edge = outs[1-j]; - if(loop_edge->Children.size() == 1 && loop_edge->Children[0] == loop_edge->Parent){ - UnhoistLoop(loop_edge,init_edge); - break; - } - } - } - } - } - - void RPFP::FuseEdges(){ - hash_map > outgoing; - for(unsigned i = 0; i < edges.size(); i++){ - outgoing[edges[i]->Parent].push_back(edges[i]); - } - hash_set edges_to_delete; - for(unsigned i = 0; i < nodes.size(); i++){ - Node *node = nodes[i]; - std::vector &outs = outgoing[node]; - if(outs.size() > 1 && outs.size() <= 16){ - std::vector trs(outs.size()); - for(unsigned j = 0; j < outs.size(); j++) - trs[j] = &outs[j]->F; - Transformer tr = Fuse(trs); - std::vector chs; - for(unsigned j = 0; j < outs.size(); j++) - for(unsigned k = 0; k < outs[j]->Children.size(); k++) - chs.push_back(outs[j]->Children[k]); - CreateEdge(node,tr,chs); - for(unsigned j = 0; j < outs.size(); j++) - edges_to_delete.insert(outs[j]); - } - } - std::vector new_edges; - hash_set all_nodes; - for(unsigned j = 0; j < edges.size(); j++){ - if(edges_to_delete.find(edges[j]) == edges_to_delete.end()){ -#if 0 - if(all_nodes.find(edges[j]->Parent) != all_nodes.end()) - throw "help!"; - all_nodes.insert(edges[j]->Parent); -#endif - new_edges.push_back(edges[j]); - } - else - delete edges[j]; - } - edges.swap(new_edges); - } - - void RPFP::MarkLiveNodes(hash_map > &outgoing, hash_set &live_nodes, Node *node){ - if(live_nodes.find(node) != live_nodes.end()) - return; - live_nodes.insert(node); - std::vector &outs = outgoing[node]; - for(unsigned i = 0; i < outs.size(); i++) - for(unsigned j = 0; j < outs[i]->Children.size(); j++) - MarkLiveNodes(outgoing, live_nodes,outs[i]->Children[j]); - } - - void RPFP::RemoveDeadNodes(){ - hash_map > outgoing; - for(unsigned i = 0; i < edges.size(); i++) - outgoing[edges[i]->Parent].push_back(edges[i]); - hash_set live_nodes; - for(unsigned i = 0; i < nodes.size(); i++) - if(!nodes[i]->Bound.IsFull()) - MarkLiveNodes(outgoing,live_nodes,nodes[i]); - std::vector new_edges; - for(unsigned j = 0; j < edges.size(); j++){ - if(live_nodes.find(edges[j]->Parent) != live_nodes.end()) - new_edges.push_back(edges[j]); - else { - Edge *edge = edges[j]; - for(unsigned int i = 0; i < edge->Children.size(); i++){ - std::vector &ic = edge->Children[i]->Incoming; - for(std::vector::iterator it = ic.begin(), en = ic.end(); it != en; ++it){ - if(*it == edge){ - ic.erase(it); - break; - } - } - } - delete edge; - } - } - edges.swap(new_edges); - std::vector new_nodes; - for(unsigned j = 0; j < nodes.size(); j++){ - if(live_nodes.find(nodes[j]) != live_nodes.end()) - new_nodes.push_back(nodes[j]); - else - delete nodes[j]; - } - nodes.swap(new_nodes); - } - - void RPFP::WriteSolution(std::ostream &s){ - for(unsigned i = 0; i < nodes.size(); i++){ - Node *node = nodes[i]; - Term asgn = (node->Name)(node->Annotation.IndParams) == node->Annotation.Formula; - s << asgn << std::endl; - } - } - - void RPFP::WriteEdgeVars(Edge *e, hash_map &memo, const Term &t, std::ostream &s) - { - std::pair foo(t,0); - std::pair::iterator, bool> bar = memo.insert(foo); - // int &res = bar.first->second; - if(!bar.second) return; - hash_map::iterator it = e->varMap.find(t); - if (it != e->varMap.end()){ - return; - } - if (t.is_app()) - { - func_decl f = t.decl(); - // int idx; - int nargs = t.num_args(); - for(int i = 0; i < nargs; i++) - WriteEdgeVars(e, memo, t.arg(i),s); - if (nargs == 0 && f.get_decl_kind() == Uninterpreted && !ls->is_constant(f)){ - Term rename = HideVariable(t,e->number); - Term value = dualModel.eval(rename); - s << " (= " << t << " " << value << ")\n"; - } - } - else if (t.is_quantifier()) - WriteEdgeVars(e,memo,t.body(),s); - return; - } - - void RPFP::WriteEdgeAssignment(std::ostream &s, Edge *e){ - s << "(\n"; - hash_map memo; - WriteEdgeVars(e, memo, e->F.Formula ,s); - s << ")\n"; - } - - void RPFP::WriteCounterexample(std::ostream &s, Node *node){ - for(unsigned i = 0; i < node->Outgoing->Children.size(); i++){ - Node *child = node->Outgoing->Children[i]; - if(!Empty(child)) - WriteCounterexample(s,child); - } - s << "(" << node->number << " : " << EvalNode(node) << " <- "; - for(unsigned i = 0; i < node->Outgoing->Children.size(); i++){ - Node *child = node->Outgoing->Children[i]; - if(!Empty(child)) - s << " " << node->Outgoing->Children[i]->number; - } - s << ")" << std::endl; - WriteEdgeAssignment(s,node->Outgoing); - } - - RPFP::Term RPFP::ToRuleRec(Edge *e, hash_map &memo, const Term &t, std::vector &quants) - { - std::pair foo(t,expr(ctx)); - std::pair::iterator, bool> bar = memo.insert(foo); - Term &res = bar.first->second; - if(!bar.second) return res; - if (t.is_app()) - { - func_decl f = t.decl(); - // int idx; - std::vector args; - int nargs = t.num_args(); - args.reserve(nargs); - for(int i = 0; i < nargs; i++) - args.push_back(ToRuleRec(e, memo, t.arg(i),quants)); - hash_map::iterator rit = e->relMap.find(f); - if(rit != e->relMap.end()){ - Node* child = e->Children[rit->second]; - FuncDecl op = child->Name; - res = op(args.size(), VEC2PTR(args)); - } - else { - res = f(args.size(), VEC2PTR(args)); - if(nargs == 0 && t.decl().get_decl_kind() == Uninterpreted) - quants.push_back(t); - } - } - else if (t.is_quantifier()) - { - Term body = ToRuleRec(e,memo,t.body(),quants); - res = CloneQuantifier(t,body); - } - else res = t; - return res; - } - - - void RPFP::ToClauses(std::vector &cnsts, FileFormat format){ - cnsts.resize(edges.size()); - for(unsigned i = 0; i < edges.size(); i++){ - Edge *edge = edges[i]; - SetEdgeMaps(edge); - std::vector quants; - hash_map memo; - Term lhs = ToRuleRec(edge, memo, edge->F.Formula,quants); - Term rhs = (edge->Parent->Name)(edge->F.IndParams.size(),&edge->F.IndParams[0]); - for(unsigned j = 0; j < edge->F.IndParams.size(); j++) - ToRuleRec(edge,memo,edge->F.IndParams[j],quants); // just to get quants - Term cnst = implies(lhs,rhs); -#if 0 - for(unsigned i = 0; i < quants.size(); i++){ - std::cout << expr(ctx,(Z3_ast)quants[i]) << " : " << sort(ctx,Z3_get_sort(ctx,(Z3_ast)quants[i])) << std::endl; - } -#endif - if(format != DualityFormat) - cnst= forall(quants,cnst); - cnsts[i] = cnst; - } - // int num_rules = cnsts.size(); - - for(unsigned i = 0; i < nodes.size(); i++){ - Node *node = nodes[i]; - if(!node->Bound.IsFull()){ - Term lhs = (node->Name)(node->Bound.IndParams) && !node->Bound.Formula; - Term cnst = implies(lhs,ctx.bool_val(false)); - if(format != DualityFormat){ - std::vector quants; - for(unsigned j = 0; j < node->Bound.IndParams.size(); j++) - quants.push_back(node->Bound.IndParams[j]); - if(format == HornFormat) - cnst= exists(quants,!cnst); - else - cnst= forall(quants, cnst); - } - cnsts.push_back(cnst); - } - } - - } - - - bool RPFP::proof_core_contains(const expr &e){ - return proof_core->find(e) != proof_core->end(); - } - - bool RPFP_caching::proof_core_contains(const expr &e){ - std::vector foo; - GetAssumptionLits(e,foo); - for(unsigned i = 0; i < foo.size(); i++) - if(proof_core->find(foo[i]) != proof_core->end()) - return true; - return false; - } - - bool RPFP::EdgeUsedInProof(Edge *edge){ - ComputeProofCore(); - if(!edge->dual.null() && proof_core_contains(edge->dual)) - return true; - for(unsigned i = 0; i < edge->constraints.size(); i++) - if(proof_core_contains(edge->constraints[i])) - return true; - return false; - } - - RPFP::~RPFP(){ - ClearProofCore(); - for(unsigned i = 0; i < nodes.size(); i++) - delete nodes[i]; - for(unsigned i = 0; i < edges.size(); i++) - delete edges[i]; - } -} - -#if 0 -void show_ast(expr *a){ - std::cout << *a; -} -#endif diff --git a/src/duality/duality_solver.cpp b/src/duality/duality_solver.cpp deleted file mode 100644 index 7782f4a8b..000000000 --- a/src/duality/duality_solver.cpp +++ /dev/null @@ -1,3601 +0,0 @@ -/*++ - Copyright (c) 2012 Microsoft Corporation - - Module Name: - - duality_solver.h - - Abstract: - - implements relational post-fixedpoint problem - (RPFP) solver - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - - --*/ - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#endif - -#include "duality/duality.h" -#include "duality/duality_profiling.h" - -#include -#include -#include -#include -#include -#include - -// TODO: make these official options or get rid of them - -#define NEW_CAND_SEL -// #define LOCALIZE_CONJECTURES -// #define CANDS_FROM_UPDATES -#define CANDS_FROM_COVER_FAIL -#define DEPTH_FIRST_EXPAND -#define MINIMIZE_CANDIDATES -// #define MINIMIZE_CANDIDATES_HARDER -#define BOUNDED -// #define CHECK_CANDS_FROM_IND_SET -#define UNDERAPPROX_NODES -#define NEW_EXPAND -#define EARLY_EXPAND -// #define TOP_DOWN -// #define EFFORT_BOUNDED_STRAT -#define SKIP_UNDERAPPROX_NODES -// #define KEEP_EXPANSIONS -// #define USE_CACHING_RPFP -// #define PROPAGATE_BEFORE_CHECK -#define NEW_STRATIFIED_INLINING - -#define USE_RPFP_CLONE -#define USE_NEW_GEN_CANDS - -//#define NO_PROPAGATE -//#define NO_GENERALIZE -//#define NO_DECISIONS - -namespace Duality { - - // TODO: must be a better place for this... - static char string_of_int_buffer[20]; - - static const char *string_of_int(int n){ - sprintf(string_of_int_buffer,"%d",n); - return string_of_int_buffer; - } - - /** Generic object for producing diagnostic output. */ - - class Reporter { - protected: - RPFP *rpfp; - public: - Reporter(RPFP *_rpfp){ - rpfp = _rpfp; - } - virtual void Extend(RPFP::Node *node){} - virtual void Update(RPFP::Node *node, const RPFP::Transformer &update, bool eager){} - virtual void Bound(RPFP::Node *node){} - virtual void Expand(RPFP::Edge *edge){} - virtual void AddCover(RPFP::Node *covered, std::vector &covering){} - virtual void RemoveCover(RPFP::Node *covered, RPFP::Node *covering){} - virtual void Conjecture(RPFP::Node *node, const RPFP::Transformer &t){} - virtual void Forcing(RPFP::Node *covered, RPFP::Node *covering){} - virtual void Dominates(RPFP::Node *node, RPFP::Node *other){} - virtual void InductionFailure(RPFP::Edge *edge, const std::vector &children){} - virtual void UpdateUnderapprox(RPFP::Node *node, const RPFP::Transformer &update){} - virtual void Reject(RPFP::Edge *edge, const std::vector &Children){} - virtual void Message(const std::string &msg){} - virtual void Depth(int){} - virtual ~Reporter(){} - }; - - Reporter *CreateStdoutReporter(RPFP *rpfp); - Reporter *CreateConjectureFileReporter(RPFP *rpfp, const std::string &fname); - - /** Object we throw in case of catastrophe. */ - - struct InternalError { - std::string msg; - InternalError(const std::string & _msg) - : msg(_msg) {} - }; - - - /** This is the main solver. It takes an arbitrary (possibly cyclic) - RPFP and either annotates it with a solution, or returns a - counterexample derivation in the form of an embedded RPFP tree. */ - - class Duality : public Solver { - - public: - Duality(RPFP *_rpfp) - : ctx(_rpfp->ctx), - slvr(_rpfp->slvr()), - nodes(_rpfp->nodes), - edges(_rpfp->edges) - { - rpfp = _rpfp; - reporter = nullptr; - conj_reporter = nullptr; - heuristic = nullptr; - unwinding = nullptr; - FullExpand = false; - NoConj = false; - FeasibleEdges = true; - UseUnderapprox = true; - Report = false; - StratifiedInlining = false; - RecursionBound = -1; - BatchExpand = false; - { - scoped_no_proof no_proofs_please(ctx.m()); -#ifdef USE_RPFP_CLONE - clone_rpfp = new RPFP_caching(rpfp->ls); - clone_rpfp->Clone(rpfp); -#endif -#ifdef USE_NEW_GEN_CANDS - gen_cands_rpfp = new RPFP_caching(rpfp->ls); - gen_cands_rpfp->Clone(rpfp); -#endif - } - } - - ~Duality() override { -#ifdef USE_RPFP_CLONE - delete clone_rpfp; -#endif -#ifdef USE_NEW_GEN_CANDS - delete gen_cands_rpfp; -#endif - if(unwinding) delete unwinding; - } - -#ifdef USE_RPFP_CLONE - RPFP_caching *clone_rpfp; -#endif -#ifdef USE_NEW_GEN_CANDS - RPFP_caching *gen_cands_rpfp; -#endif - - - typedef RPFP::Node Node; - typedef RPFP::Edge Edge; - - /** This struct represents a candidate for extending the - unwinding. It consists of an edge to instantiate - and a vector of children for the new instance. */ - - struct Candidate { - Edge *edge; std::vector - Children; - }; - - /** Comparison operator, allowing us to sort Nodes - by their number field. */ - - struct lnode - { - bool operator()(const Node* s1, const Node* s2) const - { - return s1->number < s2->number; - } - }; - - typedef std::set Unexpanded; // sorted set of Nodes - - /** This class provides a heuristic for expanding a derivation - tree. */ - - class Heuristic { - RPFP *rpfp; - - /** Heuristic score for unwinding nodes. Currently this - counts the number of updates. */ - struct score { - int updates; - score() : updates(0) {} - }; - hash_map scores; - - public: - Heuristic(RPFP *_rpfp){ - rpfp = _rpfp; - } - - virtual ~Heuristic(){} - - virtual void Update(RPFP::Node *node){ - scores[node].updates++; - } - - /** Heuristic choice of nodes to expand. Takes a set "choices" - and returns a subset "best". We currently choose the - nodes with the fewest updates. - */ -#if 0 - virtual void ChooseExpand(const std::set &choices, std::set &best){ - int best_score = INT_MAX; - for(std::set::iterator it = choices.begin(), en = choices.end(); it != en; ++it){ - Node *node = (*it)->map; - int score = scores[node].updates; - best_score = std::min(best_score,score); - } - for(std::set::iterator it = choices.begin(), en = choices.end(); it != en; ++it) - if(scores[(*it)->map].updates == best_score) - best.insert(*it); - } -#else - virtual void ChooseExpand(const std::set &choices, std::set &best, bool high_priority=false, bool best_only=false){ - if(high_priority) return; - int best_score = INT_MAX; - int worst_score = 0; - for(std::set::iterator it = choices.begin(), en = choices.end(); it != en; ++it){ - Node *node = (*it)->map; - int score = scores[node].updates; - best_score = std::min(best_score,score); - worst_score = std::max(worst_score,score); - } - int cutoff = best_only ? best_score : (best_score + (worst_score-best_score)/2); - for(std::set::iterator it = choices.begin(), en = choices.end(); it != en; ++it) - if(scores[(*it)->map].updates <= cutoff) - best.insert(*it); - } -#endif - - /** Called when done expanding a tree */ - virtual void Done() {} - - /** Ask whether a node should be used/unused in the tree. Returns, - 1 if yes, -1 if no, and 0 if don't care. */ - - virtual int UseNode(Node *node){ - return 0; - } - }; - - /** The Proposer class proposes conjectures eagerly. These can come - from any source, including predicate abstraction, templates, or - previous solver runs. The proposed conjectures are checked - with low effort when the unwinding is expanded. - */ - - class Proposer { - public: - /** Given a node in the unwinding, propose some conjectures */ - virtual std::vector &Propose(Node *node) = 0; - virtual ~Proposer(){}; - }; - - - class Covering; // see below - - // These members represent the state of the algorithm. - - RPFP *rpfp; // the input RPFP - Reporter *reporter; // object for logging - Reporter *conj_reporter; // object for logging conjectures - Heuristic *heuristic; // expansion heuristic - context &ctx; // Z3 context - solver &slvr; // Z3 solver - std::vector &nodes; // Nodes of input RPFP - std::vector &edges; // Edges of input RPFP - std::vector leaves; // leaf nodes of unwinding (unused) - Unexpanded unexpanded; // unexpanded nodes - std::list candidates; // candidates for expansion - // maps children to edges in input RPFP - hash_map > edges_by_child; - // maps each node in input RPFP to its expanded instances - hash_map > insts_of_node; - // maps each node in input RPFP to all its instances - hash_map > all_of_node; - RPFP *unwinding; // the unwinding - Covering *indset; // proposed inductive subset - Counterexample cex; // counterexample - std::list to_expand; - hash_set updated_nodes; - hash_map underapprox_map; // maps underapprox nodes to the nodes they approximate - int last_decisions; - hash_set overapproxes; - std::vector proposers; - std::string ConjectureFile; - bool stratified_inlining_done; - -#ifdef BOUNDED - struct Counter { - unsigned val; - Counter(){val = 0;} - }; - typedef std::map NodeToCounter; - hash_map back_edges; // counts of back edges -#endif - - /** Solve the problem. */ - bool Solve() override { - PreSolve(); - bool res = SolveMain(); // does the actual work - PostSolve(); - return res; - } - - void PreSolve(){ - reporter = Report ? CreateStdoutReporter(rpfp) : new Reporter(rpfp); - conj_reporter = ConjectureFile.empty() ? nullptr : CreateConjectureFileReporter(rpfp,ConjectureFile); -#ifndef LOCALIZE_CONJECTURES - heuristic = !cex.get_tree() ? new Heuristic(rpfp) : new ReplayHeuristic(rpfp,cex); -#else - heuristic = !cex.get_tree() ? (Heuristic *)(new LocalHeuristic(rpfp)) - : (Heuristic *)(new ReplayHeuristic(rpfp,cex)); -#endif - // determine if we are recursion bounded - for(unsigned i = 0; i < rpfp->nodes.size(); i++) - if(rpfp->nodes[i]->recursion_bound < UINT_MAX) - RecursionBound = 0; - cex.clear(); // in case we didn't use it for heuristic - if(unwinding) delete unwinding; - unwinding = new RPFP(rpfp->ls); - unwinding->HornClauses = rpfp->HornClauses; - indset = new Covering(this); - last_decisions = 0; - CreateEdgesByChildMap(); -#ifndef TOP_DOWN - CreateInitialUnwinding(); -#else - CreateLeaves(); - for(unsigned i = 0; i < leaves.size(); i++) - if(!SatisfyUpperBound(leaves[i])) - return false; -#endif - StratifiedLeafCount = -1; - stratified_inlining_done = false; - } - - void PostSolve(){ - // print_profile(std::cout); - delete indset; - delete heuristic; - // delete unwinding; // keep the unwinding for future mining of predicates - delete reporter; - if(conj_reporter) - delete conj_reporter; - for(unsigned i = 0; i < proposers.size(); i++) - delete proposers[i]; - } - - bool RecheckBounds(){ - for(unsigned i = 0; i < unwinding->nodes.size(); i++){ - Node *node = unwinding->nodes[i]; - node->Bound = node->map->Bound; - if(!SatisfyUpperBound(node)) - return false; - } - return true; - } - - void CreateInitialUnwinding(){ - if(!StratifiedInlining){ - CreateLeaves(); - if(FeasibleEdges)NullaryCandidates(); - else InstantiateAllEdges(); - } - else { -#ifdef NEW_STRATIFIED_INLINING - -#else - CreateLeaves(); -#endif - } - - } - - void Cancel() override { - // TODO - } - -#if 0 - virtual void Restart(RPFP *_rpfp){ - rpfp = _rpfp; - delete unwinding; - nodes = _rpfp->nodes; - edges = _rpfp->edges; - leaves.clear(); - unexpanded.clear(); // unexpanded nodes - candidates.clear(); // candidates for expansion - edges_by_child.clear(); - insts_of_node.clear(); - all_of_node.clear(); - to_expand.clear(); - } -#endif - - void LearnFrom(Solver *other_solver) override { - // get the counterexample as a guide - cex.swap(other_solver->GetCounterexample()); - - // propose conjectures based on old unwinding - Duality *old_duality = dynamic_cast(other_solver); - if(old_duality) - proposers.push_back(new HistoryProposer(old_duality,this)); - } - - /** Return a reference to the counterexample */ - Counterexample &GetCounterexample() override { - return cex; - } - - // options - bool FullExpand; // do not use partial expansion of derivation tree - bool NoConj; // do not use conjectures (no forced covering) - bool FeasibleEdges; // use only feasible edges in unwinding - bool UseUnderapprox; // use underapproximations - bool Report; // spew on stdout - bool StratifiedInlining; // Do stratified inlining as preprocessing step - int RecursionBound; // Recursion bound for bounded verification - bool BatchExpand; - bool EnableRestarts; - - bool SetBoolOption(bool &opt, const std::string &value){ - if(value == "0") { - opt = false; - return true; - } - if(value == "1") { - opt = true; - return true; - } - return false; - } - - bool SetIntOption(int &opt, const std::string &value){ - opt = atoi(value.c_str()); - return true; - } - - /** Set options (not currently used) */ - bool SetOption(const std::string &option, const std::string &value) override { - if(option == "full_expand"){ - return SetBoolOption(FullExpand,value); - } - if(option == "no_conj"){ - return SetBoolOption(NoConj,value); - } - if(option == "feasible_edges"){ - return SetBoolOption(FeasibleEdges,value); - } - if(option == "use_underapprox"){ - return SetBoolOption(UseUnderapprox,value); - } - if(option == "report"){ - return SetBoolOption(Report,value); - } - if(option == "stratified_inlining"){ - return SetBoolOption(StratifiedInlining,value); - } - if(option == "batch_expand"){ - return SetBoolOption(BatchExpand,value); - } - if(option == "recursion_bound"){ - return SetIntOption(RecursionBound,value); - } - if(option == "conjecture_file"){ - ConjectureFile = value; - } - if(option == "enable_restarts"){ - return SetBoolOption(EnableRestarts,value); - } - return false; - } - - /** Create an instance of a node in the unwinding. Set its - annotation to true, and mark it unexpanded. */ - Node* CreateNodeInstance(Node *node, int number = 0){ - RPFP::Node *inst = unwinding->CloneNode(node); - inst->Annotation.SetFull(); - if(number < 0) inst->number = number; - unexpanded.insert(inst); - all_of_node[node].push_back(inst); - return inst; - } - - /** Create an instance of an edge in the unwinding, with given - parent and children. */ - void CreateEdgeInstance(Edge *edge, Node *parent, const std::vector &children){ - RPFP::Edge *inst = unwinding->CreateEdge(parent,edge->F,children); - inst->map = edge; - } - - void MakeLeaf(Node *node, bool do_not_expand = false){ - node->Annotation.SetEmpty(); - Edge *e = unwinding->CreateLowerBoundEdge(node); -#ifdef TOP_DOWN - node->Annotation.SetFull(); // allow this node to cover others -#endif - if(StratifiedInlining) - node->Annotation.SetFull(); // allow this node to cover others - else - updated_nodes.insert(node); - e->map = nullptr; - reporter->Extend(node); -#ifdef EARLY_EXPAND - if(!do_not_expand) - TryExpandNode(node); -#endif - // e->F.SetEmpty(); - } - - void MakeOverapprox(Node *node){ - node->Annotation.SetFull(); - Edge *e = unwinding->CreateLowerBoundEdge(node); - overapproxes.insert(node); - e->map = nullptr; - } - - /** We start the unwinding with leaves that under-approximate - each relation with false. */ - void CreateLeaves(){ - unexpanded.clear(); - leaves.clear(); - for(unsigned i = 0; i < nodes.size(); i++){ - RPFP::Node *node = CreateNodeInstance(nodes[i]); - if(0 && nodes[i]->Outgoing->Children.size() == 0) - CreateEdgeInstance(nodes[i]->Outgoing,node,std::vector()); - else { - if(!StratifiedInlining) - MakeLeaf(node); - else { - MakeOverapprox(node); - LeafMap[nodes[i]] = node; - } - } - leaves.push_back(node); - } - } - - /** Create the map from children to edges in the input RPFP. This - is used to generate candidates for expansion. */ - void CreateEdgesByChildMap(){ - edges_by_child.clear(); - for(unsigned i = 0; i < edges.size(); i++){ - Edge *e = edges[i]; - std::set done; - for(unsigned j = 0; j < e->Children.size(); j++){ - Node *c = e->Children[j]; - if(done.find(c) == done.end()) // avoid duplicates - edges_by_child[c].push_back(e); - done.insert(c); - } - } - } - - void NullaryCandidates(){ - for(unsigned i = 0; i < edges.size(); i++){ - RPFP::Edge *edge = edges[i]; - if(edge->Children.size() == 0){ - Candidate cand; - cand.edge = edge; - candidates.push_back(cand); - } - } - } - - void InstantiateAllEdges(){ - hash_map leaf_map; - for(unsigned i = 0; i < leaves.size(); i++){ - leaf_map[leaves[i]->map] = leaves[i]; - insts_of_node[leaves[i]->map].push_back(leaves[i]); - } - unexpanded.clear(); - for(unsigned i = 0; i < edges.size(); i++){ - Edge *edge = edges[i]; - Candidate c; c.edge = edge; - c.Children.resize(edge->Children.size()); - for(unsigned j = 0; j < c.Children.size(); j++) - c.Children[j] = leaf_map[edge->Children[j]]; - Node *new_node; - Extend(c,new_node); -#ifdef EARLY_EXPAND - TryExpandNode(new_node); -#endif - } - for(Unexpanded::iterator it = unexpanded.begin(), en = unexpanded.end(); it != en; ++it) - indset->Add(*it); - for(unsigned i = 0; i < leaves.size(); i++){ - std::vector &foo = insts_of_node[leaves[i]->map]; - foo.erase(foo.begin()); - } - } - - bool ProducedBySI(Edge *edge, std::vector &children){ - if(LeafMap.find(edge->Parent) == LeafMap.end()) return false; - Node *other = LeafMap[edge->Parent]; - if(other->Outgoing->map != edge) return false; - std::vector &ochs = other->Outgoing->Children; - for(unsigned i = 0; i < children.size(); i++) - if(ochs[i] != children[i]) return false; - return true; - } - - /** Add a candidate for expansion, but not if Stratified inlining has already - produced it */ - - void AddCandidate(Edge *edge, std::vector &children){ - if(StratifiedInlining && ProducedBySI(edge,children)) - return; - candidates.push_back(Candidate()); - candidates.back().edge = edge; - candidates.back().Children = children; - } - - /** Generate candidates for expansion, given a vector of candidate - sets for each argument position. This recursively produces - the cross product. - */ - void GenCandidatesRec(int pos, Edge *edge, - const std::vector > &vec, - std::vector &children){ - if(pos == (int)vec.size()){ - AddCandidate(edge,children); - } - else { - for(unsigned i = 0; i < vec[pos].size(); i++){ - children[pos] = vec[pos][i]; - GenCandidatesRec(pos+1,edge,vec,children); - } - } - } - - /** Setup for above recursion. */ - void GenCandidates(int pos, Edge *edge, - const std::vector > &vec){ - std::vector children(vec.size()); - GenCandidatesRec(0,edge,vec,children); - } - - /** Expand a node. We find all the candidates for expansion using - this node and other already expanded nodes. This is a little - tricky, since a node may be used for multiple argument - positions of an edge, and we don't want to produce duplicates. - */ - -#ifndef NEW_EXPAND - void ExpandNode(Node *node){ - std::vector &nedges = edges_by_child[node->map]; - for(unsigned i = 0; i < nedges.size(); i++){ - Edge *edge = nedges[i]; - for(unsigned npos = 0; npos < edge->Children.size(); ++npos){ - if(edge->Children[npos] == node->map){ - std::vector > vec(edge->Children.size()); - vec[npos].push_back(node); - for(unsigned j = 0; j < edge->Children.size(); j++){ - if(j != npos){ - std::vector &insts = insts_of_node[edge->Children[j]]; - for(unsigned k = 0; k < insts.size(); k++) - if(indset->Candidate(insts[k])) - vec[j].push_back(insts[k]); - } - if(j < npos && edge->Children[j] == node->map) - vec[j].push_back(node); - } - GenCandidates(0,edge,vec); - } - } - } - unexpanded.erase(node); - insts_of_node[node->map].push_back(node); - } -#else - /** If the current proposed solution is not inductive, - use the induction failure to generate candidates for extension. */ - void ExpandNode(Node *node){ - unexpanded.erase(node); - insts_of_node[node->map].push_back(node); - timer_start("GenCandIndFailUsing"); - std::vector &nedges = edges_by_child[node->map]; - for(unsigned i = 0; i < nedges.size(); i++){ - Edge *edge = nedges[i]; - slvr.push(); - RPFP *checker = new RPFP(rpfp->ls); - Node *root = CheckerJustForEdge(edge,checker,true); - if(root){ - expr using_cond = ctx.bool_val(false); - for(unsigned npos = 0; npos < edge->Children.size(); ++npos) - if(edge->Children[npos] == node->map) - using_cond = using_cond || checker->Localize(root->Outgoing->Children[npos]->Outgoing,NodeMarker(node)); - slvr.add(using_cond); - if(checker->Check(root) != unsat){ - Candidate candidate; - ExtractCandidateFromCex(edge,checker,root,candidate); - reporter->InductionFailure(edge,candidate.Children); - candidates.push_back(candidate); - } - } - slvr.pop(1); - delete checker; - } - timer_stop("GenCandIndFailUsing"); - } -#endif - - void ExpandNodeFromOther(Node *node, Node *other){ - std::vector &in = other->Incoming; - for(unsigned i = 0; i < in.size(); i++){ - Edge *edge = in[i]; - Candidate cand; - cand.edge = edge->map; - cand.Children = edge->Children; - for(unsigned j = 0; j < cand.Children.size(); j++) - if(cand.Children[j] == other) - cand.Children[j] = node; - candidates.push_front(cand); - } - // unexpanded.erase(node); - // insts_of_node[node->map].push_back(node); - } - - /** Expand a node based on some uncovered node it dominates. - This pushes cahdidates onto the *front* of the candidate - queue, so these expansions are done depth-first. */ - bool ExpandNodeFromCoverFail(Node *node){ - if(!node->Outgoing || node->Outgoing->Children.size() == 0) - return false; - Node *other = indset->GetSimilarNode(node); - if(!other) - return false; -#ifdef UNDERAPPROX_NODES - Node *under_node = CreateUnderapproxNode(node); - underapprox_map[under_node] = node; - indset->CoverByNode(node,under_node); - ExpandNodeFromOther(under_node,other); - ExpandNode(under_node); -#else - ExpandNodeFromOther(node,other); - unexpanded.erase(node); - insts_of_node[node->map].push_back(node); -#endif - return true; - } - - - /** Make a boolean variable to act as a "marker" for a node. */ - expr NodeMarker(Node *node){ - std::string name = std::string("@m_") + string_of_int(node->number); - return ctx.constant(name.c_str(),ctx.bool_sort()); - } - - /** Make a boolean variable to act as a "marker" for a pair of nodes. */ - expr NodeMarker(Node *node1, Node *node2){ - std::string name = std::string("@m_") + string_of_int(node1->number); - name += std::string("_") + string_of_int(node2->number); - return ctx.constant(name.c_str(),ctx.bool_sort()); - } - - /** Union the annotation of dst into src. If with_markers is - true, we conjoin the annotation formula of dst with its - marker. This allows us to discover which disjunct is - true in a satisfying assignment. */ - void UnionAnnotations(RPFP::Transformer &dst, Node *src, bool with_markers = false){ - if(!with_markers) - dst.UnionWith(src->Annotation); - else { - RPFP::Transformer t = src->Annotation; - t.Formula = t.Formula && NodeMarker(src); - dst.UnionWith(t); - } - } - - void GenNodeSolutionFromIndSet(Node *node, RPFP::Transformer &annot, bool with_markers = false){ - annot.SetEmpty(); - std::vector &insts = insts_of_node[node]; - for(unsigned j = 0; j < insts.size(); j++) - if(indset->Contains(insts[j])) - UnionAnnotations(annot,insts[j],with_markers); - annot.Simplify(); - } - - bool NodeSolutionFromIndSetFull(Node *node){ - std::vector &insts = insts_of_node[node]; - for(unsigned j = 0; j < insts.size(); j++) - if(indset->Contains(insts[j])) - if(insts[j]->Annotation.IsFull()) - return true; - return false; - } - - bool recursionBounded; - - /** See if the solution might be bounded. */ - void TestRecursionBounded(){ - recursionBounded = false; - if(RecursionBound == -1) - return; - for(unsigned i = 0; i < nodes.size(); i++){ - Node *node = nodes[i]; - std::vector &insts = insts_of_node[node]; - for(unsigned j = 0; j < insts.size(); j++) - if(indset->Contains(insts[j])) - if(NodePastRecursionBound(insts[j],true)) - recursionBounded = true; - } - } - - bool IsResultRecursionBounded() override { - return recursionBounded; - } - - /** Generate a proposed solution of the input RPFP from - the unwinding, by unioning the instances of each node. */ - void GenSolutionFromIndSet(bool with_markers = false){ - for(unsigned i = 0; i < nodes.size(); i++){ - Node *node = nodes[i]; - GenNodeSolutionFromIndSet(node,node->Annotation,with_markers); - } - } - -#ifdef BOUNDED - bool NodePastRecursionBound(Node *node, bool report = false){ - if(RecursionBound < 0) return false; - NodeToCounter &backs = back_edges[node]; - for(NodeToCounter::iterator it = backs.begin(), en = backs.end(); it != en; ++it){ - if(it->second.val > it->first->recursion_bound){ - if(report){ - std::ostringstream os; - os << "cut off " << it->first->Name.name() << " at depth " << it->second.val; - reporter->Message(os.str()); - } - return true; - } - } - return false; - } -#endif - - /** Test whether a given extension candidate actually represents - an induction failure. Right now we approximate this: if - the resulting node in the unwinding could be labeled false, - it clearly is not an induction failure. */ - - bool CandidateFeasible(const Candidate &cand){ - if(!FeasibleEdges) return true; - timer_start("CandidateFeasible"); - RPFP *checker = new RPFP(rpfp->ls); - // std::cout << "Checking feasibility of extension " << cand.edge->Parent->number << std::endl; - checker->Push(); - std::vector chs(cand.Children.size()); - Node *root = checker->CloneNode(cand.edge->Parent); -#ifdef BOUNDED - for(unsigned i = 0; i < cand.Children.size(); i++) - if(NodePastRecursionBound(cand.Children[i])){ - timer_stop("CandidateFeasible"); - return false; - } -#endif -#ifdef NEW_CAND_SEL - GenNodeSolutionFromIndSet(cand.edge->Parent,root->Bound); -#else - root->Bound.SetEmpty(); -#endif - checker->AssertNode(root); - for(unsigned i = 0; i < cand.Children.size(); i++) - chs[i] = checker->CloneNode(cand.Children[i]); - Edge *e = checker->CreateEdge(root,cand.edge->F,chs); - checker->AssertEdge(e,0,true); - // std::cout << "Checking SAT: " << e->dual << std::endl; - bool res = checker->Check(root) != unsat; - // std::cout << "Result: " << res << std::endl; - if(!res)reporter->Reject(cand.edge,cand.Children); - checker->Pop(1); - delete checker; - timer_stop("CandidateFeasible"); - return res; - } - - - hash_map TopoSort; - int TopoSortCounter; - std::vector SortedEdges; - - void DoTopoSortRec(Node *node){ - if(TopoSort.find(node) != TopoSort.end()) - return; - TopoSort[node] = INT_MAX; // just to break cycles - Edge *edge = node->Outgoing; // note, this is just *one* outgoing edge - if(edge){ - std::vector &chs = edge->Children; - for(unsigned i = 0; i < chs.size(); i++) - DoTopoSortRec(chs[i]); - } - TopoSort[node] = TopoSortCounter++; - SortedEdges.push_back(edge); - } - - void DoTopoSort(){ - TopoSort.clear(); - SortedEdges.clear(); - TopoSortCounter = 0; - for(unsigned i = 0; i < nodes.size(); i++) - DoTopoSortRec(nodes[i]); - } - - - int StratifiedLeafCount; - -#ifdef NEW_STRATIFIED_INLINING - - /** Stratified inlining builds an initial layered unwinding before - switching to the LAWI strategy. Currently the number of layers - is one. Only nodes that are the targets of back edges are - consider to be leaves. This assumes we have already computed a - topological sort. - */ - - bool DoStratifiedInlining(){ - if(stratified_inlining_done) - return true; - stratified_inlining_done = true; - DoTopoSort(); - int depth = 1; // TODO: make this an option - std::vector > unfolding_levels(depth+1); - for(int level = 1; level <= depth; level++) - for(unsigned i = 0; i < SortedEdges.size(); i++){ - Edge *edge = SortedEdges[i]; - Node *parent = edge->Parent; - std::vector &chs = edge->Children; - std::vector my_chs(chs.size()); - for(unsigned j = 0; j < chs.size(); j++){ - Node *child = chs[j]; - int ch_level = TopoSort[child] >= TopoSort[parent] ? level-1 : level; - if(unfolding_levels[ch_level].find(child) == unfolding_levels[ch_level].end()){ - if(ch_level == 0) - unfolding_levels[0][child] = CreateLeaf(child); - else - throw InternalError("in levelized unwinding"); - } - my_chs[j] = unfolding_levels[ch_level][child]; - } - Candidate cand; cand.edge = edge; cand.Children = my_chs; - Node *new_node; - bool ok = Extend(cand,new_node); - MarkExpanded(new_node); // we don't expand here -- just mark it done - if(!ok) return false; // got a counterexample - unfolding_levels[level][parent] = new_node; - } - return true; - } - - Node *CreateLeaf(Node *node){ - RPFP::Node *nchild = CreateNodeInstance(node); - MakeLeaf(nchild, /* do_not_expand = */ true); - nchild->Annotation.SetEmpty(); - return nchild; - } - - void MarkExpanded(Node *node){ - if(unexpanded.find(node) != unexpanded.end()){ - unexpanded.erase(node); - insts_of_node[node->map].push_back(node); - } - } - -#else - - /** In stratified inlining, we build the unwinding from the bottom - down, trying to satisfy the node bounds. We do this as a pre-pass, - limiting the expansion. If we get a counterexample, we are done, - else we continue as usual expanding the unwinding upward. - */ - - bool DoStratifiedInlining(){ - timer_start("StratifiedInlining"); - DoTopoSort(); - for(unsigned i = 0; i < leaves.size(); i++){ - Node *node = leaves[i]; - bool res = SatisfyUpperBound(node); - if(!res){ - timer_stop("StratifiedInlining"); - return false; - } - } - // don't leave any dangling nodes! -#ifndef EFFORT_BOUNDED_STRAT - for(unsigned i = 0; i < leaves.size(); i++) - if(!leaves[i]->Outgoing) - MakeLeaf(leaves[i],true); -#endif - timer_stop("StratifiedInlining"); - return true; - } - -#endif - - /** Here, we do the downward expansion for stratified inlining */ - - hash_map LeafMap, StratifiedLeafMap; - - Edge *GetNodeOutgoing(Node *node, int last_decs = 0){ - if(overapproxes.find(node) == overapproxes.end()) return node->Outgoing; /* already expanded */ - overapproxes.erase(node); -#ifdef EFFORT_BOUNDED_STRAT - if(last_decs > 5000){ - // RPFP::Transformer save = node->Annotation; - node->Annotation.SetEmpty(); - Edge *e = unwinding->CreateLowerBoundEdge(node); - // node->Annotation = save; - insts_of_node[node->map].push_back(node); - // std::cout << "made leaf: " << node->number << std::endl; - return e; - } -#endif - Edge *edge = node->map->Outgoing; - std::vector &chs = edge->Children; - - // make sure we don't create a covered node in this process! - - for(unsigned i = 0; i < chs.size(); i++){ - Node *child = chs[i]; - if(TopoSort[child] < TopoSort[node->map]){ - Node *leaf = LeafMap[child]; - if(!indset->Contains(leaf)){ - node->Outgoing->F.Formula = ctx.bool_val(false); // make this a proper leaf, else bogus cex - return node->Outgoing; - } - } - } - - std::vector nchs(chs.size()); - for(unsigned i = 0; i < chs.size(); i++){ - Node *child = chs[i]; - if(TopoSort[child] < TopoSort[node->map]){ - Node *leaf = LeafMap[child]; - nchs[i] = leaf; - if(unexpanded.find(leaf) != unexpanded.end()){ - unexpanded.erase(leaf); - insts_of_node[child].push_back(leaf); - } - } - else { - if(StratifiedLeafMap.find(child) == StratifiedLeafMap.end()){ - RPFP::Node *nchild = CreateNodeInstance(child,StratifiedLeafCount--); - MakeLeaf(nchild); - nchild->Annotation.SetEmpty(); - StratifiedLeafMap[child] = nchild; - indset->SetDominated(nchild); - } - nchs[i] = StratifiedLeafMap[child]; - } - } - CreateEdgeInstance(edge,node,nchs); - reporter->Extend(node); - return node->Outgoing; - } - - void SetHeuristicOldNode(Node *node){ - LocalHeuristic *h = dynamic_cast(heuristic); - if(h) - h->SetOldNode(node); - } - - bool SolveMain(){ - timer_start("SolveMain"); - bool res = SolveMainInt(); // does the actual work - timer_stop("SolveMain"); - return res; - } - - /** This does the actual solving work. We try to generate - candidates for extension. If we succed, we extend the - unwinding. If we fail, we have a solution. */ - bool SolveMainInt(){ - if(StratifiedInlining && !DoStratifiedInlining()) - return false; -#ifdef BOUNDED - DoTopoSort(); -#endif - while(true){ - timer_start("ProduceCandidatesForExtension"); - ProduceCandidatesForExtension(); - timer_stop("ProduceCandidatesForExtension"); - if(candidates.empty()){ - GenSolutionFromIndSet(); - TestRecursionBounded(); - return true; - } - Candidate cand = candidates.front(); - candidates.pop_front(); - if(CandidateFeasible(cand)){ - Node *new_node; - if(!Extend(cand,new_node)) - return false; -#ifdef EARLY_EXPAND - TryExpandNode(new_node); -#endif - } - } - } - - // hack: put something local into the underapproximation formula - // without this, interpolants can be pretty bad - void AddThing(expr &conj){ - std::string name = "@thing"; - expr thing = ctx.constant(name.c_str(),ctx.bool_sort()); - if(conj.is_app() && conj.decl().get_decl_kind() == And){ - std::vector conjs(conj.num_args()+1); - for(unsigned i = 0; i+1 < conjs.size(); i++) - conjs[i] = conj.arg(i); - conjs[conjs.size()-1] = thing; - conj = rpfp->conjoin(conjs); - } - } - - Node *CreateUnderapproxNode(Node *node){ - // cex.get_tree()->ComputeUnderapprox(cex.get_root(),0); - RPFP::Node *under_node = CreateNodeInstance(node->map /* ,StratifiedLeafCount-- */); - under_node->Annotation.IntersectWith(cex.get_root()->Underapprox); - AddThing(under_node->Annotation.Formula); - Edge *e = unwinding->CreateLowerBoundEdge(under_node); - under_node->Annotation.SetFull(); // allow this node to cover others - back_edges[under_node] = back_edges[node]; - e->map = nullptr; - reporter->Extend(under_node); - return under_node; - } - - /** Try to prove a conjecture about a node. If successful - update the unwinding annotation appropriately. */ - bool ProveConjecture(Node *node, const RPFP::Transformer &t,Node *other = nullptr, Counterexample *_cex = nullptr){ - reporter->Conjecture(node,t); - timer_start("ProveConjecture"); - RPFP::Transformer save = node->Bound; - node->Bound.IntersectWith(t); - -#ifndef LOCALIZE_CONJECTURES - bool ok = SatisfyUpperBound(node); -#else - SetHeuristicOldNode(other); - bool ok = SatisfyUpperBound(node); - SetHeuristicOldNode(0); -#endif - - if(ok){ - timer_stop("ProveConjecture"); - return true; - } -#ifdef UNDERAPPROX_NODES - if(UseUnderapprox && last_decisions > 500){ - std::cout << "making an underapprox\n"; - ExpandNodeFromCoverFail(node); - } -#endif - if(_cex) (*_cex).swap(cex); // return the cex if asked - cex.clear(); // throw away the useless cex - node->Bound = save; // put back original bound - timer_stop("ProveConjecture"); - return false; - } - - /** If a node is part of the inductive subset, expand it. - We ask the inductive subset to exclude the node if possible. - */ - void TryExpandNode(RPFP::Node *node){ - if(indset->Close(node)) return; - if(!NoConj && indset->Conjecture(node)){ -#ifdef UNDERAPPROX_NODES - /* TODO: temporary fix. this prevents an infinite loop in case - the node is covered by multiple others. This should be - removed when covering by a set is implemented. - */ - if(indset->Contains(node)){ - unexpanded.erase(node); - insts_of_node[node->map].push_back(node); - } -#endif - return; - } -#ifdef UNDERAPPROX_NODES - if(!indset->Contains(node)) - return; // could be covered by an underapprox node -#endif - indset->Add(node); -#if defined(CANDS_FROM_COVER_FAIL) && !defined(UNDERAPPROX_NODES) - if(ExpandNodeFromCoverFail(node)) - return; -#endif - ExpandNode(node); - } - - /** Make the conjunction of markers for all (expanded) instances of - a node in the input RPFP. */ - expr AllNodeMarkers(Node *node){ - expr res = ctx.bool_val(true); - std::vector &insts = insts_of_node[node]; - for(int k = insts.size()-1; k >= 0; k--) - res = res && NodeMarker(insts[k]); - return res; - } - - void RuleOutNodesPastBound(Node *node, RPFP::Transformer &t){ -#ifdef BOUNDED - if(RecursionBound < 0)return; - std::vector &insts = insts_of_node[node]; - for(unsigned i = 0; i < insts.size(); i++) - if(NodePastRecursionBound(insts[i])) - t.Formula = t.Formula && !NodeMarker(insts[i]); -#endif - } - - - void GenNodeSolutionWithMarkersAux(Node *node, RPFP::Transformer &annot, expr &marker_disjunction, Node *other_node){ -#ifdef BOUNDED - if(RecursionBound >= 0 && NodePastRecursionBound(node)) - return; -#endif - RPFP::Transformer temp = node->Annotation; - expr marker = (!other_node) ? NodeMarker(node) : NodeMarker(node, other_node); - temp.Formula = (!marker || temp.Formula); - annot.IntersectWith(temp); - marker_disjunction = marker_disjunction || marker; - } - - bool GenNodeSolutionWithMarkers(Node *node, RPFP::Transformer &annot, bool expanded_only = false, Node *other_node = nullptr){ - bool res = false; - annot.SetFull(); - expr marker_disjunction = ctx.bool_val(false); - std::vector &insts = expanded_only ? insts_of_node[node] : all_of_node[node]; - for(unsigned j = 0; j < insts.size(); j++){ - Node *node = insts[j]; - if(indset->Contains(insts[j])){ - GenNodeSolutionWithMarkersAux(node, annot, marker_disjunction, other_node); res = true; - } - } - annot.Formula = annot.Formula && marker_disjunction; - annot.Simplify(); - return res; - } - - /** Make a checker to determine if an edge in the input RPFP - is satisfied. */ - Node *CheckerJustForEdge(Edge *edge, RPFP *checker, bool expanded_only = false){ - Node *root = checker->CloneNode(edge->Parent); - GenNodeSolutionFromIndSet(edge->Parent, root->Bound); - if(root->Bound.IsFull()) - return nullptr; - checker->AssertNode(root); - std::vector cs; - for(unsigned j = 0; j < edge->Children.size(); j++){ - Node *oc = edge->Children[j]; - Node *nc = checker->CloneNode(oc); - if(!GenNodeSolutionWithMarkers(oc,nc->Annotation,expanded_only)) - return nullptr; - Edge *e = checker->CreateLowerBoundEdge(nc); - checker->AssertEdge(e); - cs.push_back(nc); - } - checker->AssertEdge(checker->CreateEdge(root,edge->F,cs)); - return root; - } - -#ifndef MINIMIZE_CANDIDATES_HARDER - -#if 0 - /** Make a checker to detheermine if an edge in the input RPFP - is satisfied. */ - Node *CheckerForEdge(Edge *edge, RPFP *checker){ - Node *root = checker->CloneNode(edge->Parent); - root->Bound = edge->Parent->Annotation; - root->Bound.Formula = (!AllNodeMarkers(edge->Parent)) || root->Bound.Formula; - checker->AssertNode(root); - std::vector cs; - for(unsigned j = 0; j < edge->Children.size(); j++){ - Node *oc = edge->Children[j]; - Node *nc = checker->CloneNode(oc); - nc->Annotation = oc->Annotation; - RuleOutNodesPastBound(oc,nc->Annotation); - Edge *e = checker->CreateLowerBoundEdge(nc); - checker->AssertEdge(e); - cs.push_back(nc); - } - checker->AssertEdge(checker->CreateEdge(root,edge->F,cs)); - return root; - } - -#else - /** Make a checker to determine if an edge in the input RPFP - is satisfied. */ - Node *CheckerForEdge(Edge *edge, RPFP *checker){ - Node *root = checker->CloneNode(edge->Parent); - GenNodeSolutionFromIndSet(edge->Parent, root->Bound); -#if 0 - if(root->Bound.IsFull()) - return = 0; -#endif - checker->AssertNode(root); - std::vector cs; - for(unsigned j = 0; j < edge->Children.size(); j++){ - Node *oc = edge->Children[j]; - Node *nc = checker->CloneNode(oc); - GenNodeSolutionWithMarkers(oc,nc->Annotation,true); - Edge *e = checker->CreateLowerBoundEdge(nc); - checker->AssertEdge(e); - cs.push_back(nc); - } - checker->AssertEdge(checker->CreateEdge(root,edge->F,cs)); - return root; - } -#endif - - /** If an edge is not satisfied, produce an extension candidate - using instances of its children that violate the parent annotation. - We find these using the marker predicates. */ - void ExtractCandidateFromCex(Edge *edge, RPFP *checker, Node *root, Candidate &candidate){ - candidate.edge = edge; - for(unsigned j = 0; j < edge->Children.size(); j++){ - Node *node = root->Outgoing->Children[j]; - Edge *lb = node->Outgoing; - std::vector &insts = insts_of_node[edge->Children[j]]; -#ifndef MINIMIZE_CANDIDATES - for(int k = insts.size()-1; k >= 0; k--) -#else - for(unsigned k = 0; k < insts.size(); k++) -#endif - { - Node *inst = insts[k]; - if(indset->Contains(inst)){ - if(checker->Empty(node) || - eq(lb ? checker->Eval(lb,NodeMarker(inst)) : checker->dualModel.eval(NodeMarker(inst,node)),ctx.bool_val(true))){ - candidate.Children.push_back(inst); - goto next_child; - } - } - } - throw InternalError("No candidate from induction failure"); - next_child:; - } - } -#else - - - /** Make a checker to determine if an edge in the input RPFP - is satisfied. */ - Node *CheckerForEdge(Edge *edge, RPFP *checker){ - Node *root = checker->CloneNode(edge->Parent); - GenNodeSolutionFromIndSet(edge->Parent, root->Bound); - if(root->Bound.IsFull()) - return = 0; - checker->AssertNode(root); - std::vector cs; - for(unsigned j = 0; j < edge->Children.size(); j++){ - Node *oc = edge->Children[j]; - Node *nc = checker->CloneNode(oc); - GenNodeSolutionWithMarkers(oc,nc->Annotation,true); - Edge *e = checker->CreateLowerBoundEdge(nc); - checker->AssertEdge(e); - cs.push_back(nc); - } - checker->AssertEdge(checker->CreateEdge(root,edge->F,cs)); - return root; - } - - /** If an edge is not satisfied, produce an extension candidate - using instances of its children that violate the parent annotation. - We find these using the marker predicates. */ - void ExtractCandidateFromCex(Edge *edge, RPFP *checker, Node *root, Candidate &candidate){ - candidate.edge = edge; - std::vector assumps; - for(unsigned j = 0; j < edge->Children.size(); j++){ - Edge *lb = root->Outgoing->Children[j]->Outgoing; - std::vector &insts = insts_of_node[edge->Children[j]]; - for(unsigned k = 0; k < insts.size(); k++) - { - Node *inst = insts[k]; - expr marker = NodeMarker(inst); - if(indset->Contains(inst)){ - if(checker->Empty(lb->Parent) || - eq(checker->Eval(lb,marker),ctx.bool_val(true))){ - candidate.Children.push_back(inst); - assumps.push_back(checker->Localize(lb,marker)); - goto next_child; - } - assumps.push_back(checker->Localize(lb,marker)); - if(checker->CheckUpdateModel(root,assumps) != unsat){ - candidate.Children.push_back(inst); - goto next_child; - } - assumps.pop_back(); - } - } - throw InternalError("No candidate from induction failure"); - next_child:; - } - } - -#endif - - - Node *CheckerForEdgeClone(Edge *edge, RPFP_caching *checker){ - Edge *gen_cands_edge = checker->GetEdgeClone(edge); - Node *root = gen_cands_edge->Parent; - root->Outgoing = gen_cands_edge; - GenNodeSolutionFromIndSet(edge->Parent, root->Bound); -#if 0 - if(root->Bound.IsFull()) - return = 0; -#endif - checker->AssertNode(root); - for(unsigned j = 0; j < edge->Children.size(); j++){ - Node *oc = edge->Children[j]; - Node *nc = gen_cands_edge->Children[j]; - GenNodeSolutionWithMarkers(oc,nc->Annotation,true,nc); - } - checker->AssertEdge(gen_cands_edge,1,true); - return root; - } - - /** If the current proposed solution is not inductive, - use the induction failure to generate candidates for extension. */ - void GenCandidatesFromInductionFailure(bool full_scan = false){ - timer_start("GenCandIndFail"); - GenSolutionFromIndSet(true /* add markers */); - for(unsigned i = 0; i < edges.size(); i++){ - Edge *edge = edges[i]; - if(!full_scan && updated_nodes.find(edge->Parent) == updated_nodes.end()) - continue; -#ifndef USE_NEW_GEN_CANDS - slvr.push(); - RPFP *checker = new RPFP(rpfp->ls); - Node *root = CheckerForEdge(edge,checker); - if(checker->Check(root) != unsat){ - Candidate candidate; - ExtractCandidateFromCex(edge,checker,root,candidate); - reporter->InductionFailure(edge,candidate.Children); - candidates.push_back(candidate); - } - slvr.pop(1); - delete checker; -#else - if(!NodeSolutionFromIndSetFull(edge->Parent)){ - RPFP_caching::scoped_solver_for_edge ssfe(gen_cands_rpfp,edge,true /* models */, true /*axioms*/); - gen_cands_rpfp->Push(); - Node *root = CheckerForEdgeClone(edge,gen_cands_rpfp); - if(gen_cands_rpfp->Check(root) != unsat){ - Candidate candidate; - ExtractCandidateFromCex(edge,gen_cands_rpfp,root,candidate); - reporter->InductionFailure(edge,candidate.Children); - candidates.push_back(candidate); - } - gen_cands_rpfp->Pop(1); - } -#endif - } - updated_nodes.clear(); - timer_stop("GenCandIndFail"); -#ifdef CHECK_CANDS_FROM_IND_SET - for(std::list::iterator it = candidates.begin(), en = candidates.end(); it != en; ++it){ - if(!CandidateFeasible(*it)) - throw "produced infeasible candidate"; - } -#endif - if(!full_scan && candidates.empty()){ - reporter->Message("No candidates from updates. Trying full scan."); - GenCandidatesFromInductionFailure(true); - } - } - -#ifdef CANDS_FROM_UPDATES - /** If the given edge is not inductive in the current proposed solution, - use the induction failure to generate candidates for extension. */ - void GenCandidatesFromEdgeInductionFailure(RPFP::Edge *edge){ - GenSolutionFromIndSet(true /* add markers */); - for(unsigned i = 0; i < edges.size(); i++){ - slvr.push(); - Edge *edge = edges[i]; - RPFP *checker = new RPFP(rpfp->ls); - Node *root = CheckerForEdge(edge,checker); - if(checker->Check(root) != unsat){ - Candidate candidate; - ExtractCandidateFromCex(edge,checker,root,candidate); - reporter->InductionFailure(edge,candidate.Children); - candidates.push_back(candidate); - } - slvr.pop(1); - delete checker; - } - } -#endif - - /** Find the unexpanded nodes in the inductive subset. */ - void FindNodesToExpand(){ - for(Unexpanded::iterator it = unexpanded.begin(), en = unexpanded.end(); it != en; ++it){ - Node *node = *it; - if(indset->Candidate(node)) - to_expand.push_back(node); - } - } - - /** Try to create some extension candidates from the unexpanded - nodes. */ - void ProduceSomeCandidates(){ - while(candidates.empty() && !to_expand.empty()){ - Node *node = to_expand.front(); - to_expand.pop_front(); - TryExpandNode(node); - } - } - - std::list postponed_candidates; - - /** Try to produce some extension candidates, first from unexpanded - nides, and if this fails, from induction failure. */ - void ProduceCandidatesForExtension(){ - if(candidates.empty()) - ProduceSomeCandidates(); - while(candidates.empty()){ - FindNodesToExpand(); - if(to_expand.empty()) break; - ProduceSomeCandidates(); - } - if(candidates.empty()){ -#ifdef DEPTH_FIRST_EXPAND - if(postponed_candidates.empty()){ - GenCandidatesFromInductionFailure(); - postponed_candidates.swap(candidates); - } - if(!postponed_candidates.empty()){ - candidates.push_back(postponed_candidates.front()); - postponed_candidates.pop_front(); - } -#else - GenCandidatesFromInductionFailure(); -#endif - } - } - - bool Update(Node *node, const RPFP::Transformer &fact, bool eager=false){ - if(!node->Annotation.SubsetEq(fact)){ - reporter->Update(node,fact,eager); - if(conj_reporter) - conj_reporter->Update(node,fact,eager); - indset->Update(node,fact); - updated_nodes.insert(node->map); - node->Annotation.IntersectWith(fact); - return true; - } - return false; - } - - bool UpdateNodeToNode(Node *node, Node *top){ - return Update(node,top->Annotation); - } - - /** Update the unwinding solution, using an interpolant for the - derivation tree. */ - void UpdateWithInterpolant(Node *node, RPFP *tree, Node *top){ - if(top->Outgoing) - for(unsigned i = 0; i < top->Outgoing->Children.size(); i++) - UpdateWithInterpolant(node->Outgoing->Children[i],tree,top->Outgoing->Children[i]); - UpdateNodeToNode(node, top); - heuristic->Update(node); - } - - /** Update unwinding lower bounds, using a counterexample. */ - - void UpdateWithCounterexample(Node *node, RPFP *tree, Node *top){ - if(top->Outgoing) - for(unsigned i = 0; i < top->Outgoing->Children.size(); i++) - UpdateWithCounterexample(node->Outgoing->Children[i],tree,top->Outgoing->Children[i]); - if(!top->Underapprox.SubsetEq(node->Underapprox)){ - reporter->UpdateUnderapprox(node,top->Underapprox); - // indset->Update(node,top->Annotation); - node->Underapprox.UnionWith(top->Underapprox); - heuristic->Update(node); - } - } - - /** Try to update the unwinding to satisfy the upper bound of a - node. */ - bool SatisfyUpperBound(Node *node){ - if(node->Bound.IsFull()) return true; -#ifdef PROPAGATE_BEFORE_CHECK - Propagate(); -#endif - reporter->Bound(node); - int start_decs = rpfp->CumulativeDecisions(); - DerivationTree *dtp = new DerivationTreeSlow(this,unwinding,reporter,heuristic,FullExpand); - DerivationTree &dt = *dtp; - bool res = dt.Derive(unwinding,node,UseUnderapprox); - int end_decs = rpfp->CumulativeDecisions(); - // std::cout << "decisions: " << (end_decs - start_decs) << std::endl; - last_decisions = end_decs - start_decs; - if(res){ - cex.set(dt.tree,dt.top); // note tree is now owned by cex - if(UseUnderapprox){ - UpdateWithCounterexample(node,dt.tree,dt.top); - } - } - else { - UpdateWithInterpolant(node,dt.tree,dt.top); - delete dt.tree; - } - delete dtp; - return !res; - } - - /* For a given nod in the unwinding, get conjectures from the - proposers and check them locally. Update the node with any true - conjectures. - */ - - void DoEagerDeduction(Node *node){ - for(unsigned i = 0; i < proposers.size(); i++){ - const std::vector &conjectures = proposers[i]->Propose(node); - for(unsigned j = 0; j < conjectures.size(); j++){ - const RPFP::Transformer &conjecture = conjectures[j]; - RPFP::Transformer bound(conjecture); - std::vector conj_vec; - unwinding->CollectConjuncts(bound.Formula,conj_vec); - for(unsigned k = 0; k < conj_vec.size(); k++){ - bound.Formula = conj_vec[k]; - if(CheckEdgeCaching(node->Outgoing,bound) == unsat) - Update(node,bound, /* eager = */ true); - //else - //std::cout << "conjecture failed\n"; - } - } - } - } - - - check_result CheckEdge(RPFP *checker, Edge *edge){ - Node *root = edge->Parent; - checker->Push(); - checker->AssertNode(root); - checker->AssertEdge(edge,1,true); - check_result res = checker->Check(root); - checker->Pop(1); - return res; - } - - check_result CheckEdgeCaching(Edge *unwinding_edge, const RPFP::Transformer &bound){ - - // use a dedicated solver for this edge - // TODO: can this mess be hidden somehow? - - RPFP_caching *checker = gen_cands_rpfp; // TODO: a good choice? - Edge *edge = unwinding_edge->map; // get the edge in the original RPFP - RPFP_caching::scoped_solver_for_edge ssfe(checker,edge,true /* models */, true /*axioms*/); - Edge *checker_edge = checker->GetEdgeClone(edge); - - // copy the annotations and bound to the clone - Node *root = checker_edge->Parent; - root->Bound = bound; - for(unsigned j = 0; j < checker_edge->Children.size(); j++){ - Node *oc = unwinding_edge->Children[j]; - Node *nc = checker_edge->Children[j]; - nc->Annotation = oc->Annotation; - } - - return CheckEdge(checker,checker_edge); - } - - - /* If the counterexample derivation is partial due to - use of underapproximations, complete it. */ - - void BuildFullCex(Node *node){ - DerivationTree dt(this,unwinding,reporter,heuristic,FullExpand); - bool res = dt.Derive(unwinding,node,UseUnderapprox,true); // build full tree - if(!res) throw "Duality internal error in BuildFullCex"; - cex.set(dt.tree,dt.top); - } - - void UpdateBackEdges(Node *node){ -#ifdef BOUNDED - std::vector &chs = node->Outgoing->Children; - for(unsigned i = 0; i < chs.size(); i++){ - Node *child = chs[i]; - bool is_back = TopoSort[child->map] >= TopoSort[node->map]; - NodeToCounter &nov = back_edges[node]; - NodeToCounter chv = back_edges[child]; - if(is_back) - chv[child->map].val++; - for(NodeToCounter::iterator it = chv.begin(), en = chv.end(); it != en; ++it){ - Node *back = it->first; - Counter &c = nov[back]; - c.val = std::max(c.val,it->second.val); - } - } -#endif - } - - /** Extend the unwinding, keeping it solved. */ - bool Extend(Candidate &cand, Node *&node){ - timer_start("Extend"); - node = CreateNodeInstance(cand.edge->Parent); - CreateEdgeInstance(cand.edge,node,cand.Children); - UpdateBackEdges(node); - reporter->Extend(node); - DoEagerDeduction(node); // first be eager... - bool res = SatisfyUpperBound(node); // then be lazy - if(res) indset->CloseDescendants(node); - else { -#ifdef UNDERAPPROX_NODES - ExpandUnderapproxNodes(cex.get_tree(), cex.get_root()); -#endif - if(UseUnderapprox) BuildFullCex(node); - timer_stop("Extend"); - return res; - } - timer_stop("Extend"); - return res; - } - - void ExpandUnderapproxNodes(RPFP *tree, Node *root){ - Node *node = root->map; - if(underapprox_map.find(node) != underapprox_map.end()){ - RPFP::Transformer cnst = root->Annotation; - tree->EvalNodeAsConstraint(root, cnst); - cnst.Complement(); - Node *orig = underapprox_map[node]; - RPFP::Transformer save = orig->Bound; - orig->Bound = cnst; - DerivationTree dt(this,unwinding,reporter,heuristic,FullExpand); - bool res = dt.Derive(unwinding,orig,UseUnderapprox,true,tree); - if(!res){ - UpdateWithInterpolant(orig,dt.tree,dt.top); - throw "bogus underapprox!"; - } - ExpandUnderapproxNodes(tree,dt.top); - } - else if(root->Outgoing){ - std::vector &chs = root->Outgoing->Children; - for(unsigned i = 0; i < chs.size(); i++) - ExpandUnderapproxNodes(tree,chs[i]); - } - } - - // Propagate conjuncts up the unwinding - void Propagate(){ - reporter->Message("beginning propagation"); - timer_start("Propagate"); - std::vector sorted_nodes = unwinding->nodes; - std::sort(sorted_nodes.begin(),sorted_nodes.end(),std::less()); // sorts by sequence number - hash_map > facts; - for(unsigned i = 0; i < sorted_nodes.size(); i++){ - Node *node = sorted_nodes[i]; - std::set &node_facts = facts[node->map]; - if(!(node->Outgoing && indset->Contains(node))) - continue; - std::vector conj_vec; - unwinding->CollectConjuncts(node->Annotation.Formula,conj_vec); - std::set conjs; - std::copy(conj_vec.begin(),conj_vec.end(),std::inserter(conjs,conjs.begin())); - if(!node_facts.empty()){ - RPFP *checker = new RPFP(rpfp->ls); - slvr.push(); - Node *root = checker->CloneNode(node); - Edge *edge = node->Outgoing; - // checker->AssertNode(root); - std::vector cs; - for(unsigned j = 0; j < edge->Children.size(); j++){ - Node *oc = edge->Children[j]; - Node *nc = checker->CloneNode(oc); - nc->Annotation = oc->Annotation; // is this needed? - cs.push_back(nc); - } - Edge *checker_edge = checker->CreateEdge(root,edge->F,cs); - checker->AssertEdge(checker_edge, 0, true, false); - std::vector propagated; - for(std::set ::iterator it = node_facts.begin(), en = node_facts.end(); it != en;){ - const expr &fact = *it; - if(conjs.find(fact) == conjs.end()){ - root->Bound.Formula = fact; - slvr.push(); - checker->AssertNode(root); - check_result res = checker->Check(root); - slvr.pop(); - if(res != unsat){ - std::set ::iterator victim = it; - ++it; - node_facts.erase(victim); // if it ain't true, nix it - continue; - } - propagated.push_back(fact); - } - ++it; - } - slvr.pop(); - for(unsigned i = 0; i < propagated.size(); i++){ - root->Annotation.Formula = propagated[i]; - UpdateNodeToNode(node,root); - } - delete checker; - } - for(std::set ::iterator it = conjs.begin(), en = conjs.end(); it != en; ++it){ - expr foo = *it; - node_facts.insert(foo); - } - } - timer_stop("Propagate"); - } - - - /** This class represents a derivation tree. */ - class DerivationTree { - public: - - virtual ~DerivationTree(){} - - DerivationTree(Duality *_duality, RPFP *rpfp, Reporter *_reporter, Heuristic *_heuristic, bool _full_expand) - : slvr(rpfp->slvr()), - ctx(rpfp->ctx) - { - duality = _duality; - reporter = _reporter; - heuristic = _heuristic; - full_expand = _full_expand; - } - - Duality *duality; - Reporter *reporter; - Heuristic *heuristic; - solver &slvr; - context &ctx; - RPFP *tree; - RPFP::Node *top; - std::list leaves; - bool full_expand; - bool underapprox; - bool constrained; - bool false_approx; - std::vector underapprox_core; - int start_decs, last_decs; - - /* We build derivation trees in one of three modes: - - 1) In normal mode, we build the full tree without considering - underapproximations. - - 2) In underapprox mode, we use underapproximations to cut off - the tree construction. THis means the resulting tree may not - be complete. - - 3) In constrained mode, we build the full tree but use - underapproximations as upper bounds. This mode is used to - complete the partial derivation constructed in underapprox - mode. - */ - - bool Derive(RPFP *rpfp, RPFP::Node *root, bool _underapprox, bool _constrained = false, RPFP *_tree = nullptr){ - underapprox = _underapprox; - constrained = _constrained; - false_approx = true; - timer_start("Derive"); -#ifndef USE_CACHING_RPFP - tree = _tree ? _tree : new RPFP(rpfp->ls); -#else - RPFP::LogicSolver *cache_ls = new RPFP::iZ3LogicSolver(ctx); - cache_ls->slvr->push(); - tree = _tree ? _tree : new RPFP_caching(cache_ls); -#endif - tree->HornClauses = rpfp->HornClauses; - tree->Push(); // so we can clear out the solver later when finished - top = CreateApproximatedInstance(root); - tree->AssertNode(top); // assert the negation of the top-level spec - timer_start("Build"); - bool res = Build(); - heuristic->Done(); - timer_stop("Build"); - timer_start("Pop"); - tree->Pop(1); - timer_stop("Pop"); -#ifdef USE_CACHING_RPFP - cache_ls->slvr->pop(1); - delete cache_ls; - tree->ls = rpfp->ls; -#endif - timer_stop("Derive"); - return res; - } - -#define WITH_CHILDREN - - void InitializeApproximatedInstance(RPFP::Node *to){ - to->Annotation = to->map->Annotation; -#ifndef WITH_CHILDREN - tree->CreateLowerBoundEdge(to); -#endif - leaves.push_back(to); - } - - Node *CreateApproximatedInstance(RPFP::Node *from){ - Node *to = tree->CloneNode(from); - InitializeApproximatedInstance(to); - return to; - } - - bool CheckWithUnderapprox(){ - timer_start("CheckWithUnderapprox"); - std::vector leaves_vector(leaves.size()); - std::copy(leaves.begin(),leaves.end(),leaves_vector.begin()); - check_result res = tree->Check(top,leaves_vector); - timer_stop("CheckWithUnderapprox"); - return res != unsat; - } - - virtual bool Build(){ -#ifdef EFFORT_BOUNDED_STRAT - start_decs = tree->CumulativeDecisions(); -#endif - while(ExpandSomeNodes(true)); // do high-priority expansions - while (true) - { -#ifndef WITH_CHILDREN - timer_start("asserting leaves"); - timer_start("pushing"); - tree->Push(); - timer_stop("pushing"); - for(std::list::iterator it = leaves.begin(), en = leaves.end(); it != en; ++it) - tree->AssertEdge((*it)->Outgoing,1); // assert the overapproximation, and keep it past pop - timer_stop("asserting leaves"); - lbool res = tree->Solve(top, 2); // incremental solve, keep interpolants for two pops - timer_start("popping leaves"); - tree->Pop(1); - timer_stop("popping leaves"); -#else - lbool res; - if((underapprox || false_approx) && top->Outgoing && CheckWithUnderapprox()){ - if(constrained) goto expand_some_nodes; // in constrained mode, keep expanding - goto we_are_sat; // else if underapprox is sat, we stop - } - // tree->Check(top); - res = tree->Solve(top, 1); // incremental solve, keep interpolants for one pop -#endif - if (res == l_false) - return false; - - expand_some_nodes: - if(ExpandSomeNodes()) - continue; - - we_are_sat: - if(underapprox && !constrained){ - timer_start("ComputeUnderapprox"); - tree->ComputeUnderapprox(top,1); - timer_stop("ComputeUnderapprox"); - } - else { -#ifdef UNDERAPPROX_NODES -#ifndef SKIP_UNDERAPPROX_NODES - timer_start("ComputeUnderapprox"); - tree->ComputeUnderapprox(top,1); - timer_stop("ComputeUnderapprox"); -#endif -#endif - } - return true; - } - } - - virtual void ExpandNode(RPFP::Node *p){ - // tree->RemoveEdge(p->Outgoing); - Edge *ne = p->Outgoing; - if(ne) { - // reporter->Message("Recycling edge..."); - std::vector &cs = ne->Children; - for(unsigned i = 0; i < cs.size(); i++) - InitializeApproximatedInstance(cs[i]); - // ne->dual = expr(); - } - else { - Edge *edge = duality->GetNodeOutgoing(p->map,last_decs); - std::vector &cs = edge->Children; - std::vector children(cs.size()); - for(unsigned i = 0; i < cs.size(); i++) - children[i] = CreateApproximatedInstance(cs[i]); - ne = tree->CreateEdge(p, p->map->Outgoing->F, children); - ne->map = p->map->Outgoing->map; - } -#ifndef WITH_CHILDREN - tree->AssertEdge(ne); // assert the edge in the solver -#else - tree->AssertEdge(ne,0,!full_expand,(underapprox || false_approx)); // assert the edge in the solver -#endif - reporter->Expand(ne); - } - -#define UNDERAPPROXCORE -#ifndef UNDERAPPROXCORE - void ExpansionChoices(std::set &best){ - std::set choices; - for(std::list::iterator it = leaves.begin(), en = leaves.end(); it != en; ++it) - if (!tree->Empty(*it)) // if used in the counter-model - choices.insert(*it); - heuristic->ChooseExpand(choices, best); - } -#else -#if 0 - - void ExpansionChoices(std::set &best){ - std::vector unused_set, used_set; - std::set choices; - for(std::list::iterator it = leaves.begin(), en = leaves.end(); it != en; ++it){ - Node *n = *it; - if (!tree->Empty(n)) - used_set.push_back(n); - else - unused_set.push_back(n); - } - if(tree->Check(top,unused_set) == unsat) - throw "error in ExpansionChoices"; - for(unsigned i = 0; i < used_set.size(); i++){ - Node *n = used_set[i]; - unused_set.push_back(n); - if(!top->Outgoing || tree->Check(top,unused_set) == unsat){ - unused_set.pop_back(); - choices.insert(n); - } - else - std::cout << "Using underapprox of " << n->number << std::endl; - } - heuristic->ChooseExpand(choices, best); - } -#else - void ExpansionChoicesFull(std::set &best, bool high_priority, bool best_only = false){ - std::set choices; - for(std::list::iterator it = leaves.begin(), en = leaves.end(); it != en; ++it) - if (high_priority || !tree->Empty(*it)) // if used in the counter-model - choices.insert(*it); - heuristic->ChooseExpand(choices, best, high_priority, best_only); - } - - void ExpansionChoicesRec(std::vector &unused_set, std::vector &used_set, - std::set &choices, int from, int to){ - if(from == to) return; - int orig_unused = unused_set.size(); - unused_set.resize(orig_unused + (to - from)); - std::copy(used_set.begin()+from,used_set.begin()+to,unused_set.begin()+orig_unused); - if(!top->Outgoing || tree->Check(top,unused_set) == unsat){ - unused_set.resize(orig_unused); - if(to - from == 1){ -#if 1 - std::cout << "Not using underapprox of " << used_set[from] ->number << std::endl; -#endif - choices.insert(used_set[from]); - } - else { - int mid = from + (to - from)/2; - ExpansionChoicesRec(unused_set, used_set, choices, from, mid); - ExpansionChoicesRec(unused_set, used_set, choices, mid, to); - } - } - else { -#if 1 - std::cout << "Using underapprox of "; - for(int i = from; i < to; i++){ - std::cout << used_set[i]->number << " "; - if(used_set[i]->map->Underapprox.IsEmpty()) - std::cout << "(false!) "; - } - std::cout << std::endl; -#endif - } - } - - std::set old_choices; - - void ExpansionChoices(std::set &best, bool high_priority, bool best_only = false){ - if(!underapprox || constrained || high_priority){ - ExpansionChoicesFull(best, high_priority,best_only); - return; - } - std::vector unused_set, used_set; - std::set choices; - for(std::list::iterator it = leaves.begin(), en = leaves.end(); it != en; ++it){ - Node *n = *it; - if (!tree->Empty(n)){ - if(old_choices.find(n) != old_choices.end() || n->map->Underapprox.IsEmpty()) - choices.insert(n); - else - used_set.push_back(n); - } - else - unused_set.push_back(n); - } - if(tree->Check(top,unused_set) == unsat) - throw "error in ExpansionChoices"; - ExpansionChoicesRec(unused_set, used_set, choices, 0, used_set.size()); - old_choices = choices; - heuristic->ChooseExpand(choices, best, high_priority); - } -#endif -#endif - - bool ExpandSomeNodes(bool high_priority = false, int max = INT_MAX){ -#ifdef EFFORT_BOUNDED_STRAT - last_decs = tree->CumulativeDecisions() - start_decs; -#endif - timer_start("ExpandSomeNodes"); - timer_start("ExpansionChoices"); - std::set choices; - ExpansionChoices(choices,high_priority,max != INT_MAX); - timer_stop("ExpansionChoices"); - std::list leaves_copy = leaves; // copy so can modify orig - leaves.clear(); - int count = 0; - for(std::list::iterator it = leaves_copy.begin(), en = leaves_copy.end(); it != en; ++it){ - if(choices.find(*it) != choices.end() && count < max){ - count++; - ExpandNode(*it); - } - else leaves.push_back(*it); - } - timer_stop("ExpandSomeNodes"); - return !choices.empty(); - } - - void RemoveExpansion(RPFP::Node *p){ - Edge *edge = p->Outgoing; - Node *parent = edge->Parent; -#ifndef KEEP_EXPANSIONS - std::vector cs = edge->Children; - tree->DeleteEdge(edge); - for(unsigned i = 0; i < cs.size(); i++) - tree->DeleteNode(cs[i]); -#endif - leaves.push_back(parent); - } - - // remove all the descendants of tree root (but not root itself) - void RemoveTree(RPFP *tree, RPFP::Node *root){ - Edge *edge = root->Outgoing; - std::vector cs = edge->Children; - tree->DeleteEdge(edge); - for(unsigned i = 0; i < cs.size(); i++){ - RemoveTree(tree,cs[i]); - tree->DeleteNode(cs[i]); - } - } - }; - - class DerivationTreeSlow : public DerivationTree { - public: - - struct stack_entry { - unsigned level; // SMT solver stack level - std::vector expansions; - }; - - std::vector stack; - - hash_map updates; - - int restart_interval; - - DerivationTreeSlow(Duality *_duality, RPFP *rpfp, Reporter *_reporter, Heuristic *_heuristic, bool _full_expand) - : DerivationTree(_duality, rpfp, _reporter, _heuristic, _full_expand) { - stack.push_back(stack_entry()); - } - - struct DoRestart {}; - - bool Build() override { - restart_interval = 3; - while (true) { - try { - return BuildMain(); - } - catch (const DoRestart &) { - // clear the statck and try again - updated_nodes.clear(); - while(stack.size() > 1) - PopLevel(); - reporter->Message("restarted"); - restart_interval += 1; - } - } - } - - - // When we check, try to use the same children that were used in the - // previous counterexample. - check_result Check(){ -#if 0 - std::vector posnodes, negnodes; - std::vector &expansions = stack.back().expansions; - for(unsigned i = 0; i < expansions.size(); i++){ - Node *node = expansions[i]; - std::vector &chs = node->Outgoing->Children; - for(unsigned j = 0; j < chs.size(); j++){ - Node *ch = chs[j]; - int use = heuristic->UseNode(ch); - if(use == 1) - posnodes.push_back(ch); - else if (use == -1) - negnodes.push_back(ch); - } - } - if(!(posnodes.empty() && negnodes.empty())){ - check_result res = tree->CheckWithConstrainedNodes(posnodes,negnodes); - if(res != unsat){ - reporter->Message("matched previous counterexample"); - return res; - } - } -#endif - return tree->Check(top); - } - - bool BuildMain(){ - - stack.back().level = tree->slvr().get_scope_level(); - bool was_sat = true; - int update_failures = 0; - int total_updates = 0; - - while (true) - { - lbool res; - - unsigned slvr_level = tree->slvr().get_scope_level(); - if(slvr_level != stack.back().level) - throw "stacks out of sync!"; - reporter->Depth(stack.size()); - - // res = tree->Solve(top, 1); // incremental solve, keep interpolants for one pop - check_result foo = Check(); - res = foo == unsat ? l_false : l_true; - - if (res == l_false) { - if (stack.empty()) // should never happen - return false; - - { - std::vector &expansions = stack.back().expansions; - int update_count = 0; - for(unsigned i = 0; i < expansions.size(); i++){ - Node *node = expansions[i]; - try { - tree->SolveSingleNode(top,node); -#ifdef NO_GENERALIZE - node->Annotation.Formula = tree->RemoveRedundancy(node->Annotation.Formula).simplify(); -#else - if(expansions.size() == 1 && NodeTooComplicated(node)) - SimplifyNode(node); - else - node->Annotation.Formula = tree->RemoveRedundancy(node->Annotation.Formula).simplify(); - Generalize(node); -#endif - } - catch(const RPFP::Bad &){ - // bad interpolants can get us here - throw DoRestart(); - } - catch(const RPFP::ReallyBad &){ - // this could be caused by incompleteness - for(unsigned i = 0; i < expansions.size(); i++){ - Node *node = expansions[i]; - node->map->Annotation.SetFull(); - std::vector &chs = node->map->Outgoing->Children; - for(unsigned j = 0; j < chs.size(); j++) - chs[j]->Annotation.SetFull(); - reporter->Message("incompleteness: cleared annotation and child annotations"); - } - throw DoRestart(); - } - catch(char const *msg){ - // bad interpolants can get us here - reporter->Message(std::string("interpolation failure:") + msg); - throw DoRestart(); - } - catch(const RPFP::greedy_reduce_failed &){ - // if we couldn't reduce, just continue (maybe should restart?) - reporter->Message("interpolant verification failed"); - } - if(RecordUpdate(node)){ - update_count++; - total_updates++; - } - else - heuristic->Update(node->map); // make it less likely to expand this node in future - } -#if 1 - if(duality->EnableRestarts) - if(total_updates >= restart_interval) - throw DoRestart(); -#endif - if(update_count == 0){ - if(was_sat){ - update_failures++; - if(update_failures > 10){ - for(unsigned i = 0; i < expansions.size(); i++){ - Node *node = expansions[i]; - node->map->Annotation.SetFull(); - reporter->Message("incompleteness: cleared annotation"); - } - throw DoRestart(); - } - } - reporter->Message("backtracked without learning"); - } - else update_failures = 0; - } - tree->ComputeProofCore(); // need to compute the proof core before popping solver - bool propagated = false; - while(1) { - bool prev_level_used = LevelUsedInProof(stack.size()-2); // need to compute this before pop - PopLevel(); - if(stack.size() == 1)break; - if(prev_level_used){ - Node *node = stack.back().expansions[0]; -#ifndef NO_PROPAGATE - if(!Propagate(node)) break; -#endif - if(!RecordUpdate(node)) break; // shouldn't happen! - RemoveUpdateNodesAtCurrentLevel(); // this level is about to be deleted -- remove its children from update list - propagated = true; - continue; - } - if(propagated) break; // propagation invalidates the proof core, so disable non-chron backtrack - RemoveUpdateNodesAtCurrentLevel(); // this level is about to be deleted -- remove its children from update list - std::vector &unused_ex = stack.back().expansions; - for(unsigned i = 0; i < unused_ex.size(); i++) - heuristic->Update(unused_ex[i]->map); // make it less likely to expand this node in future - } - HandleUpdatedNodes(); - if(stack.size() == 1){ - if(top->Outgoing) - tree->DeleteEdge(top->Outgoing); // in case we kept the tree - return false; - } - was_sat = false; - } - else { - was_sat = true; - tree->Push(); - std::vector &expansions = stack.back().expansions; -#ifndef NO_DECISIONS -#if 0 - if(expansions.size() > 0) - tree->GreedyReduceNodes(expansions[0]->Outgoing->Children); // try to reduce number of children -#endif - for(unsigned i = 0; i < expansions.size(); i++){ - tree->FixCurrentState(expansions[i]->Outgoing); - } -#endif -#if 0 - if(tree->slvr().check() == unsat) - throw "help!"; -#endif - int expand_max = 1; - if(0&&duality->BatchExpand){ - int thing = stack.size() / 10; // * 0.1; - expand_max = std::max(1,thing); - if(expand_max > 1) - std::cout << "foo!\n"; - } - - if(ExpandSomeNodes(false,expand_max)) - continue; - tree->Pop(1); - node_order.clear(); - while(stack.size() > 1){ - tree->Pop(1); - std::vector &expansions = stack.back().expansions; - for(unsigned i = 0; i < expansions.size(); i++) - node_order.push_back(expansions[i]); - stack.pop_back(); - } -#if 0 - Reduce(); -#endif - return true; - } - } - } - - std::vector node_order; - - void Reduce(){ - tree->Push(); - // tree->AssertNode(top); // assert the negation of the top-level spec - for(int i = node_order.size()-1; i >= 0; --i){ - Edge *edge = node_order[i]->Outgoing; - if(edge){ - for(unsigned j = 0; j < edge->Children.size(); j++){ - Node *ch = edge->Children[j]; - if(!ch->Outgoing) - ch->Annotation.SetEmpty(); - } - tree->AssertEdge(edge,0,true); - } - } - tree->GreedyReduceNodes(node_order); // try to reduce the counterexample size - tree->Pop(1); - } - - void PopLevel(){ - std::vector &expansions = stack.back().expansions; - tree->Pop(1); - hash_set leaves_to_remove; - for(unsigned i = 0; i < expansions.size(); i++){ - Node *node = expansions[i]; - // if(node != top) - //tree->ConstrainParent(node->Incoming[0],node); - std::vector &cs = node->Outgoing->Children; - for(unsigned i = 0; i < cs.size(); i++){ - leaves_to_remove.insert(cs[i]); - UnmapNode(cs[i]); - if(std::find(updated_nodes.begin(),updated_nodes.end(),cs[i]) != updated_nodes.end()) - throw "help!"; - } - } - RemoveLeaves(leaves_to_remove); // have to do this before actually deleting the children - for(unsigned i = 0; i < expansions.size(); i++){ - Node *node = expansions[i]; - RemoveExpansion(node); - } - stack.pop_back(); - } - - bool NodeTooComplicated(Node *node){ - int ops = tree->CountOperators(node->Annotation.Formula); - if(ops > 10) return true; - node->Annotation.Formula = tree->RemoveRedundancy(node->Annotation.Formula).simplify(); - return tree->CountOperators(node->Annotation.Formula) > 3; - } - - void SimplifyNode(Node *node){ - // have to destroy the old proof to get a new interpolant - timer_start("SimplifyNode"); - tree->PopPush(); - try { - tree->InterpolateByCases(top,node); - } - catch(const RPFP::Bad&){ - timer_stop("SimplifyNode"); - throw RPFP::Bad(); - } - timer_stop("SimplifyNode"); - } - - bool LevelUsedInProof(unsigned level){ - std::vector &expansions = stack[level].expansions; - for(unsigned i = 0; i < expansions.size(); i++) - if(tree->EdgeUsedInProof(expansions[i]->Outgoing)) - return true; - return false; - } - - void RemoveUpdateNodesAtCurrentLevel() { - for(std::list::iterator it = updated_nodes.begin(), en = updated_nodes.end(); it != en;){ - Node *node = *it; - if(AtCurrentStackLevel(node->Incoming[0]->Parent)){ - std::list::iterator victim = it; - ++it; - updated_nodes.erase(victim); - } - else - ++it; - } - } - - void RemoveLeaves(hash_set &leaves_to_remove){ - std::list leaves_copy; - leaves_copy.swap(leaves); - for(std::list::iterator it = leaves_copy.begin(), en = leaves_copy.end(); it != en; ++it){ - if(leaves_to_remove.find(*it) == leaves_to_remove.end()) - leaves.push_back(*it); - } - } - - hash_map > node_map; - std::list updated_nodes; - - void ExpandNode(RPFP::Node *p) override { - stack.push_back(stack_entry()); - stack.back().level = tree->slvr().get_scope_level(); - stack.back().expansions.push_back(p); - DerivationTree::ExpandNode(p); - std::vector &new_nodes = p->Outgoing->Children; - for(unsigned i = 0; i < new_nodes.size(); i++){ - Node *n = new_nodes[i]; - node_map[n->map].push_back(n); - } - } - - bool RecordUpdate(Node *node){ - bool res = duality->UpdateNodeToNode(node->map,node); - if(res){ - std::vector to_update = node_map[node->map]; - for(unsigned i = 0; i < to_update.size(); i++){ - Node *node2 = to_update[i]; - // maintain invariant that no nodes on updated list are created at current stack level - if(node2 == node || !(node->Incoming.size() > 0 && AtCurrentStackLevel(node2->Incoming[0]->Parent))){ - updated_nodes.push_back(node2); - if(node2 != node) - node2->Annotation = node->Annotation; - } - } - } - return res; - } - - void HandleUpdatedNodes(){ - for(std::list::iterator it = updated_nodes.begin(), en = updated_nodes.end(); it != en;){ - Node *node = *it; - node->Annotation = node->map->Annotation; - if(node->Incoming.size() > 0) - tree->ConstrainParent(node->Incoming[0],node); - if(AtCurrentStackLevel(node->Incoming[0]->Parent)){ - std::list::iterator victim = it; - ++it; - updated_nodes.erase(victim); - } - else - ++it; - } - } - - bool AtCurrentStackLevel(Node *node){ - std::vector vec = stack.back().expansions; - for(unsigned i = 0; i < vec.size(); i++) - if(vec[i] == node) - return true; - return false; - } - - void UnmapNode(Node *node){ - std::vector &vec = node_map[node->map]; - for(unsigned i = 0; i < vec.size(); i++){ - if(vec[i] == node){ - std::swap(vec[i],vec.back()); - vec.pop_back(); - return; - } - } - throw "can't unmap node"; - } - - void Generalize(Node *node){ -#ifndef USE_RPFP_CLONE - tree->Generalize(top,node); -#else - RPFP_caching *clone_rpfp = duality->clone_rpfp; - if(!node->Outgoing->map) return; - Edge *clone_edge = clone_rpfp->GetEdgeClone(node->Outgoing->map); - Node *clone_node = clone_edge->Parent; - clone_node->Annotation = node->Annotation; - for(unsigned i = 0; i < clone_edge->Children.size(); i++) - clone_edge->Children[i]->Annotation = node->map->Outgoing->Children[i]->Annotation; - clone_rpfp->GeneralizeCache(clone_edge); - node->Annotation = clone_node->Annotation; -#endif - } - - bool Propagate(Node *node){ -#ifdef USE_RPFP_CLONE - RPFP_caching *clone_rpfp = duality->clone_rpfp; - Edge *clone_edge = clone_rpfp->GetEdgeClone(node->Outgoing->map); - Node *clone_node = clone_edge->Parent; - clone_node->Annotation = node->map->Annotation; - for(unsigned i = 0; i < clone_edge->Children.size(); i++) - clone_edge->Children[i]->Annotation = node->map->Outgoing->Children[i]->Annotation; - bool res = clone_rpfp->PropagateCache(clone_edge); - if(res) - node->Annotation = clone_node->Annotation; - return res; -#else - return false; -#endif - } - - }; - - - class Covering { - - struct cover_info { - Node *covered_by; - std::list covers; - bool dominated; - std::set dominates; - cover_info(){ - covered_by = nullptr; - dominated = false; - } - }; - - typedef hash_map cover_map; - cover_map cm; - Duality *parent; - bool some_updates; - -#define NO_CONJ_ON_SIMPLE_LOOPS -#ifdef NO_CONJ_ON_SIMPLE_LOOPS - hash_set simple_loops; -#endif - - Node *&covered_by(Node *node){ - return cm[node].covered_by; - } - - std::list &covers(Node *node){ - return cm[node].covers; - } - - std::vector &insts_of_node(Node *node){ - return parent->insts_of_node[node]; - } - - Reporter *reporter(){ - return parent->reporter; - } - - std::set &dominates(Node *x){ - return cm[x].dominates; - } - - bool dominates(Node *x, Node *y){ - std::set &d = cm[x].dominates; - return d.find(y) != d.end(); - } - - bool &dominated(Node *x){ - return cm[x].dominated; - } - - public: - - Covering(Duality *_parent){ - parent = _parent; - some_updates = false; - -#ifdef NO_CONJ_ON_SIMPLE_LOOPS - hash_map > outgoing; - for(unsigned i = 0; i < parent->rpfp->edges.size(); i++) - outgoing[parent->rpfp->edges[i]->Parent].push_back(parent->rpfp->edges[i]); - for(unsigned i = 0; i < parent->rpfp->nodes.size(); i++){ - Node * node = parent->rpfp->nodes[i]; - std::vector &outs = outgoing[node]; - if(outs.size() == 2){ - for(int j = 0; j < 2; j++){ - Edge *loop_edge = outs[j]; - if(loop_edge->Children.size() == 1 && loop_edge->Children[0] == loop_edge->Parent) - simple_loops.insert(node); - } - } - } -#endif - - } - - bool IsCoveredRec(hash_set &memo, Node *node){ - if(memo.find(node) != memo.end()) - return false; - memo.insert(node); - if(covered_by(node)) return true; - for(unsigned i = 0; i < node->Outgoing->Children.size(); i++) - if(IsCoveredRec(memo,node->Outgoing->Children[i])) - return true; - return false; - } - - bool IsCovered(Node *node){ - hash_set memo; - return IsCoveredRec(memo,node); - } - -#ifndef UNDERAPPROX_NODES - void RemoveCoveringsBy(Node *node){ - std::list &cs = covers(node); - for(std::list::iterator it = cs.begin(), en = cs.end(); it != en; it++){ - covered_by(*it) = 0; - reporter()->RemoveCover(*it,node); - } - cs.clear(); - } -#else - void RemoveCoveringsBy(Node *node){ - std::vector &cs = parent->all_of_node[node->map]; - for(std::vector::iterator it = cs.begin(), en = cs.end(); it != en; it++){ - Node *other = *it; - if(covered_by(other) && CoverOrder(node,other)){ - covered_by(other) = nullptr; - reporter()->RemoveCover(*it,node); - } - } - } -#endif - - void RemoveAscendantCoveringsRec(hash_set &memo, Node *node){ - if(memo.find(node) != memo.end()) - return; - memo.insert(node); - RemoveCoveringsBy(node); - for(std::vector::iterator it = node->Incoming.begin(), en = node->Incoming.end(); it != en; ++it) - RemoveAscendantCoveringsRec(memo,(*it)->Parent); - } - - void RemoveAscendantCoverings(Node *node){ - hash_set memo; - RemoveAscendantCoveringsRec(memo,node); - } - - bool CoverOrder(Node *covering, Node *covered){ -#ifdef UNDERAPPROX_NODES - if(parent->underapprox_map.find(covered) != parent->underapprox_map.end()) - return false; - if(parent->underapprox_map.find(covering) != parent->underapprox_map.end()) - return covering->number < covered->number || parent->underapprox_map[covering] == covered; -#endif - return covering->number < covered->number; - } - - bool CheckCover(Node *covered, Node *covering){ - return - CoverOrder(covering,covered) - && covered->Annotation.SubsetEq(covering->Annotation) - && !IsCovered(covering); - } - - bool CoverByNode(Node *covered, Node *covering){ - if(CheckCover(covered,covering)){ - covered_by(covered) = covering; - covers(covering).push_back(covered); - std::vector others; others.push_back(covering); - reporter()->AddCover(covered,others); - RemoveAscendantCoverings(covered); - return true; - } - else - return false; - } - -#ifdef UNDERAPPROX_NODES - bool CoverByAll(Node *covered){ - RPFP::Transformer all = covered->Annotation; - all.SetEmpty(); - std::vector &insts = parent->insts_of_node[covered->map]; - std::vector others; - for(unsigned i = 0; i < insts.size(); i++){ - Node *covering = insts[i]; - if(CoverOrder(covering,covered) && !IsCovered(covering)){ - others.push_back(covering); - all.UnionWith(covering->Annotation); - } - } - if(others.size() && covered->Annotation.SubsetEq(all)){ - covered_by(covered) = covered; // anything non-null will do - reporter()->AddCover(covered,others); - RemoveAscendantCoverings(covered); - return true; - } - else - return false; - } -#endif - - bool Close(Node *node){ - if(covered_by(node)) - return true; -#ifndef UNDERAPPROX_NODES - std::vector &insts = insts_of_node(node->map); - for(unsigned i = 0; i < insts.size(); i++) - if(CoverByNode(node,insts[i])) - return true; -#else - if(CoverByAll(node)) - return true; -#endif - return false; - } - - bool CloseDescendantsRec(hash_set &memo, Node *node){ - if(memo.find(node) != memo.end()) - return false; - for(unsigned i = 0; i < node->Outgoing->Children.size(); i++) - if(CloseDescendantsRec(memo,node->Outgoing->Children[i])) - return true; - if(Close(node)) - return true; - memo.insert(node); - return false; - } - - bool CloseDescendants(Node *node){ - timer_start("CloseDescendants"); - hash_set memo; - bool res = CloseDescendantsRec(memo,node); - timer_stop("CloseDescendants"); - return res; - } - - bool Contains(Node *node){ - timer_start("Contains"); - bool res = !IsCovered(node); - timer_stop("Contains"); - return res; - } - - bool Candidate(Node *node){ - timer_start("Candidate"); - bool res = !IsCovered(node) && !dominated(node); - timer_stop("Candidate"); - return res; - } - - void SetDominated(Node *node){ - dominated(node) = true; - } - - bool CouldCover(Node *covered, Node *covering){ -#ifdef NO_CONJ_ON_SIMPLE_LOOPS - // Forsimple loops, we rely on propagation, not covering - if(simple_loops.find(covered->map) != simple_loops.end()) - return false; -#endif -#ifdef UNDERAPPROX_NODES - // if(parent->underapprox_map.find(covering) != parent->underapprox_map.end()) - // return parent->underapprox_map[covering] == covered; -#endif - if(CoverOrder(covering,covered) - && !IsCovered(covering)){ - RPFP::Transformer f(covering->Annotation); f.SetEmpty(); -#if defined(TOP_DOWN) || defined(EFFORT_BOUNDED_STRAT) - if(parent->StratifiedInlining) - return true; -#endif - return !covering->Annotation.SubsetEq(f); - } - return false; - } - - bool ContainsCex(Node *node, Counterexample &cex){ - expr val = cex.get_tree()->Eval(cex.get_root()->Outgoing,node->Annotation.Formula); - return eq(val,parent->ctx.bool_val(true)); - } - - /** We conjecture that the annotations of similar nodes may be - true of this one. We start with later nodes, on the - principle that their annotations are likely weaker. We save - a counterexample -- if annotations of other nodes are true - in this counterexample, we don't need to check them. - */ - -#ifndef UNDERAPPROX_NODES - bool Conjecture(Node *node){ - std::vector &insts = insts_of_node(node->map); - Counterexample cex; - for(int i = insts.size() - 1; i >= 0; i--){ - Node *other = insts[i]; - if(CouldCover(node,other)){ - reporter()->Forcing(node,other); - if(cex.get_tree() && !ContainsCex(other,cex)) - continue; - cex.clear(); - if(parent->ProveConjecture(node,other->Annotation,other,&cex)) - if(CloseDescendants(node)) - return true; - } - } - cex.clear(); - return false; - } -#else - bool Conjecture(Node *node){ - std::vector &insts = insts_of_node(node->map); - Counterexample cex; - RPFP::Transformer Bound = node->Annotation; - Bound.SetEmpty(); - bool some_other = false; - for(int i = insts.size() - 1; i >= 0; i--){ - Node *other = insts[i]; - if(CouldCover(node,other)){ - reporter()->Forcing(node,other); - Bound.UnionWith(other->Annotation); - some_other = true; - } - } - if(some_other && parent->ProveConjecture(node,Bound)){ - CloseDescendants(node); - return true; - } - return false; - } -#endif - - void Update(Node *node, const RPFP::Transformer &update){ - RemoveCoveringsBy(node); - some_updates = true; - } - -#ifndef UNDERAPPROX_NODES - Node *GetSimilarNode(Node *node){ - if(!some_updates) - return 0; - std::vector &insts = insts_of_node(node->map); - for(int i = insts.size()-1; i >= 0; i--){ - Node *other = insts[i]; - if(dominates(node,other)) - if(CoverOrder(other,node) - && !IsCovered(other)) - return other; - } - return 0; - } -#else - Node *GetSimilarNode(Node *node){ - if(!some_updates) - return nullptr; - std::vector &insts = insts_of_node(node->map); - for(int i = insts.size() - 1; i >= 0; i--){ - Node *other = insts[i]; - if(CoverOrder(other,node) - && !IsCovered(other)) - return other; - } - return nullptr; - } -#endif - - bool Dominates(Node * node, Node *other){ - if(node == other) return false; - if(other->Outgoing->map == nullptr) return true; - if(node->Outgoing->map == other->Outgoing->map){ - assert(node->Outgoing->Children.size() == other->Outgoing->Children.size()); - for(unsigned i = 0; i < node->Outgoing->Children.size(); i++){ - Node *nc = node->Outgoing->Children[i]; - Node *oc = other->Outgoing->Children[i]; - if(!(nc == oc || oc->Outgoing->map ==nullptr || dominates(nc,oc))) - return false; - } - return true; - } - return false; - } - - void Add(Node *node){ - std::vector &insts = insts_of_node(node->map); - for(unsigned i = 0; i < insts.size(); i++){ - Node *other = insts[i]; - if(Dominates(node,other)){ - cm[node].dominates.insert(other); - cm[other].dominated = true; - reporter()->Dominates(node, other); - } - } - } - - }; - - /* This expansion heuristic makes use of a previuosly obtained - counterexample as a guide. This is for use in abstraction - refinement schemes.*/ - - class ReplayHeuristic : public Heuristic { - - Counterexample old_cex; - public: - ReplayHeuristic(RPFP *_rpfp, Counterexample &_old_cex) - : Heuristic(_rpfp) - { - old_cex.swap(_old_cex); // take ownership from caller - } - - ~ReplayHeuristic() override { - } - - // Maps nodes of derivation tree into old cex - hash_map cex_map; - - void Done() override { - cex_map.clear(); - old_cex.clear(); - } - - void ShowNodeAndChildren(Node *n){ - std::cout << n->Name.name() << ": "; - std::vector &chs = n->Outgoing->Children; - for(unsigned i = 0; i < chs.size(); i++) - std::cout << chs[i]->Name.name() << " " ; - std::cout << std::endl; - } - - // HACK: When matching relation names, we drop suffixes used to - // make the names unique between runs. For compatibility - // with boggie, we drop suffixes beginning with @@ - std::string BaseName(const std::string &name){ - int pos = name.find("@@"); - if(pos >= 1) - return name.substr(0,pos); - return name; - } - - Node *MatchNode(Node *node){ - if(cex_map.find(node) == cex_map.end()){ // try to match an unmatched node - Node *parent = node->Incoming[0]->Parent; // assumes we are a tree! - if(cex_map.find(parent) == cex_map.end()) - throw "catastrophe in ReplayHeuristic::ChooseExpand"; - Node *old_parent = cex_map[parent]; - std::vector &chs = parent->Outgoing->Children; - if(old_parent && old_parent->Outgoing){ - std::vector &old_chs = old_parent->Outgoing->Children; - for(unsigned i = 0, j=0; i < chs.size(); i++){ - if(j < old_chs.size() && BaseName(chs[i]->Name.name().str()) == BaseName(old_chs[j]->Name.name().str())) - cex_map[chs[i]] = old_chs[j++]; - else { - std::cerr << "WARNING: duality: unmatched child: " << chs[i]->Name.name() << std::endl; - cex_map[chs[i]] = 0; - } - } - goto matching_done; - } - for(unsigned i = 0; i < chs.size(); i++) - cex_map[chs[i]] = 0; - } - matching_done: - return cex_map[node]; - } - - int UseNode(Node *node) override { - if (!old_cex.get_tree()) - return 0; - Node *old_node = MatchNode(node); - if(!old_node) - return 0; - return old_cex.get_tree()->Empty(old_node) ? -1 : 1; - } - - void ChooseExpand(const std::set &choices, std::set &best, bool high_priority, bool best_only) override { - if(cex_map.empty()) - cex_map[*(choices.begin())] = old_cex.get_root(); // match the root nodes - if(!high_priority || !old_cex.get_tree()){ - Heuristic::ChooseExpand(choices,best,false); - return; - } - // first, try to match the derivatino tree nodes to the old cex - std::set matched, unmatched; - for(std::set::iterator it = choices.begin(), en = choices.end(); it != en; ++it){ - Node *node = (*it); - Node *old_node = MatchNode(node); - if(!old_node) - unmatched.insert(node); - else if(old_cex.get_tree()->Empty(old_node)) - unmatched.insert(node); - else - matched.insert(node); - } - if (matched.empty() && !high_priority) - Heuristic::ChooseExpand(unmatched,best,false); - else - Heuristic::ChooseExpand(matched,best,false); - } - }; - - - class LocalHeuristic : public Heuristic { - - RPFP::Node *old_node; - public: - LocalHeuristic(RPFP *_rpfp) - : Heuristic(_rpfp) - { - old_node = nullptr; - } - - void SetOldNode(RPFP::Node *_old_node){ - old_node = _old_node; - cex_map.clear(); - } - - // Maps nodes of derivation tree into old subtree - hash_map cex_map; - - void ChooseExpand(const std::set &choices, std::set &best, bool, bool) override { - if(old_node == nullptr){ - Heuristic::ChooseExpand(choices,best); - return; - } - // first, try to match the derivatino tree nodes to the old cex - std::set matched, unmatched; - for(std::set::iterator it = choices.begin(), en = choices.end(); it != en; ++it){ - Node *node = (*it); - if(cex_map.empty()) - cex_map[node] = old_node; // match the root nodes - if(cex_map.find(node) == cex_map.end()){ // try to match an unmatched node - Node *parent = node->Incoming[0]->Parent; // assumes we are a tree! - if(cex_map.find(parent) == cex_map.end()) - throw "catastrophe in ReplayHeuristic::ChooseExpand"; - Node *old_parent = cex_map[parent]; - std::vector &chs = parent->Outgoing->Children; - if(old_parent && old_parent->Outgoing){ - std::vector &old_chs = old_parent->Outgoing->Children; - if(chs.size() == old_chs.size()){ - for(unsigned i = 0; i < chs.size(); i++) - cex_map[chs[i]] = old_chs[i]; - goto matching_done; - } - else - std::cout << "derivation tree does not match old cex" << std::endl; - } - for(unsigned i = 0; i < chs.size(); i++) - cex_map[chs[i]] = 0; - } - matching_done: - Node *old_node = cex_map[node]; - if(!old_node) - unmatched.insert(node); - else if(old_node != node->map) - unmatched.insert(node); - else - matched.insert(node); - } - Heuristic::ChooseExpand(unmatched,best); - } - }; - - /** This proposer class generates conjectures based on the - unwinding generated by a previous solver. The assumption is - that the provious solver was working on a different - abstraction of the same system. The trick is to adapt the - annotations in the old unwinding to the new predicates. We - start by generating a map from predicates and parameters in - the old problem to the new. - - HACK: mapping is done by cheesy name comparison. - */ - - class HistoryProposer : public Proposer - { - Duality *old_solver; - Duality *new_solver; - hash_map > conjectures; - - public: - /** Construct a history solver. */ - HistoryProposer(Duality *_old_solver, Duality *_new_solver) - : old_solver(_old_solver), new_solver(_new_solver) { - - // tricky: names in the axioms may have changed -- map them - hash_set &old_constants = old_solver->unwinding->ls->get_constants(); - hash_set &new_constants = new_solver->rpfp->ls->get_constants(); - hash_map cmap; - for(hash_set::iterator it = new_constants.begin(), en = new_constants.end(); it != en; ++it) - cmap[GetKey(*it)] = *it; - hash_map bckg_map; - for(hash_set::iterator it = old_constants.begin(), en = old_constants.end(); it != en; ++it){ - func_decl f = new_solver->ctx.translate(*it); // move to new context - if(cmap.find(GetKey(f)) != cmap.end()) - bckg_map[f] = cmap[GetKey(f)]; - // else - // std::cout << "constant not matched\n"; - } - - RPFP *old_unwinding = old_solver->unwinding; - hash_map > pred_match; - - // index all the predicates in the old unwinding - for(unsigned i = 0; i < old_unwinding->nodes.size(); i++){ - Node *node = old_unwinding->nodes[i]; - std::string key = GetKey(node); - pred_match[key].push_back(node); - } - - // match with predicates in the new RPFP - RPFP *rpfp = new_solver->rpfp; - for(unsigned i = 0; i < rpfp->nodes.size(); i++){ - Node *node = rpfp->nodes[i]; - std::string key = GetKey(node); - std::vector &matches = pred_match[key]; - for(unsigned j = 0; j < matches.size(); j++) - MatchNodes(node,matches[j],bckg_map); - } - } - - std::vector &Propose(Node *node) override { - return conjectures[node->map]; - } - - ~HistoryProposer() override { - }; - - private: - void MatchNodes(Node *new_node, Node *old_node, hash_map &bckg_map){ - if(old_node->Annotation.IsFull()) - return; // don't conjecture true! - hash_map var_match; - std::vector &new_params = new_node->Annotation.IndParams; - // Index the new parameters by their keys - for(unsigned i = 0; i < new_params.size(); i++) - var_match[GetKey(new_params[i])] = new_params[i]; - RPFP::Transformer &old = old_node->Annotation; - std::vector from_params = old.IndParams; - for(unsigned j = 0; j < from_params.size(); j++) - from_params[j] = new_solver->ctx.translate(from_params[j]); // get in new context - std::vector to_params = from_params; - for(unsigned j = 0; j < to_params.size(); j++){ - std::string key = GetKey(to_params[j]); - if(var_match.find(key) == var_match.end()){ - // std::cout << "unmatched parameter!\n"; - return; - } - to_params[j] = var_match[key]; - } - expr fmla = new_solver->ctx.translate(old.Formula); // get in new context - fmla = new_solver->rpfp->SubstParams(old.IndParams,to_params,fmla); // substitute parameters - hash_map memo; - fmla = new_solver->rpfp->SubstRec(memo,bckg_map,fmla); // substitute background constants - RPFP::Transformer new_annot = new_node->Annotation; - new_annot.Formula = fmla; - conjectures[new_node].push_back(new_annot); - } - - // We match names by removing suffixes beginning with double at sign - - std::string GetKey(Node *node){ - return GetKey(node->Name); - } - - std::string GetKey(const expr &var){ - return GetKey(var.decl()); - } - - std::string GetKey(const func_decl &f){ - std::string name = f.name().str(); - int idx = name.find("@@"); - if(idx >= 0) - name.erase(idx); - return name; - } - }; - }; - - static int stop_event = -1; - - class StreamReporter : public Reporter { - std::ostream &s; - public: - StreamReporter(RPFP *_rpfp, std::ostream &_s) - : Reporter(_rpfp), s(_s) {event = 0; depth = -1;} - int event; - int depth; - void ev(){ - if(stop_event == event){ - std::cout << "stop!\n"; - } - s << "[" << event++ << "]" ; - } - void Extend(RPFP::Node *node) override { - ev(); s << "node " << node->number << ": " << node->Name.name(); - std::vector &rps = node->Outgoing->Children; - for(unsigned i = 0; i < rps.size(); i++) - s << " " << rps[i]->number; - s << std::endl; - } - void Update(RPFP::Node *node, const RPFP::Transformer &update, bool eager) override { - ev(); s << "update " << node->number << " " << node->Name.name() << ": "; - rpfp->Summarize(update.Formula); - if(depth > 0) s << " (depth=" << depth << ")"; - if(eager) s << " (eager)"; - s << std::endl; - } - void Bound(RPFP::Node *node) override { - ev(); s << "check " << node->number << std::endl; - } - void Expand(RPFP::Edge *edge) override { - RPFP::Node *node = edge->Parent; - ev(); s << "expand " << node->map->number << " " << node->Name.name(); - if(depth > 0) s << " (depth=" << depth << ")"; - s << std::endl; - } - void Depth(int d) override { - depth = d; - } - void AddCover(RPFP::Node *covered, std::vector &covering) override { - ev(); s << "cover " << covered->Name.name() << ": " << covered->number << " by "; - for(unsigned i = 0; i < covering.size(); i++) - s << covering[i]->number << " "; - s << std::endl; - } - void RemoveCover(RPFP::Node *covered, RPFP::Node *covering) override { - ev(); s << "uncover " << covered->Name.name() << ": " << covered->number << " by " << covering->number << std::endl; - } - void Forcing(RPFP::Node *covered, RPFP::Node *covering) override { - ev(); s << "forcing " << covered->Name.name() << ": " << covered->number << " by " << covering->number << std::endl; - } - void Conjecture(RPFP::Node *node, const RPFP::Transformer &t) override { - ev(); s << "conjecture " << node->number << " " << node->Name.name() << ": "; - rpfp->Summarize(t.Formula); - s << std::endl; - } - void Dominates(RPFP::Node *node, RPFP::Node *other) override { - ev(); s << "dominates " << node->Name.name() << ": " << node->number << " > " << other->number << std::endl; - } - void InductionFailure(RPFP::Edge *edge, const std::vector &children) override { - ev(); s << "induction failure: " << edge->Parent->Name.name() << ", children ="; - for(unsigned i = 0; i < children.size(); i++) - s << " " << children[i]->number; - s << std::endl; - } - void UpdateUnderapprox(RPFP::Node *node, const RPFP::Transformer &update) override { - ev(); s << "underapprox " << node->number << " " << node->Name.name() << ": " << update.Formula << std::endl; - } - void Reject(RPFP::Edge *edge, const std::vector &children) override { - ev(); s << "reject " << edge->Parent->number << " " << edge->Parent->Name.name() << ": "; - for(unsigned i = 0; i < children.size(); i++) - s << " " << children[i]->number; - s << std::endl; - } - void Message(const std::string &msg) override { - ev(); s << "msg " << msg << std::endl; - } - - }; - - - class DualityDepthBounded : public Solver { - - Duality *duality; - context &ctx; // Z3 context - solver &slvr; // Z3 solver - - public: - DualityDepthBounded(RPFP *_rpfp) : - ctx(_rpfp->ctx), - slvr(_rpfp->slvr()){ - rpfp = _rpfp; - DepthBoundRPFP(); - duality = alloc(Duality,drpfp); - } - - ~DualityDepthBounded() override { - dealloc(duality); - delete drpfp; - } - - bool Solve() override { - int depth_bound = 10; - bool res; - SetMaxDepthRPFP(depth_bound); - duality->PreSolve(); - while(true){ - res = duality->SolveMain(); - if(!res || GetSolution()) - break; - depth_bound++; - SetMaxDepthRPFP(depth_bound); - res = duality->RecheckBounds(); - if(!res) - break; - } - duality->PostSolve(); - if(!res) - ConvertCex(); - return res; - } - - Counterexample &GetCounterexample() override { - return cex; - } - - bool SetOption(const std::string &option, const std::string &value) override { - return duality->SetOption(option,value); - } - - void LearnFrom(Solver *old_solver) override { - DualityDepthBounded *old = dynamic_cast(old_solver); - if(old){ - duality->LearnFrom(old->duality); - } - } - - bool IsResultRecursionBounded() override { - return duality->IsResultRecursionBounded(); - } - - void Cancel() override { - duality->Cancel(); - } - - typedef RPFP::Node Node; - typedef RPFP::Edge Edge; - RPFP *rpfp, *drpfp; - hash_map db_map, db_rev_map; - hash_map db_edge_rev_map; - std::vector db_saved_bounds; - Counterexample cex; - - expr AddParamToRels(hash_map &memo, hash_map &rmap, const expr &p, const expr &t) { - std::pair foo(t,expr(ctx)); - std::pair::iterator, bool> bar = memo.insert(foo); - expr &res = bar.first->second; - if(!bar.second) return res; - - if (t.is_app()) - { - func_decl f = t.decl(); - std::vector args; - int nargs = t.num_args(); - args.reserve(nargs); - for(int i = 0; i < nargs; i++) - args.push_back(AddParamToRels(memo, rmap, p, t.arg(i))); - hash_map::iterator rit = rmap.find(f); - if(rit != rmap.end()){ - args.push_back(p); - res = (rit->second)(args); - res = ctx.make(And,res,ctx.make(Geq,p,ctx.int_val(0))); - } - else - res = f(args); - } - else if (t.is_quantifier()) - { - expr body = AddParamToRels(memo, rmap, p, t.body()); - res = clone_quantifier(t, body); - } - else res = t; - return res; - } - - - void DepthBoundRPFP(){ - drpfp = new RPFP(rpfp->ls); - expr dvar = ctx.int_const("@depth"); - expr dmax = ctx.int_const("@depth_max"); - for(unsigned i = 0; i < rpfp->nodes.size(); i++){ - Node *node = rpfp->nodes[i]; - std::vector arg_sorts; - const std::vector ¶ms = node->Annotation.IndParams; - for(unsigned j = 0; j < params.size(); j++) - arg_sorts.push_back(params[j].get_sort()); - arg_sorts.push_back(ctx.int_sort()); - std::string new_name = std::string("@db@") + node->Name.name().str(); - func_decl f = ctx.function(new_name.c_str(),arg_sorts.size(), VEC2PTR(arg_sorts),ctx.bool_sort()); - std::vector args = params; - args.push_back(dvar); - expr pat = f(args); - Node *dnode = drpfp->CreateNode(pat); - db_map[node] = dnode; - db_rev_map[dnode] = node; - expr bound_fmla = node->Bound.Formula; - if(!eq(bound_fmla,ctx.bool_val(true))){ - bound_fmla = implies(dvar == dmax,bound_fmla); - dnode->Bound.Formula = bound_fmla; - } - db_saved_bounds.push_back(bound_fmla); - // dnode->Annotation.Formula = ctx.make(And,node->Annotation.Formula,ctx.make(Geq,dvar,ctx.int_val(0))); - } - for(unsigned i = 0; i < rpfp->edges.size(); i++){ - Edge *edge = rpfp->edges[i]; - std::vector new_children; - std::vector new_relparams; - hash_map rmap; - for(unsigned j = 0; j < edge->Children.size(); j++){ - Node *ch = edge->Children[j]; - Node *nch = db_map[ch]; - func_decl f = nch->Name; - func_decl sf = drpfp->NumberPred(f,j); - new_children.push_back(nch); - new_relparams.push_back(sf); - rmap[edge->F.RelParams[j]] = sf; - } - std::vector new_indparams = edge->F.IndParams; - new_indparams.push_back(dvar); - hash_map memo; - expr new_fmla = AddParamToRels(memo,rmap,ctx.make(Sub,dvar,ctx.int_val(1)),edge->F.Formula); - RPFP::Transformer new_t = drpfp->CreateTransformer(new_relparams,new_indparams,new_fmla); - Node *new_parent = db_map[edge->Parent]; - db_edge_rev_map[drpfp->CreateEdge(new_parent,new_t,new_children)] = edge; - } - } - - void SetMaxDepthRPFP(int depth){ - hash_map subst; - expr dmax = ctx.int_const("@depth_max"); - subst[dmax] = ctx.int_val(depth); - for(unsigned i = 0; i < drpfp->nodes.size(); i++){ - Node *node = drpfp->nodes[i]; - expr fmla = db_saved_bounds[i]; - fmla = drpfp->SubstRec(subst,fmla); - node->Bound.Formula = fmla; - } - } - - void ConvertCex(){ - cex.clear(); - RPFP *tree = new RPFP(rpfp->ls); - Node *root; - Counterexample &dctx = duality->GetCounterexample(); - hash_map ctx_node_map; - for(unsigned i = 0; i < dctx.get_tree()->nodes.size(); i++){ - Node *dnode = dctx.get_tree()->nodes[i]; - Node *onode = db_rev_map[dnode->map->map]; - Node *node = tree->CloneNode(onode); - node->number = dnode->number; // numbers have to match for model to make sense - ctx_node_map[dnode] = node; - if(dnode == dctx.get_root()) - root = node; - } - for(unsigned i = 0; i < dctx.get_tree()->edges.size(); i++){ - Edge *dedge = dctx.get_tree()->edges[i]; - Edge *oedge = db_edge_rev_map[dedge->map]; - Node *parent = ctx_node_map[dedge->Parent]; - std::vector chs; - for(unsigned j = 0; j < dedge->Children.size(); j++) - chs.push_back(ctx_node_map[dedge->Children[j]]); - Edge *edge = tree->CreateEdge(parent,oedge->F,chs); - edge->number = dedge->number; // numbers have to match for model to make sense - edge->map = oedge; - } - tree->dualModel = dctx.get_tree()->dualModel; - cex.set(tree,root); - } - - bool GetSolution(){ - for(unsigned i = 0; i < rpfp->nodes.size(); i++) - if(!drpfp->nodes[i]->Annotation.SubsetEq(rpfp->nodes[i]->Bound)) - return false; - expr dvar = ctx.int_const("@depth"); - hash_map subst; - subst[dvar] = ctx.int_val(INT_MAX); - for(unsigned i = 0; i < rpfp->nodes.size(); i++){ - expr fmla = drpfp->nodes[i]->Annotation.Formula; - fmla = drpfp->SubstRec(subst,fmla); - fmla = fmla.simplify(); - rpfp->nodes[i]->Annotation.Formula = fmla; - } - return true; - } - - void UndoDepthBoundRPFP(){ -#if 0 - if(cex.get_tree()){ - // here, need to map the cex back... - } - // also need to map the proof back, but we don't... -#endif - } - }; - - Solver *Solver::Create(const std::string &solver_class, RPFP *rpfp){ - // Solver *s = alloc(DualityDepthBounded,rpfp); - Solver *s = alloc(Duality,rpfp); - return s; - } - - Reporter *CreateStdoutReporter(RPFP *rpfp){ - return new StreamReporter(rpfp, std::cout); - } - - class ConjectureFileReporter : public Reporter { - std::ofstream s; - public: - ConjectureFileReporter(RPFP *_rpfp, const std::string &fname) - : Reporter(_rpfp), s(fname.c_str()) {} - void Update(RPFP::Node *node, const RPFP::Transformer &update, bool eager) override { - s << "(define-fun " << node->Name.name() << " ("; - for(unsigned i = 0; i < update.IndParams.size(); i++){ - if(i != 0) - s << " "; - s << "(" << update.IndParams[i] << " " << update.IndParams[i].get_sort() << ")"; - } - s << ") Bool \n"; - s << update.Formula << ")\n"; - s << std::endl; - } - }; - - Reporter *CreateConjectureFileReporter(RPFP *rpfp, const std::string &fname){ - return new ConjectureFileReporter(rpfp, fname); - } - -} - diff --git a/src/duality/duality_wrapper.cpp b/src/duality/duality_wrapper.cpp deleted file mode 100644 index 17adbdcea..000000000 --- a/src/duality/duality_wrapper.cpp +++ /dev/null @@ -1,744 +0,0 @@ -/*++ - Copyright (c) 2012 Microsoft Corporation - - Module Name: - - wrapper.cpp - - Abstract: - - wrap various objects in the style expected by duality - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - - --*/ - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#pragma warning(disable:4101) -#endif - -#include "duality/duality_wrapper.h" -#include -#include "smt/smt_solver.h" -#include "interp/iz3interp.h" -#include "util/statistics.h" -#include "ast/expr_abstract.h" -#include "util/stopwatch.h" -#include "model/model_smt2_pp.h" -#include "qe/qe_lite.h" - -namespace Duality { - - solver::solver(Duality::context& c, bool _extensional, bool models) : object(c), the_model(c) { - params_ref p; - p.set_bool("proof", true); // this is currently useless - if(models) - p.set_bool("model", true); - p.set_bool("unsat_core", true); - bool mbqi = c.get_config().get().get_bool("mbqi",true); - p.set_bool("mbqi",mbqi); // just to test - p.set_str("mbqi.id","itp"); // use mbqi for quantifiers in interpolants - p.set_uint("mbqi.max_iterations",1); // use mbqi for quantifiers in interpolants - extensional = mbqi && (true || _extensional); - if(extensional) - p.set_bool("array.extensional",true); - scoped_ptr sf = mk_smt_solver_factory(); - m_solver = (*sf)(m(), p, true, true, true, ::symbol::null); - m_solver->updt_params(p); // why do we have to do this? - canceled = false; - m_mode = m().proof_mode(); - } - - expr context::constant(const std::string &name, const sort &ty){ - symbol s = str_symbol(name.c_str()); - return cook(m().mk_const(m().mk_const_decl(s, ty))); - } - - expr context::make(decl_kind op, int n, ::expr **args){ - switch(op) { - case True: return mki(m_basic_fid,OP_TRUE,n,args); - case False: return mki(m_basic_fid,OP_FALSE,n,args); - case Equal: return mki(m_basic_fid,OP_EQ,n,args); - case Distinct: return mki(m_basic_fid,OP_DISTINCT,n,args); - case Ite: return mki(m_basic_fid,OP_ITE,n,args); - case And: return mki(m_basic_fid,OP_AND,n,args); - case Or: return mki(m_basic_fid,OP_OR,n,args); - case Iff: return mki(m_basic_fid,OP_IFF,n,args); - case Xor: return mki(m_basic_fid,OP_XOR,n,args); - case Not: return mki(m_basic_fid,OP_NOT,n,args); - case Implies: return mki(m_basic_fid,OP_IMPLIES,n,args); - case Oeq: return mki(m_basic_fid,OP_OEQ,n,args); - case Interp: return mki(m_basic_fid,OP_INTERP,n,args); - case Leq: return mki(m_arith_fid,OP_LE,n,args); - case Geq: return mki(m_arith_fid,OP_GE,n,args); - case Lt: return mki(m_arith_fid,OP_LT,n,args); - case Gt: return mki(m_arith_fid,OP_GT,n,args); - case Plus: return mki(m_arith_fid,OP_ADD,n,args); - case Sub: return mki(m_arith_fid,OP_SUB,n,args); - case Uminus: return mki(m_arith_fid,OP_UMINUS,n,args); - case Times: return mki(m_arith_fid,OP_MUL,n,args); - case Div: return mki(m_arith_fid,OP_DIV,n,args); - case Idiv: return mki(m_arith_fid,OP_IDIV,n,args); - case Rem: return mki(m_arith_fid,OP_REM,n,args); - case Mod: return mki(m_arith_fid,OP_MOD,n,args); - case Power: return mki(m_arith_fid,OP_POWER,n,args); - case ToReal: return mki(m_arith_fid,OP_TO_REAL,n,args); - case ToInt: return mki(m_arith_fid,OP_TO_INT,n,args); - case IsInt: return mki(m_arith_fid,OP_IS_INT,n,args); - case Store: return mki(m_array_fid,OP_STORE,n,args); - case Select: return mki(m_array_fid,OP_SELECT,n,args); - case ConstArray: return mki(m_array_fid,OP_CONST_ARRAY,n,args); - case ArrayDefault: return mki(m_array_fid,OP_ARRAY_DEFAULT,n,args); - case ArrayMap: return mki(m_array_fid,OP_ARRAY_MAP,n,args); - case SetUnion: return mki(m_array_fid,OP_SET_UNION,n,args); - case SetIntersect: return mki(m_array_fid,OP_SET_INTERSECT,n,args); - case SetDifference: return mki(m_array_fid,OP_SET_DIFFERENCE,n,args); - case SetComplement: return mki(m_array_fid,OP_SET_COMPLEMENT,n,args); - case SetSubSet: return mki(m_array_fid,OP_SET_SUBSET,n,args); - case AsArray: return mki(m_array_fid,OP_AS_ARRAY,n,args); - default: - assert(0); - return expr(*this); - } - } - - expr context::mki(family_id fid, ::decl_kind dk, int n, ::expr **args){ - return cook(m().mk_app(fid, dk, 0, nullptr, n, (::expr **)args)); - } - - expr context::make(decl_kind op, const std::vector &args){ - static std::vector< ::expr*> a(10); - if(a.size() < args.size()) - a.resize(args.size()); - for(unsigned i = 0; i < args.size(); i++) - a[i] = to_expr(args[i].raw()); - return make(op,args.size(), args.size() ? VEC2PTR(a) : nullptr); - } - - expr context::make(decl_kind op){ - return make(op,0,nullptr); - } - - expr context::make(decl_kind op, const expr &arg0){ - ::expr *a = to_expr(arg0.raw()); - return make(op,1,&a); - } - - expr context::make(decl_kind op, const expr &arg0, const expr &arg1){ - ::expr *args[2]; - args[0] = to_expr(arg0.raw()); - args[1] = to_expr(arg1.raw()); - return make(op,2,args); - } - - expr context::make(decl_kind op, const expr &arg0, const expr &arg1, const expr &arg2){ - ::expr *args[3]; - args[0] = to_expr(arg0.raw()); - args[1] = to_expr(arg1.raw()); - args[2] = to_expr(arg2.raw()); - return make(op,3,args); - } - - expr context::make_quant(decl_kind op, const std::vector &bvs, const expr &body){ - if(bvs.size() == 0) return body; - std::vector< ::expr *> foo(bvs.size()); - - - std::vector< ::symbol> names; - std::vector< ::sort *> types; - std::vector< ::expr *> bound_asts; - unsigned num_bound = bvs.size(); - - for (unsigned i = 0; i < num_bound; ++i) { - app* a = to_app(bvs[i].raw()); - ::symbol s(to_app(a)->get_decl()->get_name()); - names.push_back(s); - types.push_back(m().get_sort(a)); - bound_asts.push_back(a); - } - expr_ref abs_body(m()); - expr_abstract(m(), 0, num_bound, VEC2PTR(bound_asts), to_expr(body.raw()), abs_body); - expr_ref result(m()); - result = m().mk_quantifier( - op == Forall, - names.size(), VEC2PTR(types), VEC2PTR(names), abs_body.get(), - 0, - ::symbol(), - ::symbol(), - 0, nullptr, - 0, nullptr - ); - return cook(result.get()); - } - - expr context::make_quant(decl_kind op, const std::vector &_sorts, const std::vector &_names, const expr &body){ - if(_sorts.size() == 0) return body; - - - std::vector< ::symbol> names; - std::vector< ::sort *> types; - std::vector< ::expr *> bound_asts; - unsigned num_bound = _sorts.size(); - - for (unsigned i = 0; i < num_bound; ++i) { - names.push_back(_names[i]); - types.push_back(to_sort(_sorts[i].raw())); - } - expr_ref result(m()); - result = m().mk_quantifier( - op == Forall, - names.size(), VEC2PTR(types), VEC2PTR(names), to_expr(body.raw()), - 0, - ::symbol(), - ::symbol(), - 0, nullptr, - 0, nullptr - ); - return cook(result.get()); - } - - - decl_kind func_decl::get_decl_kind() const { - return ctx().get_decl_kind(*this); - } - - decl_kind context::get_decl_kind(const func_decl &t){ - ::func_decl *d = to_func_decl(t.raw()); - if (null_family_id == d->get_family_id()) - return Uninterpreted; - // return (opr)d->get_decl_kind(); - if (m_basic_fid == d->get_family_id()) { - switch(d->get_decl_kind()) { - case OP_TRUE: return True; - case OP_FALSE: return False; - case OP_EQ: return Equal; - case OP_DISTINCT: return Distinct; - case OP_ITE: return Ite; - case OP_AND: return And; - case OP_OR: return Or; - case OP_IFF: return Iff; - case OP_XOR: return Xor; - case OP_NOT: return Not; - case OP_IMPLIES: return Implies; - case OP_OEQ: return Oeq; - case OP_INTERP: return Interp; - default: - return OtherBasic; - } - } - if (m_arith_fid == d->get_family_id()) { - switch(d->get_decl_kind()) { - case OP_LE: return Leq; - case OP_GE: return Geq; - case OP_LT: return Lt; - case OP_GT: return Gt; - case OP_ADD: return Plus; - case OP_SUB: return Sub; - case OP_UMINUS: return Uminus; - case OP_MUL: return Times; - case OP_DIV: return Div; - case OP_IDIV: return Idiv; - case OP_REM: return Rem; - case OP_MOD: return Mod; - case OP_POWER: return Power; - case OP_TO_REAL: return ToReal; - case OP_TO_INT: return ToInt; - case OP_IS_INT: return IsInt; - default: - return OtherArith; - } - } - if (m_array_fid == d->get_family_id()) { - switch(d->get_decl_kind()) { - case OP_STORE: return Store; - case OP_SELECT: return Select; - case OP_CONST_ARRAY: return ConstArray; - case OP_ARRAY_DEFAULT: return ArrayDefault; - case OP_ARRAY_MAP: return ArrayMap; - case OP_SET_UNION: return SetUnion; - case OP_SET_INTERSECT: return SetIntersect; - case OP_SET_DIFFERENCE: return SetDifference; - case OP_SET_COMPLEMENT: return SetComplement; - case OP_SET_SUBSET: return SetSubSet; - case OP_AS_ARRAY: return AsArray; - default: - return OtherArray; - } - } - - return Other; - } - - - sort_kind context::get_sort_kind(const sort &s){ - family_id fid = to_sort(s.raw())->get_family_id(); - ::decl_kind k = to_sort(s.raw())->get_decl_kind(); - if (m().is_uninterp(to_sort(s.raw()))) { - return UninterpretedSort; - } - else if (fid == m_basic_fid && k == BOOL_SORT) { - return BoolSort; - } - else if (fid == m_arith_fid && k == INT_SORT) { - return IntSort; - } - else if (fid == m_arith_fid && k == REAL_SORT) { - return RealSort; - } - else if (fid == m_array_fid && k == ARRAY_SORT) { - return ArraySort; - } - else { - return UnknownSort; - } - } - - expr func_decl::operator()(unsigned n, expr const * args) const { - std::vector< ::expr *> _args(n); - for(unsigned i = 0; i < n; i++) - _args[i] = to_expr(args[i].raw()); - return ctx().cook(m().mk_app(to_func_decl(raw()),n,VEC2PTR(_args))); - } - - int solver::get_num_decisions(){ - ::statistics st; - m_solver->collect_statistics(st); - std::ostringstream ss; - st.display(ss); - std::string stats = ss.str(); - int pos = stats.find("decisions:"); - if(pos < 0) return 0; // for some reason, decisions are not reported if there are none - pos += 10; - int end = stats.find('\n',pos); - std::string val = stats.substr(pos,end-pos); - return atoi(val.c_str()); - } - - void context::print_expr(std::ostream &s, const ast &e){ - s << mk_pp(e.raw(), m()); - } - - - expr expr::simplify(const params &_p) const { - ::expr * a = to_expr(raw()); - params_ref p = _p.get(); - th_rewriter m_rw(m(), p); - expr_ref result(m()); - m_rw(a, result); - return ctx().cook(result); - } - - expr expr::simplify() const { - params p; - return simplify(p); - } - - expr context::make_var(int idx, const sort &s){ - ::sort * a = to_sort(s.raw()); - return cook(m().mk_var(idx,a)); - } - - - expr expr::qe_lite() const { - ::qe_lite qe(m(), params_ref()); - expr_ref result(to_expr(raw()),m()); - proof_ref pf(m()); - qe(result,pf); - return ctx().cook(result); - } - - expr expr::qe_lite(const std::set &idxs, bool index_of_bound) const { - ::qe_lite qe(m(), params_ref()); - expr_ref result(to_expr(raw()),m()); - proof_ref pf(m()); - uint_set uis; - for(std::set::const_iterator it=idxs.begin(), en = idxs.end(); it != en; ++it) - uis.insert(*it); - qe(uis,index_of_bound,result); - return ctx().cook(result); - } - - expr clone_quantifier(const expr &q, const expr &b){ - return q.ctx().cook(q.m().update_quantifier(to_quantifier(q.raw()), to_expr(b.raw()))); - } - - expr clone_quantifier(const expr &q, const expr &b, const std::vector &patterns){ - quantifier *thing = to_quantifier(q.raw()); - bool is_forall = thing->is_forall(); - unsigned num_patterns = patterns.size(); - std::vector< ::expr *> _patterns(num_patterns); - for(unsigned i = 0; i < num_patterns; i++) - _patterns[i] = to_expr(patterns[i].raw()); - return q.ctx().cook(q.m().update_quantifier(thing, is_forall, num_patterns, VEC2PTR(_patterns), to_expr(b.raw()))); - } - - expr clone_quantifier(decl_kind dk, const expr &q, const expr &b){ - quantifier *thing = to_quantifier(q.raw()); - bool is_forall = dk == Forall; - return q.ctx().cook(q.m().update_quantifier(thing, is_forall, to_expr(b.raw()))); - } - - void expr::get_patterns(std::vector &pats) const { - quantifier *thing = to_quantifier(raw()); - unsigned num_patterns = thing->get_num_patterns(); - :: expr * const *it = thing->get_patterns(); - pats.resize(num_patterns); - for(unsigned i = 0; i < num_patterns; i++) - pats[i] = expr(ctx(),it[i]); - } - - - unsigned func_decl::arity() const { - return (to_func_decl(raw())->get_arity()); - } - - sort func_decl::domain(unsigned i) const { - return sort(ctx(),(to_func_decl(raw())->get_domain(i))); - } - - sort func_decl::range() const { - return sort(ctx(),(to_func_decl(raw())->get_range())); - } - - func_decl context::fresh_func_decl(char const * prefix, const std::vector &domain, sort const & range){ - std::vector < ::sort * > _domain(domain.size()); - for(unsigned i = 0; i < domain.size(); i++) - _domain[i] = to_sort(domain[i].raw()); - ::func_decl* d = m().mk_fresh_func_decl(prefix, - _domain.size(), - VEC2PTR(_domain), - to_sort(range.raw())); - return func_decl(*this,d); - } - - func_decl context::fresh_func_decl(char const * prefix, sort const & range){ - ::func_decl* d = m().mk_fresh_func_decl(prefix, - 0, - nullptr, - to_sort(range.raw())); - return func_decl(*this,d); - } - - - -#if 0 - - - lbool interpolating_solver::interpolate( - const std::vector &assumptions, - std::vector &interpolants, - model &model, - Z3_literals &labels, - bool incremental) - { - Z3_model _model = 0; - Z3_literals _labels = 0; - Z3_lbool lb; - std::vector _assumptions(assumptions.size()); - std::vector _interpolants(assumptions.size()-1); - for(unsigned i = 0; i < assumptions.size(); i++) - _assumptions[i] = assumptions[i]; - std::vector _theory(theory.size()); - for(unsigned i = 0; i < theory.size(); i++) - _theory[i] = theory[i]; - - lb = Z3_interpolate( - ctx(), - _assumptions.size(), - VEC2PTR(_assumptions), - 0, - 0, - VEC2PTR(_interpolants), - &_model, - &_labels, - incremental, - _theory.size(), - VEC2PTR(_theory)); - - if(lb == Z3_L_FALSE){ - interpolants.resize(_interpolants.size()); - for (unsigned i = 0; i < _interpolants.size(); ++i) { - interpolants[i] = expr(ctx(),_interpolants[i]); - } - } - - if (_model) { - model = iz3wrapper::model(ctx(), _model); - } - - if(_labels){ - labels = _labels; - } - - return lb; - } - -#endif - - static int linearize_assumptions(int num, - TermTree *assumptions, - std::vector > &linear_assumptions, - std::vector &parents){ - for(unsigned i = 0; i < assumptions->getChildren().size(); i++) - num = linearize_assumptions(num, assumptions->getChildren()[i], linear_assumptions, parents); - // linear_assumptions[num].push_back(assumptions->getTerm()); - for(unsigned i = 0; i < assumptions->getChildren().size(); i++) - parents[assumptions->getChildren()[i]->getNumber()] = num; - parents[num] = SHRT_MAX; // in case we have no parent - linear_assumptions[num].push_back(assumptions->getTerm()); - std::vector &ts = assumptions->getTerms(); - for(unsigned i = 0; i < ts.size(); i++) - linear_assumptions[num].push_back(ts[i]); - return num + 1; - } - - static int unlinearize_interpolants(int num, - TermTree* assumptions, - const std::vector &interpolant, - TermTree * &tree_interpolant) - { - std::vector chs(assumptions->getChildren().size()); - for(unsigned i = 0; i < assumptions->getChildren().size(); i++) - num = unlinearize_interpolants(num, assumptions->getChildren()[i], interpolant,chs[i]); - expr f; - if(num < (int)interpolant.size()) // last interpolant is missing, presumed false - f = interpolant[num]; - tree_interpolant = new TermTree(f,chs); - return num + 1; - } - - - lbool interpolating_solver::interpolate_tree(TermTree *assumptions, - TermTree *&interpolant, - model &model, - literals &labels, - bool incremental - ) - - { - int size = assumptions->number(0); - std::vector > linear_assumptions(size); - std::vector parents(size); - linearize_assumptions(0,assumptions,linear_assumptions,parents); - - ptr_vector< ::ast> _interpolants(size-1); - vector >_assumptions(size); - for(int i = 0; i < size; i++) - for(unsigned j = 0; j < linear_assumptions[i].size(); j++) - _assumptions[i].push_back(linear_assumptions[i][j]); - ::vector _parents; _parents.resize(parents.size()); - for(unsigned i = 0; i < parents.size(); i++) - _parents[i] = parents[i]; - ptr_vector< ::ast> _theory(theory.size()); - for(unsigned i = 0; i < theory.size(); i++) - _theory[i] = theory[i]; - - - if(!incremental){ - push(); - for(unsigned i = 0; i < linear_assumptions.size(); i++) - for(unsigned j = 0; j < linear_assumptions[i].size(); j++) - add(linear_assumptions[i][j]); - } - - check_result res = unsat; - - if(!m_solver->get_proof()) - res = check(); - - if(res == unsat){ - - interpolation_options_struct opts; - if(weak_mode) - opts.set("weak","1"); - - ::ast *proof = m_solver->get_proof(); - try { - iz3interpolate(m(),proof,_assumptions,_parents,_interpolants,_theory,&opts); - } - // If there's an interpolation bug, throw a char * - // exception so duality can catch it and restart. - catch (const interpolation_failure &f) { - throw f.msg(); - } - - std::vector linearized_interpolants(_interpolants.size()); - for(unsigned i = 0; i < _interpolants.size(); i++) - linearized_interpolants[i] = expr(ctx(),_interpolants[i]); - - // since iz3interpolant returns interpolants with one ref count, we decrement here - for(unsigned i = 0; i < _interpolants.size(); i++) - m().dec_ref(_interpolants[i]); - - unlinearize_interpolants(0,assumptions,linearized_interpolants,interpolant); - interpolant->setTerm(ctx().bool_val(false)); - } - - model_ref _m; - m_solver->get_model(_m); - model = Duality::model(ctx(),_m.get()); - -#if 0 - if(_labels){ - labels = _labels; - } -#endif - - if(!incremental) - pop(); - - return (res == unsat) ? l_false : ((res == sat) ? l_true : l_undef); - - } - - - void interpolating_solver::SetWeakInterpolants(bool weak){ - weak_mode = weak; - } - - - void interpolating_solver::SetPrintToFile(const std::string &filename){ - print_filename = filename; - } - - void interpolating_solver::AssertInterpolationAxiom(const expr & t){ - add(t); - theory.push_back(t); - } - - - void interpolating_solver::RemoveInterpolationAxiom(const expr & t){ - // theory.remove(t); - } - - - const char *interpolating_solver::profile(){ - // return Z3_interpolation_profile(ctx()); - return ""; - } - - - static void get_assumptions_rec(stl_ext::hash_set &memo, const proof &pf, std::vector &assumps){ - if(memo.find(pf) != memo.end())return; - memo.insert(pf); - pfrule dk = pf.rule(); - if(dk == PR_ASSERTED){ - expr con = pf.conc(); - assumps.push_back(con); - } - else { - unsigned nprems = pf.num_prems(); - for(unsigned i = 0; i < nprems; i++){ - proof arg = pf.prem(i); - get_assumptions_rec(memo,arg,assumps); - } - } - } - - void proof::get_assumptions(std::vector &assumps){ - stl_ext::hash_set memo; - get_assumptions_rec(memo,*this,assumps); - } - - - void ast::show() const{ - std::cout << mk_pp(raw(), m()) << std::endl; - } - - void model::show() const { - model_smt2_pp(std::cout, m(), *m_model, 0); - std::cout << std::endl; - } - - void model::show_hash() const { - std::ostringstream ss; - model_smt2_pp(ss, m(), *m_model, 0); - hash_space::hash hasher; - unsigned h = hasher(ss.str()); - std::cout << "model hash: " << h << "\n"; - } - - void solver::show() { - unsigned n = m_solver->get_num_assertions(); - if(!n) - return; - ast_smt_pp pp(m()); - for (unsigned i = 0; i < n-1; ++i) - pp.add_assumption(m_solver->get_assertion(i)); - pp.display_smt2(std::cout, m_solver->get_assertion(n-1)); - } - - void solver::print(const char *filename) { - std::ofstream f(filename); - unsigned n = m_solver->get_num_assertions(); - if(!n) - return; - ast_smt_pp pp(m()); - for (unsigned i = 0; i < n-1; ++i) - pp.add_assumption(m_solver->get_assertion(i)); - pp.display_smt2(f, m_solver->get_assertion(n-1)); - } - - - void solver::show_assertion_ids() { -#if 0 - unsigned n = m_solver->get_num_assertions(); - std::cerr << "assertion ids: "; - for (unsigned i = 0; i < n-1; ++i) - std::cerr << " " << m_solver->get_assertion(i)->get_id(); - std::cerr << "\n"; -#else - unsigned n = m_solver->get_num_assertions(); - std::cerr << "assertion ids hash: "; - unsigned h = 0; - for (unsigned i = 0; i < n-1; ++i) - h += m_solver->get_assertion(i)->get_id(); - std::cerr << h << "\n"; -#endif - } - - void include_ast_show(ast &a){ - a.show(); - } - - void include_model_show(model &a){ - a.show(); - } - - void show_ast(::ast *a, ast_manager &m) { - std::cout << mk_pp(a, m) << std::endl; - } - - bool expr::is_label (bool &pos,std::vector &names) const { - buffer< ::symbol> _names; - bool res = m().is_label(to_expr(raw()),pos,_names); - if(res) - for(unsigned i = 0; i < _names.size(); i++) - names.push_back(symbol(ctx(),_names[i])); - return res; - } - - double current_time() - { - static stopwatch sw; - static bool started = false; - if(!started){ - sw.start(); - started = true; - } - return sw.get_current_seconds(); - } - -} - - - - diff --git a/src/duality/duality_wrapper.h b/src/duality/duality_wrapper.h deleted file mode 100644 index 69f821a08..000000000 --- a/src/duality/duality_wrapper.h +++ /dev/null @@ -1,1489 +0,0 @@ -/*++ - Copyright (c) 2012 Microsoft Corporation - - Module Name: - - duality_wrapper.h - - Abstract: - - wrap various Z3 classes in the style expected by duality - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - - --*/ -#ifndef DUALITY_WRAPPER_H_ -#define DUALITY_WRAPPER_H_ - -#include -#include -#include -#include -#include -#include -#include -#include "util/version.h" -#include - -#include "interp/iz3hash.h" -#include "model/model.h" -#include "solver/solver.h" - -#include "ast/well_sorted.h" -#include "ast/arith_decl_plugin.h" -#include "ast/bv_decl_plugin.h" -#include "ast/datatype_decl_plugin.h" -#include "ast/array_decl_plugin.h" -#include "ast/ast_translation.h" -#include "ast/ast_pp.h" -#include "ast/ast_ll_pp.h" -#include "ast/ast_smt_pp.h" -#include "ast/ast_smt2_pp.h" -#include "ast/rewriter/th_rewriter.h" -#include "ast/rewriter/var_subst.h" -#include "ast/expr_substitution.h" -#include "ast/pp.h" -#include "util/scoped_ctrl_c.h" -#include "util/cancel_eh.h" -#include "util/scoped_timer.h" -#include "ast/scoped_proof.h" - -namespace Duality { - - class exception; - class config; - class context; - class symbol; - class params; - class ast; - class sort; - class func_decl; - class expr; - class solver; - class goal; - class tactic; - class probe; - class model; - class func_interp; - class func_entry; - class statistics; - class apply_result; - class fixedpoint; - class literals; - - /** - Duality global configuration object. - */ - - class config { - params_ref m_params; - config & operator=(config const & s); - public: - config(config const & s) : m_params(s.m_params) {} - config(const params_ref &_params) : m_params(_params) {} - config() { } // TODO: create a new params object here - ~config() { } - void set(char const * param, char const * value) { m_params.set_str(param,value); } - void set(char const * param, bool value) { m_params.set_bool(param,value); } - void set(char const * param, int value) { m_params.set_uint(param,value); } - params_ref &get() {return m_params;} - const params_ref &get() const {return m_params;} - }; - - enum decl_kind { - True, - False, - And, - Or, - Not, - Iff, - Ite, - Equal, - Implies, - Distinct, - Xor, - Oeq, - Interp, - Leq, - Geq, - Lt, - Gt, - Plus, - Sub, - Uminus, - Times, - Div, - Idiv, - Rem, - Mod, - Power, - ToReal, - ToInt, - IsInt, - Select, - Store, - ConstArray, - ArrayDefault, - ArrayMap, - SetUnion, - SetIntersect, - SetDifference, - SetComplement, - SetSubSet, - AsArray, - Numeral, - Forall, - Exists, - Variable, - Uninterpreted, - OtherBasic, - OtherArith, - OtherArray, - Other - }; - - enum sort_kind {BoolSort,IntSort,RealSort,ArraySort,UninterpretedSort,UnknownSort}; - - /** - A context has an ast manager global configuration options, etc. - */ - - class context { - protected: - ast_manager &mgr; - config m_config; - - family_id m_basic_fid; - family_id m_array_fid; - family_id m_arith_fid; - family_id m_bv_fid; - family_id m_dt_fid; - family_id m_datalog_fid; - arith_util m_arith_util; - - public: - context(ast_manager &_manager, const config &_config) : mgr(_manager), m_config(_config), m_arith_util(_manager) { - m_basic_fid = m().get_basic_family_id(); - m_arith_fid = m().mk_family_id("arith"); - m_bv_fid = m().mk_family_id("bv"); - m_array_fid = m().mk_family_id("array"); - m_dt_fid = m().mk_family_id("datatype"); - m_datalog_fid = m().mk_family_id("datalog_relation"); - } - ~context() { } - - ast_manager &m() const {return *(ast_manager *)&mgr;} - - void set(char const * param, char const * value) { m_config.set(param,value); } - void set(char const * param, bool value) { m_config.set(param,value); } - void set(char const * param, int value) { m_config.set(param,value); } - config &get_config() {return m_config;} - - symbol str_symbol(char const * s); - symbol int_symbol(int n); - - sort bool_sort(); - sort int_sort(); - sort real_sort(); - sort bv_sort(unsigned sz); - sort array_sort(const sort & d, const sort & r); - - func_decl function(symbol const & name, unsigned arity, sort const * domain, sort const & range); - func_decl function(char const * name, unsigned arity, sort const * domain, sort const & range); - func_decl function(char const * name, sort const & domain, sort const & range); - func_decl function(char const * name, sort const & d1, sort const & d2, sort const & range); - func_decl function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & range); - func_decl function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & range); - func_decl function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & d5, sort const & range); - func_decl fresh_func_decl(char const * name, const std::vector &domain, sort const & range); - func_decl fresh_func_decl(char const * name, sort const & range); - - expr constant(symbol const & name, sort const & s); - expr constant(char const * name, sort const & s); - expr constant(const std::string &name, sort const & s); - expr bool_const(char const * name); - expr int_const(char const * name); - expr real_const(char const * name); - expr bv_const(char const * name, unsigned sz); - - expr bool_val(bool b); - - expr int_val(int n); - expr int_val(unsigned n); - expr int_val(char const * n); - - expr real_val(int n, int d); - expr real_val(int n); - expr real_val(unsigned n); - expr real_val(char const * n); - - expr bv_val(int n, unsigned sz); - expr bv_val(unsigned n, unsigned sz); - expr bv_val(char const * n, unsigned sz); - - expr num_val(int n, sort const & s); - - expr mki(family_id fid, ::decl_kind dk, int n, ::expr **args); - expr make(decl_kind op, int n, ::expr **args); - expr make(decl_kind op, const std::vector &args); - expr make(decl_kind op); - expr make(decl_kind op, const expr &arg0); - expr make(decl_kind op, const expr &arg0, const expr &arg1); - expr make(decl_kind op, const expr &arg0, const expr &arg1, const expr &arg2); - - expr make_quant(decl_kind op, const std::vector &bvs, const expr &body); - expr make_quant(decl_kind op, const std::vector &_sorts, const std::vector &_names, const expr &body); - expr make_var(int idx, const sort &s); - - decl_kind get_decl_kind(const func_decl &t); - - sort_kind get_sort_kind(const sort &s); - - expr translate(const expr &e); - func_decl translate(const func_decl &); - - void print_expr(std::ostream &s, const ast &e); - - fixedpoint mk_fixedpoint(); - - expr cook(::expr *a); - std::vector cook(ptr_vector< ::expr> v); - ::expr *uncook(const expr &a); - }; - - template - class z3array { - T * m_array; - unsigned m_size; - z3array(z3array const & s); - z3array & operator=(z3array const & s); - public: - z3array(unsigned sz):m_size(sz) { m_array = new T[sz]; } - ~z3array() { delete[] m_array; } - unsigned size() const { return m_size; } - T & operator[](unsigned i) { assert(i < m_size); return m_array[i]; } - T const & operator[](unsigned i) const { assert(i < m_size); return m_array[i]; } - T const * ptr() const { return m_array; } - T * ptr() { return m_array; } - }; - - class object { - protected: - context * m_ctx; - public: - object(): m_ctx((context *)nullptr) {} - object(context & c):m_ctx(&c) {} - object(object const & s):m_ctx(s.m_ctx) {} - context & ctx() const { return *m_ctx; } - friend void check_context(object const & a, object const & b) { assert(a.m_ctx == b.m_ctx); } - ast_manager &m() const {return m_ctx->m();} - }; - - class symbol : public object { - ::symbol m_sym; - public: - symbol(context & c, ::symbol s):object(c), m_sym(s) {} - symbol(symbol const & s):object(s), m_sym(s.m_sym) {} - symbol & operator=(symbol const & s) { m_ctx = s.m_ctx; m_sym = s.m_sym; return *this; } - operator ::symbol() const {return m_sym;} - std::string str() const { - if (m_sym.is_numerical()) { - std::ostringstream buffer; - buffer << m_sym.get_num(); - return buffer.str(); - } - else { - return m_sym.bare_str(); - } - } - friend std::ostream & operator<<(std::ostream & out, symbol const & s) { - return out << s.str(); - } - friend bool operator==(const symbol &x, const symbol &y) { - return x.m_sym == y.m_sym; - } - }; - - class params : public config {}; - - /** Wrapper around an ast pointer */ - class ast_i : public object { - protected: - ::ast *_ast; - public: - ::ast * const &raw() const {return _ast;} - ast_i(context & c, ::ast *a = nullptr) : object(c) {_ast = a;} - - ast_i(){_ast = nullptr;} - bool eq(const ast_i &other) const { - return _ast == other._ast; - } - bool lt(const ast_i &other) const { - return _ast < other._ast; - } - friend bool operator==(const ast_i &x, const ast_i&y){ - return x.eq(y); - } - friend bool operator!=(const ast_i &x, const ast_i&y){ - return !x.eq(y); - } - friend bool operator<(const ast_i &x, const ast_i&y){ - return x.lt(y); - } - size_t hash() const {return (size_t)_ast;} - bool null() const {return !_ast;} - }; - - /** Reference counting verison of above */ - class ast : public ast_i { - public: - operator ::ast*() const { return raw(); } - friend bool eq(ast const & a, ast const & b) { return a.raw() == b.raw(); } - - - ast(context &c, ::ast *a = nullptr) : ast_i(c,a) { - if(_ast) - m().inc_ref(a); - } - - ast() {} - - ast(const ast &other) : ast_i(other) { - if(_ast) - m().inc_ref(_ast); - } - - ast &operator=(const ast &other) { - if(_ast) - m().dec_ref(_ast); - _ast = other._ast; - m_ctx = other.m_ctx; - if(_ast) - m().inc_ref(_ast); - return *this; - } - - ~ast(){ - if(_ast) - m().dec_ref(_ast); - } - - void show() const; - - }; - - class sort : public ast { - public: - sort(context & c):ast(c) {} - sort(context & c, ::sort *s):ast(c, s) {} - sort(sort const & s):ast(s) {} - operator ::sort*() const { return to_sort(raw()); } - sort & operator=(sort const & s) { return static_cast(ast::operator=(s)); } - - bool is_bool() const { return m().is_bool(*this); } - bool is_int() const { return ctx().get_sort_kind(*this) == IntSort; } - bool is_real() const { return ctx().get_sort_kind(*this) == RealSort; } - bool is_arith() const; - bool is_array() const { return ctx().get_sort_kind(*this) == ArraySort; } - bool is_datatype() const; - bool is_relation() const; - bool is_finite_domain() const; - - - sort array_domain() const; - sort array_range() const; - - friend std::ostream & operator<<(std::ostream & out, sort const & m){ - m.ctx().print_expr(out,m); - return out; - } - }; - - - class func_decl : public ast { - public: - func_decl() : ast() {} - func_decl(context & c):ast(c) {} - func_decl(context & c, ::func_decl *n):ast(c, n) {} - func_decl(func_decl const & s):ast(s) {} - operator ::func_decl*() const { return to_func_decl(*this); } - func_decl & operator=(func_decl const & s) { return static_cast(ast::operator=(s)); } - - unsigned arity() const; - sort domain(unsigned i) const; - sort range() const; - symbol name() const {return symbol(ctx(),to_func_decl(raw())->get_name());} - decl_kind get_decl_kind() const; - - bool is_const() const { return arity() == 0; } - - expr operator()(unsigned n, expr const * args) const; - expr operator()(const std::vector &args) const; - expr operator()() const; - expr operator()(expr const & a) const; - expr operator()(int a) const; - expr operator()(expr const & a1, expr const & a2) const; - expr operator()(expr const & a1, int a2) const; - expr operator()(int a1, expr const & a2) const; - expr operator()(expr const & a1, expr const & a2, expr const & a3) const; - expr operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4) const; - expr operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5) const; - - func_decl get_func_decl_parameter(unsigned idx){ - return func_decl(ctx(),to_func_decl(to_func_decl(raw())->get_parameters()[idx].get_ast())); - } - - }; - - class expr : public ast { - public: - expr() : ast() {} - expr(context & c):ast(c) {} - expr(context & c, ::ast *n):ast(c, n) {} - expr(expr const & n):ast(n) {} - expr & operator=(expr const & n) { return static_cast(ast::operator=(n)); } - operator ::expr*() const { return to_expr(raw()); } - unsigned get_id() const {return to_expr(raw())->get_id();} - - sort get_sort() const { return sort(ctx(),m().get_sort(to_expr(raw()))); } - - bool is_bool() const { return get_sort().is_bool(); } - bool is_int() const { return get_sort().is_int(); } - bool is_real() const { return get_sort().is_real(); } - bool is_arith() const { return get_sort().is_arith(); } - bool is_array() const { return get_sort().is_array(); } - bool is_datatype() const { return get_sort().is_datatype(); } - bool is_relation() const { return get_sort().is_relation(); } - bool is_finite_domain() const { return get_sort().is_finite_domain(); } - bool is_true() const {return is_app() && decl().get_decl_kind() == True; } - - bool is_numeral() const { - return is_app() && decl().get_decl_kind() == OtherArith && m().is_unique_value(to_expr(raw())); - } - bool is_app() const {return raw()->get_kind() == AST_APP;} - bool is_quantifier() const {return raw()->get_kind() == AST_QUANTIFIER;} - bool is_var() const {return raw()->get_kind() == AST_VAR;} - bool is_label (bool &pos,std::vector &names) const ; - bool is_ground() const {return to_app(raw())->is_ground();} - bool has_quantifiers() const {return to_app(raw())->has_quantifiers();} - bool has_free(int idx) const { - used_vars proc; - proc.process(to_expr(raw())); - return proc.contains(idx); - } - unsigned get_max_var_idx_plus_1() const { - used_vars proc; - proc.process(to_expr(raw())); - return proc.get_max_found_var_idx_plus_1(); - } - - // operator Z3_app() const { assert(is_app()); return reinterpret_cast(m_ast); } - func_decl decl() const {return func_decl(ctx(),to_app(raw())->get_decl());} - unsigned num_args() const { - ast_kind dk = raw()->get_kind(); - switch(dk){ - case AST_APP: - return to_app(raw())->get_num_args(); - case AST_QUANTIFIER: - return 1; - case AST_VAR: - return 0; - default:; - } - SASSERT(0); - return 0; - } - expr arg(unsigned i) const { - ast_kind dk = raw()->get_kind(); - switch(dk){ - case AST_APP: - return ctx().cook(to_app(raw())->get_arg(i)); - case AST_QUANTIFIER: - return ctx().cook(to_quantifier(raw())->get_expr()); - default:; - } - assert(0); - return expr(); - } - - expr body() const { - return ctx().cook(to_quantifier(raw())->get_expr()); - } - - friend expr operator!(expr const & a) { - // ::expr *e = a; - return expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_NOT,a)); - } - - friend expr operator&&(expr const & a, expr const & b) { - return expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_AND,a,b)); - } - - friend expr operator||(expr const & a, expr const & b) { - return expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_OR,a,b)); - } - - friend expr implies(expr const & a, expr const & b) { - return expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_IMPLIES,a,b)); - } - - friend expr operator==(expr const & a, expr const & b) { - return expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_EQ,a,b)); - } - - friend expr operator!=(expr const & a, expr const & b) { - return expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_DISTINCT,a,b)); - } - - friend expr operator+(expr const & a, expr const & b) { - return a.ctx().make(Plus,a,b); // expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_ADD,a,b)); - } - - friend expr operator*(expr const & a, expr const & b) { - return a.ctx().make(Times,a,b); // expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_MUL,a,b)); - } - - friend expr operator/(expr const & a, expr const & b) { - return a.ctx().make(Div,a,b); // expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_DIV,a,b)); - } - - friend expr operator-(expr const & a) { - return a.ctx().make(Uminus,a); // expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_UMINUS,a)); - } - - friend expr operator-(expr const & a, expr const & b) { - return a.ctx().make(Sub,a,b); // expr(a.ctx(),a.m().mk_app(a.ctx().m_arith_fid,OP_SUB,a,b)); - } - - friend expr operator<=(expr const & a, expr const & b) { - return a.ctx().make(Leq,a,b); // expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_LE,a,b)); - } - - friend expr operator>=(expr const & a, expr const & b) { - return a.ctx().make(Geq,a,b); //expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_GE,a,b)); - } - - friend expr operator<(expr const & a, expr const & b) { - return a.ctx().make(Lt,a,b); expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_LT,a,b)); - } - - friend expr operator>(expr const & a, expr const & b) { - return a.ctx().make(Gt,a,b); expr(a.ctx(),a.m().mk_app(a.m().get_basic_family_id(),OP_GT,a,b)); - } - - expr simplify() const; - - expr simplify(params const & p) const; - - expr qe_lite() const; - - expr qe_lite(const std::set &idxs, bool index_of_bound) const; - - friend expr clone_quantifier(const expr &, const expr &); - - friend expr clone_quantifier(const expr &q, const expr &b, const std::vector &patterns); - - friend expr clone_quantifier(decl_kind, const expr &, const expr &); - - friend std::ostream & operator<<(std::ostream & out, expr const & m){ - m.ctx().print_expr(out,m); - return out; - } - - void get_patterns(std::vector &pats) const ; - - unsigned get_quantifier_num_bound() const { - return to_quantifier(raw())->get_num_decls(); - } - - unsigned get_index_value() const { - var* va = to_var(raw()); - return va->get_idx(); - } - - bool is_quantifier_forall() const { - return to_quantifier(raw())->is_forall(); - } - - sort get_quantifier_bound_sort(unsigned n) const { - return sort(ctx(),to_quantifier(raw())->get_decl_sort(n)); - } - - symbol get_quantifier_bound_name(unsigned n) const { - return symbol(ctx(),to_quantifier(raw())->get_decl_names()[n]); - } - - friend expr forall(const std::vector &quants, const expr &body); - - friend expr exists(const std::vector &quants, const expr &body); - - }; - - - typedef ::decl_kind pfrule; - - class proof : public ast { - public: - proof(context & c):ast(c) {} - proof(context & c, ::proof *s):ast(c, s) {} - proof(proof const & s):ast(s) {} - operator ::proof*() const { return to_app(raw()); } - proof & operator=(proof const & s) { return static_cast(ast::operator=(s)); } - - pfrule rule() const { - ::func_decl *d = to_app(raw())->get_decl(); - return d->get_decl_kind(); - } - - unsigned num_prems() const { - return to_app(raw())->get_num_args() - 1; - } - - expr conc() const { - return ctx().cook(to_app(raw())->get_arg(num_prems())); - } - - proof prem(unsigned i) const { - return proof(ctx(),to_app(to_app(raw())->get_arg(i))); - } - - void get_assumptions(std::vector &assumps); - }; - -#if 0 - -#if Z3_MAJOR_VERSION > 4 || Z3_MAJOR_VERSION == 4 && Z3_MINOR_VERSION >= 3 - template - class ast_vector_tpl : public object { - Z3_ast_vector m_vector; - void init(Z3_ast_vector v) { Z3_ast_vector_inc_ref(ctx(), v); m_vector = v; } - public: - ast_vector_tpl(context & c):object(c) { init(Z3_mk_ast_vector(c)); } - ast_vector_tpl(context & c, Z3_ast_vector v):object(c) { init(v); } - ast_vector_tpl(ast_vector_tpl const & s):object(s), m_vector(s.m_vector) { Z3_ast_vector_inc_ref(ctx(), m_vector); } - ~ast_vector_tpl() { /* Z3_ast_vector_dec_ref(ctx(), m_vector); */ } - operator Z3_ast_vector() const { return m_vector; } - unsigned size() const { return Z3_ast_vector_size(ctx(), m_vector); } - T operator[](unsigned i) const { Z3_ast r = Z3_ast_vector_get(ctx(), m_vector, i); check_error(); return cast_ast()(ctx(), r); } - void push_back(T const & e) { Z3_ast_vector_push(ctx(), m_vector, e); check_error(); } - void resize(unsigned sz) { Z3_ast_vector_resize(ctx(), m_vector, sz); check_error(); } - T back() const { return operator[](size() - 1); } - void pop_back() { assert(size() > 0); resize(size() - 1); } - bool empty() const { return size() == 0; } - ast_vector_tpl & operator=(ast_vector_tpl const & s) { - Z3_ast_vector_inc_ref(s.ctx(), s.m_vector); - // Z3_ast_vector_dec_ref(ctx(), m_vector); - m_ctx = s.m_ctx; - m_vector = s.m_vector; - return *this; - } - friend std::ostream & operator<<(std::ostream & out, ast_vector_tpl const & v) { out << Z3_ast_vector_to_string(v.ctx(), v); return out; } - }; - - typedef ast_vector_tpl ast_vector; - typedef ast_vector_tpl expr_vector; - typedef ast_vector_tpl sort_vector; - typedef ast_vector_tpl func_decl_vector; - -#endif - -#endif - - class func_interp : public object { - ::func_interp * m_interp; - void init(::func_interp * e) { - m_interp = e; - } - public: - func_interp(context & c, ::func_interp * e):object(c) { init(e); } - func_interp(func_interp const & s):object(s) { init(s.m_interp); } - ~func_interp() { } - operator ::func_interp *() const { return m_interp; } - func_interp & operator=(func_interp const & s) { - m_ctx = s.m_ctx; - m_interp = s.m_interp; - return *this; - } - unsigned num_entries() const { return m_interp->num_entries(); } - expr get_arg(unsigned ent, unsigned arg) const { - return expr(ctx(),m_interp->get_entry(ent)->get_arg(arg)); - } - expr get_value(unsigned ent) const { - return expr(ctx(),m_interp->get_entry(ent)->get_result()); - } - expr else_value() const { - return expr(ctx(),m_interp->get_else()); - } - }; - - - - class model : public object { - model_ref m_model; - void init(::model *m) { - m_model = m; - } - public: - model(context & c, ::model * m = nullptr):object(c), m_model(m) { } - model(model const & s):object(s), m_model(s.m_model) { } - ~model() { } - operator ::model *() const { return m_model.get(); } - model & operator=(model const & s) { - // ::model *_inc_ref(s.ctx(), s.m_model); - // ::model *_dec_ref(ctx(), m_model); - m_ctx = s.m_ctx; - m_model = s.m_model.get(); - return *this; - } - model & operator=(::model *s) { - m_model = s; - return *this; - } - bool null() const {return !m_model;} - - expr eval(expr const & n, bool model_completion=true) const { - ::model * _m = m_model.get(); - expr_ref result(ctx().m()); - _m->eval(n, result, model_completion); - return expr(ctx(), result); - } - - void show() const; - void show_hash() const; - - unsigned num_consts() const {return m_model.get()->get_num_constants();} - unsigned num_funcs() const {return m_model.get()->get_num_functions();} - func_decl get_const_decl(unsigned i) const {return func_decl(ctx(),m_model.get()->get_constant(i));} - func_decl get_func_decl(unsigned i) const {return func_decl(ctx(),m_model.get()->get_function(i));} - unsigned size() const; - func_decl operator[](unsigned i) const; - - expr get_const_interp(const func_decl & f) const { - return ctx().cook(m_model->get_const_interp(to_func_decl(f.raw()))); - } - - func_interp get_func_interp(const func_decl & f) const { - return func_interp(ctx(),m_model->get_func_interp(to_func_decl(f.raw()))); - } - -#if 0 - friend std::ostream & operator<<(std::ostream & out, model const & m) { out << Z3_model_to_string(m.ctx(), m); return out; } -#endif - }; - -#if 0 - class stats : public object { - Z3_stats m_stats; - void init(Z3_stats e) { - m_stats = e; - Z3_stats_inc_ref(ctx(), m_stats); - } - public: - stats(context & c):object(c), m_stats(0) {} - stats(context & c, Z3_stats e):object(c) { init(e); } - stats(stats const & s):object(s) { init(s.m_stats); } - ~stats() { if (m_stats) Z3_stats_dec_ref(ctx(), m_stats); } - operator Z3_stats() const { return m_stats; } - stats & operator=(stats const & s) { - Z3_stats_inc_ref(s.ctx(), s.m_stats); - if (m_stats) Z3_stats_dec_ref(ctx(), m_stats); - m_ctx = s.m_ctx; - m_stats = s.m_stats; - return *this; - } - unsigned size() const { return Z3_stats_size(ctx(), m_stats); } - std::string key(unsigned i) const { Z3_string s = Z3_stats_get_key(ctx(), m_stats, i); check_error(); return s; } - bool is_uint(unsigned i) const { Z3_bool r = Z3_stats_is_uint(ctx(), m_stats, i); check_error(); return r != 0; } - bool is_double(unsigned i) const { Z3_bool r = Z3_stats_is_double(ctx(), m_stats, i); check_error(); return r != 0; } - unsigned uint_value(unsigned i) const { unsigned r = Z3_stats_get_uint_value(ctx(), m_stats, i); check_error(); return r; } - double double_value(unsigned i) const { double r = Z3_stats_get_double_value(ctx(), m_stats, i); check_error(); return r; } - friend std::ostream & operator<<(std::ostream & out, stats const & s) { out << Z3_stats_to_string(s.ctx(), s); return out; } - }; -#endif - - enum check_result { - unsat, sat, unknown - }; - - class fixedpoint : public object { - - public: - void get_rules(std::vector &rules); - void get_assertions(std::vector &rules); - void register_relation(const func_decl &rela); - void add_rule(const expr &clause, const symbol &name); - void assert_cnst(const expr &cnst); - }; - - inline std::ostream & operator<<(std::ostream & out, check_result r) { - if (r == unsat) out << "unsat"; - else if (r == sat) out << "sat"; - else out << "unknown"; - return out; - } - - inline check_result to_check_result(lbool l) { - if (l == l_true) return sat; - else if (l == l_false) return unsat; - return unknown; - } - - class solver : public object { - protected: - ::solver *m_solver; - model the_model; - bool canceled; - proof_gen_mode m_mode; - bool extensional; - public: - solver(context & c, bool extensional = false, bool models = true); - solver(context & c, ::solver *s):object(c),the_model(c) { m_solver = s; canceled = false;} - solver(solver const & s):object(s), the_model(s.the_model) { m_solver = s.m_solver; canceled = false;} - ~solver() { - if(m_solver) - dealloc(m_solver); - } - operator ::solver*() const { return m_solver; } - solver & operator=(solver const & s) { - m_ctx = s.m_ctx; - m_solver = s.m_solver; - the_model = s.the_model; - m_mode = s.m_mode; - return *this; - } - struct cancel_exception {}; - void checkpoint(){ - if(canceled) - throw(cancel_exception()); - } - // void set(params const & p) { Z3_solver_set_params(ctx(), m_solver, p); check_error(); } - void push() { scoped_proof_mode spm(m(),m_mode); m_solver->push(); } - void pop(unsigned n = 1) { scoped_proof_mode spm(m(),m_mode); m_solver->pop(n); } - // void reset() { Z3_solver_reset(ctx(), m_solver); check_error(); } - void add(expr const & e) { scoped_proof_mode spm(m(),m_mode); m_solver->assert_expr(e); } - check_result check() { - scoped_proof_mode spm(m(),m_mode); - checkpoint(); - lbool r = m_solver->check_sat(0,nullptr); - model_ref m; - m_solver->get_model(m); - the_model = m.get(); - return to_check_result(r); - } - check_result check_keep_model(unsigned n, expr * const assumptions, unsigned *core_size = nullptr, expr *core = nullptr) { - scoped_proof_mode spm(m(),m_mode); - model old_model(the_model); - check_result res = check(n,assumptions,core_size,core); - if(the_model == nullptr) - the_model = old_model; - return res; - } - check_result check(unsigned n, expr * const assumptions, unsigned *core_size = nullptr, expr *core = nullptr) { - scoped_proof_mode spm(m(),m_mode); - checkpoint(); - std::vector< ::expr *> _assumptions(n); - for (unsigned i = 0; i < n; i++) { - _assumptions[i] = to_expr(assumptions[i]); - } - the_model = nullptr; - lbool r = m_solver->check_sat(n, VEC2PTR(_assumptions)); - - if(core_size && core){ - ptr_vector< ::expr> _core; - m_solver->get_unsat_core(_core); - *core_size = _core.size(); - for(unsigned i = 0; i < *core_size; i++) - core[i] = expr(ctx(),_core[i]); - } - - model_ref m; - m_solver->get_model(m); - the_model = m.get(); - - return to_check_result(r); - } -#if 0 - check_result check(expr_vector assumptions) { - scoped_proof_mode spm(m(),m_mode); - unsigned n = assumptions.size(); - z3array _assumptions(n); - for (unsigned i = 0; i < n; i++) { - check_context(*this, assumptions[i]); - _assumptions[i] = assumptions[i]; - } - Z3_lbool r = Z3_check_assumptions(ctx(), m_solver, n, _assumptions.ptr()); - check_error(); - return to_check_result(r); - } -#endif - model get_model() const { return model(ctx(), the_model); } - // std::string reason_unknown() const { Z3_string r = Z3_solver_get_reason_unknown(ctx(), m_solver); check_error(); return r; } - // stats statistics() const { Z3_stats r = Z3_solver_get_statistics(ctx(), m_solver); check_error(); return stats(ctx(), r); } -#if 0 - expr_vector unsat_core() const { Z3_ast_vector r = Z3_solver_get_unsat_core(ctx(), m_solver); check_error(); return expr_vector(ctx(), r); } - expr_vector assertions() const { Z3_ast_vector r = Z3_solver_get_assertions(ctx(), m_solver); check_error(); return expr_vector(ctx(), r); } -#endif - // expr proof() const { Z3_ast r = Z3_solver_proof(ctx(), m_solver); check_error(); return expr(ctx(), r); } - // friend std::ostream & operator<<(std::ostream & out, solver const & s) { out << Z3_solver_to_string(s.ctx(), s); return out; } - int get_num_decisions(); - - void cancel(){ - scoped_proof_mode spm(m(),m_mode); - canceled = true; - m().limit().cancel(); - } - - unsigned get_scope_level(){ scoped_proof_mode spm(m(),m_mode); return m_solver->get_scope_level();} - - void show(); - void print(const char *filename); - void show_assertion_ids(); - - proof get_proof(){ - scoped_proof_mode spm(m(),m_mode); - return proof(ctx(),m_solver->get_proof()); - } - - bool extensional_array_theory() {return extensional;} - }; - -#if 0 - class goal : public object { - Z3_goal m_goal; - void init(Z3_goal s) { - m_goal = s; - Z3_goal_inc_ref(ctx(), s); - } - public: - goal(context & c, bool models=true, bool unsat_cores=false, bool proofs=false):object(c) { init(Z3_mk_goal(c, models, unsat_cores, proofs)); } - goal(context & c, Z3_goal s):object(c) { init(s); } - goal(goal const & s):object(s) { init(s.m_goal); } - ~goal() { Z3_goal_dec_ref(ctx(), m_goal); } - operator Z3_goal() const { return m_goal; } - goal & operator=(goal const & s) { - Z3_goal_inc_ref(s.ctx(), s.m_goal); - Z3_goal_dec_ref(ctx(), m_goal); - m_ctx = s.m_ctx; - m_goal = s.m_goal; - return *this; - } - void add(expr const & f) { check_context(*this, f); Z3_goal_assert(ctx(), m_goal, f); check_error(); } - unsigned size() const { return Z3_goal_size(ctx(), m_goal); } - expr operator[](unsigned i) const { Z3_ast r = Z3_goal_formula(ctx(), m_goal, i); check_error(); return expr(ctx(), r); } - Z3_goal_prec precision() const { return Z3_goal_precision(ctx(), m_goal); } - bool inconsistent() const { return Z3_goal_inconsistent(ctx(), m_goal) != 0; } - unsigned depth() const { return Z3_goal_depth(ctx(), m_goal); } - void reset() { Z3_goal_reset(ctx(), m_goal); } - unsigned num_exprs() const { Z3_goal_num_exprs(ctx(), m_goal); } - bool is_decided_sat() const { return Z3_goal_is_decided_sat(ctx(), m_goal) != 0; } - bool is_decided_unsat() const { return Z3_goal_is_decided_unsat(ctx(), m_goal) != 0; } - friend std::ostream & operator<<(std::ostream & out, goal const & g) { out << Z3_goal_to_string(g.ctx(), g); return out; } - }; - - class apply_result : public object { - Z3_apply_result m_apply_result; - void init(Z3_apply_result s) { - m_apply_result = s; - Z3_apply_result_inc_ref(ctx(), s); - } - public: - apply_result(context & c, Z3_apply_result s):object(c) { init(s); } - apply_result(apply_result const & s):object(s) { init(s.m_apply_result); } - ~apply_result() { Z3_apply_result_dec_ref(ctx(), m_apply_result); } - operator Z3_apply_result() const { return m_apply_result; } - apply_result & operator=(apply_result const & s) { - Z3_apply_result_inc_ref(s.ctx(), s.m_apply_result); - Z3_apply_result_dec_ref(ctx(), m_apply_result); - m_ctx = s.m_ctx; - m_apply_result = s.m_apply_result; - return *this; - } - unsigned size() const { return Z3_apply_result_get_num_subgoals(ctx(), m_apply_result); } - goal operator[](unsigned i) const { Z3_goal r = Z3_apply_result_get_subgoal(ctx(), m_apply_result, i); check_error(); return goal(ctx(), r); } - goal operator[](int i) const { assert(i >= 0); return this->operator[](static_cast(i)); } - model convert_model(model const & m, unsigned i = 0) const { - check_context(*this, m); - Z3_model new_m = Z3_apply_result_convert_model(ctx(), m_apply_result, i, m); - check_error(); - return model(ctx(), new_m); - } - friend std::ostream & operator<<(std::ostream & out, apply_result const & r) { out << Z3_apply_result_to_string(r.ctx(), r); return out; } - }; - - class tactic : public object { - Z3_tactic m_tactic; - void init(Z3_tactic s) { - m_tactic = s; - Z3_tactic_inc_ref(ctx(), s); - } - public: - tactic(context & c, char const * name):object(c) { Z3_tactic r = Z3_mk_tactic(c, name); check_error(); init(r); } - tactic(context & c, Z3_tactic s):object(c) { init(s); } - tactic(tactic const & s):object(s) { init(s.m_tactic); } - ~tactic() { Z3_tactic_dec_ref(ctx(), m_tactic); } - operator Z3_tactic() const { return m_tactic; } - tactic & operator=(tactic const & s) { - Z3_tactic_inc_ref(s.ctx(), s.m_tactic); - Z3_tactic_dec_ref(ctx(), m_tactic); - m_ctx = s.m_ctx; - m_tactic = s.m_tactic; - return *this; - } - solver mk_solver() const { Z3_solver r = Z3_mk_solver_from_tactic(ctx(), m_tactic); check_error(); return solver(ctx(), r); } - apply_result apply(goal const & g) const { - check_context(*this, g); - Z3_apply_result r = Z3_tactic_apply(ctx(), m_tactic, g); - check_error(); - return apply_result(ctx(), r); - } - apply_result operator()(goal const & g) const { - return apply(g); - } - std::string help() const { char const * r = Z3_tactic_get_help(ctx(), m_tactic); check_error(); return r; } - friend tactic operator&(tactic const & t1, tactic const & t2) { - check_context(t1, t2); - Z3_tactic r = Z3_tactic_and_then(t1.ctx(), t1, t2); - t1.check_error(); - return tactic(t1.ctx(), r); - } - friend tactic operator|(tactic const & t1, tactic const & t2) { - check_context(t1, t2); - Z3_tactic r = Z3_tactic_or_else(t1.ctx(), t1, t2); - t1.check_error(); - return tactic(t1.ctx(), r); - } - friend tactic repeat(tactic const & t, unsigned max=UINT_MAX) { - Z3_tactic r = Z3_tactic_repeat(t.ctx(), t, max); - t.check_error(); - return tactic(t.ctx(), r); - } - friend tactic with(tactic const & t, params const & p) { - Z3_tactic r = Z3_tactic_using_params(t.ctx(), t, p); - t.check_error(); - return tactic(t.ctx(), r); - } - friend tactic try_for(tactic const & t, unsigned ms) { - Z3_tactic r = Z3_tactic_try_for(t.ctx(), t, ms); - t.check_error(); - return tactic(t.ctx(), r); - } - }; - - class probe : public object { - Z3_probe m_probe; - void init(Z3_probe s) { - m_probe = s; - Z3_probe_inc_ref(ctx(), s); - } - public: - probe(context & c, char const * name):object(c) { Z3_probe r = Z3_mk_probe(c, name); check_error(); init(r); } - probe(context & c, double val):object(c) { Z3_probe r = Z3_probe_const(c, val); check_error(); init(r); } - probe(context & c, Z3_probe s):object(c) { init(s); } - probe(probe const & s):object(s) { init(s.m_probe); } - ~probe() { Z3_probe_dec_ref(ctx(), m_probe); } - operator Z3_probe() const { return m_probe; } - probe & operator=(probe const & s) { - Z3_probe_inc_ref(s.ctx(), s.m_probe); - Z3_probe_dec_ref(ctx(), m_probe); - m_ctx = s.m_ctx; - m_probe = s.m_probe; - return *this; - } - double apply(goal const & g) const { double r = Z3_probe_apply(ctx(), m_probe, g); check_error(); return r; } - double operator()(goal const & g) const { return apply(g); } - friend probe operator<=(probe const & p1, probe const & p2) { - check_context(p1, p2); Z3_probe r = Z3_probe_le(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r); - } - friend probe operator<=(probe const & p1, double p2) { return p1 <= probe(p1.ctx(), p2); } - friend probe operator<=(double p1, probe const & p2) { return probe(p2.ctx(), p1) <= p2; } - friend probe operator>=(probe const & p1, probe const & p2) { - check_context(p1, p2); Z3_probe r = Z3_probe_ge(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r); - } - friend probe operator>=(probe const & p1, double p2) { return p1 >= probe(p1.ctx(), p2); } - friend probe operator>=(double p1, probe const & p2) { return probe(p2.ctx(), p1) >= p2; } - friend probe operator<(probe const & p1, probe const & p2) { - check_context(p1, p2); Z3_probe r = Z3_probe_lt(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r); - } - friend probe operator<(probe const & p1, double p2) { return p1 < probe(p1.ctx(), p2); } - friend probe operator<(double p1, probe const & p2) { return probe(p2.ctx(), p1) < p2; } - friend probe operator>(probe const & p1, probe const & p2) { - check_context(p1, p2); Z3_probe r = Z3_probe_gt(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r); - } - friend probe operator>(probe const & p1, double p2) { return p1 > probe(p1.ctx(), p2); } - friend probe operator>(double p1, probe const & p2) { return probe(p2.ctx(), p1) > p2; } - friend probe operator==(probe const & p1, probe const & p2) { - check_context(p1, p2); Z3_probe r = Z3_probe_eq(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r); - } - friend probe operator==(probe const & p1, double p2) { return p1 == probe(p1.ctx(), p2); } - friend probe operator==(double p1, probe const & p2) { return probe(p2.ctx(), p1) == p2; } - friend probe operator&&(probe const & p1, probe const & p2) { - check_context(p1, p2); Z3_probe r = Z3_probe_and(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r); - } - friend probe operator||(probe const & p1, probe const & p2) { - check_context(p1, p2); Z3_probe r = Z3_probe_or(p1.ctx(), p1, p2); p1.check_error(); return probe(p1.ctx(), r); - } - friend probe operator!(probe const & p) { - Z3_probe r = Z3_probe_not(p.ctx(), p); p.check_error(); return probe(p.ctx(), r); - } - }; - - inline tactic fail_if(probe const & p) { - Z3_tactic r = Z3_tactic_fail_if(p.ctx(), p); - p.check_error(); - return tactic(p.ctx(), r); - } - inline tactic when(probe const & p, tactic const & t) { - check_context(p, t); - Z3_tactic r = Z3_tactic_when(t.ctx(), p, t); - t.check_error(); - return tactic(t.ctx(), r); - } - inline tactic cond(probe const & p, tactic const & t1, tactic const & t2) { - check_context(p, t1); check_context(p, t2); - Z3_tactic r = Z3_tactic_cond(t1.ctx(), p, t1, t2); - t1.check_error(); - return tactic(t1.ctx(), r); - } - -#endif - - inline expr context::bool_val(bool b){return b ? make(True) : make(False);} - - inline symbol context::str_symbol(char const * s) { ::symbol r = ::symbol(s); return symbol(*this, r); } - inline symbol context::int_symbol(int n) { ::symbol r = ::symbol(n); return symbol(*this, r); } - - inline sort context::bool_sort() { - ::sort *s = m().mk_sort(m_basic_fid, BOOL_SORT); - return sort(*this, s); - } - inline sort context::int_sort() { - ::sort *s = m().mk_sort(m_arith_fid, INT_SORT); - return sort(*this, s); - } - inline sort context::real_sort() { - ::sort *s = m().mk_sort(m_arith_fid, REAL_SORT); - return sort(*this, s); - } - inline sort context::array_sort(const sort & d, const sort & r) { - parameter params[2] = { parameter(d), parameter(to_sort(r)) }; - ::sort * s = m().mk_sort(m_array_fid, ARRAY_SORT, 2, params); - return sort(*this, s); - } - - - inline func_decl context::function(symbol const & name, unsigned arity, sort const * domain, sort const & range) { - std::vector< ::sort *> sv(arity); - for(unsigned i = 0; i < arity; i++) - sv[i] = domain[i]; - ::func_decl* d = m().mk_func_decl(name,arity, VEC2PTR(sv),range); - return func_decl(*this,d); - } - - inline func_decl context::function(char const * name, unsigned arity, sort const * domain, sort const & range) { - return function(str_symbol(name), arity, domain, range); - } - - inline func_decl context::function(char const * name, sort const & domain, sort const & range) { - sort args[1] = { domain }; - return function(name, 1, args, range); - } - - inline func_decl context::function(char const * name, sort const & d1, sort const & d2, sort const & range) { - sort args[2] = { d1, d2 }; - return function(name, 2, args, range); - } - - inline func_decl context::function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & range) { - sort args[3] = { d1, d2, d3 }; - return function(name, 3, args, range); - } - - inline func_decl context::function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & range) { - sort args[4] = { d1, d2, d3, d4 }; - return function(name, 4, args, range); - } - - inline func_decl context::function(char const * name, sort const & d1, sort const & d2, sort const & d3, sort const & d4, sort const & d5, sort const & range) { - sort args[5] = { d1, d2, d3, d4, d5 }; - return function(name, 5, args, range); - } - - - inline expr context::constant(symbol const & name, sort const & s) { - ::expr *r = m().mk_const(m().mk_const_decl(name, s)); - return expr(*this, r); - } - inline expr context::constant(char const * name, sort const & s) { return constant(str_symbol(name), s); } - inline expr context::bool_const(char const * name) { return constant(name, bool_sort()); } - inline expr context::int_const(char const * name) { return constant(name, int_sort()); } - inline expr context::real_const(char const * name) { return constant(name, real_sort()); } - inline expr context::bv_const(char const * name, unsigned sz) { return constant(name, bv_sort(sz)); } - - inline expr func_decl::operator()(const std::vector &args) const { - return operator()(args.size(), VEC2PTR(args)); - } - inline expr func_decl::operator()() const { - return operator()(0,nullptr); - } - inline expr func_decl::operator()(expr const & a) const { - return operator()(1,&a); - } - inline expr func_decl::operator()(expr const & a1, expr const & a2) const { - expr args[2] = {a1,a2}; - return operator()(2,args); - } - inline expr func_decl::operator()(expr const & a1, expr const & a2, expr const & a3) const { - expr args[3] = {a1,a2,a3}; - return operator()(3,args); - } - inline expr func_decl::operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4) const { - expr args[4] = {a1,a2,a3,a4}; - return operator()(4,args); - } - inline expr func_decl::operator()(expr const & a1, expr const & a2, expr const & a3, expr const & a4, expr const & a5) const { - expr args[5] = {a1,a2,a3,a4,a5}; - return operator()(5,args); - } - - - inline expr select(expr const & a, expr const & i) { return a.ctx().make(Select,a,i); } - inline expr store(expr const & a, expr const & i, expr const & v) { return a.ctx().make(Store,a,i,v); } - - inline expr forall(const std::vector &quants, const expr &body){ - return body.ctx().make_quant(Forall,quants,body); - } - - inline expr exists(const std::vector &quants, const expr &body){ - return body.ctx().make_quant(Exists,quants,body); - } - - inline expr context::int_val(int n){ - :: sort *r = m().mk_sort(m_arith_fid, INT_SORT); - return cook(m_arith_util.mk_numeral(rational(n),r)); - } - - - class literals : public object { - }; - - class TermTree { - public: - - TermTree(const expr &_term){ - term = _term; - } - - TermTree(const expr &_term, const std::vector &_children){ - term = _term; - children = _children; - } - - inline expr getTerm(){return term;} - - inline std::vector &getTerms(){return terms;} - - inline std::vector &getChildren(){ - return children; - } - - inline int number(int from){ - for(unsigned i = 0; i < children.size(); i++) - from = children[i]->number(from); - num = from; - return from + 1; - } - - inline int getNumber(){ - return num; - } - - inline void setTerm(const expr &t){term = t;} - - inline void addTerm(const expr &t){terms.push_back(t);} - - inline void setChildren(const std::vector & _children){ - children = _children; - } - - inline void setNumber(int _num){ - num = _num; - } - - ~TermTree(){ - for(unsigned i = 0; i < children.size(); i++) - delete children[i]; - } - - private: - expr term; - std::vector terms; - std::vector children; - int num; - }; - - typedef context interpolating_context; - - class interpolating_solver : public solver { - public: - interpolating_solver(context &ctx, bool models = true) - : solver(ctx, true, models) - { - weak_mode = false; - } - - public: - lbool interpolate(const std::vector &assumptions, - std::vector &interpolants, - model &_model, - literals &lits, - bool incremental - ); - - lbool interpolate_tree(TermTree *assumptions, - TermTree *&interpolants, - model &_model, - literals &lits, - bool incremental - ); - - bool read_interpolation_problem(const std::string &file_name, - std::vector &assumptions, - std::vector &theory, - std::string &error_message - ); - - void write_interpolation_problem(const std::string &file_name, - const std::vector &assumptions, - const std::vector &theory - ); - - void AssertInterpolationAxiom(const expr &expr); - void RemoveInterpolationAxiom(const expr &expr); - - void SetWeakInterpolants(bool weak); - void SetPrintToFile(const std::string &file_name); - - const std::vector &GetInterpolationAxioms() {return theory;} - const char *profile(); - - private: - bool weak_mode; - std::string print_filename; - std::vector theory; - }; - - - inline expr context::cook(::expr *a) {return expr(*this,a);} - - inline std::vector context::cook(ptr_vector< ::expr> v) { - std::vector _v(v.size()); - for(unsigned i = 0; i < v.size(); i++) - _v[i] = cook(v[i]); - return _v; - } - - inline ::expr *context::uncook(const expr &a) { - m().inc_ref(a.raw()); - return to_expr(a.raw()); - } - - inline expr context::translate(const expr &e) { - ::expr *f = to_expr(e.raw()); - if(&e.ctx().m() != &m()) // same ast manager -> no translation - throw "ast manager mismatch"; - return cook(f); - } - - inline func_decl context::translate(const func_decl &e) { - ::func_decl *f = to_func_decl(e.raw()); - if(&e.ctx().m() != &m()) // same ast manager -> no translation - throw "ast manager mismatch"; - return func_decl(*this,f); - } - - typedef double clock_t; - clock_t current_time(); - inline void output_time(std::ostream &os, clock_t time){os << time;} - - template class uptr { - public: - X *ptr; - uptr(){ptr = nullptr;} - void set(X *_ptr){ - if(ptr) delete ptr; - ptr = _ptr; - } - X *get(){ return ptr;} - ~uptr(){ - if(ptr) delete ptr; - } - }; - -}; - -// to make Duality::ast hashable -namespace hash_space { - template <> - class hash { - public: - size_t operator()(const Duality::ast &s) const { - return s.raw()->get_id(); - } - }; -} - - -// to make Duality::ast usable in ordered collections -namespace std { - template <> - class less { - public: - bool operator()(const Duality::ast &s, const Duality::ast &t) const { - // return s.raw() < t.raw(); - return s.raw()->get_id() < t.raw()->get_id(); - } - }; -} - -// to make Duality::ast usable in ordered collections -namespace std { - template <> - class less { - public: - bool operator()(const Duality::expr &s, const Duality::expr &t) const { - // return s.raw() < t.raw(); - return s.raw()->get_id() < t.raw()->get_id(); - } - }; -} - -// to make Duality::func_decl hashable -namespace hash_space { - template <> - class hash { - public: - size_t operator()(const Duality::func_decl &s) const { - return s.raw()->get_id(); - } - }; -} - - -// to make Duality::func_decl usable in ordered collections -namespace std { - template <> - class less { - public: - bool operator()(const Duality::func_decl &s, const Duality::func_decl &t) const { - // return s.raw() < t.raw(); - return s.raw()->get_id() < t.raw()->get_id(); - } - }; -} - -#endif diff --git a/src/interp/CMakeLists.txt b/src/interp/CMakeLists.txt deleted file mode 100644 index c3d8e3d5e..000000000 --- a/src/interp/CMakeLists.txt +++ /dev/null @@ -1,18 +0,0 @@ -z3_add_component(interp - SOURCES - iz3base.cpp - iz3checker.cpp - iz3interp.cpp - iz3mgr.cpp - iz3pp.cpp - iz3profiling.cpp - iz3proof.cpp - iz3proof_itp.cpp - iz3scopes.cpp - iz3translate.cpp - iz3translate_direct.cpp - COMPONENT_DEPENDENCIES - solver - PYG_FILES - interp_params.pyg -) diff --git a/src/interp/interp_params.pyg b/src/interp/interp_params.pyg deleted file mode 100644 index 3116a18db..000000000 --- a/src/interp/interp_params.pyg +++ /dev/null @@ -1,6 +0,0 @@ -def_module_params('interp', - description='interpolation parameters', - export=True, - params=(('profile', BOOL, False, '(INTERP) profile interpolation'), - ('check', BOOL, False, '(INTERP) check interpolants'), - )) diff --git a/src/interp/iz3base.cpp b/src/interp/iz3base.cpp deleted file mode 100644 index 773f328ab..000000000 --- a/src/interp/iz3base.cpp +++ /dev/null @@ -1,372 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3base.cpp - - Abstract: - - Base class for interpolators. Includes an AST manager and a scoping - object as bases. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#pragma warning(disable:4101) -#endif - -#include "interp/iz3base.h" -#include -#include -#include -#include -#include "solver/solver.h" -#include "../smt/smt_solver.h" - - -using namespace stl_ext; - - -iz3base::range &iz3base::ast_range(ast t){ - return ast_ranges_hash[t].rng; -} - -iz3base::range &iz3base::sym_range(symb d){ - return sym_range_hash[d]; -} - -void iz3base::add_frame_range(int frame, ast t){ - range &rng = ast_range(t); - if(!in_range(frame,rng)){ - range_add(frame,rng); - for(int i = 0, n = num_args(t); i < n; ++i) - add_frame_range(frame,arg(t,i)); - if(op(t) == Uninterpreted) - range_add(frame,sym_range(sym(t))); - } -} - -#if 1 -iz3base::range &iz3base::ast_scope(ast t){ - ranges &rngs = ast_ranges_hash[t]; - range &rng = rngs.scp; - if(!rngs.scope_computed){ // not computed yet - rng = range_full(); - for(int i = 0, n = num_args(t); i < n; ++i) - rng = range_glb(rng,ast_scope(arg(t,i))); - if(op(t) == Uninterpreted) - if(parents.empty() || num_args(t) == 0) // in tree mode, all function syms are global - rng = range_glb(rng,sym_range(sym(t))); - rngs.scope_computed = true; - } - return rng; -} -#else -iz3base::range &iz3base::ast_scope(ast t){ - ranges &rngs = ast_ranges_hash[t]; - if(rngs.scope_computed) return rngs.scp; - range rng = range_full(); - for(int i = 0, n = num_args(t); i < n; ++i) - rng = range_glb(rng,ast_scope(arg(t,i))); - if(op(t) == Uninterpreted) - if(parents.empty() || num_args(t) == 0) // in tree mode, all function syms are global - rng = range_glb(rng,sym_range(sym(t))); - rngs = ast_ranges_hash[t]; - rngs.scope_computed = true; - rngs.scp = rng; - return rngs.scp; -} -#endif - -void iz3base::print(const std::string &filename){ - ast t = make(And,cnsts); - std::ofstream f(filename.c_str()); - print_sat_problem(f,t); - f.close(); -} - - -void iz3base::gather_conjuncts_rec(ast n, std::vector &conjuncts, stl_ext::hash_set &memo){ - if(memo.find(n) == memo.end()){ - memo.insert(n); - if(op(n) == And){ - int nargs = num_args(n); - for(int i = 0; i < nargs; i++) - gather_conjuncts_rec(arg(n,i),conjuncts,memo); - } - else - conjuncts.push_back(n); - } -} - -void iz3base::gather_conjuncts(ast n, std::vector &conjuncts){ - hash_set memo; - gather_conjuncts_rec(n,conjuncts,memo); -} - -bool iz3base::is_literal(ast n){ - if(is_not(n))n = arg(n,0); - if(is_true(n) || is_false(n)) return false; - if(op(n) == And) return false; - return true; -} - -iz3base::ast iz3base::simplify_and(std::vector &conjuncts){ - hash_set memo; - for(unsigned i = 0; i < conjuncts.size(); i++){ - if(is_false(conjuncts[i])) - return conjuncts[i]; - if(is_true(conjuncts[i]) || memo.find(conjuncts[i]) != memo.end()){ - std::swap(conjuncts[i],conjuncts.back()); - conjuncts.pop_back(); - } - else if(memo.find(mk_not(conjuncts[i])) != memo.end()) - return mk_false(); // contradiction! - else - memo.insert(conjuncts[i]); - } - if(conjuncts.empty())return mk_true(); - return make(And,conjuncts); -} - -iz3base::ast iz3base::simplify_with_lit_rec(ast n, ast lit, stl_ext::hash_map &memo, int depth){ - if(is_not(n))return mk_not(simplify_with_lit_rec(mk_not(n),lit,memo,depth)); - if(n == lit) return mk_true(); - ast not_lit = mk_not(lit); - if(n == not_lit) return mk_false(); - if(op(n) != And || depth <= 0) return n; - std::pair foo(n,ast()); - std::pair::iterator,bool> bar = memo.insert(foo); - ast &res = bar.first->second; - if(!bar.second) return res; - int nargs = num_args(n); - std::vector args(nargs); - for(int i = 0; i < nargs; i++) - args[i] = simplify_with_lit_rec(arg(n,i),lit,memo,depth-1); - res = simplify_and(args); - return res; -} - -iz3base::ast iz3base::simplify_with_lit(ast n, ast lit){ - hash_map memo; - return simplify_with_lit_rec(n,lit,memo,1); -} - -iz3base::ast iz3base::simplify(ast n){ - if(is_not(n)) return mk_not(simplify(mk_not(n))); - std::pair memo_obj(n,ast()); - std::pair::iterator,bool> memo = simplify_memo.insert(memo_obj); - ast &res = memo.first->second; - if(!memo.second) return res; - switch(op(n)){ - case And: { - std::vector conjuncts; - gather_conjuncts(n,conjuncts); - for(unsigned i = 0; i < conjuncts.size(); i++) - conjuncts[i] = simplify(conjuncts[i]); -#if 0 - for(unsigned i = 0; i < conjuncts.size(); i++) - if(is_literal(conjuncts[i])) - for(unsigned j = 0; j < conjuncts.size(); j++) - if(j != i) - conjuncts[j] = simplify_with_lit(conjuncts[j],conjuncts[i]); -#endif - res = simplify_and(conjuncts); - } - break; - case Equal: { - ast x = arg(n,0); - ast y = arg(n,1); - if(ast_id(x) > ast_id(y)) - std::swap(x,y); - res = make(Equal,x,y); - break; - } - default: - res = n; - } - return res; -} - -void iz3base::initialize(const std::vector &_parts, const std::vector &_parents, const std::vector &_theory){ - cnsts = _parts; - theory = _theory; - for(unsigned i = 0; i < cnsts.size(); i++) - add_frame_range(i, cnsts[i]); - for(unsigned i = 0; i < _theory.size(); i++){ - add_frame_range(SHRT_MIN, _theory[i]); - add_frame_range(SHRT_MAX, _theory[i]); - } - for(unsigned i = 0; i < cnsts.size(); i++) - frame_map[cnsts[i]] = i; - for(unsigned i = 0; i < theory.size(); i++) - frame_map[theory[i]] = INT_MAX; -} - -void iz3base::initialize(const std::vector > &_parts, const std::vector &_parents, const std::vector &_theory){ - cnsts.resize(_parts.size()); - theory = _theory; - for(unsigned i = 0; i < _parts.size(); i++) - for(unsigned j = 0; j < _parts[i].size(); j++){ - cnsts[i] = make(And,_parts[i]); - add_frame_range(i, _parts[i][j]); - frame_map[_parts[i][j]] = i; - } - for(unsigned i = 0; i < _theory.size(); i++){ - add_frame_range(SHRT_MIN, _theory[i]); - add_frame_range(SHRT_MAX, _theory[i]); - frame_map[theory[i]] = INT_MAX; - } -} - -void iz3base::check_interp(const std::vector &itps, std::vector &theory){ -#if 0 - Z3_config config = Z3_mk_config(); - Z3_context vctx = Z3_mk_context(config); - int frames = cnsts.size(); - std::vector foocnsts(cnsts); - for(unsigned i = 0; i < frames; i++) - foocnsts[i] = Z3_mk_implies(ctx,Z3_mk_true(ctx),cnsts[i]); - Z3_write_interpolation_problem(ctx,frames,&foocnsts[0],0, "temp_lemma.smt", theory.size(), &theory[0]); - int vframes,*vparents; - Z3_ast *vcnsts; - const char *verror; - bool ok = Z3_read_interpolation_problem(vctx,&vframes,&vcnsts,0,"temp_lemma.smt",&verror); - assert(ok); - std::vector vvcnsts(vframes); - std::copy(vcnsts,vcnsts+vframes,vvcnsts.begin()); - std::vector vitps(itps.size()); - for(unsigned i = 0; i < itps.size(); i++) - vitps[i] = Z3_mk_implies(ctx,Z3_mk_true(ctx),itps[i]); - Z3_write_interpolation_problem(ctx,itps.size(),&vitps[0],0,"temp_interp.smt"); - int iframes,*iparents; - Z3_ast *icnsts; - const char *ierror; - ok = Z3_read_interpolation_problem(vctx,&iframes,&icnsts,0,"temp_interp.smt",&ierror); - assert(ok); - const char *error = 0; - bool iok = Z3_check_interpolant(vctx, frames, &vvcnsts[0], parents.size() ? &parents[0] : 0, icnsts, &error); - assert(iok); -#endif -} - -bool iz3base::is_sat(const std::vector &q, ast &_proof, std::vector &vars){ - - params_ref p; - p.set_bool("proof", true); // this is currently useless - p.set_bool("model", true); - p.set_bool("unsat_core", true); - scoped_ptr sf = mk_smt_solver_factory(); - scoped_ptr< ::solver > solver = (*sf)(m(), p, true, true, true, ::symbol::null); - ::solver &s = *solver.get(); - - for(unsigned i = 0; i < q.size(); i++) - s.assert_expr(to_expr(q[i].raw())); - lbool res = s.check_sat(0,nullptr); - if (m().canceled()) { - throw iz3_exception(Z3_CANCELED_MSG); - } - if(res == l_false){ - ::ast *proof = s.get_proof(); - _proof = cook(proof); - } - else if(vars.size()) { - model_ref _m; - s.get_model(_m); - if (!_m.get()) { - SASSERT(l_undef == res); - throw iz3_exception("interpolation cannot proceed without a model"); - } - for(unsigned i = 0; i < vars.size(); i++){ - expr_ref r(m()); - _m.get()->eval(to_expr(vars[i].raw()),r,true); - vars[i] = cook(r.get()); - } - } - solver = nullptr; - return res != l_false; -} - - -void iz3base::find_children(const stl_ext::hash_set &cnsts_set, - const ast &tree, - std::vector &cnsts, - std::vector &parents, - std::vector &conjuncts, - std::vector &children, - std::vector &pos_map, - bool merge - ){ - std::vector my_children; - std::vector my_conjuncts; - if(op(tree) == Interp){ // if we've hit an interpolation position... - find_children(cnsts_set,arg(tree,0),cnsts,parents,my_conjuncts,my_children,pos_map,merge); - if(my_conjuncts.empty()) - my_conjuncts.push_back(mk_true()); // need at least one conjunct - int root = cnsts.size() + my_conjuncts.size() - 1; - for(unsigned i = 0; i < my_conjuncts.size(); i++){ - parents.push_back(root); - cnsts.push_back(my_conjuncts[i]); - } - for(unsigned i = 0; i < my_children.size(); i++) - parents[my_children[i]] = root; - children.push_back(root); - pos_map.push_back(root); - } - else { - if(op(tree) == And){ - int nargs = num_args(tree); - for(int i = 0; i < nargs; i++) - find_children(cnsts_set,arg(tree,i),cnsts,parents,my_conjuncts,my_children,pos_map,merge); - } - if(cnsts_set.find(tree) != cnsts_set.end()){ - if(merge && !my_conjuncts.empty()) - my_conjuncts.back() = mk_and(my_conjuncts.back(),tree); - else - my_conjuncts.push_back(tree); - } - for(unsigned i = 0; i < my_children.size(); i++) - children.push_back(my_children[i]); - for(unsigned i = 0; i < my_conjuncts.size(); i++) - conjuncts.push_back(my_conjuncts[i]); - } -} - -void iz3base::to_parents_vec_representation(const std::vector &_cnsts, - const ast &tree, - std::vector &cnsts, - std::vector &parents, - std::vector &theory, - std::vector &pos_map, - bool merge - ){ - std::vector my_children; - std::vector my_conjuncts; - hash_set cnsts_set; - for(unsigned i = 0; i < _cnsts.size(); i++) - cnsts_set.insert(_cnsts[i]); - ast _tree = (op(tree) != Interp) ? make(Interp,tree) : tree; - find_children(cnsts_set,_tree,cnsts,parents,my_conjuncts,my_children,pos_map,merge); - if(op(tree) != Interp) pos_map.pop_back(); - parents[parents.size()-1] = SHRT_MAX; - - // rest of the constraints are the background theory - - hash_set used_set; - for(unsigned i = 0; i < cnsts.size(); i++) - used_set.insert(cnsts[i]); - for(unsigned i = 0; i < _cnsts.size(); i++) - if(used_set.find(_cnsts[i]) == used_set.end()) - theory.push_back(_cnsts[i]); -} - diff --git a/src/interp/iz3base.h b/src/interp/iz3base.h deleted file mode 100755 index 15f613730..000000000 --- a/src/interp/iz3base.h +++ /dev/null @@ -1,195 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3base.h - - Abstract: - - Base class for interpolators. Includes an AST manager and a scoping - object as bases. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifndef IZ3BASE_H -#define IZ3BASE_H - -#include "interp/iz3mgr.h" -#include "interp/iz3scopes.h" - -namespace hash_space { - template <> - class hash { - public: - size_t operator()(func_decl * const &s) const { - return (size_t) s; - } - }; -} - -/* Base class for interpolators. Includes an AST manager and a scoping - object as bases. */ - -class iz3base : public iz3mgr, public scopes { - - public: - - /** Get the range in which an expression occurs. This is the - smallest subtree containing all occurrences of the - expression. */ - range &ast_range(ast); - - /** Get the scope of an expression. This is the set of tree nodes in - which all of the expression's symbols are in scope. */ - range &ast_scope(ast); - - /** Get the range of a symbol. This is the smallest subtree containing - all occurrences of the symbol. */ - range &sym_range(symb); - - /** Is an expression local (in scope in some frame)? */ - - bool is_local(ast node){ - return !range_is_empty(ast_scope(node)); - } - - /** Simplify an expression */ - - ast simplify(ast); - - /** Constructor */ - - iz3base(ast_manager &_m_manager, - const std::vector &_cnsts, - const std::vector &_parents, - const std::vector &_theory) - : iz3mgr(_m_manager), scopes(_parents) { - initialize(_cnsts,_parents,_theory); - weak = false; - } - - iz3base(const iz3mgr& other, - const std::vector &_cnsts, - const std::vector &_parents, - const std::vector &_theory) - : iz3mgr(other), scopes(_parents) { - initialize(_cnsts,_parents,_theory); - weak = false; - } - - iz3base(const iz3mgr& other, - const std::vector > &_cnsts, - const std::vector &_parents, - const std::vector &_theory) - : iz3mgr(other), scopes(_parents) { - initialize(_cnsts,_parents,_theory); - weak = false; - } - - iz3base(const iz3mgr& other) - : iz3mgr(other), scopes() { - weak = false; - } - - /* Set our options */ - void set_option(const std::string &name, const std::string &value){ - if(name == "weak" && value == "1") weak = true; - } - - /* Are we doing weak interpolants? */ - bool weak_mode(){return weak;} - - /** Print interpolation problem to an SMTLIB format file */ - void print(const std::string &filename); - - /** Check correctness of a solutino to this problem. */ - void check_interp(const std::vector &itps, std::vector &theory); - - /** For convenience -- is this formula SAT? */ - bool is_sat(const std::vector &consts, ast &_proof, std::vector &vars); - - /** Interpolator for clauses, to be implemented */ - virtual void interpolate_clause(std::vector &lits, std::vector &itps){ - throw iz3_exception("no interpolator"); - } - - ast get_proof_check_assump(range &rng){ - std::vector cs(theory); - cs.push_back(cnsts[rng.hi]); - return make(And,cs); - } - - int frame_of_assertion(const ast &ass){ - stl_ext::hash_map::iterator it = frame_map.find(ass); - if(it == frame_map.end()) - throw iz3_exception("unknown assertion"); - return it->second; - } - - - void to_parents_vec_representation(const std::vector &_cnsts, - const ast &tree, - std::vector &cnsts, - std::vector &parents, - std::vector &theory, - std::vector &pos_map, - bool merge = false - ); - - protected: - std::vector cnsts; - std::vector theory; - - private: - - struct ranges { - range rng; - range scp; - bool scope_computed; - ranges(){scope_computed = false;} - }; - - stl_ext::hash_map sym_range_hash; - stl_ext::hash_map ast_ranges_hash; - stl_ext::hash_map simplify_memo; - stl_ext::hash_map frame_map; // map assertions to frames - - // int frames; // number of frames - - protected: - void add_frame_range(int frame, ast t); - - private: - void initialize(const std::vector &_parts, const std::vector &_parents, const std::vector &_theory); - - void initialize(const std::vector > &_parts, const std::vector &_parents, const std::vector &_theory); - - bool is_literal(ast n); - void gather_conjuncts_rec(ast n, std::vector &conjuncts, stl_ext::hash_set &memo); - void gather_conjuncts(ast n, std::vector &conjuncts); - ast simplify_and(std::vector &conjuncts); - ast simplify_with_lit_rec(ast n, ast lit, stl_ext::hash_map &memo, int depth); - ast simplify_with_lit(ast n, ast lit); - void find_children(const stl_ext::hash_set &cnsts_set, - const ast &tree, - std::vector &cnsts, - std::vector &parents, - std::vector &conjuncts, - std::vector &children, - std::vector &pos_map, - bool merge - ); - bool weak; - -}; - - - -#endif diff --git a/src/interp/iz3checker.cpp b/src/interp/iz3checker.cpp deleted file mode 100644 index 511342819..000000000 --- a/src/interp/iz3checker.cpp +++ /dev/null @@ -1,227 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3checker.cpp - - Abstract: - - check correctness of interpolant - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#pragma warning(disable:4101) -#endif - -#include "interp/iz3base.h" -#include "interp/iz3checker.h" - -#include -#include -#include -#include -#include -#include -#include - - -using namespace stl_ext; - -struct iz3checker : iz3base { - - /* HACK: for tree interpolants, we assume that uninterpreted functions - are global. This is because in the current state of the tree interpolation - code, symbols that appear in sibling sub-trees have to be global, and - we have no way to eliminate such function symbols. When tree interpolation is - fixed, we can tree function symbols the same as constant symbols. */ - - bool is_tree; - - void support(const ast &t, std::set &res, hash_set &memo){ - if(memo.find(t) != memo.end()) return; - memo.insert(t); - - int nargs = num_args(t); - for(int i = 0; i < nargs; i++) - support(arg(t,i),res,memo); - - switch(op(t)){ - case Uninterpreted: - if(nargs == 0 || !is_tree) { - std::string name = string_of_symbol(sym(t)); - res.insert(name); - } - break; - case Forall: - case Exists: - support(get_quantifier_body(t),res,memo); - break; - default:; - } - } - - bool check(solver *s, std::ostream &err, - const std::vector &cnsts, - const std::vector &parents, - const std::vector &itp, - const std::vector &theory){ - - is_tree = !parents.empty(); - int num = cnsts.size(); - std::vector > children(num); - - for(int i = 0; i < num-1; i++){ - if(parents.size()) - children[parents[i]].push_back(i); - else - children[i+1].push_back(i); - } - - for(int i = 0; i < num; i++){ - s->push(); - for(unsigned j = 0; j < theory.size(); j++) - s->assert_expr(to_expr(theory[j].raw())); - s->assert_expr(to_expr(cnsts[i].raw())); - std::vector &cs = children[i]; - for(unsigned j = 0; j < cs.size(); j++) - s->assert_expr(to_expr(itp[cs[j]].raw())); - if(i != num-1) - s->assert_expr(to_expr(mk_not(itp[i]).raw())); - lbool result = s->check_sat(0,nullptr); - if(result != l_false){ - err << "interpolant " << i << " is incorrect"; - - s->pop(1); - for(unsigned j = 0; j < theory.size(); j++) - s->assert_expr(to_expr(theory[j].raw())); - for(unsigned j = 0; j < cnsts.size(); j++) - if(in_range(j,range_downward(i))) - s->assert_expr(to_expr(cnsts[j].raw())); - if(i != num-1) - s->assert_expr(to_expr(mk_not(itp[i]).raw())); - lbool result = s->check_sat(0,nullptr); - if(result != l_false) - err << "interpolant " << i << " is not implied by its downeard closurn"; - - return false; - } - s->pop(1); - } - - std::vector > supports(num); - for(int i = 0; i < num; i++){ - hash_set memo; - support(cnsts[i],supports[i],memo); - } - for(int i = 0; i < num-1; i++){ - std::vector Bside(num); - for(int j = num-1; j >= 0; j--) - Bside[j] = j != i; - for(int j = num-1; j >= 0; j--) - if(!Bside[j]){ - std::vector &cs = children[i]; - for(unsigned k = 0; k < cs.size(); k++) - Bside[cs[k]] = false; - } - std::set Asup, Bsup,common,Isup,bad; - for(int j = num-1; j >= 0; j--){ - std::set &side = Bside[j] ? Bsup : Asup; - side.insert(supports[j].begin(),supports[j].end()); - } - std::set_intersection(Asup.begin(),Asup.end(),Bsup.begin(),Bsup.end(),std::inserter(common,common.begin())); - { - hash_set tmemo; - for(unsigned j = 0; j < theory.size(); j++) - support(theory[j],common,tmemo); // all theory symbols allowed in interps - } - hash_set memo; - support(itp[i],Isup,memo); - std::set_difference(Isup.begin(),Isup.end(),common.begin(),common.end(),std::inserter(bad,bad.begin())); - if(!bad.empty()){ - err << "bad symbols in interpolant " << i << ":"; - std::copy(bad.begin(),bad.end(),std::ostream_iterator(err,",")); - return false; - } - } - return true; - } - - bool check(solver *s, std::ostream &err, - const std::vector &_cnsts, - const ast &tree, - const std::vector &itp){ - - std::vector pos_map; - - // convert to the parents vector representation - - to_parents_vec_representation(_cnsts, tree, cnsts, parents, theory, pos_map); - - //use the parents vector representation to compute interpolant - return check(s,err,cnsts,parents,itp,theory); - } - - iz3checker(ast_manager &_m) - : iz3base(_m) { - } - - iz3checker(iz3mgr &_m) - : iz3base(_m) { - } - -}; - -template -std::vector to_std_vector(const ::vector &v){ - std::vector _v(v.size()); - for(unsigned i = 0; i < v.size(); i++) - _v[i] = v[i]; - return _v; -} - - -bool iz3check(ast_manager &_m_manager, - solver *s, - std::ostream &err, - const ptr_vector &cnsts, - const ::vector &parents, - const ptr_vector &interps, - const ptr_vector &theory) -{ - iz3checker chk(_m_manager); - return chk.check(s,err,chk.cook(cnsts),to_std_vector(parents),chk.cook(interps),chk.cook(theory)); -} - -bool iz3check(iz3mgr &mgr, - solver *s, - std::ostream &err, - const std::vector &cnsts, - const std::vector &parents, - const std::vector &interps, - const std::vector &theory) -{ - iz3checker chk(mgr); - return chk.check(s,err,cnsts,parents,interps,theory); -} - -bool iz3check(ast_manager &_m_manager, - solver *s, - std::ostream &err, - const ptr_vector &_cnsts, - ast *tree, - const ptr_vector &interps) -{ - iz3checker chk(_m_manager); - return chk.check(s,err,chk.cook(_cnsts),chk.cook(tree),chk.cook(interps)); -} diff --git a/src/interp/iz3checker.h b/src/interp/iz3checker.h deleted file mode 100644 index d89db3011..000000000 --- a/src/interp/iz3checker.h +++ /dev/null @@ -1,49 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3checker.h - - Abstract: - - check correctness of an interpolant - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifndef IZ3_CHECKER_H -#define IZ3_CHECKER_H - -#include "interp/iz3mgr.h" -#include "solver/solver.h" - -bool iz3check(ast_manager &_m_manager, - solver *s, - std::ostream &err, - const ptr_vector &cnsts, - const ::vector &parents, - const ptr_vector &interps, - const ptr_vector &theory); - -bool iz3check(ast_manager &_m_manager, - solver *s, - std::ostream &err, - const ptr_vector &cnsts, - ast *tree, - const ptr_vector &interps); - -bool iz3check(iz3mgr &mgr, - solver *s, - std::ostream &err, - const std::vector &cnsts, - const std::vector &parents, - const std::vector &interps, - const ptr_vector &theory); - -#endif diff --git a/src/interp/iz3exception.h b/src/interp/iz3exception.h deleted file mode 100644 index b3f841565..000000000 --- a/src/interp/iz3exception.h +++ /dev/null @@ -1,28 +0,0 @@ -/*++ -Copyright (c) 2015 Microsoft Corporation - -Module Name: - - iz3exception.h - -Abstract: - - Base class for exceptions raised by interpolation routines - -Author: - -Notes: - ---*/ -#ifndef _IZ3EXCEPTION_H_ -#define _IZ3EXCEPTION_H_ - -#include "util/z3_exception.h" -#include "util/error_codes.h" - -class iz3_exception: public default_exception { -public: - iz3_exception(const std::string &msg): default_exception(msg) {} -}; - -#endif diff --git a/src/interp/iz3hash.h b/src/interp/iz3hash.h deleted file mode 100644 index f85242ed1..000000000 --- a/src/interp/iz3hash.h +++ /dev/null @@ -1,479 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3hash.h - - Abstract: - - Simple implementation of bucket-list hash tables conforming to SGI - hash_map and hash_set interfaces. Just enough members are - implemented to support iz3 and duality. - - iz3 and duality need this package because they assume that insert - preserves iterators and references to elements, which is not true - of the hashtable packages in util. - - This package lives in namespace hash_space. Specializations of - class "hash" should be made in this namespace. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifndef IZ3_HASH_H -#define IZ3_HASH_H - -#ifdef _WINDOWS -#pragma warning(disable:4267) -#endif - -#include -#include -#include -#include "util/hash.h" - -#define stl_ext hash_space - -namespace hash_space { - - template class hash {}; - - - template <> - class hash { - public: - size_t operator()(const int &s) const { - return s; - } - }; - - template <> - class hash { - public: - size_t operator()(const std::string &s) const { - return string_hash(s.c_str(), s.size(), 0); - } - }; - - template <> - class hash > { - public: - size_t operator()(const std::pair &p) const { - return p.first + p.second; - } - }; - - template - class hash > { - public: - size_t operator()(const std::pair &p) const { - return (size_t)p.first + (size_t)p.second; - } - }; - - enum { num_primes = 29 }; - - static const unsigned long primes[num_primes] = - { - 7ul, - 53ul, - 97ul, - 193ul, - 389ul, - 769ul, - 1543ul, - 3079ul, - 6151ul, - 12289ul, - 24593ul, - 49157ul, - 98317ul, - 196613ul, - 393241ul, - 786433ul, - 1572869ul, - 3145739ul, - 6291469ul, - 12582917ul, - 25165843ul, - 50331653ul, - 100663319ul, - 201326611ul, - 402653189ul, - 805306457ul, - 1610612741ul, - 3221225473ul, - 4294967291ul - }; - - inline unsigned long next_prime(unsigned long n) { - const unsigned long* to = primes + (int)num_primes; - for(const unsigned long* p = primes; p < to; p++) - if(*p >= n) return *p; - return primes[num_primes-1]; - } - - template - class hashtable - { - public: - - typedef Value &reference; - typedef const Value &const_reference; - - struct Entry - { - Entry* next; - Value val; - - Entry(const Value &_val) : val(_val) {next = nullptr;} - }; - - - struct iterator - { - Entry* ent; - hashtable* tab; - - typedef std::forward_iterator_tag iterator_category; - typedef Value value_type; - typedef std::ptrdiff_t difference_type; - typedef size_t size_type; - typedef Value& reference; - typedef Value* pointer; - - iterator(Entry* _ent, hashtable* _tab) : ent(_ent), tab(_tab) { } - - iterator() { } - - Value &operator*() const { return ent->val; } - - Value *operator->() const { return &(operator*()); } - - iterator &operator++() { - Entry *old = ent; - ent = ent->next; - if (!ent) { - size_t bucket = tab->get_bucket(old->val); - while (!ent && ++bucket < tab->buckets.size()) - ent = tab->buckets[bucket]; - } - return *this; - } - - iterator operator++(int) { - iterator tmp = *this; - operator++(); - return tmp; - } - - - bool operator==(const iterator& it) const { - return ent == it.ent; - } - - bool operator!=(const iterator& it) const { - return ent != it.ent; - } - }; - - struct const_iterator - { - const Entry* ent; - const hashtable* tab; - - typedef std::forward_iterator_tag iterator_category; - typedef Value value_type; - typedef std::ptrdiff_t difference_type; - typedef size_t size_type; - typedef const Value& reference; - typedef const Value* pointer; - - const_iterator(const Entry* _ent, const hashtable* _tab) : ent(_ent), tab(_tab) { } - - const_iterator() { } - - const Value &operator*() const { return ent->val; } - - const Value *operator->() const { return &(operator*()); } - - const_iterator &operator++() { - Entry *old = ent; - ent = ent->next; - if (!ent) { - size_t bucket = tab->get_bucket(old->val); - while (!ent && ++bucket < tab->buckets.size()) - ent = tab->buckets[bucket]; - } - return *this; - } - - const_iterator operator++(int) { - const_iterator tmp = *this; - operator++(); - return tmp; - } - - - bool operator==(const const_iterator& it) const { - return ent == it.ent; - } - - bool operator!=(const const_iterator& it) const { - return ent != it.ent; - } - }; - - private: - - typedef std::vector Table; - - Table buckets; - size_t entries; - HashFun hash_fun ; - GetKey get_key; - KeyEqFun key_eq_fun; - - public: - - hashtable(size_t init_size) : buckets(init_size,(Entry *)nullptr) { - entries = 0; - } - - hashtable(const hashtable& other) { - dup(other); - } - - hashtable& operator= (const hashtable& other) { - if (&other != this) - dup(other); - return *this; - } - - ~hashtable() { - clear(); - } - - size_t size() const { - return entries; - } - - bool empty() const { - return size() == 0; - } - - void swap(hashtable& other) { - buckets.swap(other.buckets); - std::swap(entries, other.entries); - } - - iterator begin() { - for (size_t i = 0; i < buckets.size(); ++i) - if (buckets[i]) - return iterator(buckets[i], this); - return end(); - } - - iterator end() { - return iterator(nullptr, this); - } - - const_iterator begin() const { - for (size_t i = 0; i < buckets.size(); ++i) - if (buckets[i]) - return const_iterator(buckets[i], this); - return end(); - } - - const_iterator end() const { - return const_iterator(nullptr, this); - } - - size_t get_bucket(const Value& val, size_t n) const { - return hash_fun(get_key(val)) % n; - } - - size_t get_key_bucket(const Key& key) const { - return hash_fun(key) % buckets.size(); - } - - size_t get_bucket(const Value& val) const { - return get_bucket(val,buckets.size()); - } - - Entry *lookup(const Value& val, bool ins = false) - { - resize(entries + 1); - - size_t n = get_bucket(val); - Entry* from = buckets[n]; - - for (Entry* ent = from; ent; ent = ent->next) - if (key_eq_fun(get_key(ent->val), get_key(val))) - return ent; - - if(!ins) return nullptr; - - Entry* tmp = new Entry(val); - tmp->next = from; - buckets[n] = tmp; - ++entries; - return tmp; - } - - Entry *lookup_key(const Key& key) const - { - size_t n = get_key_bucket(key); - Entry* from = buckets[n]; - - for (Entry* ent = from; ent; ent = ent->next) - if (key_eq_fun(get_key(ent->val), key)) - return ent; - - return nullptr; - } - - const_iterator find(const Key& key) const { - return const_iterator(lookup_key(key),this); - } - - iterator find(const Key& key) { - return iterator(lookup_key(key),this); - } - - std::pair insert(const Value& val){ - size_t old_entries = entries; - Entry *ent = lookup(val,true); - return std::pair(iterator(ent,this),entries > old_entries); - } - - iterator insert(const iterator &it, const Value& val){ - Entry *ent = lookup(val,true); - return iterator(ent,this); - } - - size_t erase(const Key& key) - { - Entry** p = &(buckets[get_key_bucket(key)]); - size_t count = 0; - while(*p){ - Entry *q = *p; - if (key_eq_fun(get_key(q->val), key)) { - ++count; - *p = q->next; - delete q; - } - else - p = &(q->next); - } - entries -= count; - return count; - } - - void resize(size_t new_size) { - const size_t old_n = buckets.size(); - if (new_size <= old_n) return; - const size_t n = next_prime(new_size); - if (n <= old_n) return; - Table tmp(n, (Entry*)nullptr); - for (size_t i = 0; i < old_n; ++i) { - Entry* ent = buckets[i]; - while (ent) { - size_t new_bucket = get_bucket(ent->val, n); - buckets[i] = ent->next; - ent->next = tmp[new_bucket]; - tmp[new_bucket] = ent; - ent = buckets[i]; - } - } - buckets.swap(tmp); - } - - void clear() - { - for (size_t i = 0; i < buckets.size(); ++i) { - for (Entry* ent = buckets[i]; ent != nullptr;) { - Entry* next = ent->next; - delete ent; - ent = next; - } - buckets[i] = nullptr; - } - entries = 0; - } - - void dup(const hashtable& other) - { - buckets.resize(other.buckets.size()); - for (size_t i = 0; i < other.buckets.size(); ++i) { - Entry** to = &buckets[i]; - for (Entry* from = other.buckets[i]; from; from = from->next) - to = &((*to = new Entry(from->val))->next); - } - entries = other.entries; - } - }; - - template - class equal { - public: - bool operator()(const T& x, const T &y) const { - return x == y; - } - }; - - template - class identity { - public: - const T &operator()(const T &x) const { - return x; - } - }; - - template - class proj1 { - public: - const T &operator()(const std::pair &x) const { - return x.first; - } - }; - - template , - class EqFun = equal > - class hash_set - : public hashtable,EqFun> { - - public: - - typedef Element value_type; - - hash_set() - : hashtable,EqFun>(7) {} - }; - - template , - class EqFun = equal > - class hash_map - : public hashtable,Key,HashFun,proj1,EqFun> { - - public: - - hash_map() - : hashtable,Key,HashFun,proj1,EqFun>(7) {} - - Value &operator[](const Key& key) { - std::pair kvp(key,Value()); - return - hashtable,Key,HashFun,proj1,EqFun>:: - lookup(kvp,true)->val.second; - } - }; - -} -#endif diff --git a/src/interp/iz3interp.cpp b/src/interp/iz3interp.cpp deleted file mode 100644 index 41c968bd8..000000000 --- a/src/interp/iz3interp.cpp +++ /dev/null @@ -1,578 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3interp.cpp - - Abstract: - - Interpolation based on proof translation. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -/* Copyright 2011 Microsoft Research. */ - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#pragma warning(disable:4101) -#endif - -#include -#include -#include -#include -#include -#include - -#include "interp/iz3profiling.h" -#include "interp/iz3translate.h" -#include "interp/iz3proof.h" -#include "interp/iz3hash.h" -#include "interp/iz3interp.h" - -#include "ast/scoped_proof.h" - - -using namespace stl_ext; - - - -#if 1 - -struct frame_reducer : public iz3mgr { - - int frames; - hash_map frame_map; - std::vector assertions_map; - std::vector orig_parents_copy; - std::vector used_frames; - - - frame_reducer(const iz3mgr &other) - : iz3mgr(other) {} - - void get_proof_assumptions_rec(z3pf proof, hash_set &memo, std::vector &used_frames){ - if(memo.find(proof) != memo.end())return; - memo.insert(proof); - pfrule dk = pr(proof); - if(dk == PR_ASSERTED){ - ast con = conc(proof); - if(frame_map.find(con) != frame_map.end()){ // false for theory facts - int frame = frame_map[con]; - used_frames[frame] = true; - } - } - else { - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - z3pf arg = prem(proof,i); - get_proof_assumptions_rec(arg,memo,used_frames); - } - } - } - - void get_frames(const std::vector >&z3_preds, - const std::vector &orig_parents, - std::vector >&assertions, - std::vector &parents, - z3pf proof){ - frames = z3_preds.size(); - orig_parents_copy = orig_parents; - for(unsigned i = 0; i < z3_preds.size(); i++) - for(unsigned j = 0; j < z3_preds[i].size(); j++) - frame_map[z3_preds[i][j]] = i; - used_frames.resize(frames); - hash_set memo; - get_proof_assumptions_rec(proof,memo,used_frames); - std::vector assertions_back_map(frames); - - // if multiple children of a tree node are used, we can't delete it - std::vector used_children; - used_children.reserve(frames); - for(int i = 0; i < frames; i++) - used_children.push_back(0); - for(int i = 0; i < frames; i++) - if(orig_parents[i] != SHRT_MAX) - if(used_frames[i] || used_children[i]){ - if(used_children[i] > 1) - used_frames[i] = true; - used_children[orig_parents[i]]++; - } - - for(unsigned i = 0; i < z3_preds.size(); i++) - if(used_frames[i] || i == z3_preds.size() - 1){ - assertions.push_back(z3_preds[i]); - assertions_map.push_back(i); - assertions_back_map[i] = assertions.size() - 1; - } - - if(orig_parents.size()){ - parents.resize(assertions.size()); - for(unsigned i = 0; i < assertions.size(); i++){ - int p = orig_parents[assertions_map[i]]; - while(p != SHRT_MAX && !used_frames[p]) - p = orig_parents[p]; - parents[i] = p == SHRT_MAX ? p : assertions_back_map[p]; - } - } - - // std::cout << "used frames = " << frames << "\n"; - } - - void fix_interpolants(std::vector &interpolants){ - std::vector unfixed = interpolants; - interpolants.resize(frames - 1); - for(int i = 0; i < frames - 1; i++) - interpolants[i] = mk_true(); - for(unsigned i = 0; i < unfixed.size(); i++) - interpolants[assertions_map[i]] = unfixed[i]; - for(int i = 0; i < frames-2; i++){ - int p = orig_parents_copy.size() == 0 ? i+1 : orig_parents_copy[i]; - if(p < frames - 1 && !used_frames[p]) - interpolants[p] = mk_and(interpolants[i],interpolants[p]); - } - } -}; - -#else -struct frame_reducer { - - - - frame_reducer(context _ctx){ - } - - void get_frames(const std::vector &z3_preds, - const std::vector &orig_parents, - std::vector &assertions, - std::vector &parents, - ast proof){ - assertions = z3_preds; - parents = orig_parents; - } - - void fix_interpolants(std::vector &interpolants){ - } -}; - -#endif - - - -template -struct killme { - T *p; - killme(){p = nullptr;} - void set(T *_p) {p = _p;} - ~killme(){ - if(p) - delete p; - } -}; - - -class iz3interp : public iz3base { -public: - - killme sp_killer; - killme tr_killer; - - bool is_linear(std::vector &parents){ - for(int i = 0; i < ((int)parents.size())-1; i++) - if(parents[i] != i+1) - return false; - return true; - } - - void test_secondary(const std::vector &cnsts, - const std::vector &parents, - std::vector &interps - ){ - throw iz3_exception("secondary interpolating prover not supported"); - } - - void proof_to_interpolant(z3pf proof, - const std::vector > &cnsts, - const std::vector &parents, - std::vector &interps, - const std::vector &theory, - interpolation_options_struct *options = nullptr - ){ -#if 0 - test_secondary(cnsts,parents,interps); - return; -#endif - - profiling::timer_start("Interpolation prep"); - - // get rid of frames not used in proof - - std::vector > cnsts_vec; - std::vector parents_vec; - frame_reducer fr(*this); - fr.get_frames(cnsts,parents,cnsts_vec,parents_vec,proof); - - int num = cnsts_vec.size(); - std::vector interps_vec(num-1); - - // if this is really a sequence problem, we can make it easier - if(is_linear(parents_vec)) - parents_vec.clear(); - - // secondary prover no longer supported - iz3secondary *sp = nullptr; - -#define BINARY_INTERPOLATION -#ifndef BINARY_INTERPOLATION - // create a translator - iz3translation *tr = iz3translation::create(*this,sp,cnsts_vec,parents_vec,theory); - tr_killer.set(tr); - - // set the translation options, if needed - if(options) - for(hash_map::iterator it = options->map.begin(), en = options->map.end(); it != en; ++it) - tr->set_option(it->first, it->second); - - // create a proof object to hold the translation - iz3proof pf(tr); - - profiling::timer_stop("Interpolation prep"); - - // translate into an interpolatable proof - profiling::timer_start("Proof translation"); - try { - tr->translate(proof,pf); - } - catch (const char *msg) { - throw interpolation_failure(msg); - } - catch (const iz3translation::unsupported & ex) { - TRACE("iz3", tout << "unsupported " << "\n";); - throw interpolation_error(); - } - catch (const iz3proof::proof_error & ex) { - TRACE("iz3", tout << "proof error " << "\n";); - throw interpolation_error(); - } - profiling::timer_stop("Proof translation"); - - // translate the proof into interpolants - profiling::timer_start("Proof interpolation"); - for(int i = 0; i < num-1; i++){ - interps_vec[i] = pf.interpolate(tr->range_downward(i),tr->weak_mode()); - interps_vec[i] = tr->quantify(interps_vec[i],tr->range_downward(i)); - } - profiling::timer_stop("Proof interpolation"); -#else - iz3base the_base(*this,cnsts_vec,parents_vec,theory); - - profiling::timer_stop("Interpolation prep"); - - for(int i = 0; i < num-1; i++){ - range rng = the_base.range_downward(i); - std::vector > cnsts_vec_vec(2); - for(unsigned j = 0; j < cnsts_vec.size(); j++){ - bool is_A = the_base.in_range(j,rng); - for(unsigned k = 0; k < cnsts_vec[j].size(); k++) - cnsts_vec_vec[is_A ? 0 : 1].push_back(cnsts_vec[j][k]); - } - - killme tr_killer_i; - iz3translation *tr = iz3translation::create(*this,sp,cnsts_vec_vec,std::vector(),theory); - tr_killer_i.set(tr); - - // set the translation options, if needed - if(options) - for(hash_map::iterator it = options->map.begin(), en = options->map.end(); it != en; ++it) - tr->set_option(it->first, it->second); - - // create a proof object to hold the translation - iz3proof pf(tr); - - // translate into an interpolatable proof - profiling::timer_start("Proof translation"); - try { - tr->translate(proof,pf); - } - catch (const char *msg) { - throw interpolation_failure(msg); - } - catch (const iz3translation::unsupported & ex) { - TRACE("iz3", tout << "unsupported " << "\n";); - throw interpolation_error(); - } - catch (const iz3proof::proof_error &) { - TRACE("iz3", tout << "proof error\n";); - throw interpolation_error(); - } - profiling::timer_stop("Proof translation"); - - // translate the proof into interpolants - profiling::timer_start("Proof interpolation"); - interps_vec[i] = pf.interpolate(tr->range_downward(0),tr->weak_mode()); - interps_vec[i] = tr->quantify(interps_vec[i],tr->range_downward(0)); - profiling::timer_stop("Proof interpolation"); - } -#endif - // put back in the removed frames - fr.fix_interpolants(interps_vec); - - interps = interps_vec; - - } - - - void proof_to_interpolant(z3pf proof, - std::vector &cnsts, - const std::vector &parents, - std::vector &interps, - const std::vector &theory, - interpolation_options_struct *options = nullptr - ){ - std::vector > cnsts_vec(cnsts.size()); - for(unsigned i = 0; i < cnsts.size(); i++) - cnsts_vec[i].push_back(cnsts[i]); - proof_to_interpolant(proof,cnsts_vec,parents,interps,theory,options); - } - - // same as above, but represents the tree using an ast - - void proof_to_interpolant(const z3pf &proof, - const std::vector &_cnsts, - const ast &tree, - std::vector &interps, - interpolation_options_struct *options = nullptr - ){ - std::vector pos_map; - - // convert to the parents vector representation - - to_parents_vec_representation(_cnsts, tree, cnsts, parents, theory, pos_map); - - //use the parents vector representation to compute interpolant - proof_to_interpolant(proof,cnsts,parents,interps,theory,options); - - // get the interps for the tree positions - std::vector _interps = interps; - interps.resize(pos_map.size()); - for(unsigned i = 0; i < pos_map.size(); i++){ - unsigned j = pos_map[i]; - interps[i] = j < _interps.size() ? _interps[j] : mk_false(); - } - } - - bool has_interp(hash_map &memo, const ast &t){ - if(memo.find(t) != memo.end()) - return memo[t]; - bool res = false; - if(op(t) == Interp) - res = true; - else if(op(t) == And){ - int nargs = num_args(t); - for(int i = 0; i < nargs; i++) - res |= has_interp(memo, arg(t,i)); - } - memo[t] = res; - return res; - } - - void collect_conjuncts(std::vector &cnsts, hash_map &memo, const ast &t){ - if(!has_interp(memo,t)) - cnsts.push_back(t); - else { - int nargs = num_args(t); - for(int i = 0; i < nargs; i++) - collect_conjuncts(cnsts, memo, arg(t,i)); - } - } - - void assert_conjuncts(solver &s, std::vector &cnsts, const ast &t){ - hash_map memo; - collect_conjuncts(cnsts,memo,t); - for(unsigned i = 0; i < cnsts.size(); i++) - s.assert_expr(to_expr(cnsts[i].raw())); - } - - void get_proof_assumptions(z3pf proof, std::vector &cnsts, hash_set &memo){ - if(memo.find(proof) != memo.end())return; - memo.insert(proof); - pfrule dk = pr(proof); - if(dk == PR_ASSERTED) - cnsts.push_back(conc(proof)); - else { - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - z3pf arg = prem(proof,i); - get_proof_assumptions(arg,cnsts,memo); - } - } - } - - iz3interp(ast_manager &_m_manager) - : iz3base(_m_manager) {} -}; - - - -void iz3interpolate(ast_manager &_m_manager, - ast *proof, - const ptr_vector &cnsts, - const ::vector &parents, - ptr_vector &interps, - const ptr_vector &theory, - interpolation_options_struct * options) -{ - iz3interp itp(_m_manager); - if(options) - options->apply(itp); - std::vector _cnsts(cnsts.size()); - std::vector _parents(parents.size()); - std::vector _interps; - std::vector _theory(theory.size()); - for(unsigned i = 0; i < cnsts.size(); i++) - _cnsts[i] = itp.cook(cnsts[i]); - for(unsigned i = 0; i < parents.size(); i++) - _parents[i] = parents[i]; - for(unsigned i = 0; i < theory.size(); i++) - _theory[i] = itp.cook(theory[i]); - iz3mgr::ast _proof = itp.cook(proof); - itp.proof_to_interpolant(_proof,_cnsts,_parents,_interps,_theory,options); - interps.resize(_interps.size()); - for(unsigned i = 0; i < interps.size(); i++) - interps[i] = itp.uncook(_interps[i]); -} - -void iz3interpolate(ast_manager &_m_manager, - ast *proof, - const ::vector > &cnsts, - const ::vector &parents, - ptr_vector &interps, - const ptr_vector &theory, - interpolation_options_struct * options) -{ - iz3interp itp(_m_manager); - if(options) - options->apply(itp); - std::vector > _cnsts(cnsts.size()); - std::vector _parents(parents.size()); - std::vector _interps; - std::vector _theory(theory.size()); - for(unsigned i = 0; i < cnsts.size(); i++) - for(unsigned j = 0; j < cnsts[i].size(); j++) - _cnsts[i].push_back(itp.cook(cnsts[i][j])); - for(unsigned i = 0; i < parents.size(); i++) - _parents[i] = parents[i]; - for(unsigned i = 0; i < theory.size(); i++) - _theory[i] = itp.cook(theory[i]); - iz3mgr::ast _proof = itp.cook(proof); - itp.proof_to_interpolant(_proof,_cnsts,_parents,_interps,_theory,options); - interps.resize(_interps.size()); - for(unsigned i = 0; i < interps.size(); i++) - interps[i] = itp.uncook(_interps[i]); -} - -void iz3interpolate(ast_manager &_m_manager, - ast *proof, - const ptr_vector &cnsts, - ast *tree, - ptr_vector &interps, - interpolation_options_struct * options) -{ - iz3interp itp(_m_manager); - if(options) - options->apply(itp); - std::vector _cnsts(cnsts.size()); - std::vector _interps; - for(unsigned i = 0; i < cnsts.size(); i++) - _cnsts[i] = itp.cook(cnsts[i]); - iz3mgr::ast _proof = itp.cook(proof); - iz3mgr::ast _tree = itp.cook(tree); - - // if consts isn't provided, we can reconstruct it - if(_cnsts.empty()){ - hash_set memo; - itp.get_proof_assumptions(_proof,_cnsts,memo); - } - - itp.proof_to_interpolant(_proof,_cnsts,_tree,_interps,options); - interps.resize(_interps.size()); - for(unsigned i = 0; i < interps.size(); i++) - interps[i] = itp.uncook(_interps[i]); -} - -lbool iz3interpolate(ast_manager &_m_manager, - solver &s, - ast *tree, - ptr_vector &cnsts, - ptr_vector &interps, - model_ref &m, - interpolation_options_struct * options) -{ - iz3interp itp(_m_manager); - if(options) - options->apply(itp); - iz3mgr::ast _tree = itp.cook(tree); - std::vector _cnsts; - itp.assert_conjuncts(s,_cnsts,_tree); - profiling::timer_start("solving"); - lbool res = s.check_sat(0,nullptr); - profiling::timer_stop("solving"); - if(res == l_false){ - ast *proof = s.get_proof(); - iz3mgr::ast _proof = itp.cook(proof); - std::vector _interps; - itp.proof_to_interpolant(_proof,_cnsts,_tree,_interps,options); - interps.resize(_interps.size()); - for(unsigned i = 0; i < interps.size(); i++) - interps[i] = itp.uncook(_interps[i]); - } - else if(m){ - s.get_model(m); - } - cnsts.resize(_cnsts.size()); - for(unsigned i = 0; i < cnsts.size(); i++) - cnsts[i] = itp.uncook(_cnsts[i]); - return res; -} - - - -void interpolation_options_struct::apply(iz3base &b){ - for(stl_ext::hash_map::iterator it = map.begin(), en = map.end(); - it != en; - ++it) - b.set_option((*it).first,(*it).second); -} - -// On linux and mac, unlimit stack space so we get recursion - -#if defined(_WINDOWS) || defined(_CYGWIN) || defined(_MINGW) - -#else - -#include -#include - -class iz3stack_unlimiter { -public: - iz3stack_unlimiter() { - struct rlimit rl = {RLIM_INFINITY, RLIM_INFINITY}; - setrlimit(RLIMIT_STACK, &rl); - // nothing to be done if above fails - } -}; - -// initializing this will unlimit stack - -iz3stack_unlimiter the_iz3stack_unlimiter; - -#endif diff --git a/src/interp/iz3interp.h b/src/interp/iz3interp.h deleted file mode 100644 index 909703bed..000000000 --- a/src/interp/iz3interp.h +++ /dev/null @@ -1,123 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3interp.h - - Abstract: - - Interpolation based on proof translation. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifndef IZ3_INTERP_H -#define IZ3_INTERP_H - -#include "interp/iz3hash.h" -#include "interp/iz3exception.h" -#include "solver/solver.h" - -class iz3base; - -struct interpolation_options_struct { - stl_ext::hash_map map; -public: - void set(const std::string &name, const std::string &value){ - map[name] = value; - } - void apply(iz3base &b); -}; - -/** This object is thrown if a tree interpolation problem is mal-formed */ -struct iz3_bad_tree: public iz3_exception { - iz3_bad_tree(): iz3_exception("iz3_bad_tree") {} -}; - -/** This object is thrown when iz3 fails due to an incompleteness in - the secondary solver. */ -struct iz3_incompleteness: public iz3_exception { - iz3_incompleteness(): iz3_exception("iz3_incompleteness") {} -}; - -// This is thrown if there is some bug in the -// interpolation procedure -class interpolation_failure : public default_exception { - public: - interpolation_failure(const char *msg) - : default_exception(msg) - { - } -}; - -// This is thrown if we cannot derive an interpolant from a proof -// because it contains unsupported theories or if the proof contains -// errors -class interpolation_error : public default_exception { - public: - interpolation_error() - : default_exception("theory not supported by interpolation or bad proof" ) - { - } -}; - -typedef interpolation_options_struct *interpolation_options; - -/* Compute an interpolant from a proof. This version uses the parents vector - representation, for compatibility with the old API. */ - -void iz3interpolate(ast_manager &_m_manager, - ast *proof, - const ptr_vector &cnsts, - const ::vector &parents, - ptr_vector &interps, - const ptr_vector &theory, - interpolation_options_struct * options = nullptr); - -/* Same as above, but each constraint is a vector of formulas. */ - -void iz3interpolate(ast_manager &_m_manager, - ast *proof, - const vector > &cnsts, - const ::vector &parents, - ptr_vector &interps, - const ptr_vector &theory, - interpolation_options_struct * options = nullptr); - -/* Compute an interpolant from a proof. This version uses the ast - representation, for compatibility with the new API. Here, cnsts is - a vector of all the assertions in the proof. This can be - over-approximated by the set of all assertions in the - solver. However, if it is empty it will be reconstructed from the - proof, so it can be considered a hint. */ - -void iz3interpolate(ast_manager &_m_manager, - ast *proof, - const ptr_vector &cnsts, - ast *tree, - ptr_vector &interps, - interpolation_options_struct * options); - - -/* Compute an interpolant from an ast representing an interpolation - problem, if unsat, else return a model (if enabled). Uses the - given solver to produce the proof/model. Also returns a vector - of the constraints in the problem, helpful for checking correctness. -*/ - -lbool iz3interpolate(ast_manager &_m_manager, - solver &s, - ast *tree, - ptr_vector &cnsts, - ptr_vector &interps, - model_ref &m, - interpolation_options_struct * options); - - -#endif diff --git a/src/interp/iz3mgr.cpp b/src/interp/iz3mgr.cpp deleted file mode 100644 index bb37d7f48..000000000 --- a/src/interp/iz3mgr.cpp +++ /dev/null @@ -1,969 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3mgr.cpp - - Abstract: - - A wrapper around an ast manager, providing convenience methods. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#pragma warning(disable:4101) -#pragma warning(disable:4805) -#pragma warning(disable:4800) -#endif - -#include "interp/iz3mgr.h" - -#include -#include -#include -#include -#include - -#include "ast/expr_abstract.h" -#include "util/params.h" -#include "ast/used_vars.h" - - -using namespace stl_ext; - - -std::ostream &operator <<(std::ostream &s, const iz3mgr::ast &a){ - return s; -} - - -iz3mgr::ast iz3mgr::make_var(const std::string &name, type ty){ - symbol s = symbol(name.c_str()); - return cook(m().mk_const(m().mk_const_decl(s, ty))); -} - -iz3mgr::ast iz3mgr::make(opr op, int n, raw_ast **args){ - switch(op) { - case True: return mki(m_basic_fid,OP_TRUE,n,args); - case False: return mki(m_basic_fid,OP_FALSE,n,args); - case Equal: return mki(m_basic_fid,OP_EQ,n,args); - case Distinct: return mki(m_basic_fid,OP_DISTINCT,n,args); - case Ite: return mki(m_basic_fid,OP_ITE,n,args); - case And: return mki(m_basic_fid,OP_AND,n,args); - case Or: return mki(m_basic_fid,OP_OR,n,args); - case Iff: return mki(m_basic_fid,OP_IFF,n,args); - case Xor: return mki(m_basic_fid,OP_XOR,n,args); - case Not: return mki(m_basic_fid,OP_NOT,n,args); - case Implies: return mki(m_basic_fid,OP_IMPLIES,n,args); - case Oeq: return mki(m_basic_fid,OP_OEQ,n,args); - case Interp: return mki(m_basic_fid,OP_INTERP,n,args); - case Leq: return mki(m_arith_fid,OP_LE,n,args); - case Geq: return mki(m_arith_fid,OP_GE,n,args); - case Lt: return mki(m_arith_fid,OP_LT,n,args); - case Gt: return mki(m_arith_fid,OP_GT,n,args); - case Plus: return mki(m_arith_fid,OP_ADD,n,args); - case Sub: return mki(m_arith_fid,OP_SUB,n,args); - case Uminus: return mki(m_arith_fid,OP_UMINUS,n,args); - case Times: return mki(m_arith_fid,OP_MUL,n,args); - case Div: return mki(m_arith_fid,OP_DIV,n,args); - case Idiv: return mki(m_arith_fid,OP_IDIV,n,args); - case Rem: return mki(m_arith_fid,OP_REM,n,args); - case Mod: return mki(m_arith_fid,OP_MOD,n,args); - case Power: return mki(m_arith_fid,OP_POWER,n,args); - case ToReal: return mki(m_arith_fid,OP_TO_REAL,n,args); - case ToInt: return mki(m_arith_fid,OP_TO_INT,n,args); - case IsInt: return mki(m_arith_fid,OP_IS_INT,n,args); - case Store: return mki(m_array_fid,OP_STORE,n,args); - case Select: return mki(m_array_fid,OP_SELECT,n,args); - case ConstArray: return mki(m_array_fid,OP_CONST_ARRAY,n,args); - case ArrayDefault: return mki(m_array_fid,OP_ARRAY_DEFAULT,n,args); - case ArrayMap: return mki(m_array_fid,OP_ARRAY_MAP,n,args); - case SetUnion: return mki(m_array_fid,OP_SET_UNION,n,args); - case SetIntersect: return mki(m_array_fid,OP_SET_INTERSECT,n,args); - case SetDifference: return mki(m_array_fid,OP_SET_DIFFERENCE,n,args); - case SetComplement: return mki(m_array_fid,OP_SET_COMPLEMENT,n,args); - case SetSubSet: return mki(m_array_fid,OP_SET_SUBSET,n,args); - case AsArray: return mki(m_array_fid,OP_AS_ARRAY,n,args); - default: - assert(0); - return ast(); - } -} - -iz3mgr::ast iz3mgr::mki(family_id fid, decl_kind dk, int n, raw_ast **args){ - return cook(m().mk_app(fid, dk, 0, nullptr, n, (expr **)args)); -} - -iz3mgr::ast iz3mgr::make(opr op, const std::vector &args){ - static std::vector a(10); - if(a.size() < args.size()) - a.resize(args.size()); - for(unsigned i = 0; i < args.size(); i++) - a[i] = args[i].raw(); - return make(op,args.size(), args.size() ? &a[0] : nullptr); -} - -iz3mgr::ast iz3mgr::make(opr op){ - return make(op,0,nullptr); -} - -iz3mgr::ast iz3mgr::make(opr op, const ast &arg0){ - raw_ast *a = arg0.raw(); - return make(op,1,&a); -} - -iz3mgr::ast iz3mgr::make(opr op, const ast &arg0, const ast &arg1){ - raw_ast *args[2]; - args[0] = arg0.raw(); - args[1] = arg1.raw(); - return make(op,2,args); -} - -iz3mgr::ast iz3mgr::make(opr op, const ast &arg0, const ast &arg1, const ast &arg2){ - raw_ast *args[3]; - args[0] = arg0.raw(); - args[1] = arg1.raw(); - args[2] = arg2.raw(); - return make(op,3,args); -} - -iz3mgr::ast iz3mgr::make(symb sym, int n, raw_ast **args){ - return cook(m().mk_app(sym, n, (expr **) args)); -} - -iz3mgr::ast iz3mgr::make(symb sym, const std::vector &args){ - static std::vector a(10); - if(a.size() < args.size()) - a.resize(args.size()); - for(unsigned i = 0; i < args.size(); i++) - a[i] = args[i].raw(); - return make(sym,args.size(), args.size() ? &a[0] : nullptr); -} - -iz3mgr::ast iz3mgr::make(symb sym){ - return make(sym,0,nullptr); -} - -iz3mgr::ast iz3mgr::make(symb sym, const ast &arg0){ - raw_ast *a = arg0.raw(); - return make(sym,1,&a); -} - -iz3mgr::ast iz3mgr::make(symb sym, const ast &arg0, const ast &arg1){ - raw_ast *args[2]; - args[0] = arg0.raw(); - args[1] = arg1.raw(); - return make(sym,2,args); -} - -iz3mgr::ast iz3mgr::make(symb sym, const ast &arg0, const ast &arg1, const ast &arg2){ - raw_ast *args[3]; - args[0] = arg0.raw(); - args[1] = arg1.raw(); - args[2] = arg2.raw(); - return make(sym,3,args); -} - -iz3mgr::ast iz3mgr::make_quant(opr op, const std::vector &bvs, ast &body){ - if(bvs.size() == 0) return body; - std::vector foo(bvs.size()); - - - std::vector names; - std::vector types; - std::vector bound_asts; - unsigned num_bound = bvs.size(); - - for (unsigned i = 0; i < num_bound; ++i) { - app* a = to_app(bvs[i].raw()); - symbol s(to_app(a)->get_decl()->get_name()); - names.push_back(s); - types.push_back(m().get_sort(a)); - bound_asts.push_back(a); - } - expr_ref abs_body(m()); - expr_abstract(m(), 0, num_bound, &bound_asts[0], to_expr(body.raw()), abs_body); - expr_ref result(m()); - result = m().mk_quantifier( - op == Forall, - names.size(), &types[0], &names[0], abs_body.get(), - 0, - symbol("itp"), - symbol(), - 0, nullptr, - 0, nullptr - ); - return cook(result.get()); -} - -// FIXME replace this with existing Z3 functionality - -iz3mgr::ast iz3mgr::clone(const ast &t, const std::vector &_args){ - if(_args.size() == 0) - return t; - - ast_manager& m = m_manager; - expr* a = to_expr(t.raw()); - static std::vector rargs(10); - if(rargs.size() < _args.size()) - rargs.resize(_args.size()); - for(unsigned i = 0; i < _args.size(); i++) - rargs[i] = _args[i].raw(); - expr* const* args = (expr **)&rargs[0]; - switch(a->get_kind()) { - case AST_APP: { - app* e = to_app(a); - if (e->get_num_args() != _args.size()) { - assert(0); - } - else { - a = m.mk_app(e->get_decl(), _args.size(), args); - } - break; - } - case AST_QUANTIFIER: { - if (_args.size() != 1) { - assert(0); - } - else { - a = m.update_quantifier(to_quantifier(a), args[0]); - } - break; - } - default: - break; - } - return cook(a); -} - - -void iz3mgr::show(ast t){ - if(t.null()){ - std::cout << "(null)" << std::endl; - } - params_ref p; - p.set_bool("flat_assoc",false); - std::cout << mk_pp(t.raw(), m(), p) << std::endl; -} - -void iz3mgr::show_symb(symb s){ - std::cout << mk_pp(s, m()) << std::endl; -} - -void iz3mgr::print_expr(std::ostream &s, const ast &e){ - params_ref p; - p.set_bool("flat_assoc",false); - s << mk_pp(e.raw(), m(), p); -} - - -void iz3mgr::print_clause(std::ostream &s, std::vector &cls){ - s << "("; - for(unsigned i = 0; i < cls.size(); i++){ - if(i > 0) s << ","; - print_expr(s,cls[i]); - } - s << ")"; -} - -void iz3mgr::show_clause(std::vector &cls){ - print_clause(std::cout,cls); - std::cout << std::endl; -} - -void iz3mgr::print_lit(ast lit){ - ast abslit = is_not(lit) ? arg(lit,0) : lit; - int f = op(abslit); - if(f == And || f == Or || f == Iff){ - if(is_not(lit)) std::cout << "~"; - std::cout << "[" << abslit << "]"; - } - else - std::cout << lit; -} - - -static int pretty_cols = 79; -static int pretty_indent_chars = 2; - -static int pretty_find_delim(const std::string &s, int pos){ - int level = 0; - int end = s.size(); - for(; pos < end; pos++){ - int ch = s[pos]; - if(ch == '(')level++; - if(ch == ')')level--; - if(level < 0 || (level == 0 && ch == ','))break; - } - return pos; -} - -static void pretty_newline(std::ostream &f, int indent){ - f << std::endl; - for(int i = 0; i < indent; i++) - f << " "; -} - -void iz3mgr::pretty_print(std::ostream &f, const std::string &s){ - int cur_indent = 0; - int indent = 0; - int col = 0; - int pos = 0; - while(pos < (int)s.size()){ - int delim = pretty_find_delim(s,pos); - if(s[pos] != ')' && s[pos] != ',' && cur_indent > indent){ - pretty_newline(f,indent); - cur_indent = indent; - col = indent; - continue; - } - if (col + delim - pos > pretty_cols) { - if (col > indent) { - pretty_newline(f,indent); - cur_indent = indent; - col = indent; - continue; - } - int paren = s.find('(',pos); - if(paren != (int)std::string::npos){ - int chars = paren - pos + 1; - f << s.substr(pos,chars); - indent += pretty_indent_chars; - if(col) pretty_newline(f,indent); - cur_indent = indent; - pos += chars; - col = indent; - continue; - } - } - int chars = delim - pos + 1; - f << s.substr(pos,chars); - pos += chars; - col += chars; - if(s[delim] == ')') - indent -= pretty_indent_chars; - } -} - - -iz3mgr::opr iz3mgr::op(const ast &t){ - ast_kind dk = t.raw()->get_kind(); - switch(dk){ - case AST_APP: { - expr * e = to_expr(t.raw()); - func_decl *d = to_app(t.raw())->get_decl(); - if (null_family_id == d->get_family_id()) - return Uninterpreted; - // return (opr)d->get_decl_kind(); - if (m_basic_fid == d->get_family_id()) { - switch(d->get_decl_kind()) { - case OP_TRUE: return True; - case OP_FALSE: return False; - case OP_EQ: return Equal; - case OP_DISTINCT: return Distinct; - case OP_ITE: return Ite; - case OP_AND: return And; - case OP_OR: return Or; - case OP_IFF: return Iff; - case OP_XOR: return Xor; - case OP_NOT: return Not; - case OP_IMPLIES: return Implies; - case OP_OEQ: return Oeq; - case OP_INTERP: return Interp; - default: - return Other; - } - } - if (m_arith_fid == d->get_family_id()) { - switch(d->get_decl_kind()) { - case OP_LE: return Leq; - case OP_GE: return Geq; - case OP_LT: return Lt; - case OP_GT: return Gt; - case OP_ADD: return Plus; - case OP_SUB: return Sub; - case OP_UMINUS: return Uminus; - case OP_MUL: return Times; - case OP_DIV: return Div; - case OP_IDIV: return Idiv; - case OP_REM: return Rem; - case OP_MOD: return Mod; - case OP_POWER: return Power; - case OP_TO_REAL: return ToReal; - case OP_TO_INT: return ToInt; - case OP_IS_INT: return IsInt; - default: - if (m().is_unique_value(e)) - return Numeral; - return Other; - } - } - if (m_array_fid == d->get_family_id()) { - switch(d->get_decl_kind()) { - case OP_STORE: return Store; - case OP_SELECT: return Select; - case OP_CONST_ARRAY: return ConstArray; - case OP_ARRAY_DEFAULT: return ArrayDefault; - case OP_ARRAY_MAP: return ArrayMap; - case OP_SET_UNION: return SetUnion; - case OP_SET_INTERSECT: return SetIntersect; - case OP_SET_DIFFERENCE: return SetDifference; - case OP_SET_COMPLEMENT: return SetComplement; - case OP_SET_SUBSET: return SetSubSet; - case OP_AS_ARRAY: return AsArray; - default: - return Other; - } - } - - return Other; - } - - - case AST_QUANTIFIER: - return to_quantifier(t.raw())->is_forall() ? Forall : Exists; - case AST_VAR: - return Variable; - default:; - } - return Other; -} - - -iz3mgr::pfrule iz3mgr::pr(const ast &t){ - func_decl *d = to_app(t.raw())->get_decl(); - assert(m_basic_fid == d->get_family_id()); - return d->get_decl_kind(); -} - -void iz3mgr::print_sat_problem(std::ostream &out, const ast &t){ - ast_smt_pp pp(m()); - pp.set_simplify_implies(false); - pp.display_smt2(out, to_expr(t.raw())); -} - -iz3mgr::ast iz3mgr::z3_simplify(const ast &e){ - ::expr * a = to_expr(e.raw()); - params_ref p; - th_rewriter m_rw(m(), p); - expr_ref result(m()); - m_rw(a, result); - return cook(result); -} - -iz3mgr::ast iz3mgr::z3_really_simplify(const ast &e){ - ::expr * a = to_expr(e.raw()); - params_ref simp_params; - simp_params.set_bool(":som",true); - simp_params.set_bool(":sort-sums",true); - th_rewriter m_rw(m(), simp_params); - expr_ref result(m()); - m_rw(a, result); - return cook(result); -} - - -#if 0 -static rational lcm(const rational &x, const rational &y){ - int a = x.numerator(); - int b = y.numerator(); - return rational(a * b / gcd(a, b)); -} -#endif - -static rational extract_lcd(std::vector &res){ - if(res.size() == 0) return rational(1); // shouldn't happen - rational lcd = denominator(res[0]); - for(unsigned i = 1; i < res.size(); i++) - lcd = lcm(lcd,denominator(res[i])); - for(unsigned i = 0; i < res.size(); i++) - res[i] *= lcd; - return lcd; -} - -void iz3mgr::get_farkas_coeffs(const ast &proof, std::vector& coeffs){ - std::vector rats; - get_farkas_coeffs(proof,rats); - coeffs.resize(rats.size()); - for(unsigned i = 0; i < rats.size(); i++){ - class sort *is = m().mk_sort(m_arith_fid, INT_SORT); - ast coeff = cook(m_arith_util.mk_numeral(rats[i],is)); - coeffs[i] = coeff; - } -} - -static void abs_rat(std::vector &rats){ - // check that they are all non-neg -- if neg, take abs val and warn! - for(unsigned i = 0; i < rats.size(); i++) - if(rats[i].is_neg()){ - // std::cout << "negative Farkas coeff!\n"; - rats[i] = -rats[i]; - } -} - -bool iz3mgr::is_farkas_coefficient_negative(const ast &proof, int n){ - rational r; - symb s = sym(proof); - bool ok = s->get_parameter(n+2).is_rational(r); - if(!ok) - throw iz3_exception("Bad Farkas coefficient"); - return r.is_neg(); -} - -void iz3mgr::get_farkas_coeffs(const ast &proof, std::vector& rats){ - symb s = sym(proof); - int numps = s->get_num_parameters(); - rats.resize(numps-2); -#if 0 - if(num_prems(proof) < numps-2){ - std::cout << "bad farkas rule: " << num_prems(proof) << " premises should be " << numps-2 << "\n"; - } -#endif - for(int i = 2; i < numps; i++){ - rational r; - bool ok = s->get_parameter(i).is_rational(r); - if(!ok) - throw iz3_exception("Bad Farkas coefficient"); -#if 0 - { - ast con = conc(prem(proof,i-2)); - ast temp = make_real(r); // for debugging - opr o = is_not(con) ? op(arg(con,0)) : op(con); - if(is_not(con) ? (o == Leq || o == Lt) : (o == Geq || o == Gt)) - r = -r; - } -#endif - rats[i-2] = r; - } -#if 0 - if(rats.size() != 0 && rats[0].is_neg()){ - for(unsigned i = 0; i < rats.size(); i++){ - assert(rats[i].is_neg()); - rats[i] = -rats[i]; - } - } -#endif - abs_rat(rats); - extract_lcd(rats); -} - -void iz3mgr::get_broken_gcd_test_coeffs(const ast &proof, std::vector& rats){ - symb s = sym(proof); - int numps = s->get_num_parameters(); - rats.resize(numps-2); - for(int i = 2; i < numps; i++){ - rational r; - bool ok = s->get_parameter(i).is_rational(r); - if(!ok) - throw "Bad Farkas coefficient"; - rats[i-2] = r; - } - extract_lcd(rats); -} - -void iz3mgr::get_assign_bounds_coeffs(const ast &proof, std::vector& coeffs){ - std::vector rats; - get_assign_bounds_coeffs(proof,rats); - coeffs.resize(rats.size()); - for(unsigned i = 0; i < rats.size(); i++){ - coeffs[i] = make_int(rats[i]); - } -} - -void iz3mgr::get_assign_bounds_coeffs(const ast &proof, std::vector& rats){ - symb s = sym(proof); - int numps = s->get_num_parameters(); - rats.resize(numps-1); - rats[0] = rational(1); - ast conseq = arg(conc(proof),0); - opr conseq_o = is_not(conseq) ? op(arg(conseq,0)) : op(conseq); - bool conseq_neg = is_not(conseq) ? (conseq_o == Leq || conseq_o == Lt) : (conseq_o == Geq || conseq_o == Gt); - for(int i = 2; i < numps; i++){ - rational r; - bool ok = s->get_parameter(i).is_rational(r); - if(!ok) - throw iz3_exception("Bad Farkas coefficient"); - { - ast con = arg(conc(proof),i-1); - ast temp = make_real(r); // for debugging - opr o = is_not(con) ? op(arg(con,0)) : op(con); - if(is_not(con) ? (o == Leq || o == Lt) : (o == Geq || o == Gt)) - r = -r; - if(conseq_neg) - r = -r; - } - rats[i-1] = r; - } -#if 0 - if(rats[1].is_neg()){ // work around bug -- if all coeffs negative, negate them - for(unsigned i = 1; i < rats.size(); i++){ - if(!rats[i].is_neg()) - throw iz3_exception("Bad Farkas coefficients"); - rats[i] = -rats[i]; - } - } -#endif - abs_rat(rats); - extract_lcd(rats); -} - -void iz3mgr::get_gomory_cut_coeffs(const ast &proof, std::vector& coeffs){ - std::vector rats; - get_gomory_cut_coeffs(proof,rats); - coeffs.resize(rats.size()); - for(unsigned i = 0; i < rats.size(); i++){ - coeffs[i] = make_int(rats[i]); - } -} - -void iz3mgr::get_gomory_cut_coeffs(const ast &proof, std::vector& rats){ - symb s = sym(proof); - int numps = s->get_num_parameters(); - rats.resize(numps-2); - for(int i = 2; i < numps; i++){ - rational r; - bool ok = s->get_parameter(i).is_rational(r); - if(!ok) - throw "Bad Farkas coefficient"; - rats[i-2] = r; - } - abs_rat(rats); - extract_lcd(rats); -} - -void iz3mgr::get_assign_bounds_rule_coeffs(const ast &proof, std::vector& coeffs){ - std::vector rats; - get_assign_bounds_rule_coeffs(proof,rats); - coeffs.resize(rats.size()); - for(unsigned i = 0; i < rats.size(); i++){ - coeffs[i] = make_int(rats[i]); - } -} - -void iz3mgr::get_assign_bounds_rule_coeffs(const ast &proof, std::vector& rats){ - symb s = sym(proof); - int numps = s->get_num_parameters(); - rats.resize(numps-1); - rats[0] = rational(1); - ast conseq = arg(conc(proof),0); - opr conseq_o = is_not(conseq) ? op(arg(conseq,0)) : op(conseq); - bool conseq_neg = is_not(conseq) ? (conseq_o == Leq || conseq_o == Lt) : (conseq_o == Geq || conseq_o == Gt); - for(int i = 2; i < numps; i++){ - rational r; - bool ok = s->get_parameter(i).is_rational(r); - if(!ok) - throw iz3_exception("Bad Farkas coefficient"); - { - ast con = conc(prem(proof,i-2)); - ast temp = make_real(r); // for debugging - opr o = is_not(con) ? op(arg(con,0)) : op(con); - if(is_not(con) ? (o == Leq || o == Lt) : (o == Geq || o == Gt)) - r = -r; - if(conseq_neg) - r = -r; - } - rats[i-1] = r; - } -#if 0 - if(rats[1].is_neg()){ // work around bug -- if all coeffs negative, negate them - for(unsigned i = 1; i < rats.size(); i++){ - if(!rats[i].is_neg()) - throw iz3_exception("Bad Farkas coefficients"); - rats[i] = -rats[i]; - } - } -#endif - abs_rat(rats); - extract_lcd(rats); -} - -/** Set P to P + cQ, where P and Q are linear inequalities. Assumes P is 0 <= y or 0 < y. */ - -void iz3mgr::linear_comb(ast &P, const ast &c, const ast &Q, bool round_off){ - ast Qrhs; - bool qstrict = false; - if(is_not(Q)){ - ast nQ = arg(Q,0); - switch(op(nQ)){ - case Gt: - Qrhs = make(Sub,arg(nQ,1),arg(nQ,0)); - break; - case Lt: - Qrhs = make(Sub,arg(nQ,0),arg(nQ,1)); - break; - case Geq: - Qrhs = make(Sub,arg(nQ,1),arg(nQ,0)); - qstrict = true; - break; - case Leq: - Qrhs = make(Sub,arg(nQ,0),arg(nQ,1)); - qstrict = true; - break; - default: - throw iz3_exception("not an inequality"); - } - } - else { - switch(op(Q)){ - case Leq: - Qrhs = make(Sub,arg(Q,1),arg(Q,0)); - break; - case Geq: - Qrhs = make(Sub,arg(Q,0),arg(Q,1)); - break; - case Lt: - Qrhs = make(Sub,arg(Q,1),arg(Q,0)); - qstrict = true; - break; - case Gt: - Qrhs = make(Sub,arg(Q,0),arg(Q,1)); - qstrict = true; - break; - default: - throw iz3_exception("not an inequality"); - } - } - bool pstrict = op(P) == Lt; - if (round_off && get_type(Qrhs) != int_type()) - round_off = false; - if(qstrict && round_off && (pstrict || !(c == make_int(rational(1))))){ - Qrhs = make(Sub,Qrhs,make_int(rational(1))); - qstrict = false; - } - Qrhs = make(Times,c,Qrhs); - bool strict = pstrict || qstrict; - if(strict) - P = make(Lt,arg(P,0),make(Plus,arg(P,1),Qrhs)); - else - P = make(Leq,arg(P,0),make(Plus,arg(P,1),Qrhs)); -} - -iz3mgr::ast iz3mgr::sum_inequalities(const std::vector &coeffs, const std::vector &ineqs, bool round_off){ - ast zero = make_int("0"); - ast thing = make(Leq,zero,zero); - for(unsigned i = 0; i < ineqs.size(); i++){ - linear_comb(thing,coeffs[i],ineqs[i], round_off); - } - thing = simplify_ineq(thing); - return thing; -} - -void iz3mgr::mk_idiv(const ast& t, const rational &d, ast &whole, ast &frac){ - opr o = op(t); - if(o == Plus){ - int nargs = num_args(t); - for(int i = 0; i < nargs; i++) - mk_idiv(arg(t,i),d,whole,frac); - return; - } - else if(o == Times){ - rational coeff; - if(is_numeral(arg(t,0),coeff)){ - if(gcd(coeff,d) == d){ - whole = make(Plus,whole,make(Times,make_int(coeff/d),arg(t,1))); - return; - } - } - } - frac = make(Plus,frac,t); -} - -iz3mgr::ast iz3mgr::mk_idiv(const ast& q, const rational &d){ - ast t = z3_simplify(q); - if(d == rational(1)) - return t; - else { - ast whole = make_int("0"); - ast frac = whole; - mk_idiv(t,d,whole,frac); - return z3_simplify(make(Plus,whole,make(Idiv,z3_simplify(frac),make_int(d)))); - } -} - -iz3mgr::ast iz3mgr::mk_idiv(const ast& t, const ast &d){ - rational r; - if(is_numeral(d,r)) - return mk_idiv(t,r); - return make(Idiv,t,d); -} - - -// does variable occur in expression? -int iz3mgr::occurs_in1(stl_ext::hash_map &occurs_in_memo,ast var, ast e){ - std::pair foo(e,false); - std::pair::iterator,bool> bar = occurs_in_memo.insert(foo); - bool &res = bar.first->second; - if(bar.second){ - if(e == var) res = true; - int nargs = num_args(e); - for(int i = 0; i < nargs; i++) - res |= occurs_in1(occurs_in_memo,var,arg(e,i)); - } - return res; -} - -int iz3mgr::occurs_in(ast var, ast e){ - hash_map memo; - return occurs_in1(memo,var,e); -} - - -bool iz3mgr::solve_arith(const ast &v, const ast &x, const ast &y, ast &res){ - if(occurs_in(v,y)) - return false; - if(op(x) == Plus){ - int n = num_args(x); - for(int i = 0; i < n; i++){ - if(arg(x,i) == v){ - res = z3_simplify(make(Sub, y, make(Sub, x, v))); - return true; - } - } - } - return false; -} - -// find a controlling equality for a given variable v in a term -// a controlling equality is of the form v = t, which, being -// false would force the formula to have the specifid truth value -// returns t, or null if no such - -iz3mgr::ast iz3mgr::cont_eq(stl_ext::hash_set &cont_eq_memo, bool truth, ast v, ast e){ - if(is_not(e)) return cont_eq(cont_eq_memo, !truth,v,arg(e,0)); - if(cont_eq_memo.find(e) != cont_eq_memo.end()) - return ast(); - cont_eq_memo.insert(e); - if(!truth && op(e) == Equal){ - if(arg(e,0) == v && !occurs_in(v,arg(e,1))) return(arg(e,1)); - if(arg(e,1) == v && !occurs_in(v,arg(e,0))) return(arg(e,0)); - ast res; - if(solve_arith(v,arg(e,0),arg(e,1),res)) return res; - if(solve_arith(v,arg(e,1),arg(e,0),res)) return res; - } - if((!truth && op(e) == And) || (truth && op(e) == Or)){ - int nargs = num_args(e); - for(int i = 0; i < nargs; i++){ - ast res = cont_eq(cont_eq_memo, truth, v, arg(e,i)); - if(!res.null()) return res; - } - } - if(truth && op(e) == Implies){ - ast res = cont_eq(cont_eq_memo, !truth, v, arg(e,0)); - if(!res.null()) return res; - res = cont_eq(cont_eq_memo, truth, v, arg(e,1)); - if(!res.null()) return res; - } - return ast(); -} - -// substitute a term t for unbound occurrences of variable v in e - -iz3mgr::ast iz3mgr::subst(stl_ext::hash_map &subst_memo, ast var, ast t, ast e){ - if(e == var) return t; - std::pair foo(e,ast()); - std::pair::iterator,bool> bar = subst_memo.insert(foo); - ast &res = bar.first->second; - if(bar.second){ - int nargs = num_args(e); - std::vector args(nargs); - for(int i = 0; i < nargs; i++) - args[i] = subst(subst_memo,var,t,arg(e,i)); - opr f = op(e); - if(f == Equal && args[0] == args[1]) res = mk_true(); - else res = clone(e,args); - } - return res; -} - -iz3mgr::ast iz3mgr::subst(ast var, ast t, ast e){ - hash_map memo; - return subst(memo,var,t,e); -} - -iz3mgr::ast iz3mgr::subst(stl_ext::hash_map &subst_memo,ast e){ - std::pair foo(e,ast()); - std::pair::iterator,bool> bar = subst_memo.insert(foo); - ast &res = bar.first->second; - if(bar.second){ - int nargs = num_args(e); - std::vector args(nargs); - for(int i = 0; i < nargs; i++) - args[i] = subst(subst_memo,arg(e,i)); - opr f = op(e); - if(f == Equal && args[0] == args[1]) res = mk_true(); - else res = clone(e,args); - } - return res; -} - -// apply a quantifier to a formula, with some optimizations -// 1) bound variable does not occur -> no quantifier -// 2) bound variable must be equal to some term -> substitute - -iz3mgr::ast iz3mgr::apply_quant(opr quantifier, ast var, ast e){ - if((quantifier == Forall && op(e) == And) - || (quantifier == Exists && op(e) == Or)){ - int n = num_args(e); - std::vector args(n); - for(int i = 0; i < n; i++) - args[i] = apply_quant(quantifier,var,arg(e,i)); - return make(op(e),args); - } - if(!occurs_in(var,e))return e; - hash_set cont_eq_memo; - ast cterm = cont_eq(cont_eq_memo, quantifier == Forall, var, e); - if(!cterm.null()){ - return subst(var,cterm,e); - } - std::vector bvs; bvs.push_back(var); - return make_quant(quantifier,bvs,e); -} - -#if 0 -void iz3mgr::get_bound_substitutes(stl_ext::hash_map &memo, const ast &e, const ast &var, std::vector &substs){ - std::pair foo(e,false); - std::pair::iterator,bool> bar = memo.insert(foo); - if(bar.second){ - if(op(e) == - } - - } -#endif - -unsigned iz3mgr::num_free_variables(const ast &e){ - used_vars uv; - uv(to_expr(e.raw())); - return uv.get_num_vars(); -} - -iz3mgr::ast iz3mgr::close_universally (ast e){ - used_vars uv; - uv(to_expr(e.raw())); - std::vector bvs; - stl_ext::hash_map subst_memo; - for (unsigned i = 0; i < uv.get_max_found_var_idx_plus_1(); i++){ - if (uv.get(i)) { - std::ostringstream os; - os << "%%" << i; - ast c = make_var(os.str(),uv.get(i)); - ast v = cook(m().mk_var(i,uv.get(i))); - subst_memo[v] = c; - bvs.push_back(c); - } - } - e = subst(subst_memo,e); - for (unsigned i = 0; i < bvs.size(); i++) - e = apply_quant(Forall,bvs[i],e); - return e; -} diff --git a/src/interp/iz3mgr.h b/src/interp/iz3mgr.h deleted file mode 100644 index 49552f92f..000000000 --- a/src/interp/iz3mgr.h +++ /dev/null @@ -1,738 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3mgr.h - - Abstract: - - A wrapper around an ast manager, providing convenience methods. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifndef IZ3MGR_H -#define IZ3MGR_H - - -#include -#include -#include - -#include "interp/iz3hash.h" -#include "interp/iz3exception.h" - -#include "ast/well_sorted.h" -#include "ast/arith_decl_plugin.h" -#include "ast/bv_decl_plugin.h" -#include "ast/datatype_decl_plugin.h" -#include "ast/array_decl_plugin.h" -#include "ast/ast_translation.h" -#include "ast/ast_pp.h" -#include "ast/ast_ll_pp.h" -#include "ast/ast_smt_pp.h" -#include "ast/ast_smt2_pp.h" -#include "ast/rewriter/th_rewriter.h" -#include "ast/rewriter/var_subst.h" -#include "ast/expr_substitution.h" -#include "ast/pp.h" -#include "util/scoped_ctrl_c.h" -#include "util/cancel_eh.h" -#include "util/scoped_timer.h" - -/* A wrapper around an ast manager, providing convenience methods. */ - -/** Shorthands for some built-in operators. */ - - - -// rename this to keep it accessible, as we use ast for something else -typedef ast raw_ast; - -/** Wrapper around an ast pointer */ -class ast_i { -protected: - raw_ast *_ast; -public: - raw_ast * const &raw() const {return _ast;} - ast_i(raw_ast *a){_ast = a;} - - ast_i(){_ast = nullptr;} - bool eq(const ast_i &other) const { - return _ast == other._ast; - } - bool lt(const ast_i &other) const { - return _ast->get_id() < other._ast->get_id(); - } - friend bool operator==(const ast_i &x, const ast_i&y){ - return x.eq(y); - } - friend bool operator!=(const ast_i &x, const ast_i&y){ - return !x.eq(y); - } - friend bool operator<(const ast_i &x, const ast_i&y){ - return x.lt(y); - } - size_t hash() const {return _ast->get_id();} - bool null() const {return !_ast;} -}; - -/** Reference counting verison of above */ -class ast_r : public ast_i { - ast_manager *_m; -public: - ast_r(ast_manager *m, raw_ast *a) : ast_i(a) { - _m = m; - m->inc_ref(a); - } - - ast_r() {_m = nullptr;} - - ast_r(const ast_r &other) : ast_i(other) { - _m = other._m; - if (_m) _m->inc_ref(_ast); - } - - ast_r &operator=(const ast_r &other) { - if(_ast) - _m->dec_ref(_ast); - _ast = other._ast; - _m = other._m; - if (_m) _m->inc_ref(_ast); - return *this; - } - - ~ast_r() { - if(_ast) - _m->dec_ref(_ast); - } - - ast_manager *mgr() const {return _m;} - -}; - -// to make ast_r hashable -namespace hash_space { - template <> - class hash { - public: - size_t operator()(const ast_r &s) const { - return s.raw()->get_id(); - } - }; -} - - -// to make ast_r usable in ordered collections -namespace std { - template <> - class less { - public: - bool operator()(const ast_r &s, const ast_r &t) const { - // return s.raw() < t.raw(); - return s.raw()->get_id() < t.raw()->get_id(); - } - }; -} - - -/** Wrapper around an AST manager, providing convenience methods. */ - -class iz3mgr { - - public: - typedef ast_r ast; - // typedef decl_kind opr; - typedef func_decl *symb; - typedef sort *type; - typedef ast_r z3pf; - typedef decl_kind pfrule; - - enum opr { - True, - False, - And, - Or, - Not, - Iff, - Ite, - Equal, - Implies, - Distinct, - Xor, - Oeq, - Interp, - Leq, - Geq, - Lt, - Gt, - Plus, - Sub, - Uminus, - Times, - Div, - Idiv, - Rem, - Mod, - Power, - ToReal, - ToInt, - IsInt, - Select, - Store, - ConstArray, - ArrayDefault, - ArrayMap, - SetUnion, - SetIntersect, - SetDifference, - SetComplement, - SetSubSet, - AsArray, - Numeral, - Forall, - Exists, - Variable, - Uninterpreted, - Other - }; - - opr op(const ast &t); - - unsigned ast_id(const ast &x) - { - return to_expr(x.raw())->get_id(); - } - - /** Overloads for constructing ast. */ - - ast make_var(const std::string &name, type ty); - ast make(opr op, const std::vector &args); - ast make(opr op); - ast make(opr op, const ast &arg0); - ast make(opr op, const ast &arg0, const ast &arg1); - ast make(opr op, const ast &arg0, const ast &arg1, const ast &arg2); - ast make(symb sym, const std::vector &args); - ast make(symb sym); - ast make(symb sym, const ast &arg0); - ast make(symb sym, const ast &arg0, const ast &arg1); - ast make(symb sym, const ast &arg0, const ast &arg1, const ast &arg2); - ast make_quant(opr op, const std::vector &bvs, ast &body); - ast clone(const ast &t, const std::vector &args); - - ast_manager &m() {return m_manager;} - - ast cook(raw_ast *a) {return ast(&m_manager,a);} - - std::vector cook(ptr_vector v) { - std::vector _v(v.size()); - for(unsigned i = 0; i < v.size(); i++) - _v[i] = cook(v[i]); - return _v; - } - - raw_ast *uncook(const ast &a) { - m_manager.inc_ref(a.raw()); - return a.raw(); - } - - /** Methods for destructing ast. */ - - - int num_args(const ast& t){ - ast_kind dk = t.raw()->get_kind(); - switch(dk){ - case AST_APP: - return to_app(t.raw())->get_num_args(); - case AST_QUANTIFIER: - return 1; - case AST_VAR: - return 0; - default:; - } - assert(0); - return 0; - } - - ast arg(const ast &t, int i){ - ast_kind dk = t.raw()->get_kind(); - switch(dk){ - case AST_APP: - return cook(to_app(t.raw())->get_arg(i)); - case AST_QUANTIFIER: - return cook(to_quantifier(t.raw())->get_expr()); - default:; - } - assert(0); - return ast(); - } - - void get_args(const ast &t, std::vector &res){ - res.resize(num_args(t)); - for(unsigned i = 0; i < res.size(); i++) - res[i] = arg(t,i); - } - - std::vector args(const ast &t){ - std::vector res; - get_args(t,res); - return res; - } - - symb sym(const ast& t){ - raw_ast *_ast = t.raw(); - return is_app(_ast) ? to_app(_ast)->get_decl() : nullptr; - } - - std::string string_of_symbol(symb s){ - symbol _s = s->get_name(); - if (_s.is_numerical()) { - std::ostringstream buffer; - buffer << _s.get_num(); - return buffer.str(); - } - else { - return _s.bare_str(); - } - } - - type get_type(const ast& t){ - return m().get_sort(to_expr(t.raw())); - } - - std::string string_of_numeral(const ast& t){ - rational r; - expr* e = to_expr(t.raw()); - assert(e); - if (m_arith_util.is_numeral(e, r)) - return r.to_string(); - assert(0); - return "NaN"; - } - - bool is_numeral(const ast& t, rational &r){ - expr* e = to_expr(t.raw()); - assert(e); - return m_arith_util.is_numeral(e, r); - } - - rational get_coeff(const ast& t){ - rational res; - if(op(t) == Times && is_numeral(arg(t,0),res)) - return res; - return rational(1); - } - - ast get_linear_var(const ast& t){ - rational res; - if(op(t) == Times && is_numeral(arg(t,0),res)) - return arg(t,1); - return t; - } - - int get_quantifier_num_bound(const ast &t) { - return to_quantifier(t.raw())->get_num_decls(); - } - - std::string get_quantifier_bound_name(const ast &t, unsigned i) { - return to_quantifier(t.raw())->get_decl_names()[i].bare_str(); - } - - type get_quantifier_bound_type(const ast &t, unsigned i) { - return to_quantifier(t.raw())->get_decl_sort(i); - } - - ast get_quantifier_body(const ast &t) { - return cook(to_quantifier(t.raw())->get_expr()); - } - - unsigned get_variable_index_value(const ast &t) { - var* va = to_var(t.raw()); - return va->get_idx(); - } - - bool is_bool_type(type t){ - family_id fid = to_sort(t)->get_family_id(); - decl_kind k = to_sort(t)->get_decl_kind(); - return fid == m().get_basic_family_id() && k == BOOL_SORT; - } - - bool is_array_type(type t){ - family_id fid = to_sort(t)->get_family_id(); - decl_kind k = to_sort(t)->get_decl_kind(); - return fid == m_array_fid && k == ARRAY_SORT; - } - - type get_range_type(symb s){ - return to_func_decl(s)->get_range(); - } - - int get_num_parameters(const symb &s){ - return to_func_decl(s)->get_num_parameters(); - } - - ast get_ast_parameter(const symb &s, int idx){ - return cook(to_func_decl(s)->get_parameters()[idx].get_ast()); - } - - enum lemma_theory {ArithTheory,ArrayTheory,UnknownTheory}; - - lemma_theory get_theory_lemma_theory(const ast &proof){ - symb s = sym(proof); - ::symbol p0; - bool ok = s->get_parameter(0).is_symbol(p0); - if(!ok) return UnknownTheory; - std::string foo(p0.bare_str()); - if(foo == "arith") - return ArithTheory; - if(foo == "array") - return ArrayTheory; - return UnknownTheory; - } - - enum lemma_kind {FarkasKind,Leq2EqKind,Eq2LeqKind,GCDTestKind,AssignBoundsKind,EqPropagateKind,GomoryCutKind,ArithMysteryKind,UnknownKind}; - - lemma_kind get_theory_lemma_kind(const ast &proof){ - symb s = sym(proof); - if(s->get_num_parameters() < 2) { - return ArithMysteryKind; // Bad -- Z3 hasn't told us - } - ::symbol p0; - bool ok = s->get_parameter(1).is_symbol(p0); - if(!ok) return UnknownKind; - std::string foo(p0.bare_str()); - if(foo == "farkas") - return FarkasKind; - if(foo == "triangle-eq") - return is_not(arg(conc(proof),0)) ? Eq2LeqKind : Leq2EqKind; - if(foo == "gcd-test") - return GCDTestKind; - if(foo == "assign-bounds") - return AssignBoundsKind; - if(foo == "eq-propagate") - return EqPropagateKind; - if(foo == "gomory-cut") - return GomoryCutKind; - return UnknownKind; - } - - void get_farkas_coeffs(const ast &proof, std::vector& coeffs); - - void get_farkas_coeffs(const ast &proof, std::vector& rats); - - void get_broken_gcd_test_coeffs(const ast &proof, std::vector& rats); - - void get_assign_bounds_coeffs(const ast &proof, std::vector& rats); - - void get_assign_bounds_coeffs(const ast &proof, std::vector& rats); - - void get_assign_bounds_rule_coeffs(const ast &proof, std::vector& rats); - - void get_assign_bounds_rule_coeffs(const ast &proof, std::vector& rats); - - void get_gomory_cut_coeffs(const ast &proof, std::vector& rats); - - void get_gomory_cut_coeffs(const ast &proof, std::vector& rats); - - bool is_farkas_coefficient_negative(const ast &proof, int n); - - bool is_true(const ast& t){ - return op(t) == True; - } - - bool is_false(const ast& t){ - return op(t) == False; - } - - bool is_iff(const ast& t){ - return op(t) == Iff; - } - - bool is_or(const ast& t){ - return op(t) == Or; - } - - bool is_not(const ast& t){ - return op(t) == Not; - } - - /** Simplify an expression using z3 simplifier */ - - ast z3_simplify(const ast& e); - - /** Simplify, sorting sums */ - ast z3_really_simplify(const ast &e); - - - // Some constructors that simplify things - - ast mk_not(const ast& x){ - opr o = op(x); - if(o == True) return make(False); - if(o == False) return make(True); - if(o == Not) return arg(x,0); - return make(Not,x); - } - - ast mk_and(const ast& x, const ast& y){ - opr ox = op(x); - opr oy = op(y); - if(ox == True) return y; - if(oy == True) return x; - if(ox == False) return x; - if(oy == False) return y; - if(x == y) return x; - return make(And,x,y); - } - - ast mk_or(const ast& x, const ast& y){ - opr ox = op(x); - opr oy = op(y); - if(ox == False) return y; - if(oy == False) return x; - if(ox == True) return x; - if(oy == True) return y; - if(x == y) return x; - return make(Or,x,y); - } - - ast mk_implies(const ast& x, const ast& y){ - opr ox = op(x); - opr oy = op(y); - if(ox == True) return y; - if(oy == False) return mk_not(x); - if(ox == False) return mk_true(); - if(oy == True) return y; - if(x == y) return mk_true(); - return make(Implies,x,y); - } - - ast mk_or(const std::vector &x){ - ast res = mk_false(); - for(unsigned i = 0; i < x.size(); i++) - res = mk_or(res,x[i]); - return res; - } - - ast mk_and(const std::vector &x){ - std::vector conjs; - for(unsigned i = 0; i < x.size(); i++){ - const ast &e = x[i]; - opr o = op(e); - if(o == False) - return mk_false(); - if(o != True) - conjs.push_back(e); - } - if(conjs.size() == 0) - return mk_true(); - if(conjs.size() == 1) - return conjs[0]; - return make(And,conjs); - } - - ast mk_equal(const ast& x, const ast& y){ - if(x == y) return make(True); - opr ox = op(x); - opr oy = op(y); - if(ox == True) return y; - if(oy == True) return x; - if(ox == False) return mk_not(y); - if(oy == False) return mk_not(x); - if(ox == False && oy == True) return make(False); - if(oy == False && ox == True) return make(False); - return make(Equal,x,y); - } - - ast z3_ite(const ast& x, const ast& y, const ast& z){ - opr ox = op(x); - opr oy = op(y); - opr oz = op(z); - if(ox == True) return y; - if(ox == False) return z; - if(y == z) return y; - if(oy == True && oz == False) return x; - if(oz == True && oy == False) return mk_not(x); - return make(Ite,x,y,z); - } - - ast make_int(const std::string &s) { - sort *r = m().mk_sort(m_arith_fid, INT_SORT); - return cook(m_arith_util.mk_numeral(rational(s.c_str()),r)); - } - - ast make_int(const rational &s) { - sort *r = m().mk_sort(m_arith_fid, INT_SORT); - return cook(m_arith_util.mk_numeral(s,r)); - } - - ast make_real(const std::string &s) { - sort *r = m().mk_sort(m_arith_fid, REAL_SORT); - return cook(m_arith_util.mk_numeral(rational(s.c_str()),r)); - } - - ast make_real(const rational &s) { - sort *r = m().mk_sort(m_arith_fid, REAL_SORT); - return cook(m_arith_util.mk_numeral(s,r)); - } - - ast mk_false() { return make(False); } - - ast mk_true() { return make(True); } - - ast mk_fresh_constant(char const * prefix, type s){ - return cook(m().mk_fresh_const(prefix, s)); - } - - type bool_type() { - ::sort *s = m().mk_sort(m_basic_fid, BOOL_SORT); - return s; - } - - type int_type() { - ::sort *s = m().mk_sort(m_arith_fid, INT_SORT); - return s; - } - - type real_type() { - ::sort *s = m().mk_sort(m_arith_fid, REAL_SORT); - return s; - } - - type array_type(type d, type r) { - parameter params[2] = { parameter(d), parameter(to_sort(r)) }; - ::sort * s = m().mk_sort(m_array_fid, ARRAY_SORT, 2, params); - return s; - } - - symb function(const std::string &str_name, unsigned arity, type *domain, type range) { - ::symbol name = ::symbol(str_name.c_str()); - std::vector< ::sort *> sv(arity); - for(unsigned i = 0; i < arity; i++) - sv[i] = domain[i]; - ::func_decl* d = m().mk_func_decl(name,arity,&sv[0],range); - return d; - } - - void linear_comb(ast &P, const ast &c, const ast &Q, bool round_off = false); - - ast sum_inequalities(const std::vector &coeffs, const std::vector &ineqs, bool round_off = false); - - ast simplify_ineq(const ast &ineq){ - ast res = make(op(ineq),arg(ineq,0),z3_simplify(arg(ineq,1))); - return res; - } - - void mk_idiv(const ast& t, const rational &d, ast &whole, ast &frac); - - ast mk_idiv(const ast& t, const rational &d); - - ast mk_idiv(const ast& t, const ast &d); - - /** methods for destructing proof terms */ - - pfrule pr(const z3pf &t); - - int num_prems(const z3pf &t){return to_app(t.raw())->get_num_args()-1;} - - z3pf prem(const z3pf &t, int n){return arg(t,n);} - - z3pf conc(const z3pf &t){return arg(t,num_prems(t));} - - - /* quantifier handling */ - - // substitute a term t for unbound occurrences of variable v in e - - ast subst(ast var, ast t, ast e); - - // apply a substitution defined by a map - ast subst(stl_ext::hash_map &map, ast e); - - // apply a quantifier to a formula, with some optimizations - // 1) bound variable does not occur -> no quantifier - // 2) bound variable must be equal to some term -> substitute - - ast apply_quant(opr quantifier, ast var, ast e); - - // Universally quantify all the free variables in a formula. - // Makes up names for the quntifiers. - - ast close_universally (ast e); - - unsigned num_free_variables(const ast &e); - - /** For debugging */ - void show(ast); - - void show_symb(symb s); - - /** Constructor */ - - void print_lit(ast lit); - - void print_expr(std::ostream &s, const ast &e); - - void print_clause(std::ostream &s, std::vector &cls); - - void print_sat_problem(std::ostream &out, const ast &t); - - void show_clause(std::vector &cls); - - static void pretty_print(std::ostream &f, const std::string &s); - - iz3mgr(ast_manager &_m_manager) - : m_manager(_m_manager), - m_arith_util(_m_manager) - { - m_basic_fid = m().get_basic_family_id(); - m_arith_fid = m().mk_family_id("arith"); - m_bv_fid = m().mk_family_id("bv"); - m_array_fid = m().mk_family_id("array"); - m_dt_fid = m().mk_family_id("datatype"); - m_datalog_fid = m().mk_family_id("datalog_relation"); - } - - iz3mgr(const iz3mgr& other) - : m_manager(other.m_manager), - m_arith_util(other.m_manager) - { - m_basic_fid = m().get_basic_family_id(); - m_arith_fid = m().mk_family_id("arith"); - m_bv_fid = m().mk_family_id("bv"); - m_array_fid = m().mk_family_id("array"); - m_dt_fid = m().mk_family_id("datatype"); - m_datalog_fid = m().mk_family_id("datalog_relation"); - } - - protected: - ast_manager &m_manager; - int occurs_in(ast var, ast e); - - private: - ast mki(family_id fid, decl_kind sk, int n, raw_ast **args); - ast make(opr op, int n, raw_ast **args); - ast make(symb sym, int n, raw_ast **args); - int occurs_in1(stl_ext::hash_map &occurs_in_memo, ast var, ast e); - bool solve_arith(const ast &v, const ast &x, const ast &y, ast &res); - ast cont_eq(stl_ext::hash_set &cont_eq_memo, bool truth, ast v, ast e); - ast subst(stl_ext::hash_map &subst_memo, ast var, ast t, ast e); - - - family_id m_basic_fid; - family_id m_array_fid; - family_id m_arith_fid; - family_id m_bv_fid; - family_id m_dt_fid; - family_id m_datalog_fid; - arith_util m_arith_util; -}; - -#endif - diff --git a/src/interp/iz3pp.cpp b/src/interp/iz3pp.cpp deleted file mode 100644 index 787fa4ec7..000000000 --- a/src/interp/iz3pp.cpp +++ /dev/null @@ -1,185 +0,0 @@ -/*++ - Copyright (c) 2013 Microsoft Corporation - - Module Name: - - iz3pp.cpp - - Abstract: - - Pretty-print interpolation problems - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -/* Copyright 2011 Microsoft Research. */ -#include -#include -#include -#include -#include -#include -#include - -#include "interp/iz3mgr.h" -#include "interp/iz3pp.h" -#include "ast/func_decl_dependencies.h" -#include "ast/for_each_expr.h" -#include "ast/ast_smt_pp.h" -#include "ast/ast_smt2_pp.h" -#include "ast/expr_functors.h" -#include "ast/expr_abstract.h" - - -using namespace stl_ext; - -// We promise not to use this for hash_map with range destructor -namespace stl_ext { - template <> - class hash { - public: - size_t operator()(const expr *p) const { - return (size_t) p; - } - }; -} - - -// TBD: algebraic data-types declarations will not be printed. -class free_func_visitor { - ast_manager& m; - func_decl_set m_funcs; - obj_hashtable m_sorts; -public: - free_func_visitor(ast_manager& m): m(m) {} - void operator()(var * n) { } - void operator()(app * n) { - m_funcs.insert(n->get_decl()); - class sort* s = m.get_sort(n); - if (s->get_family_id() == null_family_id) { - m_sorts.insert(s); - } - } - void operator()(quantifier * n) { } - func_decl_set& funcs() { return m_funcs; } - obj_hashtable& sorts() { return m_sorts; } -}; - -class iz3pp_helper : public iz3mgr { -public: - - void print_tree(const ast &tree, hash_map &cnames, std::ostream &out){ - hash_map::iterator foo = cnames.find(to_expr(tree.raw())); - if(foo != cnames.end()){ - symbol nm = foo->second; - if (is_smt2_quoted_symbol(nm)) { - out << mk_smt2_quoted_symbol(nm); - } - else { - out << nm; - } - } - else if(op(tree) == And){ - out << "(and"; - int nargs = num_args(tree); - for(int i = 0; i < nargs; i++){ - out << " "; - print_tree(arg(tree,i), cnames, out); - } - out << ")"; - } - else if(op(tree) == Interp){ - out << "(interp "; - print_tree(arg(tree,0), cnames, out); - out << ")"; - } - else throw iz3pp_bad_tree(); - } - - - iz3pp_helper(ast_manager &_m_manager) - : iz3mgr(_m_manager) {} -}; - -void iz3pp(ast_manager &m, - const ptr_vector &cnsts_vec, - expr *tree, - std::ostream& out) { - - unsigned sz = cnsts_vec.size(); - expr* const* cnsts = &cnsts_vec[0]; - - out << "(set-option :produce-interpolants true)\n"; - - free_func_visitor visitor(m); - expr_mark visited; - bool print_low_level = true; // m_params.print_low_level_smt2(); - -#define PP(_e_) if (print_low_level) out << mk_smt_pp(_e_, m); else ast_smt2_pp(out, _e_, env); - - smt2_pp_environment_dbg env(m); - - for (unsigned i = 0; i < sz; ++i) { - expr* e = cnsts[i]; - for_each_expr(visitor, visited, e); - } - - // name all the constraints - hash_map cnames; - int ctr = 1; - for(unsigned i = 0; i < sz; i++){ - symbol nm; - std::ostringstream s; - s << "f!" << (ctr++); - cnames[cnsts[i]] = symbol(s.str().c_str()); - } - - func_decl_set &funcs = visitor.funcs(); - func_decl_set::iterator it = funcs.begin(), end = funcs.end(); - - obj_hashtable& sorts = visitor.sorts(); - obj_hashtable::iterator sit = sorts.begin(), send = sorts.end(); - - - - for (; sit != send; ++sit) { - PP(*sit); - } - - for (; it != end; ++it) { - func_decl* f = *it; - if(f->get_family_id() == null_family_id){ - PP(f); - out << "\n"; - } - } - - for (unsigned i = 0; i < sz; ++i) { - out << "(assert "; - expr* r = cnsts[i]; - symbol nm = cnames[r]; - out << "(! "; - PP(r); - out << " :named "; - if (is_smt2_quoted_symbol(nm)) { - out << mk_smt2_quoted_symbol(nm); - } - else { - out << nm; - } - out << ")"; - out << ")\n"; - } - out << "(check-sat)\n"; - out << "(get-interpolant "; - iz3pp_helper pp(m); - pp.print_tree(pp.cook(tree),cnames,out); - out << ")\n"; -} - - diff --git a/src/interp/iz3pp.h b/src/interp/iz3pp.h deleted file mode 100644 index 7b3405f9b..000000000 --- a/src/interp/iz3pp.h +++ /dev/null @@ -1,36 +0,0 @@ -/*++ - Copyright (c) 2013 Microsoft Corporation - - Module Name: - - iz3pp.cpp - - Abstract: - - Pretty-print interpolation problems - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifndef IZ3_PP_H -#define IZ3_PP_H - -#include "interp/iz3mgr.h" - -/** Exception thrown in case of mal-formed tree interpoloation - specification */ - -struct iz3pp_bad_tree: public iz3_exception { - iz3pp_bad_tree(): iz3_exception("iz3pp_bad_tree") {} -}; - -void iz3pp(ast_manager &m, - const ptr_vector &cnsts_vec, - expr *tree, - std::ostream& out); -#endif diff --git a/src/interp/iz3profiling.cpp b/src/interp/iz3profiling.cpp deleted file mode 100644 index ba4fd0206..000000000 --- a/src/interp/iz3profiling.cpp +++ /dev/null @@ -1,153 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3profiling.h - - Abstract: - - Some routines for measuring performance. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#pragma warning(disable:4101) -#endif - -#include "interp/iz3profiling.h" - -#include -#include -#include -#include -#include -#include "util/stopwatch.h" - - -// FIXME fill in these stubs - -#define clock_t double - -static double current_time() -{ - static stopwatch sw; - static bool started = false; - if(!started){ - sw.start(); - started = true; - } - return sw.get_current_seconds(); -} - -static void output_time(std::ostream &os, clock_t time){ - os << time; -} - - -namespace profiling { - - void show_time(){ - output_time(std::cout,current_time()); - std::cout << "\n"; - } - - typedef std::map nmap; - - struct node { - std::string name; - clock_t time; - clock_t start_time; - nmap sub; - struct node *parent; - - node(); - } top; - - node::node(){ - time = 0; - parent = nullptr; - } - - struct node *current; - - struct init { - init(){ - top.name = "TOTAL"; - current = ⊤ - } - } initializer; - - struct time_entry { - clock_t t; - time_entry(){t = 0;}; - void add(clock_t incr){t += incr;} - }; - - struct ltstr - { - bool operator()(const char* s1, const char* s2) const - { - return strcmp(s1, s2) < 0; - } - }; - - typedef std::map tmap; - - static std::ostream *pfs; - - void print_node(node &top, int indent, tmap &totals){ - for(int i = 0; i < indent; i++) (*pfs) << " "; - (*pfs) << top.name; - int dots = 70 - 2 * indent - top.name.size(); - for(int i = 0; i second,indent+1,totals); - } - - void print(std::ostream &os) { - pfs = &os; - top.time = 0; - for(nmap::iterator it = top.sub.begin(); it != top.sub.end(); it++) - top.time += it->second.time; - tmap totals; - print_node(top,0,totals); - (*pfs) << "TOTALS:" << std::endl; - for(tmap::iterator it = totals.begin(); it != totals.end(); it++){ - (*pfs) << (it->first) << " "; - output_time(*pfs, it->second.t); - (*pfs) << std::endl; - } - } - - void timer_start(const char *name){ - node &child = current->sub[name]; - if(child.name.empty()){ // a new node - child.parent = current; - child.name = name; - } - child.start_time = current_time(); - current = &child; - } - - void timer_stop(const char *name){ - if(current->name != name || !current->parent){ - std::cerr << "imbalanced timer_start and timer_stop"; - exit(1); - } - current->time += (current_time() - current->start_time); - current = current->parent; - } -} diff --git a/src/interp/iz3profiling.h b/src/interp/iz3profiling.h deleted file mode 100755 index 6b9b07f25..000000000 --- a/src/interp/iz3profiling.h +++ /dev/null @@ -1,37 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3profiling.h - - Abstract: - - Some routines for measuring performance. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifndef IZ3PROFILING_H -#define IZ3PROFILING_H - -#include - -namespace profiling { - /** Start a timer with given name */ - void timer_start(const char *); - /** Stop a timer with given name */ - void timer_stop(const char *); - /** Print out timings */ - void print(std::ostream &s); - /** Show the current time. */ - void show_time(); -} - -#endif - diff --git a/src/interp/iz3proof.cpp b/src/interp/iz3proof.cpp deleted file mode 100755 index bc046ceff..000000000 --- a/src/interp/iz3proof.cpp +++ /dev/null @@ -1,628 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3proof.cpp - - Abstract: - - This class defines a simple interpolating proof system. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#pragma warning(disable:4101) -#endif - -#include "interp/iz3proof.h" -#include "interp/iz3profiling.h" - -#include -#include -#include -#include - -// #define FACTOR_INTERPS -// #define CHECK_PROOFS - - -void iz3proof::resolve(ast pivot, std::vector &cls1, const std::vector &cls2){ -#ifdef CHECK_PROOFS - std::vector orig_cls1 = cls1; -#endif - ast neg_pivot = pv->mk_not(pivot); - bool found_pivot1 = false, found_pivot2 = false; - for(unsigned i = 0; i < cls1.size(); i++){ - if(cls1[i] == neg_pivot){ - cls1[i] = cls1.back(); - cls1.pop_back(); - found_pivot1 = true; - break; - } - } - { - std::set memo; - memo.insert(cls1.begin(),cls1.end()); - for(unsigned j = 0; j < cls2.size(); j++){ - if(cls2[j] == pivot) - found_pivot2 = true; - else - if(memo.find(cls2[j]) == memo.end()) - cls1.push_back(cls2[j]); - } - } - if(found_pivot1 && found_pivot2) - return; - -#ifdef CHECK_PROOFS - std::cerr << "resolution anomaly: " << nodes.size()-1 << "\n"; -#if 0 - std::cerr << "pivot: "; {pv->print_lit(pivot); std::cout << "\n";} - std::cerr << "left clause:\n"; - for(unsigned i = 0; i < orig_cls1.size(); i++) - {pv->print_lit(orig_cls1[i]); std::cout << "\n";} - std::cerr << "right clause:\n"; - for(unsigned i = 0; i < cls2.size(); i++) - {pv->print_lit(cls2[i]); std::cout << "\n";} - throw proof_error(); -#endif -#endif -} - -iz3proof::node iz3proof::make_resolution(ast pivot, node premise1, node premise2) -{ - if(nodes[premise1].rl == Hypothesis) return premise2; // resolve with hyp is noop - if(nodes[premise2].rl == Hypothesis) return premise1; - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = Resolution; - n.aux = pivot; - n.premises.resize(2); - n.premises[0] = (premise1); - n.premises[1] = (premise2); -#ifdef CHECK_PROOFS - n.conclusion = nodes[premise1].conclusion; - resolve(pivot,n.conclusion,nodes[premise2].conclusion); - n.frame = 1; -#else - n.frame = 0; // compute conclusion lazily -#endif - return res; -} - -iz3proof::node iz3proof::resolve_lemmas(ast pivot, node premise1, node premise2) -{ - std::vector lits(nodes[premise1].conclusion), itp; // no interpolant - resolve(pivot,lits,nodes[premise2].conclusion); - return make_lemma(lits,itp); -} - - -iz3proof::node iz3proof::make_assumption(int frame, const std::vector &assumption){ -#if 0 - std::cout << "assumption: \n"; - for(unsigned i = 0; i < assumption.size(); i++) - pv->show(assumption[i]); - std::cout << "\n"; -#endif - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = Assumption; - n.conclusion.resize(1); - n.conclusion = assumption; - n.frame = frame; - return res; -} - -iz3proof::node iz3proof::make_hypothesis(ast hypothesis){ - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = Hypothesis; - n.conclusion.resize(2); - n.conclusion[0] = hypothesis; - n.conclusion[1] = pv->mk_not(hypothesis); - return res; -} - -iz3proof::node iz3proof::make_theory(const std::vector &conclusion, std::vector premises){ - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = Theory; - n.conclusion = conclusion; - n.premises = premises; - return res; -} - -iz3proof::node iz3proof::make_axiom(const std::vector &conclusion){ - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = Axiom; - n.conclusion = conclusion; - return res; -} - -iz3proof::node iz3proof::make_contra(node prem, const std::vector &conclusion){ - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = Contra; - n.conclusion = conclusion; -#ifdef CHECK_PROOFS - //if(!(conclusion == nodes[prem].conclusion)){ - //std::cerr << "internal error: proof error\n"; - //assert(0 && "proof error"); - //} -#endif - n.premises.push_back(prem); - return res; -} - - -iz3proof::node iz3proof::make_lemma(const std::vector &conclusion, const std::vector &interpolation){ - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = Lemma; - n.conclusion = conclusion; - n.frame = interps.size(); - interps.push_back(interpolation); - return res; -} - -/** Make a Reflexivity node. This rule produces |- x = x */ - -iz3proof::node iz3proof::make_reflexivity(ast con){ - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = Reflexivity; - n.conclusion.push_back(con); - return res; -} - -/** Make a Symmetry node. This takes a derivation of |- x = y and - produces | y = x */ - -iz3proof::node iz3proof::make_symmetry(ast con, node prem){ - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = Reflexivity; - n.conclusion.push_back(con); - n.premises.push_back(prem); - return res; -} - -/** Make a transitivity node. This takes derivations of |- x = y - and |- y = z produces | x = z */ - -iz3proof::node iz3proof::make_transitivity(ast con, node prem1, node prem2){ - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = Transitivity; - n.conclusion.push_back(con); - n.premises.push_back(prem1); - n.premises.push_back(prem2); - return res; -} - - -/** Make a congruence node. This takes derivations of |- x_i = y_i - and produces |- f(x_1,...,x_n) = f(y_1,...,y_n) */ - -iz3proof::node iz3proof::make_congruence(ast con, const std::vector &prems){ - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = Congruence; - n.conclusion.push_back(con); - n.premises = prems; - return res; -} - - -/** Make an equality contradicition node. This takes |- x = y - and |- !(x = y) and produces false. */ - -iz3proof::node iz3proof::make_eqcontra(node prem1, node prem2){ - node res = make_node(); - node_struct &n = nodes[res]; - n.rl = EqContra; - n.premises.push_back(prem1); - n.premises.push_back(prem2); - return res; -} - -iz3proof::node iz3proof::copy_rec(stl_ext::hash_map &memo, iz3proof &src, node n){ - stl_ext::hash_map::iterator it = memo.find(n); - if(it != memo.end()) return (*it).second; - node_struct &ns = src.nodes[n]; - std::vector prems(ns.premises.size()); - for(unsigned i = 0; i < prems.size(); i++) - prems[i] = copy_rec(memo,src,ns.premises[i]); - nodes.push_back(ns); - nodes.back().premises.swap(prems); - if(ns.rl == Lemma){ - nodes.back().frame = interps.size(); - interps.push_back(src.interps[ns.frame]); - } - int res = nodes.size()-1; - memo[n] = res; - return res; -} - -iz3proof::node iz3proof::copy(iz3proof &src, node n){ - stl_ext::hash_map memo; - return copy_rec(memo, src, n); -} - -bool iz3proof::pred_in_A(ast id){ - return weak - ? pv->ranges_intersect(pv->ast_range(id),rng) : - pv->range_contained(pv->ast_range(id),rng); -} - -bool iz3proof::term_in_B(ast id){ - prover::range r = pv->ast_scope(id); - if(weak) { - if(pv->range_min(r) == SHRT_MIN) - return !pv->range_contained(r,rng); - else - return !pv->ranges_intersect(r,rng); - } - else - return !pv->range_contained(r,rng); -} - -bool iz3proof::frame_in_A(int frame){ - return pv->in_range(frame,rng); -} - -bool iz3proof::lit_in_B(ast lit){ - return - b_lits.find(lit) != b_lits.end() - || b_lits.find(pv->mk_not(lit)) != b_lits.end(); -} - -iz3proof::ast iz3proof::my_or(ast x, ast y){ - return pv->mk_not(pv->mk_and(pv->mk_not(x),pv->mk_not(y))); -} - -iz3proof::ast iz3proof::get_A_lits(std::vector &cls){ - ast foo = pv->mk_false(); - for(unsigned i = 0; i < cls.size(); i++){ - ast lit = cls[i]; - if(b_lits.find(pv->mk_not(lit)) == b_lits.end()){ - if(pv->range_max(pv->ast_scope(lit)) == pv->range_min(pv->ast_scope(lit))){ - std::cout << "bad lit: " << pv->range_max(rng) << " : " << pv->range_max(pv->ast_scope(lit)) << " : " << (pv->ast_id(lit)) << " : "; - pv->show(lit); - } - foo = my_or(foo,lit); - } - } - return foo; -} - -iz3proof::ast iz3proof::get_B_lits(std::vector &cls){ - ast foo = pv->mk_false(); - for(unsigned i = 0; i < cls.size(); i++){ - ast lit = cls[i]; - if(b_lits.find(pv->mk_not(lit)) != b_lits.end()) - foo = my_or(foo,lit); - } - return foo; -} - -void iz3proof::set_of_B_lits(std::vector &cls, std::set &res){ - for(unsigned i = 0; i < cls.size(); i++){ - ast lit = cls[i]; - if(b_lits.find(pv->mk_not(lit)) != b_lits.end()) - res.insert(lit); - } -} - -void iz3proof::set_of_A_lits(std::vector &cls, std::set &res){ - for(unsigned i = 0; i < cls.size(); i++){ - ast lit = cls[i]; - if(b_lits.find(pv->mk_not(lit)) == b_lits.end()) - res.insert(lit); - } -} - -void iz3proof::find_B_lits(){ - b_lits.clear(); - for(unsigned i = 0; i < nodes.size(); i++){ - node_struct &n = nodes[i]; - std::vector &cls = n.conclusion; - if(n.rl == Assumption){ - if(weak) goto lemma; - if(!frame_in_A(n.frame)) - for(unsigned j = 0; j < cls.size(); j++) - b_lits.insert(cls[j]); - } - else if(n.rl == Lemma) { - lemma: - for(unsigned j = 0; j < cls.size(); j++) - if(term_in_B(cls[j])) - b_lits.insert(cls[j]); - } - } -} - -iz3proof::ast iz3proof::disj_of_set(std::set &s){ - ast res = pv->mk_false(); - for(std::set::iterator it = s.begin(), en = s.end(); it != en; ++it) - res = my_or(*it,res); - return res; -} - -void iz3proof::mk_and_factor(int p1, int p2, int i, std::vector &itps, std::vector > &disjs){ -#ifdef FACTOR_INTERPS - std::set &d1 = disjs[p1]; - std::set &d2 = disjs[p2]; - if(!weak){ - if(pv->is_true(itps[p1])){ - itps[i] = itps[p2]; - disjs[i] = disjs[p2]; - } - else if(pv->is_true(itps[p2])){ - itps[i] = itps[p1]; - disjs[i] = disjs[p1]; - } - else { - std::set p1only,p2only; - std::insert_iterator > p1o(p1only,p1only.begin()); - std::insert_iterator > p2o(p2only,p2only.begin()); - std::insert_iterator > dio(disjs[i],disjs[i].begin()); - std::set_difference(d1.begin(),d1.end(),d2.begin(),d2.end(),p1o); - std::set_difference(d2.begin(),d2.end(),d1.begin(),d1.end(),p2o); - std::set_intersection(d1.begin(),d1.end(),d2.begin(),d2.end(),dio); - ast p1i = my_or(itps[p1],disj_of_set(p1only)); - ast p2i = my_or(itps[p2],disj_of_set(p2only)); - itps[i] = pv->mk_and(p1i,p2i); - } - } - else { - itps[i] = pv->mk_and(itps[p1],itps[p2]); - std::insert_iterator > dio(disjs[i],disjs[i].begin()); - std::set_union(d1.begin(),d1.end(),d2.begin(),d2.end(),dio); - } -#endif -} - -void iz3proof::mk_or_factor(int p1, int p2, int i, std::vector &itps, std::vector > &disjs){ -#ifdef FACTOR_INTERPS - std::set &d1 = disjs[p1]; - std::set &d2 = disjs[p2]; - if(weak){ - if(pv->is_false(itps[p1])){ - itps[i] = itps[p2]; - disjs[i] = disjs[p2]; - } - else if(pv->is_false(itps[p2])){ - itps[i] = itps[p1]; - disjs[i] = disjs[p1]; - } - else { - std::set p1only,p2only; - std::insert_iterator > p1o(p1only,p1only.begin()); - std::insert_iterator > p2o(p2only,p2only.begin()); - std::insert_iterator > dio(disjs[i],disjs[i].begin()); - std::set_difference(d1.begin(),d1.end(),d2.begin(),d2.end(),p1o); - std::set_difference(d2.begin(),d2.end(),d1.begin(),d1.end(),p2o); - std::set_intersection(d1.begin(),d1.end(),d2.begin(),d2.end(),dio); - ast p1i = pv->mk_and(itps[p1],pv->mk_not(disj_of_set(p1only))); - ast p2i = pv->mk_and(itps[p2],pv->mk_not(disj_of_set(p2only))); - itps[i] = my_or(p1i,p2i); - } - } - else { - itps[i] = my_or(itps[p1],itps[p2]); - std::insert_iterator > dio(disjs[i],disjs[i].begin()); - std::set_union(d1.begin(),d1.end(),d2.begin(),d2.end(),dio); - } -#endif -} - -void iz3proof::interpolate_lemma(node_struct &n){ - if(interps[n.frame].size()) - return; // already computed - pv->interpolate_clause(n.conclusion,interps[n.frame]); -} - -iz3proof::ast iz3proof::interpolate(const prover::range &_rng, bool _weak -#ifdef CHECK_PROOFS - , ast assump - , std::vector *parents -#endif - ){ - // std::cout << "proof size: " << nodes.size() << "\n"; - rng = _rng; - weak = _weak; -#ifdef CHECK_PROOFS - if(nodes[nodes.size()-1].conclusion.size() != 0) - std::cerr << "internal error: proof conclusion is not empty clause\n"; - if(!child_interps.size()){ - child_interps.resize(nodes.size()); - for(unsigned j = 0; j < nodes.size(); j++) - child_interps[j] = pv->mk_true(); - } -#endif - std::vector itps(nodes.size()); -#ifdef FACTOR_INTERPS - std::vector > disjs(nodes.size()); -#endif - profiling::timer_start("Blits"); - find_B_lits(); - profiling::timer_stop("Blits"); - profiling::timer_start("interp_proof"); - // strengthen(); - for(unsigned i = 0; i < nodes.size(); i++){ - node_struct &n = nodes[i]; - ast &q = itps[i]; - switch(n.rl){ - case Assumption: { - - if(frame_in_A(n.frame)){ - /* HypC-A */ - if(!weak) -#ifdef FACTOR_INTERPS - { - q = pv->mk_false(); - set_of_B_lits(n.conclusion,disjs[i]); - } -#else - q = get_B_lits(n.conclusion); -#endif - else - q = pv->mk_false(); - } - else { - /* HypEq-B */ - if(!weak) - q = pv->mk_true(); - else -#ifdef FACTOR_INTERPS - { - q = pv->mk_true(); - set_of_A_lits(n.conclusion,disjs[i]); - } -#else - q = pv->mk_not(get_A_lits(n.conclusion)); -#endif - } - break; - } - case Resolution: { - ast p = n.aux; - p = pv->is_not(p) ? pv->mk_not(p) : p; // should be positive, but just in case - if(lit_in_B(p)) -#ifdef FACTOR_INTERPS - mk_and_factor(n.premises[0],n.premises[1],i,itps,disjs); -#else - q = pv->mk_and(itps[n.premises[0]],itps[n.premises[1]]); -#endif - else -#ifdef FACTOR_INTERPS - mk_or_factor(n.premises[0],n.premises[1],i,itps,disjs); -#else - q = my_or(itps[n.premises[0]],itps[n.premises[1]]); -#endif - break; - } - case Lemma: { - interpolate_lemma(n); // make sure lemma interpolants have been computed - q = interps[n.frame][pv->range_max(rng)]; - break; - } - case Contra: { - q = itps[n.premises[0]]; -#ifdef FACTOR_INTERPS - disjs[i] = disjs[n.premises[0]]; -#endif - break; - } - default: - assert(0 && "rule not allowed in interpolated proof"); - } -#ifdef CHECK_PROOFS - int this_frame = pv->range_max(rng); - if(0 && this_frame == 39) { - std::vector alits; - ast s = pv->mk_true(); - for(unsigned j = 0; j < n.conclusion.size(); j++) - if(pred_in_A(n.conclusion[j])){ - int scpmax = pv->range_max(pv->ast_scope(n.conclusion[j])); - if(scpmax == this_frame) - s = pv->mk_and(s,pv->mk_not(n.conclusion[j])); - } - ast ci = child_interps[i]; - s = pv->mk_and(pv->mk_and(s,pv->mk_and(assump,pv->mk_not(q))),ci); - if(pv->is_sat(s)){ - std::cout << "interpolation invariant violated at step " << i << "\n"; - assert(0 && "interpolation invariant violated"); - } - } - if((*parents)[this_frame] == 39) - child_interps[i] = pv->mk_and(child_interps[i],q); -#endif - } - ast &bar = itps[nodes.size()-1]; -#ifdef FACTOR_INTERPS - if(!weak) - bar = my_or(bar,disj_of_set(disjs[nodes.size()-1])); - else - bar = pv->mk_and(bar,pv->mk_not(disj_of_set(disjs[nodes.size()-1]))); -#endif - profiling::timer_stop("interp_proof"); - profiling::timer_start("simplifying"); - bar = pv->simplify(bar); - profiling::timer_stop("simplifying"); - return bar; -} - - -void iz3proof::print(std::ostream &s, int id){ - node_struct &n = nodes[id]; - switch(n.rl){ - case Assumption: - s << "Assumption("; - pv->print_clause(s,n.conclusion); - s << ")"; - break; - case Hypothesis: - s << "Hyp("; pv->print_expr(s,n.conclusion[0]); s << ")"; break; - case Reflexivity: - s << "Refl("; pv->print_expr(s,n.conclusion[0]); s << ")"; break; - case Symmetry: - s << "Symm("; print(s,n.premises[0]); s << ")"; break; - case Transitivity: - s << "Trans("; print(s,n.premises[0]); s << ","; print(s,n.premises[1]); s << ")"; break; - case Congruence: - s << "Cong("; pv->print_expr(s,n.conclusion[0]); - for(unsigned i = 0; i < n.premises.size(); i++){ - s << ","; - print(s,n.premises[i]); - } - s << ")"; break; - case EqContra: - s << "EqContra("; print(s,n.premises[0]); s << ","; print(s,n.premises[1]); s << ")"; break; - case Resolution: - s << "Res("; - pv->print_expr(s,n.aux); s << ","; - print(s,n.premises[0]); s << ","; print(s,n.premises[1]); s << ")"; - break; - case Lemma: - s << "Lemma("; - pv->print_clause(s,n.conclusion); - for(unsigned i = 0; i < n.premises.size(); i++){ - s << ","; - print(s,n.premises[i]); - } - s << ")"; - break; - case Contra: - s << "Contra("; - print(s,n.premises[0]); - s << ")"; - break; - default:; - } -} - - -void iz3proof::show(int id){ - std::ostringstream ss; - print(ss,id); - iz3base::pretty_print(std::cout,ss.str()); - // std::cout << ss.str(); - std::cout << "\n"; -} - - diff --git a/src/interp/iz3proof.h b/src/interp/iz3proof.h deleted file mode 100644 index a7dcb9b75..000000000 --- a/src/interp/iz3proof.h +++ /dev/null @@ -1,274 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3proof.h - - Abstract: - - This class defines a simple interpolating proof system. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifndef IZ3PROOF_H -#define IZ3PROOF_H - -#include - -#include "interp/iz3base.h" -#include "interp/iz3secondary.h" - -// #define CHECK_PROOFS - -/** This class defines a simple proof system. - - A proof is a dag consisting of "nodes". The children of each node - are its "premises". Each node has a "conclusion" that is a clause, - represented as a vector of literals. - - The literals are represented by abstract syntax trees. Operations - on these, including computation of scopes are provided by iz3base. - - A proof can be interpolated, provided it is restricted to the - rules Resolution, Assumption, Contra and Lemma, and that all - clauses are strict (i.e., each literal in each clause is local). - -*/ - -class iz3proof { - public: - /** The type of proof nodes (nodes in the derivation tree). */ - typedef int node; - - /** Enumeration of proof rules. */ - enum rule {Resolution,Assumption,Hypothesis,Theory,Axiom,Contra,Lemma,Reflexivity,Symmetry,Transitivity,Congruence,EqContra}; - - /** Interface to prover. */ - typedef iz3base prover; - - /** Ast type. */ - typedef prover::ast ast; - - /** Object thrown in case of a proof error. */ - struct proof_error: public iz3_exception { - proof_error(): iz3_exception("proof_error") {} - }; - - /* Null proof node */ - static const node null = -1; - - /** Make a resolution node with given pivot liter and premises. - The conclusion of premise1 should contain the negation of the - pivot literal, while the conclusion of premise2 should containe the - pivot literal. - */ - node make_resolution(ast pivot, node premise1, node premise2); - - /** Make an assumption node. The given clause is assumed in the given frame. */ - node make_assumption(int frame, const std::vector &assumption); - - /** Make a hypothesis node. If phi is the hypothesis, this is - effectively phi |- phi. */ - node make_hypothesis(ast hypothesis); - - /** Make a theory node. This can be any inference valid in the theory. */ - node make_theory(const std::vector &conclusion, std::vector premises); - - /** Make an axiom node. The conclusion must be an instance of an axiom. */ - node make_axiom(const std::vector &conclusion); - - /** Make a Contra node. This rule takes a derivation of the form - Gamma |- False and produces |- \/~Gamma. */ - - node make_contra(node prem, const std::vector &conclusion); - - /** Make a lemma node. A lemma node must have an interpolation. */ - node make_lemma(const std::vector &conclusion, const std::vector &interpolation); - - /** Make a Reflexivity node. This rule produces |- x = x */ - - node make_reflexivity(ast con); - - /** Make a Symmetry node. This takes a derivation of |- x = y and - produces | y = x */ - - node make_symmetry(ast con, node prem); - - /** Make a transitivity node. This takes derivations of |- x = y - and |- y = z produces | x = z */ - - node make_transitivity(ast con, node prem1, node prem2); - - /** Make a congruence node. This takes derivations of |- x_i = y_i - and produces |- f(x_1,...,x_n) = f(y_1,...,y_n) */ - - node make_congruence(ast con, const std::vector &prems); - - /** Make an equality contradicition node. This takes |- x = y - and |- !(x = y) and produces false. */ - - node make_eqcontra(node prem1, node prem2); - - /** Get the rule of a node in a proof. */ - rule get_rule(node n){ - return nodes[n].rl; - } - - /** Get the pivot of a resolution node. */ - ast get_pivot(node n){ - return nodes[n].aux; - } - - /** Get the frame of an assumption node. */ - int get_frame(node n){ - return nodes[n].frame; - } - - /** Get the number of literals of the conclusion of a node. */ - int get_num_conclusion_lits(node n){ - return get_conclusion(n).size(); - } - - /** Get the nth literal of the conclusion of a node. */ - ast get_nth_conclusion_lit(node n, int i){ - return get_conclusion(n)[i]; - } - - /** Get the conclusion of a node. */ - void get_conclusion(node n, std::vector &result){ - result = get_conclusion(n); - } - - /** Get the number of premises of a node. */ - int get_num_premises(node n){ - return nodes[n].premises.size(); - } - - /** Get the nth premise of a node. */ - int get_nth_premise(node n, int i){ - return nodes[n].premises[i]; - } - - /** Get all the premises of a node. */ - void get_premises(node n, std::vector &result){ - result = nodes[n].premises; - } - - /** Create a new proof node, replacing the premises of an old - one. */ - - node clone(node n, std::vector &premises){ - if(premises == nodes[n].premises) - return n; - nodes.push_back(nodes[n]); - nodes.back().premises = premises; - return nodes.size()-1; - } - - /** Copy a proof node from src */ - node copy(iz3proof &src, node n); - - /** Resolve two lemmas on a given literal. */ - - node resolve_lemmas(ast pivot, node left, node right); - - /** Swap two proofs. */ - void swap(iz3proof &other){ - std::swap(pv,other.pv); - nodes.swap(other.nodes); - interps.swap(other.interps); - } - - /** Compute an interpolant for a proof, where the "A" side is defined by - the given range of frames. Parameter "weak", when true, uses different - interpolation system that resutls in generally weaker interpolants. - */ - ast interpolate(const prover::range &_rng, bool weak = false -#ifdef CHECK_PROOFS - , Z3_ast assump = (Z3_ast)0, std::vector *parents = 0 - -#endif - ); - - /** print proof node to a stream */ - - void print(std::ostream &s, node n); - - /** show proof node on stdout */ - void show(node n); - - /** Construct a proof, with a given prover. */ - iz3proof(prover *p){ - pv = p; - } - - /** Default constructor */ - iz3proof(){pv = nullptr;} - - - protected: - - struct node_struct { - rule rl; - ast aux; - int frame; - std::vector conclusion; - std::vector premises; - }; - - std::vector nodes; - std::vector > interps; // interpolations of lemmas - prover *pv; - - node make_node(){ - nodes.push_back(node_struct()); - return nodes.size()-1; - } - - void resolve(ast pivot, std::vector &cls1, const std::vector &cls2); - - node copy_rec(stl_ext::hash_map &memo, iz3proof &src, node n); - - void interpolate_lemma(node_struct &n); - - // lazily compute the result of resolution - // the node member "frame" indicates result is computed - const std::vector &get_conclusion(node x){ - node_struct &n = nodes[x]; - if(n.rl == Resolution && !n.frame){ - n.conclusion = get_conclusion(n.premises[0]); - resolve(n.aux,n.conclusion,get_conclusion(n.premises[1])); - n.frame = 1; - } - return n.conclusion; - } - - prover::range rng; - bool weak; - stl_ext::hash_set b_lits; - ast my_or(ast x, ast y); -#ifdef CHECK_PROOFS - std::vector child_interps; -#endif - bool pred_in_A(ast id); - bool term_in_B(ast id); - bool frame_in_A(int frame); - bool lit_in_B(ast lit); - ast get_A_lits(std::vector &cls); - ast get_B_lits(std::vector &cls); - void find_B_lits(); - ast disj_of_set(std::set &s); - void mk_or_factor(int p1, int p2, int i, std::vector &itps, std::vector > &disjs); - void mk_and_factor(int p1, int p2, int i, std::vector &itps, std::vector > &disjs); - void set_of_B_lits(std::vector &cls, std::set &res); - void set_of_A_lits(std::vector &cls, std::set &res); -}; - -#endif diff --git a/src/interp/iz3proof_itp.cpp b/src/interp/iz3proof_itp.cpp deleted file mode 100755 index bbeb8d072..000000000 --- a/src/interp/iz3proof_itp.cpp +++ /dev/null @@ -1,3117 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3proof.cpp - - Abstract: - - This class defines a simple interpolating proof system. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#pragma warning(disable:4101) -#endif - -#include "interp/iz3proof_itp.h" - -using namespace stl_ext; - -// #define INVARIANT_CHECKING - -class iz3proof_itp_impl : public iz3proof_itp { - - prover *pv; - prover::range rng; - bool weak; - - enum LitType {LitA,LitB,LitMixed}; - - hash_map placeholders; - - // These symbols represent deduction rules - - /* This symbol represents a proof by contradiction. That is, - contra(p,l1 /\ ... /\ lk) takes a proof p of - - l1,...,lk |- false - - and returns a proof of - - |- ~l1,...,~l2 - */ - symb contra; - - /* The summation rule. The term sum(p,c,i) takes a proof p of an - inequality i', an integer coefficient c and an inequality i, and - yields a proof of i' + ci. */ - symb sum; - - /* Proof rotation. The proof term rotate(q,p) takes a - proof p of: - - Gamma, q |- false - - and yields a proof of: - - Gamma |- ~q - */ - symb rotate_sum; - - /* Inequalities to equality. leq2eq(p, q, r) takes a proof - p of ~x=y, a proof q of x <= y and a proof r of y <= x - and yields a proof of false. */ - symb leq2eq; - - /* Equality to inequality. eq2leq(p, q) takes a proof p of x=y, and - a proof q ~(x <= y) and yields a proof of false. */ - symb eq2leq; - - /* Proof term cong(p,q) takes a proof p of x=y and a proof - q of t != t and returns a proof of false. */ - symb cong; - - - /* Excluded middle. exmid(phi,p,q) takes a proof p of phi and a - proof q of ~\phi and returns a proof of false. */ - symb exmid; - - /* Symmetry. symm(p) takes a proof p of x=y and produces - a proof of y=x. */ - symb symm; - - /* Modus ponens. modpon(p,e,q) takes proofs p of P, e of P=Q - and q of ~Q and returns a proof of false. */ - symb modpon; - - /* This oprerator represents a concatenation of rewrites. The term - a=b;c=d represents an A rewrite from a to b, followed by a B - rewrite from b to c, followed by an A rewrite from c to d. - */ - symb concat; - - /* This represents a lack of a proof */ - ast no_proof; - - // This is used to represent an infinitessimal value - ast epsilon; - - // Represents the top position of a term - ast top_pos; - - // add_pos(i,pos) represents position pos if the ith argument - symb add_pos; - - // rewrite proof rules - - /* rewrite_A(pos,cond,x=y) derives A |- cond => t[x]_p = t[y]_p - where t is an arbitrary term */ - symb rewrite_A; - - /* rewrite_B(pos,cond,x=y) derives B |- cond => t[x]_p = t[y]_p, - where t is an arbitrary term */ - symb rewrite_B; - - /* a normalization step is of the form (lhs=rhs) : proof, where "proof" - is a proof of lhs=rhs and lhs is a mixed term. If rhs is a mixed term - then it must have a greater index than lhs. */ - symb normal_step; - - /* A chain of normalization steps is either "true" (the null chain) - or normal_chain( ), where step is a normalization step - and tail is a normalization chain. The lhs of must have - a less term index than any lhs in the chain. Moreover, the rhs of - may not occur as the lhs of step in . If we wish to - add lhs=rhs to the beginning of and rhs=rhs' occurs in - we must apply transitivity, transforming to lhs=rhs'. */ - - symb normal_chain; - - /* If p is a proof of Q and c is a normalization chain, then normal(p,c) - is a proof of Q(c) (that is, Q with all substitutions in c performed). */ - - symb normal; - - /** Stand-ins for quantifiers */ - - symb sforall, sexists; - - - ast get_placeholder(ast t){ - hash_map::iterator it = placeholders.find(t); - if(it != placeholders.end()) - return it->second; - ast &res = placeholders[t]; - res = mk_fresh_constant("@p",get_type(t)); -#if 0 - std::cout << "placeholder "; - print_expr(std::cout,res); - std::cout << " = "; - print_expr(std::cout,t); - std::cout << std::endl; -#endif - return res; - } - - ast make_contra_node(const ast &pf, const std::vector &lits, int pfok = -1){ - if(lits.size() == 0) - return pf; - std::vector reslits; - reslits.push_back(make(contra,pf,mk_false())); - for(unsigned i = 0; i < lits.size(); i++){ - ast bar; - if(pfok & (1 << i)) bar = make(rotate_sum,lits[i],pf); - else bar = no_proof; - ast foo = make(contra,bar,lits[i]); - reslits.push_back(foo); - } - return make(And,reslits); - } - - LitType get_term_type(const ast &lit){ - prover::range r = pv->ast_scope(lit); - if(pv->range_is_empty(r)) - return LitMixed; - if(weak) { - if(pv->range_min(r) == SHRT_MIN) - return pv->range_contained(r,rng) ? LitA : LitB; - else - return pv->ranges_intersect(r,rng) ? LitA : LitB; - } - else - return pv->range_contained(r,rng) ? LitA : LitB; - } - - bool term_common(const ast &t){ - prover::range r = pv->ast_scope(t); - return pv->ranges_intersect(r,rng) && !pv->range_contained(r,rng); - } - - bool term_in_vocab(LitType ty, const ast &lit){ - prover::range r = pv->ast_scope(lit); - if(ty == LitA){ - return pv->ranges_intersect(r,rng); - } - return !pv->range_contained(r,rng); - } - - /** Make a resolution node with given pivot literal and premises. - The conclusion of premise1 should contain the negation of the - pivot literal, while the conclusion of premise2 should contain the - pivot literal. - */ - node make_resolution(ast pivot, const std::vector &conc, node premise1, node premise2) override { - LitType lt = get_term_type(pivot); - if(lt == LitA) - return my_or(premise1,premise2); - if(lt == LitB) - return my_and(premise1,premise2); - - /* the mixed case is a bit complicated */ - - static int non_local_count = 0; - ast res = resolve_arith(pivot,conc,premise1,premise2); -#ifdef INVARIANT_CHECKING - check_contra(conc,res); -#endif - non_local_count++; - return res; - } - - - /* Handles the case of resolution on a mixed arith atom. */ - - ast resolve_arith(const ast &pivot, const std::vector &conc, node premise1, node premise2){ - ast atom = get_lit_atom(pivot); - hash_map memo; - ast neg_pivot_lit = mk_not(atom); - if(op(pivot) != Not) - std::swap(premise1,premise2); - if(op(pivot) == Equal && op(arg(pivot,0)) == Select && op(arg(pivot,1)) == Select){ - neg_pivot_lit = mk_not(neg_pivot_lit); - std::swap(premise1,premise2); - } - return resolve_arith_rec1(memo, neg_pivot_lit, premise1, premise2); - } - - - ast apply_coeff(const ast &coeff, const ast &t){ -#if 0 - rational r; - if(!is_integer(coeff,r)) - throw iz3_exception("ack!"); - ast n = make_int(r.numerator()); - ast res = make(Times,n,t); - if(!r.is_int()) { - ast d = make_int(r.numerator()); - res = mk_idiv(res,d); - } - return res; -#endif - return make(Times,coeff,t); - } - - ast sum_ineq(const ast &coeff1, const ast &ineq1, const ast &coeff2, const ast &ineq2){ - opr sum_op = Leq; - if(op(ineq1) == Lt || op(ineq2) == Lt) - sum_op = Lt; - ast sum_sides[2]; - for(int i = 0; i < 2; i++){ - sum_sides[i] = make(Plus,apply_coeff(coeff1,arg(ineq1,i)),apply_coeff(coeff2,arg(ineq2,i))); - sum_sides[i] = z3_simplify(sum_sides[i]); - } - return make(sum_op,sum_sides[0],sum_sides[1]); - } - - - void collect_contra_resolvents(int from, const ast &pivot1, const ast &pivot, const ast &conj, std::vector &res){ - int nargs = num_args(conj); - for(int i = from; i < nargs; i++){ - ast f = arg(conj,i); - if(!(f == pivot)){ - ast ph = get_placeholder(mk_not(arg(pivot1,1))); - ast pf = arg(pivot1,0); - ast thing = pf == no_proof ? no_proof : subst_term_and_simp(ph,pf,arg(f,0)); - ast newf = make(contra,thing,arg(f,1)); - res.push_back(newf); - } - } - } - - bool is_negative_equality(const ast &e){ - if(op(e) == Not){ - opr o = op(arg(e,0)); - return o == Equal || o == Iff; - } - return false; - } - - int count_negative_equalities(const std::vector &resolvent){ - int res = 0; - for(unsigned i = 0; i < resolvent.size(); i++) - if(is_negative_equality(arg(resolvent[i],1))) - res++; - return res; - } - - ast resolve_contra_nf(const ast &pivot1, const ast &conj1, - const ast &pivot2, const ast &conj2){ - std::vector resolvent; - collect_contra_resolvents(0,pivot1,pivot2,conj2,resolvent); - collect_contra_resolvents(1,pivot2,pivot1,conj1,resolvent); - if(count_negative_equalities(resolvent) > 1) - throw proof_error(); - if(resolvent.size() == 1) // we have proved a contradiction - return simplify(arg(resolvent[0],0)); // this is the proof -- get interpolant - return make(And,resolvent); - } - - ast resolve_contra(const ast &pivot1, const ast &conj1, - const ast &pivot2, const ast &conj2){ - if(arg(pivot1,0) != no_proof) - return resolve_contra_nf(pivot1, conj1, pivot2, conj2); - if(arg(pivot2,0) != no_proof) - return resolve_contra_nf(pivot2, conj2, pivot1, conj1); - return resolve_with_quantifier(pivot1, conj1, pivot2, conj2); - } - - - bool is_contra_itp(const ast &pivot1, ast itp2, ast &pivot2){ - if(op(itp2) == And){ - int nargs = num_args(itp2); - for(int i = 1; i < nargs; i++){ - ast foo = arg(itp2,i); - if(op(foo) == Uninterpreted && sym(foo) == contra){ - if(arg(foo,1) == pivot1){ - pivot2 = foo; - return true; - } - } - else break; - } - } - return false; - } - - ast resolve_arith_rec2(hash_map &memo, const ast &pivot1, const ast &conj1, const ast &itp2){ - ast &res = memo[itp2]; - if(!res.null()) - return res; - - ast pivot2; - if(is_contra_itp(mk_not(arg(pivot1,1)),itp2,pivot2)) - res = resolve_contra(pivot1,conj1,pivot2,itp2); - else { - switch(op(itp2)){ - case Or: - case And: - case Implies: { - unsigned nargs = num_args(itp2); - std::vector args; args.resize(nargs); - for(unsigned i = 0; i < nargs; i++) - args[i] = resolve_arith_rec2(memo, pivot1, conj1, arg(itp2,i)); - ast foo = itp2; // get rid of const - res = clone(foo,args); - break; - } - default: - { - opr o = op(itp2); - if(o == Uninterpreted){ - symb s = sym(itp2); - if(s == sforall || s == sexists) - res = make(s,arg(itp2,0),resolve_arith_rec2(memo, pivot1, conj1, arg(itp2,1))); - else - res = itp2; - } - else { - res = itp2; - } - } - } - } - return res; - } - - - ast resolve_arith_rec1(hash_map &memo, const ast &neg_pivot_lit, const ast &itp1, const ast &itp2){ - ast &res = memo[itp1]; - if(!res.null()) - return res; - ast pivot1; - if(is_contra_itp(neg_pivot_lit,itp1,pivot1)){ - hash_map memo2; - res = resolve_arith_rec2(memo2,pivot1,itp1,itp2); - } - else { - switch(op(itp1)){ - case Or: - case And: - case Implies: { - unsigned nargs = num_args(itp1); - std::vector args; args.resize(nargs); - for(unsigned i = 0; i < nargs; i++) - args[i] = resolve_arith_rec1(memo, neg_pivot_lit, arg(itp1,i), itp2); - ast foo = itp1; // get rid of const - res = clone(foo,args); - break; - } - default: - { - opr o = op(itp1); - if(o == Uninterpreted){ - symb s = sym(itp1); - if(s == sforall || s == sexists) - res = make(s,arg(itp1,0),resolve_arith_rec1(memo, neg_pivot_lit, arg(itp1,1), itp2)); - else - res = itp1; - } - else { - res = itp1; - } - } - } - } - return res; - } - - void check_contra(hash_set &memo, hash_set &neg_lits, const ast &foo){ - if(memo.find(foo) != memo.end()) - return; - memo.insert(foo); - if(op(foo) == Uninterpreted && sym(foo) == contra){ - ast neg_lit = arg(foo,1); - if(!is_false(neg_lit) && neg_lits.find(neg_lit) == neg_lits.end()) - throw iz3_exception("lost a literal"); - return; - } - else { - switch(op(foo)){ - case Or: - case And: - case Implies: { - unsigned nargs = num_args(foo); - std::vector args; args.resize(nargs); - for(unsigned i = 0; i < nargs; i++) - check_contra(memo, neg_lits, arg(foo,i)); - break; - } - default: break; - } - } - } - - void check_contra(const std::vector &neg_lits, const ast &foo){ - hash_set memo; - hash_set neg_lits_set; - for(unsigned i = 0; i < neg_lits.size(); i++) - if(get_term_type(neg_lits[i]) == LitMixed) - neg_lits_set.insert(mk_not(neg_lits[i])); - check_contra(memo,neg_lits_set,foo); - } - - hash_map subst_memo; // memo of subst function - - ast subst_term_and_simp(const ast &var, const ast &t, const ast &e){ - subst_memo.clear(); - return subst_term_and_simp_rec(var,t,e); - } - - ast subst_term_and_simp_rec(const ast &var, const ast &t, const ast &e){ - if(e == var) return t; - std::pair foo(e,ast()); - std::pair::iterator,bool> bar = subst_memo.insert(foo); - ast &res = bar.first->second; - if(bar.second){ - if(op(e) == Uninterpreted){ - symb g = sym(e); - if(g == rotate_sum){ - if(var == get_placeholder(arg(e,0))){ - res = e; - } - else - res = make(rotate_sum,arg(e,0),subst_term_and_simp_rec(var,t,arg(e,1))); - return res; - } - if(g == concat){ - res = e; - return res; - } - } - int nargs = num_args(e); - std::vector args(nargs); - for(int i = 0; i < nargs; i++) - args[i] = subst_term_and_simp_rec(var,t,arg(e,i)); - opr f = op(e); - if(f == Equal && args[0] == args[1]) res = mk_true(); - else if(f == And) res = my_and(args); - else if(f == Or) res = my_or(args); - else if(f == Idiv) res = mk_idiv(args[0],args[1]); - else res = clone(e,args); - } - return res; - } - - /* This is where the real work happens. Here, we simplify the - proof obtained by cut elimination, obtaining an interpolant. */ - - struct cannot_simplify: public iz3_exception { - cannot_simplify(): iz3_exception("cannot_simplify") {} - }; - hash_map simplify_memo; - - ast simplify(const ast &t){ - ast res = normalize(simplify_rec(t)); -#ifdef BOGUS_QUANTS - if(localization_vars.size()) - res = add_quants(z3_simplify(res)); -#endif - return res; - } - - ast simplify_rec(const ast &e){ - std::pair foo(e,ast()); - std::pair::iterator,bool> bar = simplify_memo.insert(foo); - ast &res = bar.first->second; - if(bar.second){ - int nargs = num_args(e); - std::vector args(nargs); - bool placeholder_arg = false; - symb g = sym(e); - if(g == concat){ - res = e; - return res; - } - for(int i = 0; i < nargs; i++){ - if(i == 0 && g == rotate_sum) - args[i] = arg(e,i); - else - args[i] = simplify_rec(arg(e,i)); - placeholder_arg |= is_placeholder(args[i]); - } - try { - TRACE("duality", print_expr(tout, e); tout << "\n";); - opr f = op(e); - if(f == Equal && args[0] == args[1]) res = mk_true(); - else if(f == And) res = my_and(args); - else if(f == Or) - res = my_or(args); - else if(f == Idiv) res = mk_idiv(args[0],args[1]); - else if(f == Uninterpreted && !placeholder_arg){ - if(g == rotate_sum) res = simplify_rotate(args); - else if(g == symm) res = simplify_symm(args); - else if(g == modpon) res = simplify_modpon(args); - else if(g == sum) res = simplify_sum(args); - else if(g == exmid) res = simplify_exmid(args); - else if(g == cong) res = simplify_cong(args); -#if 0 - else if(g == modpon) res = simplify_modpon(args); - else if(g == leq2eq) res = simplify_leq2eq(args); - else if(g == eq2leq) res = simplify_eq2leq(args); -#endif - else res = clone(e,args); - } - else res = clone(e,args); - } - catch (const cannot_simplify &){ - if(g == sum) - res = clone(e,args); - else - throw "interpolation failure"; - } - } - return res; - } - - - ast simplify_rotate(const std::vector &args){ - const ast &pf = args[1]; - ast pl = get_placeholder(args[0]); - if(op(pf) == Uninterpreted){ - symb g = sym(pf); - if(g == sum) return simplify_rotate_sum(pl,pf); - if(g == leq2eq) return simplify_rotate_leq2eq(pl,args[0],pf); - if(g == eq2leq) return simplify_rotate_eq2leq(pl,args[0],pf); - if(g == cong) return simplify_rotate_cong(pl,args[0],pf); - if(g == modpon) return simplify_rotate_modpon(pl,args[0],pf); - // if(g == symm) return simplify_rotate_symm(pl,args[0],pf); - } - if(op(pf) == Leq) - throw iz3_exception("foo!"); - throw cannot_simplify(); - } - - bool is_normal_ineq(const ast &ineq){ - if(sym(ineq) == normal) - return is_ineq(arg(ineq,0)); - return is_ineq(ineq); - } - - ast destruct_cond_ineq(const ast &ineq, ast &Aproves, ast &Bproves){ - ast res = ineq; - opr o = op(res); - if(o == And){ - Aproves = my_and(Aproves,arg(res,0)); - res = arg(res,1); - o = op(res); - } - if(o == Implies){ - Bproves = my_and(Bproves,arg(res,0)); - res = arg(res,1); - } - return res; - } - - ast distribute_coeff(const ast &coeff, const ast &s){ - if(sym(s) == sum){ - if(sym(arg(s,2)) == sum) - return make(sum, - distribute_coeff(coeff,arg(s,0)), - make_int(rational(1)), - distribute_coeff(make(Times,coeff,arg(s,1)), arg(s,2))); - else - return make(sum, - distribute_coeff(coeff,arg(s,0)), - make(Times,coeff,arg(s,1)), - arg(s,2)); - } - if(op(s) == Leq && arg(s,1) == make_int(rational(0)) && arg(s,2) == make_int(rational(0))) - return s; - return make(sum,make(Leq,make_int(rational(0)),make_int(rational(0))),coeff,s); - } - - ast simplify_sum(std::vector &args){ - if(args[1] != make_int(rational(1))){ - if(sym(args[2]) == sum) - return make(sum,args[0],make_int(rational(1)),distribute_coeff(args[1],args[2])); - } - ast Aproves = mk_true(), Bproves = mk_true(); - ast ineq = destruct_cond_ineq(args[0],Aproves,Bproves); - if(!is_normal_ineq(ineq)) throw cannot_simplify(); - sum_cond_ineq(ineq,args[1],args[2],Aproves,Bproves); - return my_and(Aproves,my_implies(Bproves,ineq)); - } - - ast simplify_rotate_sum(const ast &pl, const ast &pf){ - ast Aproves = mk_true(), Bproves = mk_true(); - ast ineq = make(Leq,make_int("0"),make_int("0")); - ineq = rotate_sum_rec(pl,pf,Aproves,Bproves,ineq); - if(is_true(Aproves) && is_true(Bproves)) - return ineq; - return my_and(Aproves,my_implies(Bproves,ineq)); - } - - bool is_rewrite_chain(const ast &chain){ - return sym(chain) == concat; - } - -#if 0 - ast ineq_from_chain_simple(const ast &chain, ast &cond){ - if(is_true(chain)) - return chain; - ast last = chain_last(chain); - ast rest = chain_rest(chain); - if(is_true(rest) && is_rewrite_side(LitA,last) - && is_true(rewrite_lhs(last))){ - cond = my_and(cond,rewrite_cond(last)); - return rewrite_rhs(last); - } - if(is_rewrite_side(LitB,last) && is_true(rewrite_cond(last))) - return ineq_from_chain_simple(rest,cond); - return chain; - } -#endif - - ast ineq_from_chain(const ast &chain, ast &Aproves, ast &Bproves){ - if(is_rewrite_chain(chain)) - return rewrite_chain_to_normal_ineq(chain,Aproves,Bproves); - return chain; - } - - - void sum_cond_ineq(ast &ineq, const ast &coeff2, const ast &ineq2, ast &Aproves, ast &Bproves){ - opr o = op(ineq2); - if(o == And){ - sum_cond_ineq(ineq,coeff2,arg(ineq2,1),Aproves,Bproves); - Aproves = my_and(Aproves,arg(ineq2,0)); - } - else if(o == Implies){ - sum_cond_ineq(ineq,coeff2,arg(ineq2,1),Aproves,Bproves); - Bproves = my_and(Bproves,arg(ineq2,0)); - } - else { - ast the_ineq = ineq_from_chain(ineq2,Aproves,Bproves); - if(sym(ineq) == normal || sym(the_ineq) == normal){ - sum_normal_ineq(ineq,coeff2,the_ineq,Aproves,Bproves); - return; - } - if(is_ineq(the_ineq)) - linear_comb(ineq,coeff2,the_ineq); - else - throw cannot_simplify(); - } - } - - void destruct_normal(const ast &pf, ast &p, ast &n){ - if(sym(pf) == normal){ - p = arg(pf,0); - n = arg(pf,1); - } - else { - p = pf; - n = mk_true(); - } - } - - void sum_normal_ineq(ast &ineq, const ast &coeff2, const ast &ineq2, ast &Aproves, ast &Bproves){ - ast in1,in2,n1,n2; - destruct_normal(ineq,in1,n1); - destruct_normal(ineq2,in2,n2); - ast dummy1, dummy2; - sum_cond_ineq(in1,coeff2,in2,dummy1,dummy2); - n1 = merge_normal_chains(n1,n2, Aproves, Bproves); - ineq = is_true(n1) ? in1 : make_normal(in1,n1); - } - - bool is_ineq(const ast &ineq){ - opr o = op(ineq); - if(o == Not) o = op(arg(ineq,0)); - return o == Leq || o == Lt || o == Geq || o == Gt; - } - - // divide both sides of inequality by a non-negative integer divisor - ast idiv_ineq(const ast &ineq1, const ast &divisor){ - if(sym(ineq1) == normal){ - ast in1,n1; - destruct_normal(ineq1,in1,n1); - in1 = idiv_ineq(in1,divisor); - return make_normal(in1,n1); - } - if(divisor == make_int(rational(1))) - return ineq1; - ast ineq = ineq1; - if(op(ineq) == Lt) - ineq = simplify_ineq(make(Leq,arg(ineq,0),make(Sub,arg(ineq,1),make_int("1")))); - return make(op(ineq),mk_idiv(arg(ineq,0),divisor),mk_idiv(arg(ineq,1),divisor)); - } - - ast rotate_sum_rec(const ast &pl, const ast &pf, ast &Aproves, ast &Bproves, ast &ineq){ - if(pf == pl){ - if(sym(ineq) == normal) - return ineq; - return simplify_ineq(ineq); - } - if(op(pf) == Uninterpreted && sym(pf) == sum){ - if(arg(pf,2) == pl){ - sum_cond_ineq(ineq,make_int("1"),arg(pf,0),Aproves,Bproves); - ineq = idiv_ineq(ineq,arg(pf,1)); - return ineq; - } - sum_cond_ineq(ineq,arg(pf,1),arg(pf,2),Aproves,Bproves); - return rotate_sum_rec(pl,arg(pf,0),Aproves,Bproves,ineq); - } - throw cannot_simplify(); - } - - ast simplify_rotate_leq2eq(const ast &pl, const ast &neg_equality, const ast &pf){ - if(pl == arg(pf,0)){ - ast equality = arg(neg_equality,0); - ast x = arg(equality,0); - ast y = arg(equality,1); - ast Aproves1 = mk_true(), Bproves1 = mk_true(); - ast pf1 = destruct_cond_ineq(arg(pf,1), Aproves1, Bproves1); - ast pf2 = destruct_cond_ineq(arg(pf,2), Aproves1, Bproves1); - ast xleqy = round_ineq(ineq_from_chain(pf1,Aproves1,Bproves1)); - ast yleqx = round_ineq(ineq_from_chain(pf2,Aproves1,Bproves1)); - ast ineq1 = make(Leq,make_int("0"),make_int("0")); - sum_cond_ineq(ineq1,make_int("-1"),xleqy,Aproves1,Bproves1); - sum_cond_ineq(ineq1,make_int("-1"),yleqx,Aproves1,Bproves1); - ast Acond = my_implies(Aproves1,my_and(Bproves1,z3_simplify(ineq1))); - ast Aproves2 = mk_true(), Bproves2 = mk_true(); - ast ineq2 = make(Leq,make_int("0"),make_int("0")); - sum_cond_ineq(ineq2,make_int("1"),xleqy,Aproves2,Bproves2); - sum_cond_ineq(ineq2,make_int("1"),yleqx,Aproves2,Bproves2); - ast Bcond = my_implies(Bproves1,my_and(Aproves1,z3_simplify(ineq2))); - // if(!is_true(Aproves1) || !is_true(Bproves1)) - // std::cout << "foo!\n";; - if(y == make_int(rational(0)) && op(x) == Plus && num_args(x) == 2){ - if(get_term_type(arg(x,0)) == LitA){ - ast iter = z3_simplify(make(Plus,arg(x,0),get_ineq_rhs(xleqy))); - ast rewrite1 = make_rewrite(LitA,pos_add(0,top_pos),Acond,make(Equal,arg(x,0),iter)); - iter = make(Plus,iter,arg(x,1)); - ast rewrite2 = make_rewrite(LitB,top_pos,Bcond,make(Equal,iter,y)); - return chain_cons(chain_cons(mk_true(),rewrite1),rewrite2); - } - if(get_term_type(arg(x,1)) == LitA){ - ast iter = z3_simplify(make(Plus,arg(x,1),get_ineq_rhs(xleqy))); - ast rewrite1 = make_rewrite(LitA,pos_add(1,top_pos),Acond,make(Equal,arg(x,1),iter)); - iter = make(Plus,arg(x,0),iter); - ast rewrite2 = make_rewrite(LitB,top_pos,Bcond,make(Equal,iter,y)); - return chain_cons(chain_cons(mk_true(),rewrite1),rewrite2); - } - } - if(get_term_type(x) == LitA){ - ast iter = z3_simplify(make(Plus,x,get_ineq_rhs(xleqy))); - ast rewrite1 = make_rewrite(LitA,top_pos,Acond,make(Equal,x,iter)); - ast rewrite2 = make_rewrite(LitB,top_pos,Bcond,make(Equal,iter,y)); - return chain_cons(chain_cons(mk_true(),rewrite1),rewrite2); - } - if(get_term_type(y) == LitA){ - ast iter = z3_simplify(make(Plus,y,get_ineq_rhs(yleqx))); - ast rewrite2 = make_rewrite(LitA,top_pos,Acond,make(Equal,iter,y)); - ast rewrite1 = make_rewrite(LitB,top_pos,Bcond,make(Equal,x,iter)); - return chain_cons(chain_cons(mk_true(),rewrite1),rewrite2); - } - throw cannot_simplify(); - } - throw cannot_simplify(); - } - - ast round_ineq(const ast &ineq){ - if(sym(ineq) == normal) - return make_normal(round_ineq(arg(ineq,0)),arg(ineq,1)); - if(!is_ineq(ineq)) - throw cannot_simplify(); - ast res = simplify_ineq(ineq); - if(op(res) == Lt) - res = make(Leq,arg(res,0),make(Sub,arg(res,1),make_int("1"))); - return res; - } - - ast unmixed_eq2ineq(const ast &lhs, const ast &rhs, opr comp_op, const ast &equa, ast &cond){ - ast ineqs= chain_ineqs(comp_op,LitA,equa,lhs,rhs); // chain must be from lhs to rhs - cond = my_and(cond,chain_conditions(LitA,equa)); - ast Bconds = z3_simplify(chain_conditions(LitB,equa)); - if(is_true(Bconds) && op(ineqs) != And) - return my_implies(cond,ineqs); - if(op(ineqs) != And) - return my_and(Bconds,my_implies(cond,ineqs)); - throw iz3_exception("help!"); - } - - ast add_mixed_eq2ineq(const ast &lhs, const ast &rhs, const ast &equa, const ast &itp){ - if(is_true(equa)) - return itp; - std::vector args(3); - args[0] = itp; - args[1] = make_int("1"); - ast ineq = make(Leq,make_int(rational(0)),make_int(rational(0))); - args[2] = make_normal(ineq,cons_normal(fix_normal(lhs,rhs,equa),mk_true())); - return simplify_sum(args); - } - - - ast simplify_rotate_eq2leq(const ast &pl, const ast &neg_equality, const ast &pf){ - if(pl == arg(pf,1)){ - TRACE("duality", print_expr(tout, pl); print_expr(tout << "\n", neg_equality); print_expr(tout << "\n", pf); tout << "\n";); - ast cond = mk_true(); - ast equa = sep_cond(arg(pf,0),cond); - if(is_equivrel_chain(equa)){ - ast lhs,rhs; eq_from_ineq(arg(neg_equality,0),lhs,rhs); // get inequality we need to prove - if(!rewrites_from_to(equa,lhs,rhs)){ - lhs = arg(arg(neg_equality,0),0); // the equality proved is ambiguous, sadly - rhs = arg(arg(neg_equality,0),1); - } - LitType lhst = get_term_type(lhs), rhst = get_term_type(rhs); - if(lhst != LitMixed && rhst != LitMixed) - return unmixed_eq2ineq(lhs, rhs, op(arg(neg_equality,0)), equa, cond); - else { - ast left, left_term, middle, right_term, right; - left = get_left_movers(equa,lhs,middle,left_term); - middle = get_right_movers(middle,rhs,right,right_term); - ast itp = unmixed_eq2ineq(left_term, right_term, op(arg(neg_equality,0)), middle, cond); - // itp = my_implies(cond,itp); - itp = add_mixed_eq2ineq(lhs, left_term, left, itp); - itp = add_mixed_eq2ineq(right_term, rhs, right, itp); - return itp; - } - } - } - throw iz3_exception("help!"); - } - - void reverse_modpon(std::vector &args){ - std::vector sargs(1); sargs[0] = args[1]; - args[1] = simplify_symm(sargs); - if(is_equivrel_chain(args[2])) - args[1] = down_chain(args[1]); - std::swap(args[0],args[2]); - } - - ast simplify_rotate_modpon(const ast &pl, const ast &neg_equality, const ast &pf){ - std::vector args; args.resize(3); - args[0] = arg(pf,0); - args[1] = arg(pf,1); - args[2] = arg(pf,2); - if(pl == args[0]) - reverse_modpon(args); - if(pl == args[2]){ - ast cond = mk_true(); - ast chain = simplify_modpon_fwd(args, cond); - return my_implies(cond,chain); - } - throw cannot_simplify(); - } - - ast get_ineq_rhs(const ast &ineq2){ - opr o = op(ineq2); - if(o == Implies) - return get_ineq_rhs(arg(ineq2,1)); - else if(o == Leq || o == Lt) - return arg(ineq2,1); - throw cannot_simplify(); - } - - ast simplify_rotate_cong(const ast &pl, const ast &neg_equality, const ast &pf){ - if(pl == arg(pf,2)){ - if(op(arg(pf,0)) == True) - return mk_true(); - rational pos; - if(is_numeral(arg(pf,1),pos)){ - int ipos = pos.get_unsigned(); - ast cond = mk_true(); - ast equa = sep_cond(arg(pf,0),cond); -#if 0 - if(op(equa) == Equal){ - ast pe = mk_not(neg_equality); - ast lhs = subst_in_arg_pos(ipos,arg(equa,0),arg(pe,0)); - ast rhs = subst_in_arg_pos(ipos,arg(equa,1),arg(pe,1)); - ast res = make(Equal,lhs,rhs); - return my_implies(cond,res); - } -#endif - ast res = chain_pos_add(ipos,equa); - return my_implies(cond,res); - } - } - throw cannot_simplify(); - } - - ast simplify_symm(const std::vector &args){ - if(op(args[0]) == True) - return mk_true(); - ast cond = mk_true(); - ast equa = sep_cond(args[0],cond); - if(is_equivrel_chain(equa)) - return my_implies(cond,reverse_chain(equa)); - if(is_negation_chain(equa)) - return commute_negation_chain(equa); - throw cannot_simplify(); - } - - ast simplify_modpon_fwd(const std::vector &args, ast &cond){ - ast P = sep_cond(args[0],cond); - ast PeqQ = sep_cond(args[1],cond); - ast chain; - if(is_equivrel_chain(P)){ - try { - ast split[2]; - split_chain(PeqQ,split); - chain = reverse_chain(split[0]); - chain = concat_rewrite_chain(chain,P); - chain = concat_rewrite_chain(chain,split[1]); - } - catch(const cannot_split &){ - static int this_count = 0; - this_count++; - ast tail, pref = get_head_chain(PeqQ,tail,false); // pref is x=y, tail is x=y -> x'=y' - ast split[2]; split_chain(tail,split); // rewrites from x to x' and y to y' - ast head = chain_last(pref); - ast prem = make_rewrite(rewrite_side(head),top_pos,rewrite_cond(head),make(Iff,mk_true(),mk_not(rewrite_lhs(head)))); - ast back_chain = chain_cons(mk_true(),prem); - back_chain = concat_rewrite_chain(back_chain,chain_pos_add(0,reverse_chain(chain_rest(pref)))); - ast cond = contra_chain(back_chain,P); - if(is_rewrite_side(LitA,head)) - cond = mk_not(cond); - ast fwd_rewrite = make_rewrite(rewrite_side(head),top_pos,cond,rewrite_rhs(head)); - P = chain_cons(mk_true(),fwd_rewrite); - chain = reverse_chain(split[0]); - chain = concat_rewrite_chain(chain,P); - chain = concat_rewrite_chain(chain,split[1]); - } - } - else { // if not an equivalence, must be of form T <-> pred - chain = concat_rewrite_chain(P,PeqQ); - } - return chain; - } - - struct subterm_normals_failed: public iz3_exception { - subterm_normals_failed(): iz3_exception("subterm_normals_failed") {} - }; - - void get_subterm_normals(const ast &ineq1, const ast &ineq2, const ast &chain, ast &normals, - const ast &pos, hash_set &memo, ast &Aproves, ast &Bproves){ - opr o1 = op(ineq1); - opr o2 = op(ineq2); - if(o1 == Not || o1 == Leq || o1 == Lt || o1 == Geq || o1 == Gt || o1 == Plus || o1 == Times){ - int n = num_args(ineq1); - if(o2 != o1 || num_args(ineq2) != n) - throw iz3_exception("bad inequality rewriting"); - for(int i = 0; i < n; i++){ - ast new_pos = add_pos_to_end(pos,i); - get_subterm_normals(arg(ineq1,i), arg(ineq2,i), chain, normals, new_pos, memo, Aproves, Bproves); - } - } - else if(get_term_type(ineq2) == LitMixed){ - if(memo.find(ineq2) == memo.end()){ - memo.insert(ineq2); - ast sub_chain = extract_rewrites(chain,pos); - if(is_true(sub_chain)) - throw iz3_exception("bad inequality rewriting"); - ast new_normal = make_normal_step(ineq2,ineq1,reverse_chain(sub_chain)); - normals = merge_normal_chains(normals,cons_normal(new_normal,mk_true()), Aproves, Bproves); - } - } - else if(!(ineq1 == ineq2)) - throw subterm_normals_failed(); - } - - ast rewrites_to_normals(const ast &ineq1, const ast &chain, ast &normals, ast &Aproves, ast &Bproves, ast &Aineqs){ - if(is_true(chain)) - return ineq1; - ast last = chain_last(chain); - ast rest = chain_rest(chain); - ast new_ineq1 = rewrites_to_normals(ineq1, rest, normals, Aproves, Bproves, Aineqs); - ast p1 = rewrite_pos(last); - ast term1; - ast coeff = arith_rewrite_coeff(new_ineq1,p1,term1); - ast res = subst_in_pos(new_ineq1,rewrite_pos(last),rewrite_rhs(last)); - ast rpos; - pos_diff(p1,rewrite_pos(last),rpos); - ast term2 = subst_in_pos(term1,rpos,rewrite_rhs(last)); - if(get_term_type(term1) != LitMixed && get_term_type(term2) != LitMixed){ - if(is_rewrite_side(LitA,last)) - linear_comb(Aineqs,coeff,make(Leq,make_int(rational(0)),make(Sub,term2,term1))); - } - else { - ast pf = extract_rewrites(make(concat,mk_true(),last),p1); - ast new_normal = fix_normal(term1,term2,pf); - normals = merge_normal_chains(normals,cons_normal(new_normal,mk_true()), Aproves, Bproves); - } - return res; - } - - ast arith_rewrite_coeff(const ast &ineq, ast &p1, ast &term){ - ast coeff = make_int(rational(1)); - if(p1 == top_pos){ - term = ineq; - return coeff; - } - int argpos = pos_arg(p1); - opr o = op(ineq); - switch(o){ - case Leq: - case Lt: - coeff = argpos ? make_int(rational(1)) : make_int(rational(-1)); - break; - case Geq: - case Gt: - coeff = argpos ? make_int(rational(-1)) : make_int(rational(1)); - break; - case Not: - coeff = make_int(rational(-1)); - case Plus: - break; - case Times: - coeff = arg(ineq,0); - break; - default: - p1 = top_pos; - term = ineq; - return coeff; - } - p1 = arg(p1,1); - ast res = arith_rewrite_coeff(arg(ineq,argpos),p1,term); - p1 = pos_add(argpos,p1); - return coeff == make_int(rational(1)) ? res : make(Times,coeff,res); - } - - ast rewrite_chain_to_normal_ineq(const ast &chain, ast &Aproves, ast &Bproves){ - ast tail, pref = get_head_chain(chain,tail,false); // pref is x=y, tail is x=y -> x'=y' - ast head = chain_last(pref); - ast ineq1 = rewrite_rhs(head); - ast ineq2 = apply_rewrite_chain(ineq1,tail); - ast nc = mk_true(); - hash_set memo; - ast itp = make(Leq,make_int(rational(0)),make_int(rational(0))); - ast Aproves_save = Aproves, Bproves_save = Bproves; try { - get_subterm_normals(ineq1,ineq2,tail,nc,top_pos,memo, Aproves, Bproves); - } - catch (const subterm_normals_failed &){ Aproves = Aproves_save; Bproves = Bproves_save; nc = mk_true(); - rewrites_to_normals(ineq1, tail, nc, Aproves, Bproves, itp); - } - if(is_rewrite_side(LitA,head)){ - linear_comb(itp,make_int("1"),ineq1); // make sure it is normal form - //itp = ineq1; - ast mc = z3_simplify(chain_side_proves(LitB,pref)); - Bproves = my_and(Bproves,mc); - } - else { - ast mc = z3_simplify(chain_side_proves(LitA,pref)); - Aproves = my_and(Aproves,mc); - } - if(is_true(nc)) - return itp; - return make_normal(itp,nc); - } - - /* Given a chain rewrite chain deriving not P and a rewrite chain deriving P, return an interpolant. */ - ast contra_chain(const ast &neg_chain, const ast &pos_chain){ - // equality is a special case. we use the derivation of x=y to rewrite not(x=y) to not(y=y) - if(is_equivrel_chain(pos_chain)){ - ast tail, pref = get_head_chain(neg_chain,tail); // pref is not(x=y), tail is not(x,y) -> not(x',y') - ast split[2]; split_chain(down_chain(tail),split); // rewrites from x to x' and y to y' - ast chain = split[0]; - chain = concat_rewrite_chain(chain,pos_chain); // rewrites from x to y' - chain = concat_rewrite_chain(chain,reverse_chain(split[1])); // rewrites from x to y - chain = concat_rewrite_chain(pref,chain_pos_add(0,chain_pos_add(0,chain))); // rewrites t -> not(y=y) - ast head = chain_last(pref); - if(is_rewrite_side(LitB,head)){ - ast condition = chain_conditions(LitB,chain); - return my_and(my_implies(chain_conditions(LitA,chain),chain_formulas(LitA,chain)),condition); - } - else { - ast condition = chain_conditions(LitA,chain); - return my_and(chain_conditions(LitB,chain),my_implies(condition,mk_not(chain_formulas(LitB,chain)))); - } - // ast chain = concat_rewrite_chain(neg_chain,chain_pos_add(0,chain_pos_add(0,pos_chain))); - // return my_and(my_implies(chain_conditions(LitA,chain),chain_formulas(LitA,chain)),chain_conditions(LitB,chain)); - } - // otherwise, we reverse the derivation of t = P and use it to rewrite not(P) to not(t) - ast chain = concat_rewrite_chain(neg_chain,chain_pos_add(0,reverse_chain(pos_chain))); - return my_and(my_implies(chain_conditions(LitA,chain),chain_formulas(LitA,chain)),chain_conditions(LitB,chain)); - } - - ast simplify_modpon(const std::vector &args){ - ast Aproves = mk_true(), Bproves = mk_true(); - ast chain = simplify_modpon_fwd(args,Bproves); - ast Q2 = destruct_cond_ineq(args[2],Aproves,Bproves); - ast interp; - if(is_normal_ineq(Q2)){ // inequalities are special - ast nQ2 = rewrite_chain_to_normal_ineq(chain,Aproves,Bproves); - sum_cond_ineq(nQ2,make_int(rational(1)),Q2,Aproves,Bproves); - interp = normalize(nQ2); - } - else - interp = is_negation_chain(chain) ? contra_chain(chain,Q2) : contra_chain(Q2,chain); - return my_and(Aproves,my_implies(Bproves,interp)); - } - - - ast simplify_exmid(const std::vector &args){ - if(is_equivrel(args[0])){ - ast Aproves = mk_true(), Bproves = mk_true(); - ast chain = destruct_cond_ineq(args[1],Aproves,Bproves); - ast Q2 = destruct_cond_ineq(args[2],Aproves,Bproves); - ast interp = contra_chain(Q2,chain); - return my_and(Aproves,my_implies(Bproves,interp)); - } - throw iz3_exception("bad exmid"); - } - - ast simplify_cong(const std::vector &args){ - ast Aproves = mk_true(), Bproves = mk_true(); - ast chain = destruct_cond_ineq(args[0],Aproves,Bproves); - rational pos; - if(is_numeral(args[1],pos)){ - int ipos = pos.get_unsigned(); - chain = chain_pos_add(ipos,chain); - ast Q2 = destruct_cond_ineq(args[2],Aproves,Bproves); - ast interp = contra_chain(Q2,chain); - return my_and(Aproves,my_implies(Bproves,interp)); - } - throw iz3_exception("bad cong"); - } - - bool is_equivrel(const ast &p){ - opr o = op(p); - return o == Equal || o == Iff; - } - - struct rewrites_failed: public iz3_exception { - rewrites_failed(): iz3_exception("rewrites_failed") {} - }; - - /* Suppose p in Lang(B) and A |- p -> q and B |- q -> r. Return a z in Lang(B) such that - B |- p -> z and A |- z -> q. Collect any side conditions in "rules". */ - - ast commute_rewrites(const ast &p, const ast &q, const ast &r, ast &rules){ - if(q == r) - return p; - if(p == q) - return r; - else { - ast rew = make(Equal,q,r); - if(get_term_type(rew) == LitB){ - apply_common_rewrites(p,p,q,rules); // A rewrites must be over comon vocab - return r; - } - } - if(sym(p) != sym(q) || sym(q) != sym(r)) - throw rewrites_failed(); - int nargs = num_args(p); - if(nargs != num_args(q) || nargs != num_args(r)) - throw rewrites_failed(); - std::vector args; args.resize(nargs); - for(int i = 0; i < nargs; i++) - args[i] = commute_rewrites(arg(p,i),arg(q,i),arg(r,i),rules); - return clone(p,args); - } - - ast apply_common_rewrites(const ast &p, const ast &q, const ast &r, ast &rules){ - if(q == r) - return p; - ast rew = make(Equal,q,r); - if(term_common(rew)){ - if(p != q) - throw rewrites_failed(); - rules = my_and(rules,rew); - return r; - } - if(sym(p) != sym(q) || sym(q) != sym(r)) - return p; - int nargs = num_args(p); - if(nargs != num_args(q) || nargs != num_args(r)) - return p; - std::vector args; args.resize(nargs); - for(int i = 0; i < nargs; i++) - args[i] = apply_common_rewrites(arg(p,i),arg(q,i),arg(r,i),rules); - return clone(p,args); - } - - ast apply_all_rewrites(const ast &p, const ast &q, const ast &r){ - if(q == r) - return p; - if(p == q) - return r; - if(sym(p) != sym(q) || sym(q) != sym(r)) - throw rewrites_failed(); - int nargs = num_args(p); - if(nargs != num_args(q) || nargs != num_args(r)) - throw rewrites_failed(); - std::vector args; args.resize(nargs); - for(int i = 0; i < nargs; i++) - args[i] = apply_all_rewrites(arg(p,i),arg(q,i),arg(r,i)); - return clone(p,args); - } - - ast delta(const ast &x, const ast &y){ - if(op(x) != op(y) || (op(x) == Uninterpreted && sym(x) != sym(y)) || num_args(x) != num_args(y)) - return make(Equal,x,y); - ast res = mk_true(); - int nargs = num_args(x); - for(int i = 0; i < nargs; i++) - res = my_and(res,delta(arg(x,i),arg(y,i))); - return res; - } - - bool diff_rec(LitType t, const ast &p, const ast &q, ast &pd, ast &qd){ - if(p == q) - return false; - if(term_in_vocab(t,p) && term_in_vocab(t,q)){ - pd = p; - qd = q; - return true; - } - else { - if(sym(p) != sym(q)) return false; - int nargs = num_args(p); - if(num_args(q) != nargs) return false; - for(int i = 0; i < nargs; i++) - if(diff_rec(t,arg(p,i),arg(q,i),pd,qd)) - return true; - return false; - } - } - - void diff(LitType t, const ast &p, const ast &q, ast &pd, ast &qd){ - if(!diff_rec(t,p,q,pd,qd)) - throw cannot_simplify(); - } - - bool apply_diff_rec(LitType t, const ast &inp, const ast &p, const ast &q, ast &out){ - if(p == q) - return false; - if(term_in_vocab(t,p) && term_in_vocab(t,q)){ - if(inp != p) - throw cannot_simplify(); - out = q; - return true; - } - else { - int nargs = num_args(p); - if(sym(p) != sym(q)) throw cannot_simplify(); - if(num_args(q) != nargs) throw cannot_simplify(); - if(sym(p) != sym(inp)) throw cannot_simplify(); - if(num_args(inp) != nargs) throw cannot_simplify(); - for(int i = 0; i < nargs; i++) - if(apply_diff_rec(t,arg(inp,i),arg(p,i),arg(q,i),out)) - return true; - return false; - } - } - - ast apply_diff(LitType t, const ast &inp, const ast &p, const ast &q){ - ast out; - if(!apply_diff_rec(t,inp,p,q,out)) - throw cannot_simplify(); - return out; - } - - bool merge_A_rewrites(const ast &A1, const ast &A2, ast &merged) { - if(arg(A1,1) == arg(A2,0)){ - merged = make(op(A1),arg(A1,0),arg(A2,1)); - return true; - } - ast diff1l, diff1r, diff2l, diff2r,diffBl,diffBr; - diff(LitA,arg(A1,0),arg(A1,1),diff1l,diff1r); - diff(LitA,arg(A2,0),arg(A2,1),diff2l,diff2r); - diff(LitB,arg(A1,1),arg(A2,0),diffBl,diffBr); - if(!term_common(diff2l) && !term_common(diffBr)){ - ast A1r = apply_diff(LitB,arg(A2,1),arg(A2,0),arg(A1,1)); - merged = make(op(A1),arg(A1,0),A1r); - return true; - } - if(!term_common(diff1r) && !term_common(diffBl)){ - ast A2l = apply_diff(LitB,arg(A1,0),arg(A1,1),arg(A2,0)); - merged = make(op(A1),A2l,arg(A2,1)); - return true; - } - return false; - } - - void collect_A_rewrites(const ast &t, std::vector &res){ - if(is_true(t)) - return; - if(sym(t) == concat){ - res.push_back(arg(t,0)); - collect_A_rewrites(arg(t,0),res); - return; - } - res.push_back(t); - } - - ast concat_A_rewrites(const std::vector &rew){ - if(rew.size() == 0) - return mk_true(); - ast res = rew[0]; - for(unsigned i = 1; i < rew.size(); i++) - res = make(concat,res,rew[i]); - return res; - } - - ast merge_concat_rewrites(const ast &A1, const ast &A2){ - std::vector rew; - collect_A_rewrites(A1,rew); - int first = rew.size(), last = first; // range that might need merging - collect_A_rewrites(A2,rew); - while(first > 0 && first < (int)rew.size() && first <= last){ - ast merged; - if(merge_A_rewrites(rew[first-1],rew[first],merged)){ - rew[first] = merged; - first--; - rew.erase(rew.begin()+first); - last--; - if(first >= last) last = first+1; - } - else - first++; - } - return concat_A_rewrites(rew); - } - - ast sep_cond(const ast &t, ast &cond){ - if(op(t) == Implies){ - cond = my_and(cond,arg(t,0)); - return arg(t,1); - } - return t; - } - - - /* operations on term positions */ - - /** Finds the difference between two positions. If p1 < p2 (p1 is a - position below p2), returns -1 and sets diff to p2-p1 (the psath - from position p2 to position p1). If p2 < p1 (p2 is a position - below p1), returns 1 and sets diff to p1-p2 (the psath from - position p1 to position p2). If equal, return 0 and set diff to - top_pos. Else (if p1 and p2 are independent) returns 2 and - leaves diff unchanged. */ - - int pos_diff(const ast &p1, const ast &p2, ast &diff){ - if(p1 == top_pos && p2 != top_pos){ - diff = p2; - return 1; - } - if(p2 == top_pos && p1 != top_pos){ - diff = p1; - return -1; - } - if(p1 == top_pos && p2 == top_pos){ - diff = p1; - return 0; - } - if(arg(p1,0) == arg(p2,0)) // same argument position, recur - return pos_diff(arg(p1,1),arg(p2,1),diff); - return 2; - } - - /* return the position of pos in the argth argument */ - ast pos_add(int arg, const ast &pos){ - return make(add_pos,make_int(rational(arg)),pos); - } - - ast add_pos_to_end(const ast &pos, int i){ - if(pos == top_pos) - return pos_add(i,pos); - return make(add_pos,arg(pos,0),add_pos_to_end(arg(pos,1),i)); - } - - /* return the argument number of position, if not top */ - int pos_arg(const ast &pos){ - rational r; - if(is_numeral(arg(pos,0),r)) - return r.get_unsigned(); - throw iz3_exception("bad position!"); - } - - /* substitute y into position pos in x */ - ast subst_in_pos(const ast &x, const ast &pos, const ast &y){ - if(pos == top_pos) - return y; - int p = pos_arg(pos); - int nargs = num_args(x); - if(p >= 0 && p < nargs){ - std::vector args(nargs); - for(int i = 0; i < nargs; i++) - args[i] = i == p ? subst_in_pos(arg(x,i),arg(pos,1),y) : arg(x,i); - return clone(x,args); - } - throw iz3_exception("bad term position!"); - } - - ast diff_chain(LitType t, const ast &pos, const ast &x, const ast &y, const ast &prefix){ - int nargs = num_args(x); - if(x == y) return prefix; - if(sym(x) == sym(y) && nargs == num_args(y)){ - ast res = prefix; - for(int i = 0; i < nargs; i++) - res = diff_chain(t,pos_add(i,pos),arg(x,i),arg(y,i),res); - return res; - } - return chain_cons(prefix,make_rewrite(t,pos,mk_true(),make_equiv_rel(x,y))); - } - - /* operations on rewrites */ - ast make_rewrite(LitType t, const ast &pos, const ast &cond, const ast &equality){ -#if 0 - if(pos == top_pos && op(equality) == Iff && !is_true(arg(equality,0))) - throw iz3_exception("bad rewrite"); -#endif - if(!is_equivrel(equality)) - throw iz3_exception("bad rewrite"); - return make(t == LitA ? rewrite_A : rewrite_B, pos, cond, equality); - } - - ast rewrite_pos(const ast &rew){ - return arg(rew,0); - } - - ast rewrite_cond(const ast &rew){ - return arg(rew,1); - } - - ast rewrite_equ(const ast &rew){ - return arg(rew,2); - } - - ast rewrite_lhs(const ast &rew){ - return arg(arg(rew,2),0); - } - - ast rewrite_rhs(const ast &rew){ - return arg(arg(rew,2),1); - } - - /* operations on rewrite chains */ - - ast chain_cons(const ast &chain, const ast &elem){ - return make(concat,chain,elem); - } - - ast chain_rest(const ast &chain){ - return arg(chain,0); - } - - ast chain_last(const ast &chain){ - return arg(chain,1); - } - - ast rewrite_update_rhs(const ast &rew, const ast &pos, const ast &new_rhs, const ast &new_cond){ - ast foo = subst_in_pos(rewrite_rhs(rew),pos,new_rhs); - ast equality = arg(rew,2); - return make(sym(rew),rewrite_pos(rew),my_and(rewrite_cond(rew),new_cond),make(op(equality),arg(equality,0),foo)); - } - - ast rewrite_update_lhs(const ast &rew, const ast &pos, const ast &new_lhs, const ast &new_cond){ - ast foo = subst_in_pos(rewrite_lhs(rew),pos,new_lhs); - ast equality = arg(rew,2); - return make(sym(rew),rewrite_pos(rew),my_and(rewrite_cond(rew),new_cond),make(op(equality),foo,arg(equality,1))); - } - - bool is_common_rewrite(const ast &rew){ - return term_common(arg(rew,2)); - } - - bool is_right_mover(const ast &rew){ - return term_common(rewrite_lhs(rew)) && !term_common(rewrite_rhs(rew)); - } - - bool is_left_mover(const ast &rew){ - return term_common(rewrite_rhs(rew)) && !term_common(rewrite_lhs(rew)); - } - - bool same_side(const ast &rew1, const ast &rew2){ - return sym(rew1) == sym(rew2); - } - - bool is_rewrite_side(LitType t, const ast &rew){ - if(t == LitA) - return sym(rew) == rewrite_A; - return sym(rew) == rewrite_B; - } - - LitType rewrite_side(const ast &rew){ - return (sym(rew) == rewrite_A) ? LitA : LitB; - } - - ast rewrite_to_formula(const ast &rew){ - return my_implies(arg(rew,1),arg(rew,2)); - } - - // make rewrite rew condition on rewrite cond - ast rewrite_conditional(const ast &cond, const ast &rew){ - ast cf = rewrite_to_formula(cond); - return make(sym(rew),arg(rew,0),my_and(arg(rew,1),cf),arg(rew,2)); - } - - ast reverse_rewrite(const ast &rew){ - ast equ = arg(rew,2); - return make(sym(rew),arg(rew,0),arg(rew,1),make(op(equ),arg(equ,1),arg(equ,0))); - } - - ast rewrite_pos_add(int apos, const ast &rew){ - return make(sym(rew),pos_add(apos,arg(rew,0)),arg(rew,1),arg(rew,2)); - } - - ast rewrite_pos_set(const ast &pos, const ast &rew){ - return make(sym(rew),pos,arg(rew,1),arg(rew,2)); - } - - ast rewrite_up(const ast &rew){ - return make(sym(rew),arg(arg(rew,0),1),arg(rew,1),arg(rew,2)); - } - - /** Adds a rewrite to a chain of rewrites, keeping the chain in - normal form. An empty chain is represented by true.*/ - - ast add_rewrite_to_chain(const ast &chain, const ast &rewrite){ - if(is_true(chain)) - return chain_cons(chain,rewrite); - ast last = chain_last(chain); - ast rest = chain_rest(chain); - if(same_side(last,rewrite)){ - ast p1 = rewrite_pos(last); - ast p2 = rewrite_pos(rewrite); - ast diff; - switch(pos_diff(p1,p2,diff)){ - case 1: { - ast absorb = rewrite_update_rhs(last,diff,rewrite_rhs(rewrite),rewrite_cond(rewrite)); - return add_rewrite_to_chain(rest,absorb); - } - case 0: - case -1: { - ast absorb = rewrite_update_lhs(rewrite,diff,rewrite_lhs(last),rewrite_cond(last)); - return add_rewrite_to_chain(rest,absorb); - } - default: {// independent case - bool rm = is_right_mover(last); - bool lm = is_left_mover(rewrite); - if((lm && !rm) || (rm && !lm)) - return chain_swap(rest,last,rewrite); - } - } - } - else { - if(is_left_mover(rewrite)){ - if(is_common_rewrite(last)) - return add_rewrite_to_chain(chain_cons(rest,flip_rewrite(last)),rewrite); - if(!is_left_mover(last)) - return chain_swap(rest,last,rewrite); - } - if(is_right_mover(last)){ - if(is_common_rewrite(rewrite)) - return add_rewrite_to_chain(chain,flip_rewrite(rewrite)); - if(!is_right_mover(rewrite)) - return chain_swap(rest,last,rewrite); - } - } - return chain_cons(chain,rewrite); - } - - ast chain_swap(const ast &rest, const ast &last, const ast &rewrite){ - return chain_cons(add_rewrite_to_chain(rest,rewrite),last); - } - - ast flip_rewrite(const ast &rew){ - symb flip_sym = (sym(rew) == rewrite_A) ? rewrite_B : rewrite_A; - ast cf = rewrite_to_formula(rew); - return make(flip_sym,arg(rew,0),my_implies(arg(rew,1),cf),arg(rew,2)); - } - - /** concatenates two rewrite chains, keeping result in normal form. */ - - ast concat_rewrite_chain(const ast &chain1, const ast &chain2){ - if(is_true(chain2)) return chain1; - if(is_true(chain1)) return chain2; - ast foo = concat_rewrite_chain(chain1,chain_rest(chain2)); - return add_rewrite_to_chain(foo,chain_last(chain2)); - } - - /** reverse a chain of rewrites */ - - ast reverse_chain_rec(const ast &chain, const ast &prefix){ - if(is_true(chain)) - return prefix; - ast last = reverse_rewrite(chain_last(chain)); - ast rest = chain_rest(chain); - return reverse_chain_rec(rest,chain_cons(prefix,last)); - } - - ast reverse_chain(const ast &chain){ - return reverse_chain_rec(chain,mk_true()); - } - - bool is_equivrel_chain(const ast &chain){ - if(is_true(chain)) - return true; - ast last = chain_last(chain); - ast rest = chain_rest(chain); - if(is_true(rest)) - return !is_true(rewrite_lhs(last)); - return is_equivrel_chain(rest); - } - - bool is_negation_chain(const ast &chain){ - if(is_true(chain)) - return false; - ast last = chain_last(chain); - ast rest = chain_rest(chain); - if(is_true(rest)) - return op(rewrite_rhs(last)) == Not; - return is_negation_chain(rest); - } - - ast commute_negation_chain(const ast &chain){ - if(is_true(chain)) - return chain; - ast last = chain_last(chain); - ast rest = chain_rest(chain); - if(is_true(rest)){ - ast old = rewrite_rhs(last); - if(!(op(old) == Not)) - throw iz3_exception("bad negative equality chain"); - ast equ = arg(old,0); - if(!is_equivrel(equ)) - throw iz3_exception("bad negative equality chain"); - last = rewrite_update_rhs(last,top_pos,make(Not,make(op(equ),arg(equ,1),arg(equ,0))),make(True)); - return chain_cons(rest,last); - } - ast pos = rewrite_pos(last); - if(pos == top_pos) - throw iz3_exception("bad negative equality chain"); - int idx = pos_arg(pos); - if(idx != 0) - throw iz3_exception("bad negative equality chain"); - pos = arg(pos,1); - if(pos == top_pos){ - ast lhs = rewrite_lhs(last); - ast rhs = rewrite_rhs(last); - if(op(lhs) != Equal || op(rhs) != Equal) - throw iz3_exception("bad negative equality chain"); - last = make_rewrite(rewrite_side(last),rewrite_pos(last),rewrite_cond(last), - make(Iff,make(Equal,arg(lhs,1),arg(lhs,0)),make(Equal,arg(rhs,1),arg(rhs,0)))); - } - else { - idx = pos_arg(pos); - if(idx == 0) - idx = 1; - else if(idx == 1) - idx = 0; - else - throw iz3_exception("bad negative equality chain"); - pos = pos_add(0,pos_add(idx,arg(pos,1))); - last = make_rewrite(rewrite_side(last),pos,rewrite_cond(last),rewrite_equ(last)); - } - return chain_cons(commute_negation_chain(rest),last); - } - - // split a rewrite chain into head and tail at last top-level rewrite - ast get_head_chain(const ast &chain, ast &tail, bool is_not = true){ - ast last = chain_last(chain); - ast rest = chain_rest(chain); - ast pos = rewrite_pos(last); - if(pos == top_pos || (is_not && arg(pos,1) == top_pos)){ - tail = mk_true(); - return chain; - } - if(is_true(rest)) - throw iz3_exception("bad rewrite chain"); - ast head = get_head_chain(rest,tail,is_not); - tail = chain_cons(tail,last); - return head; - } - - bool has_mixed_summands(const ast &e){ - if(op(e) == Plus){ - int nargs = num_args(e); - for(int i = 0; i < nargs; i++) - if(has_mixed_summands(arg(e,i))) - return true; - return false; - } - return get_term_type(e) == LitMixed; - } - - // split a rewrite chain into head and tail at last sum with no mixed sumands - ast get_right_movers(const ast &chain, const ast &rhs, ast &tail, ast &mid){ - if(is_true(chain) || !has_mixed_summands(rhs)){ - mid = rhs; - tail = mk_true(); - return chain; - } - ast last = chain_last(chain); - ast rest = chain_rest(chain); - ast mm = subst_in_pos(rhs,rewrite_pos(last),rewrite_lhs(last)); - ast res = get_right_movers(rest,mm,tail,mid); - tail = chain_cons(tail,last); - return res; - } - - // split a rewrite chain into head and tail at first sum with no mixed sumands - ast get_left_movers(const ast &chain, const ast &lhs, ast &tail, ast &mid){ - if(is_true(chain)){ - mid = lhs; - if(!has_mixed_summands(lhs)){ - tail = mk_true(); - return chain; - } - return ast(); - } - ast last = chain_last(chain); - ast rest = chain_rest(chain); - ast res = get_left_movers(rest,lhs,tail,mid); - if(res.null()){ - mid = subst_in_pos(mid,rewrite_pos(last),rewrite_rhs(last)); - if(get_term_type(mid) != LitMixed){ - tail = mk_true(); - return chain; - } - return ast(); - } - tail = chain_cons(tail,last); - return res; - } - - - struct cannot_split: public iz3_exception { - cannot_split(): iz3_exception("cannot_split") {} - }; - - /** Split a chain of rewrites two chains, operating on positions 0 and 1. - Fail if any rewrite in the chain operates on top position. */ - void split_chain_rec(const ast &chain, ast *res){ - if(is_true(chain)) - return; - ast last = chain_last(chain); - ast rest = chain_rest(chain); - split_chain_rec(rest,res); - ast pos = rewrite_pos(last); - if(pos == top_pos){ - if(rewrite_lhs(last) == rewrite_rhs(last)) - return; // skip if it's a noop - throw cannot_split(); - } - int arg = pos_arg(pos); - if(arg<0 || arg > 1) - throw cannot_split(); - res[arg] = chain_cons(res[arg],rewrite_up(last)); - } - - void split_chain(const ast &chain, ast *res){ - res[0] = res[1] = mk_true(); - split_chain_rec(chain,res); - } - - ast extract_rewrites(const ast &chain, const ast &pos){ - if(is_true(chain)) - return chain; - ast last = chain_last(chain); - ast rest = chain_rest(chain); - ast new_rest = extract_rewrites(rest,pos); - ast p1 = rewrite_pos(last); - ast diff; - switch(pos_diff(p1,pos,diff)){ - case -1: { - ast new_last = rewrite_pos_set(diff, last); - return chain_cons(new_rest,new_last); - } - case 1: - if(rewrite_lhs(last) != rewrite_rhs(last)) - throw iz3_exception("bad rewrite chain"); - break; - default:; - } - return new_rest; - } - - ast down_chain(const ast &chain){ - ast split[2]; - split_chain(chain,split); - return split[0]; - } - - ast chain_conditions(LitType t, const ast &chain){ - if(is_true(chain)) - return mk_true(); - ast last = chain_last(chain); - ast rest = chain_rest(chain); - ast cond = chain_conditions(t,rest); - if(is_rewrite_side(t,last)) - cond = my_and(cond,rewrite_cond(last)); - return cond; - } - - ast chain_formulas(LitType t, const ast &chain){ - if(is_true(chain)) - return mk_true(); - ast last = chain_last(chain); - ast rest = chain_rest(chain); - ast cond = chain_formulas(t,rest); - if(is_rewrite_side(t,last)) - cond = my_and(cond,rewrite_equ(last)); - return cond; - } - - - bool rewrites_from_to(const ast &chain, const ast &lhs, const ast &rhs){ - if(is_true(chain)) - return lhs == rhs; - ast last = chain_last(chain); - ast rest = chain_rest(chain); - ast mid = subst_in_pos(rhs,rewrite_pos(last),rewrite_lhs(last)); - return rewrites_from_to(rest,lhs,mid); - } - - struct bad_ineq_inference: public iz3_exception { - bad_ineq_inference(): iz3_exception("bad_ineq_inference") {} - }; - - ast chain_ineqs(opr comp_op, LitType t, const ast &chain, const ast &lhs, const ast &rhs){ - if(is_true(chain)){ - if (lhs != rhs) { - TRACE("duality", print_expr(tout, lhs); tout << " "; print_expr(tout, rhs); tout << "\n";); - throw bad_ineq_inference(); - } - return make(Leq,make_int(rational(0)),make_int(rational(0))); - } - TRACE("duality", print_expr(tout, chain); print_expr(tout << "\n", lhs); tout << " "; print_expr(tout, rhs); tout << "\n";); - ast last = chain_last(chain); - ast rest = chain_rest(chain); - ast mid = subst_in_pos(rhs,rewrite_pos(last),rewrite_lhs(last)); - ast cond = chain_ineqs(comp_op,t,rest,lhs,mid); - if(is_rewrite_side(t,last)){ - ast diff; - if(comp_op == Leq) diff = make(Sub,rhs,mid); - else diff = make(Sub,mid,rhs); - ast foo = make(Leq,make_int("0"),z3_simplify(diff)); - if(is_true(cond)) - cond = foo; - else { - linear_comb(cond,make_int(rational(1)),foo); - cond = simplify_ineq(cond); - } - } - return cond; - } - - ast ineq_to_lhs(const ast &ineq){ - ast s = make(Leq,make_int(rational(0)),make_int(rational(0))); - linear_comb(s,make_int(rational(1)),ineq); - return simplify_ineq(s); - } - - void eq_from_ineq(const ast &ineq, ast &lhs, ast &rhs){ - // ast s = ineq_to_lhs(ineq); - // ast srhs = arg(s,1); - ast srhs = arg(ineq,0); - if(op(srhs) == Plus && num_args(srhs) == 2 && arg(ineq,1) == make_int(rational(0))){ - lhs = arg(srhs,0); - rhs = arg(srhs,1); - // if(op(lhs) == Times) - // std::swap(lhs,rhs); - if(op(rhs) == Times){ - rhs = arg(rhs,1); - // if(op(ineq) == Leq) - // std::swap(lhs,rhs); - return; - } - } - if(op(ineq) == Leq || op(ineq) == Geq){ - lhs = srhs; - rhs = arg(ineq,1); - return; - } - throw iz3_exception("bad ineq"); - } - - ast chain_pos_add(int arg, const ast &chain){ - if(is_true(chain)) - return mk_true(); - ast last = rewrite_pos_add(arg,chain_last(chain)); - ast rest = chain_pos_add(arg,chain_rest(chain)); - return chain_cons(rest,last); - } - - ast apply_rewrite_chain(const ast &t, const ast &chain){ - if(is_true(chain)) - return t; - ast last = chain_last(chain); - ast rest = chain_rest(chain); - ast mid = apply_rewrite_chain(t,rest); - ast res = subst_in_pos(mid,rewrite_pos(last),rewrite_rhs(last)); - return res; - } - - ast drop_rewrites(LitType t, const ast &chain, ast &remainder){ - if(!is_true(chain)){ - ast last = chain_last(chain); - ast rest = chain_rest(chain); - if(is_rewrite_side(t,last)){ - ast res = drop_rewrites(t,rest,remainder); - remainder = chain_cons(remainder,last); - return res; - } - } - remainder = mk_true(); - return chain; - } - - // Normalization chains - - ast cons_normal(const ast &first, const ast &rest){ - return make(normal_chain,first,rest); - } - - ast normal_first(const ast &t){ - return arg(t,0); - } - - ast normal_rest(const ast &t){ - return arg(t,1); - } - - ast normal_lhs(const ast &t){ - return arg(arg(t,0),0); - } - - ast normal_rhs(const ast &t){ - return arg(arg(t,0),1); - } - - ast normal_proof(const ast &t){ - return arg(t,1); - } - - ast make_normal_step(const ast &lhs, const ast &rhs, const ast &proof){ - return make(normal_step,make_equiv(lhs,rhs),proof); - } - - ast make_normal(const ast &ineq, const ast &nrml){ - if(!is_ineq(ineq)) - throw iz3_exception("what?"); - return make(normal,ineq,nrml); - } - - ast fix_normal(const ast &lhs, const ast &rhs, const ast &proof){ - LitType lhst = get_term_type(lhs); - LitType rhst = get_term_type(rhs); - if(lhst == LitMixed && (rhst != LitMixed || ast_id(lhs) < ast_id(rhs))) - return make_normal_step(lhs,rhs,proof); - if(rhst == LitMixed && (lhst != LitMixed || ast_id(rhs) < ast_id(lhs))) - return make_normal_step(rhs,lhs,reverse_chain(proof)); - throw iz3_exception("help!"); - } - - ast chain_side_proves(LitType side, const ast &chain){ - LitType other_side = side == LitA ? LitB : LitA; - return my_and(chain_conditions(other_side,chain),my_implies(chain_conditions(side,chain),chain_formulas(side,chain))); - } - - // Merge two normalization chains - ast merge_normal_chains_rec(const ast &chain1, const ast &chain2, hash_map &trans, ast &Aproves, ast &Bproves){ - if(is_true(chain1)) - return chain2; - if(is_true(chain2)) - return chain1; - ast f1 = normal_first(chain1); - ast f2 = normal_first(chain2); - ast lhs1 = normal_lhs(f1); - ast lhs2 = normal_lhs(f2); - int id1 = ast_id(lhs1); - int id2 = ast_id(lhs2); - if(id1 < id2) - return cons_normal(f1,merge_normal_chains_rec(normal_rest(chain1),chain2,trans,Aproves,Bproves)); - if(id2 < id1) - return cons_normal(f2,merge_normal_chains_rec(chain1,normal_rest(chain2),trans,Aproves,Bproves)); - ast rhs1 = normal_rhs(f1); - ast rhs2 = normal_rhs(f2); - LitType t1 = get_term_type(rhs1); - LitType t2 = get_term_type(rhs2); - int tid1 = ast_id(rhs1); - int tid2 = ast_id(rhs2); - ast pf1 = normal_proof(f1); - ast pf2 = normal_proof(f2); - ast new_normal; - if(t1 == LitMixed && (t2 != LitMixed || tid2 > tid1)){ - ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2); - new_normal = f2; - trans[rhs1] = make_normal_step(rhs1,rhs2,new_proof); - } - else if(t2 == LitMixed && (t1 != LitMixed || tid1 > tid2)) - return merge_normal_chains_rec(chain2,chain1,trans,Aproves,Bproves); - else if(t1 == LitA && t2 == LitB){ - ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2); - ast Bproof, Aproof = drop_rewrites(LitB,new_proof,Bproof); - ast mcA = chain_side_proves(LitB,Aproof); - Bproves = my_and(Bproves,mcA); - ast mcB = chain_side_proves(LitA,Bproof); - Aproves = my_and(Aproves,mcB); - ast rep = apply_rewrite_chain(rhs1,Aproof); - new_proof = concat_rewrite_chain(pf1,Aproof); - new_normal = make_normal_step(lhs1,rep,new_proof); - ast A_normal = make_normal_step(rhs1,rep,Aproof); - ast res = cons_normal(new_normal,merge_normal_chains_rec(normal_rest(chain1),normal_rest(chain2),trans,Aproves,Bproves)); - res = merge_normal_chains_rec(res,cons_normal(A_normal,make(True)),trans,Aproves,Bproves); - return res; - } - else if(t1 == LitB && t2 == LitA) - return merge_normal_chains_rec(chain2,chain1,trans,Aproves,Bproves); - else if(t1 == LitA) { - ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2); - ast mc = chain_side_proves(LitB,new_proof); - Bproves = my_and(Bproves,mc); - new_normal = f1; // choice is arbitrary - } - else { /* t1 = t2 = LitB */ - ast new_proof = concat_rewrite_chain(reverse_chain(pf1),pf2); - ast mc = chain_side_proves(LitA,new_proof); - Aproves = my_and(Aproves,mc); - new_normal = f1; // choice is arbitrary - } - return cons_normal(new_normal,merge_normal_chains_rec(normal_rest(chain1),normal_rest(chain2),trans,Aproves,Bproves)); - } - - ast trans_normal_chain(const ast &chain, hash_map &trans){ - if(is_true(chain)) - return chain; - ast f = normal_first(chain); - ast r = normal_rest(chain); - r = trans_normal_chain(r,trans); - ast rhs = normal_rhs(f); - hash_map::iterator it = trans.find(rhs); - ast new_normal; - if(it != trans.end() && get_term_type(normal_lhs(f)) == LitMixed){ - const ast &f2 = it->second; - ast pf = concat_rewrite_chain(normal_proof(f),normal_proof(f2)); - new_normal = make_normal_step(normal_lhs(f),normal_rhs(f2),pf); - } - else - new_normal = f; - if(get_term_type(normal_lhs(f)) == LitMixed) - trans[normal_lhs(f)] = new_normal; - return cons_normal(new_normal,r); - } - - ast merge_normal_chains(const ast &chain1, const ast &chain2, ast &Aproves, ast &Bproves){ - hash_map trans; - ast res = merge_normal_chains_rec(chain1,chain2,trans,Aproves,Bproves); - res = trans_normal_chain(res,trans); - return res; - } - - bool destruct_cond_ineq(ast t, ast &Aproves, ast &Bproves, ast&ineq){ - if(op(t) == And){ - Aproves = arg(t,0); - t = arg(t,1); - } - else - Aproves = mk_true(); - if(op(t) == Implies){ - Bproves = arg(t,0); - t = arg(t,1); - } - else - Bproves = mk_true(); - if(is_normal_ineq(t)){ - ineq = t; - return true; - } - return false; - } - - ast cons_cond_ineq(const ast &Aproves, const ast &Bproves, const ast &ineq){ - return my_and(Aproves,my_implies(Bproves,ineq)); - } - - ast normalize(const ast &ct){ - ast Aproves,Bproves,t; - if(!destruct_cond_ineq(ct,Aproves,Bproves,t)) - return ct; - if(sym(t) != normal) - return ct; - ast chain = arg(t,1); - hash_map map; - for(ast c = chain; !is_true(c); c = normal_rest(c)){ - ast first = normal_first(c); - ast lhs = normal_lhs(first); - ast rhs = normal_rhs(first); - map[lhs] = rhs; - } - ast res = subst(map,arg(t,0)); - return cons_cond_ineq(Aproves,Bproves,res); - } - - /** Make an assumption node. The given clause is assumed in the given frame. */ - node make_assumption(int frame, const std::vector &assumption) override { - if(!weak){ - if(pv->in_range(frame,rng)){ - std::vector itp_clause; - for(unsigned i = 0; i < assumption.size(); i++) - if(get_term_type(assumption[i]) != LitA) - itp_clause.push_back(assumption[i]); - ast res = my_or(itp_clause); - return res; - } - else { - return mk_true(); - } - } - else { - if(pv->in_range(frame,rng)){ - return mk_false(); - } - else { - std::vector itp_clause; - for(unsigned i = 0; i < assumption.size(); i++) - if(get_term_type(assumption[i]) != LitB) - itp_clause.push_back(assumption[i]); - ast res = my_or(itp_clause); - return mk_not(res); - } - } - } - - ast make_local_rewrite(LitType t, const ast &p){ - ast rew = is_equivrel(p) ? p : make(Iff,mk_true(),p); -#if 0 - if(op(rew) == Iff && !is_true(arg(rew,0))) - return diff_chain(t,top_pos,arg(rew,0),arg(rew,1), mk_true()); -#endif - return chain_cons(mk_true(),make_rewrite(t, top_pos, mk_true(), rew)); - } - - ast triv_interp(const symb &rule, const std::vector &premises, int mask_in){ - std::vector ps; ps.resize(premises.size()); - std::vector conjs; - int mask = 0; - for(unsigned i = 0; i < ps.size(); i++){ - ast p = premises[i]; - LitType t = get_term_type(p); - switch(t){ - case LitA: - case LitB: - ps[i] = make_local_rewrite(t,p); - break; - default: - ps[i] = get_placeholder(p); // can only prove consequent! - if(mask_in & (1 << i)) - mask |= (1 << conjs.size()); - conjs.push_back(p); - } - } - ast ref = make(rule,ps); - ast res = make_contra_node(ref,conjs,mask); - return res; - } - - ast triv_interp(const symb &rule, const ast &p0, const ast &p1, const ast &p2, int mask){ - std::vector ps; ps.resize(3); - ps[0] = p0; - ps[1] = p1; - ps[2] = p2; - return triv_interp(rule,ps,mask); - } - - /** Make a modus-ponens node. This takes derivations of |- x - and |- x = y and produces |- y */ - - node make_mp(const ast &p_eq_q, const ast &prem1, const ast &prem2) override { - - /* Interpolate the axiom p, p=q -> q */ - ast p = arg(p_eq_q,0); - ast q = arg(p_eq_q,1); - ast itp; - if(get_term_type(p_eq_q) == LitMixed){ - int mask = 1 << 2; - if(op(p) == Not && is_equivrel(arg(p,0))) - mask |= 1; // we may need to run this rule backward if first premise is negative equality - itp = triv_interp(modpon,p,p_eq_q,mk_not(q),mask); - } - else { - if(get_term_type(p) == LitA){ - if(get_term_type(q) == LitA){ - if(op(q) == Or) - itp = make_assumption(rng.hi,args(q)); - else - itp = mk_false(); - } - else { - if(get_term_type(p_eq_q) == LitA) - itp = q; - else - throw proof_error(); - } - } - else { - if(get_term_type(q) == LitA){ - if(get_term_type(make(Equal,p,q)) == LitA) - itp = mk_not(p); - else - throw proof_error(); - } - else - itp = mk_true(); - } - } - - /* Resolve it with the premises */ - std::vector conc; conc.push_back(q); conc.push_back(mk_not(p_eq_q)); - itp = make_resolution(p,conc,itp,prem1); - conc.pop_back(); - itp = make_resolution(p_eq_q,conc,itp,prem2); - return itp; - } - - ast capture_localization(ast e){ - // #define CAPTURE_LOCALIZATION -#ifdef CAPTURE_LOCALIZATION - for(int i = localization_vars.size() - 1; i >= 0; i--){ - LocVar &lv = localization_vars[i]; - if(occurs_in(lv.var,e)){ - symb q = (pv->in_range(lv.frame,rng)) ? sexists : sforall; - e = make(q,make(Equal,lv.var,lv.term),e); // use Equal because it is polymorphic - } - } -#endif - return e; - } - - /** Make an axiom node. The conclusion must be an instance of an axiom. */ - node make_axiom(const std::vector &conclusion, prover::range frng) override { - int nargs = conclusion.size(); - std::vector largs(nargs); - std::vector eqs; - std::vector pfs; - - for(int i = 0; i < nargs; i++){ - ast argpf; - ast lit = conclusion[i]; - largs[i] = localize_term(lit,frng,argpf); - frng = pv->range_glb(frng,pv->ast_scope(largs[i])); - if(largs[i] != lit){ - eqs.push_back(make_equiv(largs[i],lit)); - pfs.push_back(argpf); - } - } - - int frame = pv->range_max(frng); - ast itp = make_assumption(frame,largs); - - for(unsigned i = 0; i < eqs.size(); i++) - itp = make_mp(eqs[i],itp,pfs[i]); - return capture_localization(itp); - } - - node make_axiom(const std::vector &conclusion) override { - return make_axiom(conclusion,pv->range_full()); - } - - /** Make a Contra node. This rule takes a derivation of the form - Gamma |- False and produces |- \/~Gamma. */ - - node make_contra(node prem, const std::vector &conclusion) override { - return prem; - } - - /** Make hypothesis. Creates a node of the form P |- P. */ - - node make_hypothesis(const ast &P) override { - if(is_not(P)) - return make_hypothesis(arg(P,0)); - switch(get_term_type(P)){ - case LitA: - return mk_false(); - case LitB: - return mk_true(); - default: // mixed hypothesis - switch(op(P)){ - case Geq: - case Leq: - case Gt: - case Lt: { - ast zleqz = make(Leq,make_int("0"),make_int("0")); - ast fark1 = make(sum,zleqz,make_int("1"),get_placeholder(P)); - ast fark2 = make(sum,fark1,make_int("1"),get_placeholder(mk_not(P))); - ast res = make(And,make(contra,fark2,mk_false()), - make(contra,get_placeholder(mk_not(P)),P), - make(contra,get_placeholder(P),mk_not(P))); - return res; - } - default: { - ast em = make(exmid,P,get_placeholder(P),get_placeholder(mk_not(P))); - ast res = make(And,make(contra,em,mk_false()), - make(contra,get_placeholder(mk_not(P)),P), - make(contra,get_placeholder(P),mk_not(P))); - return res; - } - } - } - } - - /** Make a Reflexivity node. This rule produces |- x = x */ - - node make_reflexivity(ast con) override { - if(get_term_type(con) == LitA) - return mk_false(); - if(get_term_type(con) == LitB) - return mk_true(); - ast itp = make(And,make(contra,no_proof,mk_false()), - make(contra,mk_true(),mk_not(con))); - return itp; - } - - /** Make a Symmetry node. This takes a derivation of |- x = y and - produces | y = x. Ditto for ~(x=y) */ - - node make_symmetry(ast con, const ast &premcon, node prem) override { -#if 0 - ast x = arg(con,0); - ast y = arg(con,1); - ast p = make(op(con),y,x); -#endif - if(get_term_type(con) != LitMixed) - return prem; // symmetry shmymmetry... - ast em = make(exmid,con,make(symm,get_placeholder(premcon)),get_placeholder(mk_not(con))); - ast itp = make(And,make(contra,em,mk_false()), - make(contra,make(symm,get_placeholder(mk_not(con))),premcon), - make(contra,make(symm,get_placeholder(premcon)),mk_not(con))); - - std::vector conc; conc.push_back(con); - itp = make_resolution(premcon,conc,itp,prem); - return itp; - } - - ast make_equiv_rel(const ast &x, const ast &y){ - if(is_bool_type(get_type(x))) - return make(Iff,x,y); - return make(Equal,x,y); - } - - /** Make a transitivity node. This takes derivations of |- x = y - and |- y = z produces | x = z */ - - node make_transitivity(const ast &x, const ast &y, const ast &z, node prem1, node prem2) override { - - /* Interpolate the axiom x=y,y=z,-> x=z */ - ast p = make_equiv_rel(x,y); - ast q = make_equiv_rel(y,z); - ast r = make_equiv_rel(x,z); - ast equiv = make(Iff,p,r); - ast itp; - - itp = make_congruence(q,equiv,prem2); - itp = make_mp(equiv,prem1,itp); - - return itp; - - } - - /** Make a congruence node. This takes derivations of |- x_i = y_i - and produces |- f(x_1,...,x_n) = f(y_1,...,y_n) */ - - node make_congruence(const ast &p, const ast &con, const ast &prem1) override { - ast x = arg(p,0), y = arg(p,1); - ast itp; - LitType con_t = get_term_type(con); - if(get_term_type(p) == LitA){ - if(con_t == LitA) - itp = mk_false(); - else if(con_t == LitB) - itp = p; - else - itp = make_mixed_congruence(x, y, p, con, prem1); - } - else { - if(con_t == LitA) - itp = mk_not(p); - else{ - if(con_t == LitB) - itp = mk_true(); - else - itp = make_mixed_congruence(x, y, p, con, prem1); - } - } - std::vector conc; conc.push_back(con); - itp = make_resolution(p,conc,itp,prem1); - return itp; - } - - int find_congruence_position(const ast &p, const ast &con){ - // find the argument position of x and y - const ast &x = arg(p,0); - const ast &y = arg(p,1); - int nargs = num_args(arg(con,0)); - for(int i = 0; i < nargs; i++) - if(x == arg(arg(con,0),i) && y == arg(arg(con,1),i)) - return i; - throw proof_error(); - } - - /** Make a congruence node. This takes derivations of |- x_i1 = y_i1, |- x_i2 = y_i2,... - and produces |- f(...x_i1...x_i2...) = f(...y_i1...y_i2...) */ - - node make_congruence(const std::vector &p, const ast &con, const std::vector &prems) override { - if(p.size() == 0) - throw proof_error(); - if(p.size() == 1) - return make_congruence(p[0],con,prems[0]); - ast thing = con; - ast res = mk_true(); - for(unsigned i = 0; i < p.size(); i++){ - int pos = find_congruence_position(p[i],thing); - ast next = subst_in_arg_pos(pos,arg(p[i],1),arg(thing,0)); - ast goal = make(op(thing),arg(thing,0),next); - ast equa = make_congruence(p[i],goal,prems[i]); - if(i == 0) - res = equa; - else { - ast trace = make(op(con),arg(con,0),arg(thing,0)); - ast equiv = make(Iff,trace,make(op(trace),arg(trace,0),next)); - ast foo = make_congruence(goal,equiv,equa); - res = make_mp(equiv,res,foo); - } - thing = make(op(thing),next,arg(thing,1)); - } - return res; - } - - /* Interpolate a mixed congruence axiom. */ - - virtual ast make_mixed_congruence(const ast &x, const ast &y, const ast &p, const ast &con, const ast &prem1){ - ast foo = p; - std::vector conjs; - LitType t = get_term_type(foo); - switch(t){ - case LitA: - case LitB: - foo = make_local_rewrite(t,foo); - break; - case LitMixed: - conjs.push_back(foo); - foo = get_placeholder(foo); - } - // find the argument position of x and y - int pos = -1; - int nargs = num_args(arg(con,0)); - for(int i = 0; i < nargs; i++) - if(x == arg(arg(con,0),i) && y == arg(arg(con,1),i)) - pos = i; - if(pos == -1) - throw proof_error(); - ast bar = make(cong,foo,make_int(rational(pos)),get_placeholder(mk_not(con))); - conjs.push_back(mk_not(con)); - return make_contra_node(bar,conjs); - } - - ast subst_in_arg_pos(int pos, ast term, ast app){ - std::vector args; - get_args(app,args); - args[pos] = term; - return clone(app,args); - } - - /** Make a farkas proof node. */ - - node make_farkas(ast con, const std::vector &prems, const std::vector &prem_cons, - const std::vector &coeffs) override { - - /* Compute the interpolant for the clause */ - - ast zero = make_int("0"); - std::vector conjs; - ast thing = make(Leq,zero,zero); - for(unsigned i = 0; i < prem_cons.size(); i++){ - const ast &lit = prem_cons[i]; - if(get_term_type(lit) == LitA) - // Farkas rule seems to assume strict integer inequalities are rounded - linear_comb(thing,coeffs[i],lit,true /*round_off*/); - } - thing = simplify_ineq(thing); - for(unsigned i = 0; i < prem_cons.size(); i++){ - const ast &lit = prem_cons[i]; - if(get_term_type(lit) == LitMixed){ - thing = make(sum,thing,coeffs[i],get_placeholder(lit)); - conjs.push_back(lit); - } - } - thing = make_contra_node(thing,conjs); - - /* Resolve it with the premises */ - std::vector conc; conc.resize(prem_cons.size()); - for(unsigned i = 0; i < prem_cons.size(); i++) - conc[prem_cons.size()-i-1] = prem_cons[i]; - for(unsigned i = 0; i < prem_cons.size(); i++){ - thing = make_resolution(prem_cons[i],conc,thing,prems[i]); - conc.pop_back(); - } - return thing; - } - - /** Set P to P + cQ, where P and Q are linear inequalities. Assumes P is 0 <= y or 0 < y. */ - - void linear_comb(ast &P, const ast &c, const ast &Q, bool round_off = false){ - ast Qrhs; - bool qstrict = false; - if(is_not(Q)){ - ast nQ = arg(Q,0); - switch(op(nQ)){ - case Gt: - Qrhs = make(Sub,arg(nQ,1),arg(nQ,0)); - break; - case Lt: - Qrhs = make(Sub,arg(nQ,0),arg(nQ,1)); - break; - case Geq: - Qrhs = make(Sub,arg(nQ,1),arg(nQ,0)); - qstrict = true; - break; - case Leq: - Qrhs = make(Sub,arg(nQ,0),arg(nQ,1)); - qstrict = true; - break; - default: - throw proof_error(); - } - } - else { - switch(op(Q)){ - case Leq: - Qrhs = make(Sub,arg(Q,1),arg(Q,0)); - break; - case Geq: - Qrhs = make(Sub,arg(Q,0),arg(Q,1)); - break; - case Lt: - Qrhs = make(Sub,arg(Q,1),arg(Q,0)); - qstrict = true; - break; - case Gt: - Qrhs = make(Sub,arg(Q,0),arg(Q,1)); - qstrict = true; - break; - default: - throw proof_error(); - } - } -#if 0 - bool pstrict = op(P) == Lt, strict = pstrict || qstrict; - if(pstrict && qstrict && round_off) - Qrhs = make(Sub,Qrhs,make_int(rational(1))); -#else - if (round_off && get_type(Qrhs) != int_type()) - round_off = false; - bool pstrict = op(P) == Lt; - if(qstrict && round_off && (pstrict || !(c == make_int(rational(1))))){ - Qrhs = make(Sub,Qrhs,make_int(rational(1))); - qstrict = false; - } - Qrhs = make(Times,c,Qrhs); - bool strict = pstrict || qstrict; -#endif - if(strict) - P = make(Lt,arg(P,0),make(Plus,arg(P,1),Qrhs)); - else - P = make(Leq,arg(P,0),make(Plus,arg(P,1),Qrhs)); - } - - /* Make an axiom instance of the form |- x<=y, y<= x -> x =y */ - node make_leq2eq(ast x, ast y, const ast &xleqy, const ast &yleqx) override { - ast con = make(Equal,x,y); - ast itp; - switch(get_term_type(con)){ - case LitA: - itp = mk_false(); - break; - case LitB: - itp = mk_true(); - break; - default: { // mixed equality - if(get_term_type(x) == LitMixed || get_term_type(y) == LitMixed){ - if(y == make_int(rational(0)) && op(x) == Plus && num_args(x) == 2){ - // std::cerr << "WARNING: untested case in leq2eq\n"; - } - else { - // std::cerr << "WARNING: mixed term in leq2eq\n"; - std::vector lits; - lits.push_back(con); - lits.push_back(make(Not,xleqy)); - lits.push_back(make(Not,yleqx)); - return make_axiom(lits); - } - } - std::vector conjs; conjs.resize(3); - conjs[0] = mk_not(con); - conjs[1] = xleqy; - conjs[2] = yleqx; - itp = make_contra_node(make(leq2eq, - get_placeholder(mk_not(con)), - get_placeholder(xleqy), - get_placeholder(yleqx)), - conjs,1); - } - } - return itp; - } - - /* Make an axiom instance of the form |- x = y -> x <= y */ - node make_eq2leq(ast x, ast y, const ast &xleqy) override { - ast itp; - switch(get_term_type(xleqy)){ - case LitA: - itp = mk_false(); - break; - case LitB: - itp = mk_true(); - break; - default: { // mixed equality - std::vector conjs; conjs.resize(2); - conjs[0] = make(Equal,x,y); - conjs[1] = mk_not(xleqy); - itp = make(eq2leq,get_placeholder(conjs[0]),get_placeholder(conjs[1])); - itp = make_contra_node(itp,conjs,2); - } - } - return itp; - } - - - /* Make an inference of the form t <= c |- t/d <= floor(c/d) where t - is an affine term divisble by d and c is an integer constant */ - node make_cut_rule(const ast &tleqc, const ast &d, const ast &con, const ast &prem) override { - ast itp = mk_false(); - switch(get_term_type(con)){ - case LitA: - itp = mk_false(); - break; - case LitB: - itp = mk_true(); - break; - default: { - std::vector conjs; conjs.resize(2); - conjs[0] = tleqc; - conjs[1] = mk_not(con); - itp = make(sum,get_placeholder(conjs[0]),d,get_placeholder(conjs[1])); - itp = make_contra_node(itp,conjs); - } - } - std::vector conc; conc.push_back(con); - itp = make_resolution(tleqc,conc,itp,prem); - return itp; - } - - - - // create a fresh variable for localization - ast fresh_localization_var(const ast &term, int frame){ - std::ostringstream s; - s << "%" << (localization_vars.size()); - ast var = make_var(s.str().c_str(),get_type(term)); - pv->sym_range(sym(var)) = pv->range_full(); // make this variable global - localization_vars.push_back(LocVar(var,term,frame)); - return var; - } - - struct LocVar { // localization vars - ast var; // a fresh variable - ast term; // term it represents - int frame; // frame in which it's defined - LocVar(ast v, ast t, int f){var=v;term=t;frame=f;} - }; - - std::vector localization_vars; // localization vars in order of creation - - struct locmaps { - hash_map localization_map; // maps terms to their localization vars - hash_map localization_pf_map; // maps terms to proofs of their localizations - }; - - hash_map localization_maps_per_range; - - /* "localize" a term e to a given frame range, creating new symbols to - represent non-local subterms. This returns the localized version e_l, - as well as a proof thet e_l = l. - */ - - ast make_refl(const ast &e){ - if(get_term_type(e) == LitA) - return mk_false(); - return mk_true(); // TODO: is this right? - } - - - ast make_equiv(const ast &x, const ast &y){ - if(get_type(x) == bool_type()) - return make(Iff,x,y); - else - return make(Equal,x,y); - } - - bool range_is_global(const prover::range &r){ - if(pv->range_contained(r,rng)) - return false; - if(!pv->ranges_intersect(r,rng)) - return false; - return true; - } - - ast localize_term(ast e, const prover::range &rng, ast &pf){ - - // we need to memoize this function separately for A, B and global - prover::range map_range = rng; - if(range_is_global(map_range)) - map_range = pv->range_full(); - locmaps &maps = localization_maps_per_range[map_range]; - hash_map &localization_map = maps.localization_map; - hash_map &localization_pf_map = maps.localization_pf_map; - - ast orig_e = e; - pf = make_refl(e); // proof that e = e - - // prover::range erng = - pv->ast_scope(e); -#if 0 - if(!(erng.lo > erng.hi) && pv->ranges_intersect(pv->ast_scope(e),rng)){ - return e; // this term occurs in range, so it's O.K. - } -#endif - - hash_map::iterator it = localization_map.find(e); - - if(it != localization_map.end() && is_bool_type(get_type(e)) - && !pv->ranges_intersect(pv->ast_scope(it->second),rng)) - it = localization_map.end(); // prevent quantifiers over booleans - - if(it != localization_map.end()){ - pf = localization_pf_map[e]; - e = it->second; - } - - else { - // if it is non-local, we must first localize the arguments to - // the range of its function symbol - - int nargs = num_args(e); - if(nargs > 0 /* && (!is_local(e) || flo <= hi || fhi >= lo) */){ - prover::range frng = rng; - opr o = op(e); - if(o == Uninterpreted){ - symb f = sym(e); - prover::range srng = pv->sym_range(f); - if(pv->ranges_intersect(srng,rng)) // localize to desired range if possible - frng = pv->range_glb(srng,rng); - else - frng = srng; // this term will be localized - } - else if(o == Plus || o == Times){ // don't want bound variables inside arith ops - // std::cout << "WARNING: non-local arithmetic\n"; - // frng = erng; // this term will be localized - } - else if(o == Select){ // treat the array term like a function symbol - prover::range srng = pv->ast_scope(arg(e,0)); - if(!(srng.lo > srng.hi) && pv->ranges_intersect(srng,rng)) // localize to desired range if possible - frng = pv->range_glb(srng,rng); - else - frng = srng; // this term will be localized - } - std::vector largs(nargs); - std::vector eqs; - std::vector pfs; - for(int i = 0; i < nargs; i++){ - ast argpf; - largs[i] = localize_term(arg(e,i),frng,argpf); - frng = pv->range_glb(frng,pv->ast_scope(largs[i])); - if(largs[i] != arg(e,i)){ - eqs.push_back(make_equiv(largs[i],arg(e,i))); - pfs.push_back(argpf); - } - } - - e = clone(e,largs); - if(pfs.size()) - pf = make_congruence(eqs,make_equiv(e,orig_e),pfs); - // assert(is_local(e)); - } - - localization_pf_map[orig_e] = pf; - localization_map[orig_e] = e; - } - - if(pv->ranges_intersect(pv->ast_scope(e),rng)) - return e; // this term occurs in range, so it's O.K. - - if(is_array_type(get_type(e))) - std::cerr << "WARNING: array quantifier\n"; - - // choose a frame for the constraint that is close to range - int frame = pv->range_near(pv->ast_scope(e),rng); - - ast new_var = fresh_localization_var(e,frame); - localization_map[orig_e] = new_var; - std::vector foo; foo.push_back(make_equiv(new_var,e)); - ast bar = make_assumption(frame,foo); - pf = make_transitivity(new_var,e,orig_e,bar,pf); - localization_pf_map[orig_e] = pf; - - // HACK: try to bias this term in the future - if(!pv->range_is_full(rng)){ - prover::range rf = pv->range_full(); - locmaps &fmaps = localization_maps_per_range[rf]; - hash_map &flocalization_map = fmaps.localization_map; - hash_map &flocalization_pf_map = fmaps.localization_pf_map; - // if(flocalization_map.find(orig_e) == flocalization_map.end()) - { - flocalization_map[orig_e] = new_var; - flocalization_pf_map[orig_e] = pf; - } - } - - - return new_var; - } - - ast delete_quant(hash_map &memo, const ast &v, const ast &e){ - std::pair foo(e,ast()); - std::pair::iterator,bool> bar = memo.insert(foo); - ast &res = bar.first->second; - if(bar.second){ - opr o = op(e); - switch(o){ - case Or: - case And: - case Implies: { - unsigned nargs = num_args(e); - std::vector args; args.resize(nargs); - for(unsigned i = 0; i < nargs; i++) - args[i] = delete_quant(memo, v, arg(e,i)); - res = make(o,args); - break; - } - case Uninterpreted: { - symb s = sym(e); - ast w = arg(arg(e,0),0); - if(s == sforall || s == sexists){ - res = delete_quant(memo,v,arg(e,1)); - if(w != v) - res = make(s,w,res); - break; - } - } - default: - res = e; - } - } - return res; - } - - ast insert_quants(hash_map &memo, const ast &e){ - std::pair foo(e,ast()); - std::pair::iterator,bool> bar = memo.insert(foo); - ast &res = bar.first->second; - if(bar.second){ - opr o = op(e); - switch(o){ - case Or: - case And: - case Implies: { - unsigned nargs = num_args(e); - std::vector args; args.resize(nargs); - for(unsigned i = 0; i < nargs; i++) - args[i] = insert_quants(memo, arg(e,i)); - res = make(o,args); - break; - } - case Uninterpreted: { - symb s = sym(e); - if(s == sforall || s == sexists){ - opr q = (s == sforall) ? Forall : Exists; - ast v = arg(arg(e,0),0); - hash_map dmemo; - ast body = delete_quant(dmemo,v,arg(e,1)); - body = insert_quants(memo,body); - res = apply_quant(q,v,body); - break; - } - } - default: - res = e; - } - } - return res; - } - - ast add_quants(ast e){ -#ifdef CAPTURE_LOCALIZATION - if(!localization_vars.empty()){ - hash_map memo; - e = insert_quants(memo,e); - } -#else - for(int i = localization_vars.size() - 1; i >= 0; i--){ - LocVar &lv = localization_vars[i]; - opr quantifier = (pv->in_range(lv.frame,rng)) ? Exists : Forall; - e = apply_quant(quantifier,lv.var,e); - } -#endif - return e; - } - - node make_resolution(ast pivot, node premise1, node premise2) { - std::vector lits; - return make_resolution(pivot,lits,premise1,premise2); - } - - /* Return an interpolant from a proof of false */ - ast interpolate(const node &pf) override { - // proof of false must be a formula, with quantified symbols -#ifndef BOGUS_QUANTS - return close_universally(add_quants(z3_simplify(pf))); -#else - return close_universally(z3_simplify(pf)); -#endif - } - - ast resolve_with_quantifier(const ast &pivot1, const ast &conj1, - const ast &pivot2, const ast &conj2){ - if(is_not(arg(pivot1,1))) - return resolve_with_quantifier(pivot2,conj2,pivot1,conj1); - ast eqpf; - ast P = arg(pivot1,1); - ast Ploc = localize_term(P, rng, eqpf); - ast pPloc = make_hypothesis(Ploc); - ast pP = make_mp(make(Iff,Ploc,P),pPloc,eqpf); - ast rP = make_resolution(P,conj1,pP); - ast nP = mk_not(P); - ast nPloc = mk_not(Ploc); - ast neqpf = make_congruence(make(Iff,Ploc,P),make(Iff,nPloc,nP),eqpf); - ast npPloc = make_hypothesis(nPloc); - ast npP = make_mp(make(Iff,nPloc,nP),npPloc,neqpf); - ast nrP = make_resolution(nP,conj2,npP); - ast res = make_resolution(Ploc,rP,nrP); - return capture_localization(res); - } - - ast get_contra_coeff(const ast &f){ - ast c = arg(f,0); - // if(!is_not(arg(f,1))) - // c = make(Uminus,c); - return c; - } - - ast my_or(const ast &a, const ast &b){ - return mk_or(a,b); - } - - ast my_and(const ast &a, const ast &b){ - return mk_and(a,b); - } - - ast my_implies(const ast &a, const ast &b){ - return mk_implies(a,b); - } - - ast my_or(const std::vector &a){ - return mk_or(a); - } - - ast my_and(const std::vector &a){ - return mk_and(a); - } - - ast get_lit_atom(const ast &l){ - if(op(l) == Not) - return arg(l,0); - return l; - } - - bool is_placeholder(const ast &e){ - if(op(e) == Uninterpreted){ - std::string name = string_of_symbol(sym(e)); - if(name.size() > 2 && name[0] == '@' && name[1] == 'p') - return true; - } - return false; - } - -public: - iz3proof_itp_impl(prover *p, const prover::range &r, bool w) - : iz3proof_itp(*p) - { - pv = p; - rng = r; - weak = false ; //w; - type boolintbooldom[3] = {bool_type(),int_type(),bool_type()}; - type booldom[1] = {bool_type()}; - type boolbooldom[2] = {bool_type(),bool_type()}; - type boolboolbooldom[3] = {bool_type(),bool_type(),bool_type()}; - type intbooldom[2] = {int_type(),bool_type()}; - contra = function("@contra",2,boolbooldom,bool_type()); - m().inc_ref(contra); - sum = function("@sum",3,boolintbooldom,bool_type()); - m().inc_ref(sum); - rotate_sum = function("@rotsum",2,boolbooldom,bool_type()); - m().inc_ref(rotate_sum); - leq2eq = function("@leq2eq",3,boolboolbooldom,bool_type()); - m().inc_ref(leq2eq); - eq2leq = function("@eq2leq",2,boolbooldom,bool_type()); - m().inc_ref(eq2leq); - cong = function("@cong",3,boolintbooldom,bool_type()); - m().inc_ref(cong); - exmid = function("@exmid",3,boolboolbooldom,bool_type()); - m().inc_ref(exmid); - symm = function("@symm",1,booldom,bool_type()); - m().inc_ref(symm); - epsilon = make_var("@eps",int_type()); - modpon = function("@mp",3,boolboolbooldom,bool_type()); - m().inc_ref(modpon); - no_proof = make_var("@nop",bool_type()); - concat = function("@concat",2,boolbooldom,bool_type()); - m().inc_ref(concat); - top_pos = make_var("@top_pos",bool_type()); - add_pos = function("@add_pos",2,intbooldom,bool_type()); - m().inc_ref(add_pos); - rewrite_A = function("@rewrite_A",3,boolboolbooldom,bool_type()); - m().inc_ref(rewrite_A); - rewrite_B = function("@rewrite_B",3,boolboolbooldom,bool_type()); - m().inc_ref(rewrite_B); - normal_step = function("@normal_step",2,boolbooldom,bool_type()); - m().inc_ref(normal_step); - normal_chain = function("@normal_chain",2,boolbooldom,bool_type()); - m().inc_ref(normal_chain); - normal = function("@normal",2,boolbooldom,bool_type()); - m().inc_ref(normal); - sforall = function("@sforall",2,boolbooldom,bool_type()); - m().inc_ref(sforall); - sexists = function("@sexists",2,boolbooldom,bool_type()); - m().inc_ref(sexists); - } - - ~iz3proof_itp_impl() override { - m().dec_ref(contra); - m().dec_ref(sum); - m().dec_ref(rotate_sum); - m().dec_ref(leq2eq); - m().dec_ref(eq2leq); - m().dec_ref(cong); - m().dec_ref(exmid); - m().dec_ref(symm); - m().dec_ref(modpon); - m().dec_ref(concat); - m().dec_ref(add_pos); - m().dec_ref(rewrite_A); - m().dec_ref(rewrite_B); - m().dec_ref(normal_step); - m().dec_ref(normal_chain); - m().dec_ref(normal); - m().dec_ref(sforall); - m().dec_ref(sexists); - } -}; - -iz3proof_itp *iz3proof_itp::create(prover *p, const prover::range &r, bool w){ - return new iz3proof_itp_impl(p,r,w); -} - diff --git a/src/interp/iz3proof_itp.h b/src/interp/iz3proof_itp.h deleted file mode 100644 index c9a36e9b1..000000000 --- a/src/interp/iz3proof_itp.h +++ /dev/null @@ -1,143 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3proof.h - - Abstract: - - This class defines a simple interpolating proof system. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifndef IZ3PROOF_ITP_H -#define IZ3PROOF_ITP_H - -#include - -#include "interp/iz3base.h" -#include "interp/iz3secondary.h" - -// #define CHECK_PROOFS - -/** This class defines a simple proof system. - - As opposed to iz3proof, this class directly computes interpolants, - so the proof representation is just the interpolant itself. - -*/ - -class iz3proof_itp : public iz3mgr { - public: - - /** Enumeration of proof rules. */ - enum rule {Resolution,Assumption,Hypothesis,Theory,Axiom,Contra,Lemma,Reflexivity,Symmetry,Transitivity,Congruence,EqContra}; - - /** Interface to prover. */ - typedef iz3base prover; - - /** Ast type. */ - typedef prover::ast ast; - - /** The type of proof nodes (just interpolants). */ - typedef ast node; - - /** Object thrown in case of a proof error. */ - struct proof_error: public iz3_exception { - proof_error(): iz3_exception("proof_error") {} - }; - - - /** Make a resolution node with given pivot literal and premises. - The conclusion of premise1 should contain the negation of the - pivot literal, while the conclusion of premise2 should containe the - pivot literal. - */ - virtual node make_resolution(ast pivot, const std::vector &conc, node premise1, node premise2) = 0; - - /** Make an assumption node. The given clause is assumed in the given frame. */ - virtual node make_assumption(int frame, const std::vector &assumption) = 0; - - /** Make a hypothesis node. If phi is the hypothesis, this is - effectively phi |- phi. */ - virtual node make_hypothesis(const ast &hypothesis) = 0; - - /** Make an axiom node. The conclusion must be an instance of an axiom. */ - virtual node make_axiom(const std::vector &conclusion) = 0; - - /** Make an axiom node. The conclusion must be an instance of an axiom. Localize axiom instance to range*/ - virtual node make_axiom(const std::vector &conclusion, prover::range) = 0; - - /** Make a Contra node. This rule takes a derivation of the form - Gamma |- False and produces |- \/~Gamma. */ - - virtual node make_contra(node prem, const std::vector &conclusion) = 0; - - /** Make a Reflexivity node. This rule produces |- x = x */ - - virtual node make_reflexivity(ast con) = 0; - - /** Make a Symmetry node. This takes a derivation of |- x = y and - produces | y = x */ - - virtual node make_symmetry(ast con, const ast &premcon, node prem) = 0; - - /** Make a transitivity node. This takes derivations of |- x = y - and |- y = z produces | x = z */ - - virtual node make_transitivity(const ast &x, const ast &y, const ast &z, node prem1, node prem2) = 0; - - /** Make a congruence node. This takes a derivation of |- x_i = y_i - and produces |- f(...x_i,...) = f(...,y_i,...) */ - - virtual node make_congruence(const ast &xi_eq_yi, const ast &con, const ast &prem1) = 0; - - /** Make a congruence node. This takes derivations of |- x_i1 = y_i1, |- x_i2 = y_i2,... - and produces |- f(...x_i1...x_i2...) = f(...y_i1...y_i2...) */ - - virtual node make_congruence(const std::vector &xi_eq_yi, const ast &con, const std::vector &prems) = 0; - - /** Make a modus-ponens node. This takes derivations of |- x - and |- x = y and produces |- y */ - - virtual node make_mp(const ast &x_eq_y, const ast &prem1, const ast &prem2) = 0; - - /** Make a farkas proof node. */ - - virtual node make_farkas(ast con, const std::vector &prems, const std::vector &prem_cons, const std::vector &coeffs) = 0; - - /* Make an axiom instance of the form |- x<=y, y<= x -> x =y */ - virtual node make_leq2eq(ast x, ast y, const ast &xleqy, const ast &yleqx) = 0; - - /* Make an axiom instance of the form |- x = y -> x <= y */ - virtual node make_eq2leq(ast x, ast y, const ast &xeqy) = 0; - - /* Make an inference of the form t <= c |- t/d <= floor(c/d) where t - is an affine term divisble by d and c is an integer constant */ - virtual node make_cut_rule(const ast &tleqc, const ast &d, const ast &con, const ast &prem) = 0; - - /* Return an interpolant from a proof of false */ - virtual ast interpolate(const node &pf) = 0; - - /** Create proof object to construct an interpolant. */ - static iz3proof_itp *create(prover *p, const prover::range &r, bool _weak); - - protected: - iz3proof_itp(iz3mgr &m) - : iz3mgr(m) - { - } - - public: - virtual ~iz3proof_itp(){ - } -}; - -#endif diff --git a/src/interp/iz3scopes.cpp b/src/interp/iz3scopes.cpp deleted file mode 100755 index e3a28abdd..000000000 --- a/src/interp/iz3scopes.cpp +++ /dev/null @@ -1,321 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3scopes.cpp - - Abstract: - - Calculations with scopes, for both sequence and tree interpolation. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#include - -#include - -#include "interp/iz3scopes.h" - - -/** computes the least common ancestor of two nodes in the tree, or SHRT_MAX if none */ -int scopes::tree_lca(int n1, int n2){ - if(!tree_mode()) - return std::max(n1,n2); - if(n1 == SHRT_MIN) return n2; - if(n2 == SHRT_MIN) return n1; - if(n1 == SHRT_MAX || n2 == SHRT_MAX) return SHRT_MAX; - while(n1 != n2){ - if(n1 == SHRT_MAX || n2 == SHRT_MAX) return SHRT_MAX; - assert(n1 >= 0 && n2 >= 0 && n1 < (int)parents.size() && n2 < (int)parents.size()); - if(n1 < n2) n1 = parents[n1]; - else n2 = parents[n2]; - } - return n1; -} - -/** computes the greatest common descendant two nodes in the tree, or SHRT_MIN if none */ -int scopes::tree_gcd(int n1, int n2){ - if(!tree_mode()) - return std::min(n1,n2); - int foo = tree_lca(n1,n2); - if(foo == n1) return n2; - if(foo == n2) return n1; - return SHRT_MIN; -} - -#ifndef FULL_TREE - -/** test whether a tree node is contained in a range */ -bool scopes::in_range(int n, const range &rng){ - return tree_lca(rng.lo,n) == n && tree_gcd(rng.hi,n) == n; -} - -/** test whether two ranges of tree nodes intersect */ -bool scopes::ranges_intersect(const range &rng1, const range &rng2){ - return tree_lca(rng1.lo,rng2.hi) == rng2.hi && tree_lca(rng1.hi,rng2.lo) == rng1.hi; -} - - -bool scopes::range_contained(const range &rng1, const range &rng2){ - return tree_lca(rng2.lo,rng1.lo) == rng1.lo - && tree_lca(rng1.hi,rng2.hi) == rng2.hi; -} - -scopes::range scopes::range_lub(const range &rng1, const range &rng2){ - range res; - res.lo = tree_gcd(rng1.lo,rng2.lo); - res.hi = tree_lca(rng1.hi,rng2.hi); - return res; -} - -scopes::range scopes::range_glb(const range &rng1, const range &rng2){ - range res; - res.lo = tree_lca(rng1.lo,rng2.lo); - res.hi = tree_gcd(rng1.hi,rng2.hi); - return res; -} - -#else - - -namespace std { - template <> - class hash { - public: - size_t operator()(const scopes::range_lo &p) const { - return p.lo + (size_t)p.next; - } - }; -} - -template <> inline -size_t stdext::hash_value(const scopes::range_lo& p) -{ - std::hash h; - return h(p); -} - -namespace std { - template <> - class less { - public: - bool operator()(const scopes::range_lo &x, const scopes::range_lo &y) const { - return x.lo < y.lo || x.lo == y.lo && (size_t)x.next < (size_t)y.next; - } - }; -} - - -struct range_op { - scopes::range_lo *x, *y; - int hi; - range_op(scopes::range_lo *_x, scopes::range_lo *_y, int _hi){ - x = _x; y = _y; hi = _hi; - } -}; - -namespace std { - template <> - class hash { - public: - size_t operator()(const range_op &p) const { - return (size_t) p.x + (size_t)p.y + p.hi; - } - }; -} - -template <> inline -size_t stdext::hash_value(const range_op& p) -{ - std::hash h; - return h(p); -} - -namespace std { - template <> - class less { - public: - bool operator()(const range_op &x, const range_op &y) const { - return (size_t)x.x < (size_t)y.x || x.x == y.x && - ((size_t)x.y < (size_t)y.y || x.y == y.y && x.hi < y.hi); - } - }; -} - -struct range_tables { - hash_map unique; - hash_map lub; - hash_map glb; -}; - - -scopes::range_lo *scopes::find_range_lo(int lo, range_lo *next){ - range_lo foo(lo,next); - std::pair baz(foo,(range_lo *)0); - std::pair::iterator,bool> bar = rt->unique.insert(baz); - if(bar.second) - bar.first->second = new range_lo(lo,next); - return bar.first->second; - //std::pair::iterator,bool> bar = rt->unique.insert(foo); - // const range_lo *baz = &*(bar.first); - // return (range_lo *)baz; // coerce const -} - -scopes::range_lo *scopes::range_lub_lo(range_lo *rng1, range_lo *rng2){ - if(!rng1) return rng2; - if(!rng2) return rng1; - if(rng1->lo > rng2->lo) - std::swap(rng1,rng2); - std::pair foo(range_op(rng1,rng2,0),(range_lo *)0); - std::pair::iterator,bool> bar = rt->lub.insert(foo); - range_lo *&res = bar.first->second; - if(!bar.second) return res; - if(!(rng1->next && rng1->next->lo <= rng2->lo)){ - for(int lo = rng1->lo; lo <= rng2->lo; lo = parents[lo]) - if(lo == rng2->lo) - {rng2 = rng2->next; break;} - } - range_lo *baz = range_lub_lo(rng1->next,rng2); - res = find_range_lo(rng1->lo,baz); - return res; -} - - -scopes::range_lo *scopes::range_glb_lo(range_lo *rng1, range_lo *rng2, int hi){ - if(!rng1) return rng1; - if(!rng2) return rng2; - if(rng1->lo > rng2->lo) - std::swap(rng1,rng2); - std::pair cand(range_op(rng1,rng2,hi),(range_lo *)0); - std::pair::iterator,bool> bar = rt->glb.insert(cand); - range_lo *&res = bar.first->second; - if(!bar.second) return res; - range_lo *foo; - if(!(rng1->next && rng1->next->lo <= rng2->lo)){ - int lim = hi; - if(rng1->next) lim = std::min(lim,rng1->next->lo); - int a = rng1->lo, b = rng2->lo; - while(a != b && b <= lim){ - a = parents[a]; - if(a > b)std::swap(a,b); - } - if(a == b && b <= lim){ - foo = range_glb_lo(rng1->next,rng2->next,hi); - foo = find_range_lo(b,foo); - } - else - foo = range_glb_lo(rng2,rng1->next,hi); - } - else foo = range_glb_lo(rng1->next,rng2,hi); - res = foo; - return res; -} - -/** computes the lub (smallest containing subtree) of two ranges */ -scopes::range scopes::range_lub(const range &rng1, const range &rng2){ - int hi = tree_lca(rng1.hi,rng2.hi); - if(hi == SHRT_MAX) return range_full(); - range_lo *lo = range_lub_lo(rng1.lo,rng2.lo); - return range(hi,lo); -} - -/** computes the glb (intersection) of two ranges */ -scopes::range scopes::range_glb(const range &rng1, const range &rng2){ - if(rng1.hi == SHRT_MAX) return rng2; - if(rng2.hi == SHRT_MAX) return rng1; - int hi = tree_gcd(rng1.hi,rng2.hi); - range_lo *lo = hi == SHRT_MIN ? 0 : range_glb_lo(rng1.lo,rng2.lo,hi); - if(!lo) hi = SHRT_MIN; - return range(hi,lo); -} - -/** is this range empty? */ -bool scopes::range_is_empty(const range &rng){ - return rng.hi == SHRT_MIN; -} - -/** return an empty range */ -scopes::range scopes::range_empty(){ - return range(SHRT_MIN,0); -} - -/** return a full range */ -scopes::range scopes::range_full(){ - return range(SHRT_MAX,0); -} - -/** return the maximal element of a range */ -int scopes::range_max(const range &rng){ - return rng.hi; -} - -/** return a minimal (not necessarily unique) element of a range */ -int scopes::range_min(const range &rng){ - if(rng.hi == SHRT_MAX) return SHRT_MIN; - return rng.lo ? rng.lo->lo : SHRT_MAX; -} - - -/** return range consisting of downward closure of a point */ -scopes::range scopes::range_downward(int _hi){ - std::vector descendants(parents.size()); - for(int i = descendants.size() - 1; i >= 0 ; i--) - descendants[i] = i == _hi || parents[i] < parents.size() && descendants[parents[i]]; - for(unsigned i = 0; i < descendants.size() - 1; i++) - if(parents[i] < parents.size()) - descendants[parents[i]] = false; - range_lo *foo = 0; - for(int i = descendants.size() - 1; i >= 0; --i) - if(descendants[i]) foo = find_range_lo(i,foo); - return range(_hi,foo); -} - -/** add an element to a range */ -void scopes::range_add(int i, range &n){ - range foo = range(i, find_range_lo(i,0)); - n = range_lub(foo,n); -} - -/** Choose an element of rng1 that is near to rng2 */ -int scopes::range_near(const range &rng1, const range &rng2){ - - int frame; - int thing = tree_lca(rng1.hi,rng2.hi); - if(thing != rng1.hi) return rng1.hi; - range line = range(rng1.hi,find_range_lo(rng2.hi,(range_lo *)0)); - line = range_glb(line,rng1); - return range_min(line); -} - - -/** test whether a tree node is contained in a range */ -bool scopes::in_range(int n, const range &rng){ - range r = range_empty(); - range_add(n,r); - r = range_glb(rng,r); - return !range_is_empty(r); -} - -/** test whether two ranges of tree nodes intersect */ -bool scopes::ranges_intersect(const range &rng1, const range &rng2){ - range r = range_glb(rng1,rng2); - return !range_is_empty(r); -} - - -bool scopes::range_contained(const range &rng1, const range &rng2){ - range r = range_glb(rng1,rng2); - return r.hi == rng1.hi && r.lo == rng1.lo; -} - - -#endif - - diff --git a/src/interp/iz3scopes.h b/src/interp/iz3scopes.h deleted file mode 100755 index ece30dc25..000000000 --- a/src/interp/iz3scopes.h +++ /dev/null @@ -1,222 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3scopes.h - - Abstract: - - Calculations with scopes, for both sequence and tree interpolation. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - - -#ifndef IZ3SOPES_H -#define IZ3SOPES_H - -#include -#include -#include "interp/iz3hash.h" - -class scopes { - - public: - /** Construct from parents vector. */ - scopes(const std::vector &_parents){ - parents = _parents; - } - - scopes(){ - } - - void initialize(const std::vector &_parents){ - parents = _parents; - } - - /** The parents vector defining the tree structure */ - std::vector parents; - - // #define FULL_TREE -#ifndef FULL_TREE - struct range { - range(){ - lo = SHRT_MAX; - hi = SHRT_MIN; - } - short lo, hi; - }; - - /** computes the lub (smallest containing subtree) of two ranges */ - range range_lub(const range &rng1, const range &rng2); - - /** computes the glb (intersection) of two ranges */ - range range_glb(const range &rng1, const range &rng2); - - /** is this range empty? */ - bool range_is_empty(const range &rng){ - return rng.hi < rng.lo; - } - - /** is this range full? */ - bool range_is_full(const range &rng){ - return rng.lo == SHRT_MIN && rng.hi == SHRT_MAX; - } - - /** return an empty range */ - range range_empty(){ - range res; - res.lo = SHRT_MAX; - res.hi = SHRT_MIN; - return res; - } - - /** return an empty range */ - range range_full(){ - range res; - res.lo = SHRT_MIN; - res.hi = SHRT_MAX; - return res; - } - - /** return the maximal element of a range */ - int range_max(const range &rng){ - return rng.hi; - } - - /** return a minimal (not necessarily unique) element of a range */ - int range_min(const range &rng){ - return rng.lo; - } - - /** return range consisting of downward closure of a point */ - range range_downward(int _hi){ - range foo; - foo.lo = SHRT_MIN; - foo.hi = _hi; - return foo; - } - - void range_add(int i, range &n){ -#if 0 - if(i < n.lo) n.lo = i; - if(i > n.hi) n.hi = i; -#else - range rng; rng.lo = i; rng.hi = i; - n = range_lub(rng,n); -#endif - } - - /** Choose an element of rng1 that is near to rng2 */ - int range_near(const range &rng1, const range &rng2){ - int frame; - int thing = tree_lca(rng1.lo,rng2.hi); - if(thing == rng1.lo) frame = rng1.lo; - else frame = tree_gcd(thing,rng1.hi); - return frame; - } -#else - - struct range_lo { - int lo; - range_lo *next; - range_lo(int _lo, range_lo *_next){ - lo = _lo; - next = _next; - } - }; - - struct range { - int hi; - range_lo *lo; - range(int _hi, range_lo *_lo){ - hi = _hi; - lo = _lo; - } - range(){ - hi = SHRT_MIN; - lo = 0; - } - }; - - range_tables *rt; - - /** computes the lub (smallest containing subtree) of two ranges */ - range range_lub(const range &rng1, const range &rng2); - - /** computes the glb (intersection) of two ranges */ - range range_glb(const range &rng1, const range &rng2); - - /** is this range empty? */ - bool range_is_empty(const range &rng); - - /** return an empty range */ - range range_empty(); - - /** return a full range */ - range range_full(); - - /** return the maximal element of a range */ - int range_max(const range &rng); - - /** return a minimal (not necessarily unique) element of a range */ - int range_min(const range &rng); - - /** return range consisting of downward closure of a point */ - range range_downward(int _hi); - - /** add an element to a range */ - void range_add(int i, range &n); - - /** Choose an element of rng1 that is near to rng2 */ - int range_near(const range &rng1, const range &rng2); - - range_lo *find_range_lo(int lo, range_lo *next); - range_lo *range_lub_lo(range_lo *rng1, range_lo *rng2); - range_lo *range_glb_lo(range_lo *rng1, range_lo *rng2, int lim); - -#endif - - /** test whether a tree node is contained in a range */ - bool in_range(int n, const range &rng); - - /** test whether two ranges of tree nodes intersect */ - bool ranges_intersect(const range &rng1, const range &rng2); - - /** test whether range rng1 contained in range rng2 */ - bool range_contained(const range &rng1, const range &rng2); - - private: - int tree_lca(int n1, int n2); - int tree_gcd(int n1, int n2); - bool tree_mode(){return parents.size() != 0;} - - - -}; - -// let us hash on ranges - -#ifndef FULL_TREE -namespace hash_space { - template <> - class hash { - public: - size_t operator()(const scopes::range &p) const { - return (size_t)p.lo + (size_t)p.hi; - } - }; -} - -inline bool operator==(const scopes::range &x, const scopes::range &y){ - return x.lo == y.lo && x.hi == y.hi; -} -#endif - -#endif diff --git a/src/interp/iz3secondary.h b/src/interp/iz3secondary.h deleted file mode 100755 index a5a949b54..000000000 --- a/src/interp/iz3secondary.h +++ /dev/null @@ -1,40 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3secondary - - Abstract: - - Interface for secondary provers. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - - -#ifndef IZ3SECONDARY_H -#define IZ3SECONDARY_H - -/** Interface class for secondary provers. */ - -#include "interp/iz3base.h" -#include - -class iz3secondary : public iz3mgr { - public: - virtual int interpolate(const std::vector &frames, std::vector &interpolants) = 0; - virtual ~iz3secondary(){} - - protected: - iz3secondary(const iz3mgr &mgr) : iz3mgr(mgr) {} -}; - - - -#endif diff --git a/src/interp/iz3translate.cpp b/src/interp/iz3translate.cpp deleted file mode 100644 index 44bac0643..000000000 --- a/src/interp/iz3translate.cpp +++ /dev/null @@ -1,2200 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3translate.cpp - - Abstract: - - Translate a Z3 proof to in interpolated proof. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#pragma warning(disable:4101) -#endif - -#include "interp/iz3translate.h" -#include "interp/iz3proof.h" -#include "interp/iz3profiling.h" -#include "interp/iz3interp.h" -#include "interp/iz3proof_itp.h" -#include "ast/ast_pp.h" - -#include -#include -#include -#include -#include -#include -#include - -//using std::vector; -using namespace stl_ext; - - - -/* This translator goes directly from Z3 proofs to interpolated - proofs without an intermediate representation. No secondary - prover is used. -*/ - - -#define throw_unsupported(_e_) { TRACE("iz3", tout << expr_ref((expr*)_e_.raw(), *_e_.mgr()) << "\n";); throw unsupported(_e_); } - -class iz3translation_full : public iz3translation { -public: - - - typedef iz3proof_itp Iproof; - - Iproof *iproof; - - /* Here we have lots of hash tables for memoizing various methods and - other such global data structures. - */ - - typedef hash_map AstToInt; - AstToInt locality; // memoizes locality of Z3 proof terms - - typedef std::pair EquivEntry; - typedef hash_map EquivTab; - EquivTab equivs; // maps non-local terms to equivalent local terms, with proof - - typedef hash_set AstHashSet; - AstHashSet equivs_visited; // proofs already checked for equivalences - - typedef std::pair, hash_map > AstToIpf; - AstToIpf translation; // Z3 proof nodes to Iproof nodes - - int frames; // number of frames - - typedef std::set AstSet; - typedef hash_map AstToAstSet; - AstToAstSet hyp_map; // map proof terms to hypothesis set - - struct LocVar { // localization vars - ast var; // a fresh variable - ast term; // term it represents - int frame; // frame in which it's defined - LocVar(ast v, ast t, int f){var=v;term=t;frame=f;} - }; - - std::vector localization_vars; // localization vars in order of creation - typedef hash_map AstToAst; - AstToAst localization_map; // maps terms to their localization vars - - typedef hash_map AstToBool; - AstToBool occurs_in_memo; // memo of occurs_in function - - AstHashSet cont_eq_memo; // memo of cont_eq function - - AstToAst subst_memo; // memo of subst function - - symb commute; - -public: - - -#define from_ast(x) (x) - - // #define NEW_LOCALITY - -#ifdef NEW_LOCALITY - range rng; // the range of frames in the "A" part of the interpolant -#endif - - /* To handle skolemization, we have to scan the proof for skolem - symbols and assign each to a frame. THe assignment is heuristic. - */ - - int scan_skolems_rec(hash_map &memo, const ast &proof, int frame){ - std::pair foo(proof,INT_MAX); - std::pair bar = memo.insert(foo); - int &res = bar.first->second; - if(!bar.second) return res; - pfrule dk = pr(proof); - if(dk == PR_ASSERTED){ - ast ass = conc(proof); - res = frame_of_assertion(ass); - } - else if(dk == PR_SKOLEMIZE){ - ast quanted = arg(conc(proof),0); - if(op(quanted) == Not) - quanted = arg(quanted,0); - // range r = ast_range(quanted); - // if(range_is_empty(r)) - range r = ast_scope(quanted); - if(range_is_empty(r)) - throw iz3_exception("can't skolemize"); - if(frame == INT_MAX || !in_range(frame,r)) - frame = range_max(r); // this is desperation -- may fail - if(frame >= frames) frame = frames - 1; - add_frame_range(frame,arg(conc(proof),1)); - r = ast_scope(arg(conc(proof),1)); - } - else if(dk==PR_MODUS_PONENS_OEQ){ - frame = scan_skolems_rec(memo,prem(proof,0),frame); - scan_skolems_rec(memo,prem(proof,1),frame); - } - else { - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - int bar = scan_skolems_rec(memo,prem(proof,i),frame); - if(res == INT_MAX || res == bar) res = bar; - else if(bar != INT_MAX) res = -1; - } - } - return res; - } - - void scan_skolems(const ast &proof) { - hash_map memo; - scan_skolems_rec(memo,proof, INT_MAX); - } - - // determine locality of a proof term - // return frame of derivation if local, or -1 if not - // result INT_MAX means the proof term is a tautology - // memoized in hash_map "locality" - - int get_locality_rec(ast proof){ - std::pair foo(proof,INT_MAX); - std::pair bar = locality.insert(foo); - int &res = bar.first->second; - if(!bar.second) return res; - pfrule dk = pr(proof); - if(dk == PR_ASSERTED){ - ast ass = conc(proof); - res = frame_of_assertion(ass); -#ifdef NEW_LOCALITY - if(in_range(res,rng)) - res = range_max(rng); - else - res = frames-1; -#endif - } - else if(dk == PR_QUANT_INST){ - std::vector lits; - ast con = conc(proof); - get_Z3_lits(con, lits); - iproof->make_axiom(lits); - } -#ifdef LOCALIZATION_KLUDGE - else if(dk == PR_MODUS_PONENS && pr(prem(proof,0)) == PR_QUANT_INST - && get_locality_rec(prem(proof,1)) == INT_MAX){ - std::vector lits; - ast con = conc(proof); - get_Z3_lits(con, lits); - iproof->make_axiom(lits); - } -#endif - else { - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - int bar = get_locality_rec(arg); - if(res == INT_MAX || res == bar) res = bar; - else if(bar != INT_MAX) res = -1; - } - } - return res; - } - - - int get_locality(ast proof){ - // if(lia_z3_axioms_only) return -1; - int res = get_locality_rec(proof); - if(res != -1){ - ast con = conc(proof); - range rng = ast_scope(con); - - // hack: if a clause contains "true", it reduces to "true", - // which means we won't compute the range correctly. we handle - // this case by computing the ranges of the literals separately - - if(is_true(con)){ - std::vector lits; - get_Z3_lits(conc(proof),lits); - for(unsigned i = 0; i < lits.size(); i++) - rng = range_glb(rng,ast_scope(lits[i])); - } - - if(!range_is_empty(rng)){ - AstSet &hyps = get_hyps(proof); - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it){ - ast hyp = *it; - rng = range_glb(rng,ast_scope(hyp)); - } - } - - // if(!range_is_empty(rng)){ - // if (num_free_variables(con) > 0) - // rng = range_empty(); - // } - - if(res == INT_MAX){ - if(range_is_empty(rng)) - res = -1; - else res = range_max(rng); - } - else { - if(!in_range(res,rng)) - res = -1; - } - } - return res; - } - - - AstSet &get_hyps(ast proof){ - std::pair foo(proof,AstSet()); - std::pair bar = hyp_map.insert(foo); - AstSet &res = bar.first->second; - if(!bar.second) return res; - pfrule dk = pr(proof); - if(dk == PR_HYPOTHESIS){ - ast con = conc(proof); - res.insert(con); - } - else { - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - AstSet &arg_hyps = get_hyps(arg); - res.insert(arg_hyps.begin(),arg_hyps.end()); - } - if(dk == PR_LEMMA){ - ast con = conc(proof); - res.erase(mk_not(con)); - if(is_or(con)){ - int clause_size = num_args(con); - for(int i = 0; i < clause_size; i++){ - ast neglit = mk_not(arg(con,i)); - res.erase(neglit); - } - } - } - } -#if 0 - AstSet::iterator it = res.begin(), en = res.end(); - if(it != en){ - AstSet::iterator old = it; - ++it; - for(; it != en; ++it, ++old) - if(!(*old < *it)) - std::cout << "foo!"; - } -#endif - return res; - } - - // Find all the judgements of the form p <-> q, where - // p is local and q is non-local, recording them in "equivs" - // the map equivs_visited is used to record the already visited proof terms - - void find_equivs(ast proof){ - if(equivs_visited.find(proof) != equivs_visited.end()) - return; - equivs_visited.insert(proof); - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++) // do all the sub_terms - find_equivs(prem(proof,i)); - ast con = conc(proof); // get the conclusion - if(is_iff(con)){ - ast iff = con; - for(int i = 0; i < 2; i++) - if(!is_local(arg(iff,i)) && is_local(arg(iff,1-i))){ - std::pair > foo(arg(iff,i),std::pair(arg(iff,1-i),proof)); - equivs.insert(foo); - } - } - } - - // get the lits of a Z3 clause - void get_Z3_lits(ast t, std::vector &lits){ - opr dk = op(t); - if(dk == False) - return; // false = empty clause - if(dk == Or){ - unsigned nargs = num_args(t); - lits.resize(nargs); - for(unsigned i = 0; i < nargs; i++) // do all the sub_terms - lits[i] = arg(t,i); - } - else { - lits.push_back(t); - } - } - - // resolve two clauses represented as vectors of lits. replace first clause - void resolve(ast pivot, std::vector &cls1, std::vector &cls2){ - ast neg_pivot = mk_not(pivot); - for(unsigned i = 0; i < cls1.size(); i++){ - if(cls1[i] == pivot){ - cls1[i] = cls1.back(); - cls1.pop_back(); - bool found_pivot2 = false; - for(unsigned j = 0; j < cls2.size(); j++){ - if(cls2[j] == neg_pivot) - found_pivot2 = true; - else - cls1.push_back(cls2[j]); - } - (void)found_pivot2; - assert(found_pivot2); - return; - } - } - assert(0 && "resolve failed"); - } - - // get lits resulting from unit resolution up to and including "position" - // TODO: this is quadratic -- fix it - void do_unit_resolution(ast proof, int position, std::vector &lits){ - ast orig_clause = conc(prem(proof,0)); - get_Z3_lits(orig_clause,lits); - for(int i = 1; i <= position; i++){ - std::vector unit(1); - unit[0] = conc(prem(proof,i)); - resolve(mk_not(unit[0]),lits,unit); - } - } - -#if 0 - // clear the localization variables - void clear_localization(){ - localization_vars.clear(); - localization_map.clear(); - } - - // create a fresh variable for localization - ast fresh_localization_var(ast term, int frame){ - std::ostringstream s; - s << "%" << (localization_vars.size()); - ast var = make_var(s.str().c_str(),get_type(term)); - sym_range(sym(var)) = range_full(); // make this variable global - localization_vars.push_back(LocVar(var,term,frame)); - return var; - } - - - // "localize" a term to a given frame range by - // creating new symbols to represent non-local subterms - - ast localize_term(ast e, const range &rng){ - if(ranges_intersect(ast_scope(e),rng)) - return e; // this term occurs in range, so it's O.K. - AstToAst::iterator it = localization_map.find(e); - if(it != localization_map.end()) - return it->second; - - // if is is non-local, we must first localize the arguments to - // the range of its function symbol - - int nargs = num_args(e); - if(nargs > 0 /* && (!is_local(e) || flo <= hi || fhi >= lo) */){ - range frng = rng; - if(op(e) == Uninterpreted){ - symb f = sym(e); - range srng = sym_range(f); - if(ranges_intersect(srng,rng)) // localize to desired range if possible - frng = range_glb(srng,rng); - } - std::vector largs(nargs); - for(int i = 0; i < nargs; i++){ - largs[i] = localize_term(arg(e,i),frng); - frng = range_glb(frng,ast_scope(largs[i])); - } - e = clone(e,largs); - assert(is_local(e)); - } - - - if(ranges_intersect(ast_scope(e),rng)) - return e; // this term occurs in range, so it's O.K. - - // choose a frame for the constraint that is close to range - int frame = range_near(ast_scope(e),rng); - - ast new_var = fresh_localization_var(e,frame); - localization_map[e] = new_var; - ast cnst = make(Equal,new_var,e); - // antes.push_back(std::pair(cnst,frame)); - return new_var; - } - - // some patterm matching functions - - // match logical or with nargs arguments - // assumes AIG form - bool match_or(ast e, ast *args, int nargs){ - if(op(e) != Or) return false; - int n = num_args(e); - if(n != nargs) return false; - for(int i = 0; i < nargs; i++) - args[i] = arg(e,i); - return true; - } - - // match operator f with exactly nargs arguments - bool match_op(ast e, opr f, ast *args, int nargs){ - if(op(e) != f) return false; - int n = num_args(e); - if(n != nargs) return false; - for(int i = 0; i < nargs; i++) - args[i] = arg(e,i); - return true; - } - - // see if the given formula can be interpreted as - // an axiom instance (e.g., an array axiom instance). - // if so, add it to "antes" in an appropriate frame. - // this may require "localization" - - void get_axiom_instance(ast e){ - - // "store" axiom - // (or (= w q) (= (select (store a1 w y) q) (select a1 q))) - // std::cout << "ax: "; show(e); - ast lits[2],eq_ops_l[2],eq_ops_r[2],sel_ops[2], sto_ops[3], sel_ops2[2] ; - if(match_or(e,lits,2)) - if(match_op(lits[0],Equal,eq_ops_l,2)) - if(match_op(lits[1],Equal,eq_ops_r,2)) - for(int i = 0; i < 2; i++){ // try the second equality both ways - if(match_op(eq_ops_r[0],Select,sel_ops,2)) - if(match_op(sel_ops[0],Store,sto_ops,3)) - if(match_op(eq_ops_r[1],Select,sel_ops2,2)) - for(int j = 0; j < 2; j++){ // try the first equality both ways - if(eq_ops_l[0] == sto_ops[1] - && eq_ops_l[1] == sel_ops[1] - && eq_ops_l[1] == sel_ops2[1] - && sto_ops[0] == sel_ops2[0]) - if(is_local(sel_ops[0])) // store term must be local - { - ast sto = sel_ops[0]; - ast addr = localize_term(eq_ops_l[1],ast_scope(sto)); - ast res = make(Or, - make(Equal,eq_ops_l[0],addr), - make(Equal, - make(Select,sto,addr), - make(Select,sel_ops2[0],addr))); - // int frame = range_min(ast_scope(res)); TODO - // antes.push_back(std::pair(res,frame)); - return; - } - std::swap(eq_ops_l[0],eq_ops_l[1]); - } - std::swap(eq_ops_r[0],eq_ops_r[1]); - } - } - - // a quantifier instantation looks like (~ forall x. P) \/ P[z/x] - // we need to find a time frame for P, then localize P[z/x] in this frame - - void get_quantifier_instance(ast e){ - ast disjs[2]; - if(match_or(e,disjs,2)){ - if(is_local(disjs[0])){ - ast res = localize_term(disjs[1], ast_scope(disjs[0])); - // int frame = range_min(ast_scope(res)); TODO - // antes.push_back(std::pair(res,frame)); - return; - } - } - } - - ast get_judgement(ast proof){ - ast con = from_ast(conc(proof)); - AstSet &hyps = get_hyps(proof); - std::vector hyps_vec; - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it) - hyps_vec.push_back(*it); - if(hyps_vec.size() == 0) return con; - con = make(Or,mk_not(make(And,hyps_vec)),con); - return con; - } - - // does variable occur in expression? - int occurs_in1(ast var, ast e){ - std::pair foo(e,false); - std::pair bar = occurs_in_memo.insert(foo); - bool &res = bar.first->second; - if(bar.second){ - if(e == var) res = true; - int nargs = num_args(e); - for(int i = 0; i < nargs; i++) - res |= occurs_in1(var,arg(e,i)); - } - return res; - } - - int occurs_in(ast var, ast e){ - occurs_in_memo.clear(); - return occurs_in1(var,e); - } - - // find a controlling equality for a given variable v in a term - // a controlling equality is of the form v = t, which, being - // false would force the formula to have the specifid truth value - // returns t, or null if no such - - ast cont_eq(bool truth, ast v, ast e){ - if(is_not(e)) return cont_eq(!truth,v,arg(e,0)); - if(cont_eq_memo.find(e) != cont_eq_memo.end()) - return ast(); - cont_eq_memo.insert(e); - if(!truth && op(e) == Equal){ - if(arg(e,0) == v) return(arg(e,1)); - if(arg(e,1) == v) return(arg(e,0)); - } - if((!truth && op(e) == And) || (truth && op(e) == Or)){ - int nargs = num_args(e); - for(int i = 0; i < nargs; i++){ - ast res = cont_eq(truth, v, arg(e,i)); - if(!res.null()) return res; - } - } - return ast(); - } - - // substitute a term t for unbound occurrences of variable v in e - - ast subst(ast var, ast t, ast e){ - if(e == var) return t; - std::pair foo(e,ast()); - std::pair bar = subst_memo.insert(foo); - ast &res = bar.first->second; - if(bar.second){ - int nargs = num_args(e); - std::vector args(nargs); - for(int i = 0; i < nargs; i++) - args[i] = subst(var,t,arg(e,i)); - opr f = op(e); - if(f == Equal && args[0] == args[1]) res = mk_true(); - else res = clone(e,args); - } - return res; - } - - // apply a quantifier to a formula, with some optimizations - // 1) bound variable does not occur -> no quantifier - // 2) bound variable must be equal to some term -> substitute - - ast apply_quant(opr quantifier, ast var, ast e){ - if(!occurs_in(var,e))return e; - cont_eq_memo.clear(); - ast cterm = cont_eq(quantifier == Forall, var, e); - if(!cterm.null()){ - subst_memo.clear(); - return subst(var,cterm,e); - } - std::vector bvs; bvs.push_back(var); - return make_quant(quantifier,bvs,e); - } - - // add quantifiers over the localization vars - // to an interpolant for frames lo-hi - - ast add_quants(ast e, int lo, int hi){ - for(int i = localization_vars.size() - 1; i >= 0; i--){ - LocVar &lv = localization_vars[i]; - opr quantifier = (lv.frame >= lo && lv.frame <= hi) ? Exists : Forall; - e = apply_quant(quantifier,lv.var,e); - } - return e; - } - - int get_lits_locality(std::vector &lits){ - range rng = range_full(); - for(std::vector::iterator it = lits.begin(), en = lits.end(); it != en; ++it){ - ast lit = *it; - rng = range_glb(rng,ast_scope(lit)); - } - if(range_is_empty(rng)) return -1; - int hi = range_max(rng); - if(hi >= frames) return frames - 1; - return hi; - } -#endif - - int num_lits(ast ast){ - opr dk = op(ast); - if(dk == False) - return 0; - if(dk == Or){ - unsigned nargs = num_args(ast); - int n = 0; - for(unsigned i = 0; i < nargs; i++) // do all the sub_terms - n += num_lits(arg(ast,i)); - return n; - } - else - return 1; - } - - void symbols_out_of_scope_rec(hash_set &memo, hash_set &symb_memo, int frame, const ast &t){ - if(memo.find(t) != memo.end()) - return; - memo.insert(t); - if(op(t) == Uninterpreted){ - symb s = sym(t); - range r = sym_range(s); - if(!in_range(frame,r) && symb_memo.find(s) == symb_memo.end()){ - std::cout << string_of_symbol(s) << "\n"; - symb_memo.insert(s); - } - } - int nargs = num_args(t); - for(int i = 0; i < nargs; i++) - symbols_out_of_scope_rec(memo,symb_memo,frame,arg(t,i)); - } - - void symbols_out_of_scope(int frame, const ast &t){ - hash_set memo; - hash_set symb_memo; - symbols_out_of_scope_rec(memo,symb_memo,frame,t); - } - - void conc_symbols_out_of_scope(int frame, const ast &t){ - symbols_out_of_scope(frame,conc(t)); - } - - std::vector lit_trace; - hash_set marked_proofs; - - bool proof_has_lit(const ast &proof, const ast &lit){ - AstSet &hyps = get_hyps(proof); - if(hyps.find(mk_not(lit)) != hyps.end()) - return true; - std::vector lits; - ast con = conc(proof); - get_Z3_lits(con, lits); - for(unsigned i = 0; i < lits.size(); i++) - if(lits[i] == lit) - return true; - return false; - } - - - void trace_lit_rec(const ast &lit, const ast &proof, AstHashSet &memo){ - if(memo.find(proof) == memo.end()){ - memo.insert(proof); - AstSet &hyps = get_hyps(proof); - std::vector lits; - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it) - lits.push_back(mk_not(*it)); - ast con = conc(proof); - get_Z3_lits(con, lits); - for(unsigned i = 0; i < lits.size(); i++){ - if(lits[i] == lit){ - print_expr(std::cout,proof); - std::cout << "\n"; - marked_proofs.insert(proof); - pfrule dk = pr(proof); - if(dk == PR_UNIT_RESOLUTION || dk == PR_LEMMA){ - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - trace_lit_rec(lit,arg,memo); - } - } - else - lit_trace.push_back(proof); - } - } - } - } - - ast traced_lit; - - int trace_lit(const ast &lit, const ast &proof){ - marked_proofs.clear(); - lit_trace.clear(); - traced_lit = lit; - AstHashSet memo; - trace_lit_rec(lit,proof,memo); - return lit_trace.size(); - } - - bool is_literal_or_lit_iff(const ast &lit){ - if(my_is_literal(lit)) return true; - if(op(lit) == Iff){ - return my_is_literal(arg(lit,0)) && my_is_literal(arg(lit,1)); - } - return false; - } - - bool my_is_literal(const ast &lit){ - ast abslit = is_not(lit) ? arg(lit,0) : lit; - int f = op(abslit); - return !(f == And || f == Or || f == Iff); - } - - hash_map asts_by_id; - - void print_lit(const ast &lit){ - ast abslit = is_not(lit) ? arg(lit,0) : lit; - if(!is_literal_or_lit_iff(lit)){ - if(is_not(lit)) std::cout << "~"; - int id = ast_id(abslit); - asts_by_id[id] = abslit; - std::cout << "[" << id << "]"; - } - else - print_expr(std::cout,lit); - } - - void expand(int id){ - if(asts_by_id.find(id) == asts_by_id.end()) - std::cout << "undefined\n"; - else { - ast lit = asts_by_id[id]; - std::string s = string_of_symbol(sym(lit)); - std::cout << "(" << s; - unsigned nargs = num_args(lit); - for(unsigned i = 0; i < nargs; i++){ - std::cout << " "; - print_lit(arg(lit,i)); - } - std::cout << ")\n";; - } - } - - void show_lit(const ast &lit){ - print_lit(lit); - std::cout << "\n"; - } - - void print_z3_lit(const ast &a){ - print_lit(from_ast(a)); - } - - void show_z3_lit(const ast &a){ - print_z3_lit(a); - std::cout << "\n"; - } - - - void show_con(const ast &proof, bool brief){ - if(!traced_lit.null() && proof_has_lit(proof,traced_lit)) - std::cout << "(*) "; - ast con = conc(proof); - AstSet &hyps = get_hyps(proof); - int count = 0; - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it){ - if(brief && ++count > 5){ - std::cout << "... "; - break; - } - print_lit(*it); - std::cout << " "; - } - std::cout << "|- "; - std::vector lits; - get_Z3_lits(con,lits); - for(unsigned i = 0; i < lits.size(); i++){ - print_lit(lits[i]); - std::cout << " "; - } - range r = ast_scope(con); - std::cout << " {" << r.lo << "," << r.hi << "}"; - std::cout << "\n"; - } - - void show_step(const ast &proof){ - std::cout << "\n"; - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - std::cout << "(" << i << ") "; - ast arg = prem(proof,i); - show_con(arg,true); - } - std::cout << "|------ "; - std::cout << string_of_symbol(sym(proof)) << "\n"; - show_con(proof,false); - } - - void show_marked( const ast &proof){ - std::cout << "\n"; - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - if(!traced_lit.null() && proof_has_lit(arg,traced_lit)){ - std::cout << "(" << i << ") "; - show_con(arg,true); - } - } - } - - std::vector pfhist; - int pfhist_pos; - - void pfgoto(const ast &proof){ - if(pfhist.size() == 0) - pfhist_pos = 0; - else pfhist_pos++; - pfhist.resize(pfhist_pos); - pfhist.push_back(proof); - show_step(proof); - } - - - void pfback(){ - if(pfhist_pos > 0){ - pfhist_pos--; - show_step(pfhist[pfhist_pos]); - } - } - - void pffwd(){ - if(pfhist_pos < ((int)pfhist.size()) - 1){ - pfhist_pos++; - show_step(pfhist[pfhist_pos]); - } - } - - void pfprem(int i){ - if(pfhist.size() > 0){ - ast proof = pfhist[pfhist_pos]; - unsigned nprems = num_prems(proof); - if(i >= 0 && i < (int)nprems) - pfgoto(prem(proof,i)); - } - } - - - - // translate a unit resolution sequence - Iproof::node translate_ur(ast proof){ - ast prem0 = prem(proof,0); - Iproof::node itp = translate_main(prem0,true); - std::vector clause; - ast conc0 = conc(prem0); - int nprems = num_prems(proof); - if(nprems == 2 && conc0 == mk_not(conc(prem(proof,1)))) - clause.push_back(conc0); - else - get_Z3_lits(conc0,clause); - for(int position = 1; position < nprems; position++){ - ast ante = prem(proof,position); - ast pnode = conc(ante); - ast pnode_abs = !is_not(pnode) ? pnode : mk_not(pnode); - Iproof::node neg = itp; - Iproof::node pos = translate_main(ante, false); - if(is_not(pnode)){ - pnode = mk_not(pnode); - std::swap(neg,pos); - } - std::vector unit(1); - unit[0] = conc(ante); - resolve(mk_not(conc(ante)),clause,unit); - itp = iproof->make_resolution(pnode,clause,neg,pos); - } - return itp; - } - - // get an inequality in the form 0 <= t where t is a linear term - ast rhs_normalize_inequality(const ast &ineq){ - ast zero = make_int("0"); - ast thing = make(Leq,zero,zero); - linear_comb(thing,make_int("1"),ineq); - thing = simplify_ineq(thing); - return thing; - } - - bool check_farkas(const std::vector &prems, const ast &con){ - ast zero = make_int("0"); - ast thing = make(Leq,zero,zero); - for(unsigned i = 0; i < prems.size(); i++) - linear_comb(thing,make_int(rational(1)),prems[i]); - linear_comb(thing,make_int(rational(-1)),con); - thing = simplify_ineq(thing); - return arg(thing,1) == make_int(rational(0)); - } - - // get an inequality in the form t <= c or t < c, there t is affine and c constant - ast normalize_inequality(const ast &ineq){ - ast zero = make_int("0"); - ast thing = make(Leq,zero,zero); - linear_comb(thing,make_int("1"),ineq); - thing = simplify_ineq(thing); - ast lhs = arg(thing,0); - ast rhs = arg(thing,1); - opr o = op(rhs); - if(o != Numeral){ - if(op(rhs) == Plus){ - int nargs = num_args(rhs); - ast const_term = zero; - int i = 0; - if(nargs > 0 && op(arg(rhs,0)) == Numeral){ - const_term = arg(rhs,0); - i++; - } - if(i < nargs){ - std::vector non_const; - for(; i < nargs; i++) - non_const.push_back(arg(rhs,i)); - lhs = make(Sub,lhs,make(Plus,non_const)); - } - rhs = const_term; - } - else { - lhs = make(Sub,lhs,make(Plus,rhs)); - rhs = zero; - } - lhs = z3_simplify(lhs); - rhs = z3_simplify(rhs); - thing = make(op(thing),lhs,rhs); - } - return thing; - } - - void get_linear_coefficients(const ast &t, std::vector &coeffs){ - if(op(t) == Plus){ - int nargs = num_args(t); - for(int i = 0; i < nargs; i++) - coeffs.push_back(get_coeff(arg(t,i))); - } - else - coeffs.push_back(get_coeff(t)); - } - - /* given an affine term t, get the GCD of the coefficients in t. */ - ast gcd_of_coefficients(const ast &t){ - std::vector coeffs; - get_linear_coefficients(t,coeffs); - if(coeffs.size() == 0) - return make_int("1"); // arbitrary - rational d = abs(coeffs[0]); - for(unsigned i = 1; i < coeffs.size(); i++){ - d = gcd(d,coeffs[i]); - } - return make_int(d); - } - - ast get_bounded_variable(const ast &ineq, bool &lb){ - ast nineq = normalize_inequality(ineq); - ast lhs = arg(nineq,0); - lhs.raw(); - switch(op(lhs)){ - case Uninterpreted: - lb = false; - return lhs; - case Times: - if(arg(lhs,0) == make_int(rational(1))) - lb = false; - else if(arg(lhs,0) == make_int(rational(-1))) - lb = true; - else - throw_unsupported(lhs); - return arg(lhs,1); - default: - throw_unsupported(lhs); - } - } - - rational get_term_coefficient(const ast &t1, const ast &v){ - ast t = arg(normalize_inequality(t1),0); - if(op(t) == Plus){ - int nargs = num_args(t); - for(int i = 0; i < nargs; i++){ - if(get_linear_var(arg(t,i)) == v) - return get_coeff(arg(t,i)); - } - } - else - if(get_linear_var(t) == v) - return get_coeff(t); - return rational(0); - } - - - Iproof::node GCDtoDivRule(const ast &proof, bool pol, std::vector &coeffs, std::vector &prems, ast &cut_con){ - // gather the summands of the desired polarity - std::vector my_prems; - std::vector my_coeffs; - std::vector my_prem_cons; - for(unsigned i = pol ? 0 : 1; i < coeffs.size(); i+= 2){ - rational &c = coeffs[i]; - if(c.is_pos()){ - my_prems.push_back(prems[i]); - my_coeffs.push_back(make_int(c)); - my_prem_cons.push_back(conc(prem(proof,i))); - } - else if(c.is_neg()){ - int j = (i % 2 == 0) ? i + 1 : i - 1; - my_prems.push_back(prems[j]); - my_coeffs.push_back(make_int(-coeffs[j])); - my_prem_cons.push_back(conc(prem(proof,j))); - } - } - ast my_con = sum_inequalities(my_coeffs,my_prem_cons); - - // handle generalized GCD test. sadly, we dont' get the coefficients... - if(coeffs[0].is_zero()){ - bool lb; - int xtra_prem = 0; - ast bv = get_bounded_variable(conc(prem(proof,0)),lb); - rational bv_coeff = get_term_coefficient(my_con,bv); - if(bv_coeff.is_pos() != lb) - xtra_prem = 1; - if(bv_coeff.is_neg()) - bv_coeff = -bv_coeff; - - my_prems.push_back(prems[xtra_prem]); - my_coeffs.push_back(make_int(bv_coeff)); - my_prem_cons.push_back(conc(prem(proof,xtra_prem))); - my_con = sum_inequalities(my_coeffs,my_prem_cons); - } - - my_con = normalize_inequality(my_con); - Iproof::node hyp = iproof->make_hypothesis(mk_not(my_con)); - my_prems.push_back(hyp); - my_coeffs.push_back(make_int("1")); - my_prem_cons.push_back(mk_not(my_con)); - Iproof::node res = iproof->make_farkas(mk_false(),my_prems,my_prem_cons,my_coeffs); - - ast t = arg(my_con,0); - ast c = arg(my_con,1); - ast d = gcd_of_coefficients(t); - t = z3_simplify(mk_idiv(t,d)); - c = z3_simplify(mk_idiv(c,d)); - cut_con = make(op(my_con),t,c); - return iproof->make_cut_rule(my_con,d,cut_con,res); - } - - - rational get_first_coefficient(const ast &t, ast &v){ - if(op(t) == Plus){ - unsigned best_id = UINT_MAX; - rational best_coeff(0); - int nargs = num_args(t); - for(int i = 0; i < nargs; i++) - if(op(arg(t,i)) != Numeral){ - ast lv = get_linear_var(arg(t,i)); - unsigned id = ast_id(lv); - if(id < best_id) { - v = lv; - best_id = id; - best_coeff = get_coeff(arg(t,i)); - } - } - return best_coeff; - } - else - if(op(t) != Numeral){ - v = get_linear_var(t); - return(get_coeff(t)); - } - return rational(0); - } - - ast divide_inequalities(const ast &x, const ast&y){ - ast xvar, yvar; - rational xcoeff = get_first_coefficient(arg(x,0),xvar); - rational ycoeff = get_first_coefficient(arg(y,0),yvar); - if(xcoeff == rational(0) || ycoeff == rational(0) || xvar != yvar) - throw_unsupported(x); // can be caused by non-linear arithmetic - rational ratio = xcoeff/ycoeff; - if(denominator(ratio) != rational(1)) - throw_unsupported(y); // can this ever happen? - return make_int(ratio); // better be integer! - } - - ast AssignBounds2Farkas(const ast &proof, const ast &con){ - std::vector farkas_coeffs; - get_assign_bounds_coeffs(proof,farkas_coeffs); - int nargs = num_args(con); - if(nargs != (int)(farkas_coeffs.size())) - throw_unsupported(proof); // should never happen -#if 0 - if(farkas_coeffs[0] != make_int(rational(1))) - farkas_coeffs[0] = make_int(rational(1)); -#else - std::vector lits, lit_coeffs; - for(int i = 1; i < nargs; i++){ - lits.push_back(mk_not(arg(con,i))); - lit_coeffs.push_back(farkas_coeffs[i]); - } - ast sum = normalize_inequality(sum_inequalities(lit_coeffs,lits)); - ast conseq = normalize_inequality(arg(con,0)); - ast d = divide_inequalities(sum,conseq); -#if 0 - if(d != farkas_coeffs[0]) - std::cout << "wow!\n"; -#endif - farkas_coeffs[0] = d; -#endif - std::vector my_coeffs; - std::vector my_cons; - for(int i = 1; i < nargs; i++){ - my_cons.push_back(mk_not(arg(con,i))); - my_coeffs.push_back(farkas_coeffs[i]); - } - ast farkas_con = normalize_inequality(sum_inequalities(my_coeffs,my_cons,true /* round_off */)); - my_cons.push_back(mk_not(farkas_con)); - my_coeffs.push_back(make_int("1")); - std::vector my_hyps; - my_hyps.reserve(nargs); - for(int i = 0; i < nargs; i++) - my_hyps.push_back(iproof->make_hypothesis(my_cons[i])); - ast res = iproof->make_farkas(mk_false(),my_hyps,my_cons,my_coeffs); - res = iproof->make_cut_rule(farkas_con,farkas_coeffs[0],arg(con,0),res); - return res; - } - - ast AssignBoundsRule2Farkas(const ast &proof, const ast &con, std::vector prems){ - std::vector farkas_coeffs; - get_assign_bounds_rule_coeffs(proof,farkas_coeffs); - int nargs = num_prems(proof)+1; - if(nargs != (int)(farkas_coeffs.size())) - throw iz3_exception("bad assign-bounds theory lemma"); -#if 0 - if(farkas_coeffs[0] != make_int(rational(1))) - farkas_coeffs[0] = make_int(rational(1)); -#else - std::vector lits, lit_coeffs; - for(int i = 1; i < nargs; i++){ - lits.push_back(conc(prem(proof,i-1))); - lit_coeffs.push_back(farkas_coeffs[i]); - } - ast sum = normalize_inequality(sum_inequalities(lit_coeffs,lits)); - ast conseq = normalize_inequality(con); - ast d = divide_inequalities(sum,conseq); -#if 0 - if(d != farkas_coeffs[0]) - std::cout << "wow!\n"; -#endif - farkas_coeffs[0] = d; -#endif - std::vector my_coeffs; - std::vector my_cons; - for(int i = 1; i < nargs; i++){ - my_cons.push_back(conc(prem(proof,i-1))); - my_coeffs.push_back(farkas_coeffs[i]); - } - ast farkas_con = normalize_inequality(sum_inequalities(my_coeffs,my_cons,true /* round_off */)); - std::vector my_hyps; - for(int i = 1; i < nargs; i++) - my_hyps.push_back(prems[i-1]); - my_cons.push_back(mk_not(farkas_con)); - my_coeffs.push_back(make_int("1")); - my_hyps.push_back(iproof->make_hypothesis(mk_not(farkas_con))); - ast res = iproof->make_farkas(mk_false(),my_hyps,my_cons,my_coeffs); - res = iproof->make_cut_rule(farkas_con,farkas_coeffs[0],conc(proof),res); - return res; - } - - ast GomoryCutRule2Farkas(const ast &proof, const ast &con, std::vector prems){ - std::vector my_prems = prems; - std::vector my_coeffs; - std::vector my_prem_cons; - get_gomory_cut_coeffs(proof,my_coeffs); - int nargs = num_prems(proof); - if(nargs != (int)(my_coeffs.size())) - throw "bad gomory-cut theory lemma"; - my_prem_cons.reserve(nargs); - for(int i = 0; i < nargs; i++) - my_prem_cons.push_back(conc(prem(proof,i))); - ast my_con = normalize_inequality(sum_inequalities(my_coeffs,my_prem_cons)); - Iproof::node hyp = iproof->make_hypothesis(mk_not(my_con)); - my_prems.push_back(hyp); - my_coeffs.push_back(make_int("1")); - my_prem_cons.push_back(mk_not(my_con)); - Iproof::node res = iproof->make_farkas(mk_false(),my_prems,my_prem_cons,my_coeffs); - ast t = arg(my_con,0); - ast c = arg(my_con,1); - ast d = gcd_of_coefficients(t); - /* - t = z3_simplify(mk_idiv(t,d)); - c = z3_simplify(mk_idiv(c,d)); - ast cut_con = make(op(my_con),t,c); - */ - ast cut_con = con; - return iproof->make_cut_rule(my_con,d,cut_con,res); - } - - Iproof::node RewriteClause(Iproof::node clause, const ast &rew){ - if(pr(rew) == PR_MONOTONICITY){ - int nequivs = num_prems(rew); - for(int i = 0; i < nequivs; i++){ - Iproof::node equiv_pf = translate_main(prem(rew,i),false); - ast equiv = conc(prem(rew,i)); - clause = iproof->make_mp(equiv,clause,equiv_pf); - } - return clause; - } - if(pr(rew) == PR_TRANSITIVITY){ - clause = RewriteClause(clause,prem(rew,0)); - clause = RewriteClause(clause,prem(rew,1)); - return clause; - } - if(pr(rew) == PR_REWRITE){ - return clause; // just hope the rewrite does nothing! - } - throw_unsupported(rew); - } - - - // Following code is for elimination of "commutativity" axiom - - Iproof::node make_commuted_modus_ponens(const ast &proof, const std::vector &args){ - ast pf = arg(args[1],0); - ast comm_equiv = arg(args[1],1); // equivalence relation with possible commutations - ast P = conc(prem(proof,0)); - ast Q = conc(proof); - Iproof::node P_pf = args[0]; - ast P_comm = arg(comm_equiv,0); - ast Q_comm = arg(comm_equiv,1); - if(P != P_comm) - P_pf = iproof->make_symmetry(P_comm,P,P_pf); - Iproof::node res = iproof->make_mp(comm_equiv,P_pf,pf); - if(Q != Q_comm) - res = iproof->make_symmetry(Q,Q_comm,res); - return res; - } - - Iproof::node make_commuted_monotonicity(const ast &proof, const std::vector &args){ - ast pf = arg(args[0],0); - ast comm_equiv = arg(args[0],1); // equivalence relation with possible commutations - ast con = make(Iff,make(Not,arg(comm_equiv,0)),make(Not,arg(comm_equiv,1))); - std::vector eqs; eqs.push_back(comm_equiv); - std::vector pfs; pfs.push_back(pf); - ast res = iproof->make_congruence(eqs,con,pfs); - res = make(commute,res,con); - return res; - } - - Iproof::node make_commuted_symmetry(const ast &proof, const std::vector &args){ - ast pf = arg(args[0],0); - ast comm_equiv = arg(args[0],1); // equivalence relation with possible commutations - ast con = make(Iff,arg(comm_equiv,1),arg(comm_equiv,0)); - ast res = iproof->make_symmetry(con,comm_equiv,pf); - res = make(commute,res,con); - return res; - } - - void unpack_commuted(const ast &proof, const ast &cm, ast &pf, ast &comm_equiv){ - if(sym(cm) == commute){ - pf = arg(cm,0); - comm_equiv = arg(cm,1); - } - else { - pf = cm; - comm_equiv = conc(proof); - } - } - - Iproof::node make_commuted_transitivity(const ast &proof, const std::vector &args){ - ast pf[2], comm_equiv[2]; - for(int i = 0; i < 2; i++) - unpack_commuted(prem(proof,i),args[i],pf[i],comm_equiv[i]); - if(!(arg(comm_equiv[0],1) == arg(comm_equiv[1],0))){ - ast tw = twist(prem(proof,1)); - ast np = translate_main(tw,false); - unpack_commuted(tw,np,pf[1],comm_equiv[1]); - } - ast con = make(Iff,arg(comm_equiv[0],0),arg(comm_equiv[1],1)); - ast res = iproof->make_transitivity(arg(comm_equiv[0],0),arg(comm_equiv[0],1),arg(comm_equiv[1],1),pf[0],pf[1]); - res = make(commute,res,con); - return res; - } - - ast commute_equality(const ast &eq){ - return make(Equal,arg(eq,1),arg(eq,0)); - } - - ast commute_equality_iff(const ast &con){ - if(op(con) != Iff || op(arg(con,0)) != Equal) - throw_unsupported(con); - return make(Iff,commute_equality(arg(con,0)),commute_equality(arg(con,1))); - } - - // convert a proof of a=b <-> c=d into a proof of b=a <-> d=c - // TODO: memoize this? - ast twist(const ast &proof){ - pfrule dk = pr(proof); - ast con = commute_equality_iff(conc(proof)); - int n = num_prems(proof); - std::vector prs(n); - if(dk == PR_MONOTONICITY){ - for(int i = 0; i < n; i++) - prs[i] = prem(proof,i); - } - else - for(int i = 0; i < n; i++) - prs[i] = twist(prem(proof,i)); - switch(dk){ - case PR_MONOTONICITY: - case PR_SYMMETRY: - case PR_TRANSITIVITY: - case PR_COMMUTATIVITY: - prs.push_back(con); - return clone(proof,prs); - default: - throw_unsupported(proof); - } - } - - struct TermLt { - iz3mgr &m; - bool operator()(const ast &x, const ast &y){ - unsigned xid = m.ast_id(x); - unsigned yid = m.ast_id(y); - return xid < yid; - } - TermLt(iz3mgr &_m) : m(_m) {} - }; - - void SortTerms(std::vector &terms){ - TermLt foo(*this); - std::sort(terms.begin(),terms.end(),foo); - } - - ast SortSum(const ast &t){ - if(!(op(t) == Plus)) - return t; - int nargs = num_args(t); - if(nargs < 2) return t; - std::vector args(nargs); - for(int i = 0; i < nargs; i++) - args[i] = arg(t,i); - SortTerms(args); - return make(Plus,args); - } - - void get_sum_as_vector(const ast &t, std::vector &coeffs, std::vector &vars){ - if(!(op(t) == Plus)){ - coeffs.push_back(get_coeff(t)); - vars.push_back(get_linear_var(t)); - } - else { - int nargs = num_args(t); - for(int i = 0; i < nargs; i++) - get_sum_as_vector(arg(t,i),coeffs,vars); - } - } - - ast replace_summands_with_fresh_vars(const ast &t, hash_map &map){ - if(op(t) == Plus){ - int nargs = num_args(t); - std::vector args(nargs); - for(int i = 0; i < nargs; i++) - args[i] = replace_summands_with_fresh_vars(arg(t,i),map); - return make(Plus,args); - } - if(op(t) == Times) - return make(Times,arg(t,0),replace_summands_with_fresh_vars(arg(t,1),map)); - if(map.find(t) == map.end()) - map[t] = mk_fresh_constant("@s",get_type(t)); - return map[t]; - } - - rational lcd(const std::vector &rats){ - rational res = rational(1); - for(unsigned i = 0; i < rats.size(); i++){ - res = lcm(res,denominator(rats[i])); - } - return res; - } - - Iproof::node reconstruct_farkas_with_dual(const std::vector &prems, const std::vector &pfs, const ast &con){ - int nprems = prems.size(); - std::vector npcons(nprems); - hash_map pain_map; // not needed - for(int i = 0; i < nprems; i++){ - npcons[i] = painfully_normalize_ineq(conc(prems[i]),pain_map); - if(op(npcons[i]) == Lt){ - ast constval = z3_simplify(make(Sub,arg(npcons[i],1),make_int(rational(1)))); - npcons[i] = make(Leq,arg(npcons[i],0),constval); - } - } - ast ncon = painfully_normalize_ineq(mk_not(con),pain_map); - npcons.push_back(ncon); - - hash_map dual_map; - std::vector cvec, vars_seen; - m().enable_int_real_coercions(true); - ast rhs = make_real(rational(0)); - for(unsigned i = 0; i < npcons.size(); i++){ - ast c= mk_fresh_constant("@c",real_type()); - cvec.push_back(c); - ast lhs = arg(npcons[i],0); - std::vector coeffs; - std::vector vars; - get_sum_as_vector(lhs,coeffs,vars); - for(unsigned j = 0; j < coeffs.size(); j++){ - rational coeff = coeffs[j]; - ast var = vars[j]; - if(dual_map.find(var) == dual_map.end()){ - dual_map[var] = make_real(rational(0)); - vars_seen.push_back(var); - } - ast foo = make(Plus,dual_map[var],make(Times,make_real(coeff),c)); - dual_map[var] = foo; - } - rhs = make(Plus,rhs,make(Times,c,arg(npcons[i],1))); - } - std::vector cnstrs; - for(unsigned i = 0; i < vars_seen.size(); i++) - cnstrs.push_back(make(Equal,dual_map[vars_seen[i]],make_real(rational(0)))); - cnstrs.push_back(make(Leq,rhs,make_real(rational(0)))); - for(unsigned i = 0; i < cvec.size() - 1; i++) - cnstrs.push_back(make(Geq,cvec[i],make_real(rational(0)))); - cnstrs.push_back(make(Equal,cvec.back(),make_real(rational(1)))); - ast new_proof; - - // greedily reduce the core - for(unsigned i = 0; i < cvec.size() - 1; i++){ - std::vector dummy; - cnstrs.push_back(make(Equal,cvec[i],make_real(rational(0)))); - if(!is_sat(cnstrs,new_proof,dummy)) - cnstrs.pop_back(); - } - - std::vector vals = cvec; - if(!is_sat(cnstrs,new_proof,vals)) - throw iz3_exception("Proof error!"); - std::vector rat_farkas_coeffs; - for(unsigned i = 0; i < cvec.size(); i++){ - ast bar = vals[i]; - rational r; - if(is_numeral(bar,r)) - rat_farkas_coeffs.push_back(r); - else - throw iz3_exception("Proof error!"); - } - rational the_lcd = lcd(rat_farkas_coeffs); - std::vector farkas_coeffs; - std::vector my_prems; - std::vector my_pcons; - for(unsigned i = 0; i < prems.size(); i++){ - ast fc = make_int(rat_farkas_coeffs[i] * the_lcd); - if(!(fc == make_int(rational(0)))){ - farkas_coeffs.push_back(fc); - my_prems.push_back(pfs[i]); - my_pcons.push_back(conc(prems[i])); - } - } - farkas_coeffs.push_back(make_int(the_lcd)); - my_prems.push_back(iproof->make_hypothesis(mk_not(con))); - my_pcons.push_back(mk_not(con)); - - Iproof::node res = iproof->make_farkas(mk_false(),my_prems,my_pcons,farkas_coeffs); - return res; - } - - ast painfully_normalize_ineq(const ast &ineq, hash_map &map){ - ast res = normalize_inequality(ineq); - ast lhs = arg(res,0); - lhs = replace_summands_with_fresh_vars(lhs,map); - res = make(op(res),SortSum(lhs),arg(res,1)); - return res; - } - - Iproof::node painfully_reconstruct_farkas(const std::vector &prems, const std::vector &pfs, const ast &con){ - int nprems = prems.size(); - std::vector pcons(nprems),npcons(nprems); - hash_map pcon_to_pf, npcon_to_pcon, pain_map; - for(int i = 0; i < nprems; i++){ - pcons[i] = conc(prems[i]); - npcons[i] = painfully_normalize_ineq(pcons[i],pain_map); - pcon_to_pf[npcons[i]] = pfs[i]; - npcon_to_pcon[npcons[i]] = pcons[i]; - } - // ast leq = make(Leq,arg(con,0),arg(con,1)); - ast ncon = painfully_normalize_ineq(mk_not(con),pain_map); - pcons.push_back(mk_not(con)); - npcons.push_back(ncon); - // ast assumps = make(And,pcons); - ast new_proof; - std::vector dummy; - if(is_sat(npcons,new_proof,dummy)) - throw iz3_exception("Proof error!"); - pfrule dk = pr(new_proof); - int nnp = num_prems(new_proof); - std::vector my_prems; - std::vector farkas_coeffs, my_pcons; - - if(dk == PR_TH_LEMMA - && get_theory_lemma_theory(new_proof) == ArithTheory - && get_theory_lemma_kind(new_proof) == FarkasKind) - get_farkas_coeffs(new_proof,farkas_coeffs); - else if(dk == PR_UNIT_RESOLUTION && nnp == 2){ - for(int i = 0; i < nprems; i++) - farkas_coeffs.push_back(make_int(rational(1))); - } - else - return reconstruct_farkas_with_dual(prems,pfs,con); - - for(int i = 0; i < nnp; i++){ - ast p = conc(prem(new_proof,i)); - p = really_normalize_ineq(p); - if(pcon_to_pf.find(p) != pcon_to_pf.end()){ - my_prems.push_back(pcon_to_pf[p]); - my_pcons.push_back(npcon_to_pcon[p]); - } - else if(p == ncon){ - my_prems.push_back(iproof->make_hypothesis(mk_not(con))); - my_pcons.push_back(mk_not(con)); - } - else - return reconstruct_farkas_with_dual(prems,pfs,con); - } - Iproof::node res = iproof->make_farkas(mk_false(),my_prems,my_pcons,farkas_coeffs); - return res; - } - - - - ast really_normalize_ineq(const ast &ineq){ - ast res = normalize_inequality(ineq); - res = make(op(res),SortSum(arg(res,0)),arg(res,1)); - return res; - } - - Iproof::node reconstruct_farkas(const std::vector &prems, const std::vector &pfs, const ast &con){ - int nprems = prems.size(); - std::vector pcons(nprems),npcons(nprems); - hash_map pcon_to_pf, npcon_to_pcon; - for(int i = 0; i < nprems; i++){ - pcons[i] = conc(prems[i]); - npcons[i] = really_normalize_ineq(pcons[i]); - pcon_to_pf[npcons[i]] = pfs[i]; - npcon_to_pcon[npcons[i]] = pcons[i]; - } - // ast leq = make(Leq,arg(con,0),arg(con,1)); - ast ncon = really_normalize_ineq(mk_not(con)); - pcons.push_back(mk_not(con)); - npcons.push_back(ncon); - // ast assumps = make(And,pcons); - ast new_proof; - std::vector dummy; - if(is_sat(npcons,new_proof,dummy)) - throw iz3_exception("Proof error!"); - pfrule dk = pr(new_proof); - int nnp = num_prems(new_proof); - std::vector my_prems; - std::vector farkas_coeffs, my_pcons; - - if(dk == PR_TH_LEMMA - && get_theory_lemma_theory(new_proof) == ArithTheory - && get_theory_lemma_kind(new_proof) == FarkasKind) - get_farkas_coeffs(new_proof,farkas_coeffs); - else if(dk == PR_UNIT_RESOLUTION && nnp == 2){ - for(int i = 0; i < nprems; i++) - farkas_coeffs.push_back(make_int(rational(1))); - } - else - return painfully_reconstruct_farkas(prems,pfs,con); - - for(int i = 0; i < nnp; i++){ - ast p = conc(prem(new_proof,i)); - p = really_normalize_ineq(p); - if(pcon_to_pf.find(p) != pcon_to_pf.end()){ - my_prems.push_back(pcon_to_pf[p]); - my_pcons.push_back(npcon_to_pcon[p]); - } - else if(p == ncon){ - my_prems.push_back(iproof->make_hypothesis(mk_not(con))); - my_pcons.push_back(mk_not(con)); - } - else - return painfully_reconstruct_farkas(prems,pfs,con); - } - Iproof::node res = iproof->make_farkas(mk_false(),my_prems,my_pcons,farkas_coeffs); - return res; - } - - bool is_eq_propagate(const ast &proof){ - return pr(proof) == PR_TH_LEMMA && get_theory_lemma_theory(proof) == ArithTheory && get_theory_lemma_kind(proof) == EqPropagateKind; - } - - ast EqPropagate(const ast &con, const std::vector &prems, const std::vector &args){ - Iproof::node fps[2]; - ast ineq_con[2]; - for(int i = 0; i < 2; i++){ - opr o = i == 0 ? Leq : Geq; - ineq_con[i] = make(o, arg(con,0), arg(con,1)); - fps[i] = reconstruct_farkas(prems,args,ineq_con[i]); - } - ast res = iproof->make_leq2eq(arg(con,0), arg(con,1), ineq_con[0], ineq_con[1]); - std::vector dummy_clause; - for(int i = 0; i < 2; i++) - res = iproof->make_resolution(ineq_con[i],dummy_clause,res,fps[i]); - return res; - } - - ast ArithMysteryRule(const ast &con, const std::vector &prems, const std::vector &args){ - // Hope for the best! - Iproof::node guess = reconstruct_farkas(prems,args,con); - return guess; - } - - struct CannotCombineEqPropagate {}; - - void CombineEqPropagateRec(const ast &proof, std::vector &prems, std::vector &args, ast &eqprem){ - if(pr(proof) == PR_TRANSITIVITY && is_eq_propagate(prem(proof,1))){ - CombineEqPropagateRec(prem(proof,0), prems, args, eqprem); - ast dummy; - CombineEqPropagateRec(prem(proof,1), prems, args, dummy); - return; - } - if(is_eq_propagate(proof)){ - int nprems = num_prems(proof); - for(int i = 0; i < nprems; i++){ - prems.push_back(prem(proof,i)); - ast ppf = translate_main(prem(proof,i),false); - args.push_back(ppf); - } - return; - } - eqprem = proof; - } - - ast CombineEqPropagate(const ast &proof){ - std::vector prems, args; - ast eq1; - CombineEqPropagateRec(proof, prems, args, eq1); - ast eq2con = conc(proof); - if(!eq1.null()) - eq2con = make(Equal,arg(conc(eq1),1),arg(conc(proof),1)); - ast eq2 = EqPropagate(eq2con,prems,args); - if(!eq1.null()){ - Iproof::node foo = translate_main(eq1,false); - eq2 = iproof->make_transitivity(arg(conc(eq1),0), arg(conc(eq1),1), arg(conc(proof),1), foo, eq2); - } - return eq2; - } - - bool get_store_array(const ast &t, ast &res){ - if(op(t) == Store){ - res = t; - return true; - } - int nargs = num_args(t); - for(int i = 0; i < nargs; i++) - if(get_store_array(arg(t,i),res)) - return true; - return false; - } - - // translate a Z3 proof term into interpolating proof system - - Iproof::node translate_main(ast proof, bool expect_clause = true){ - AstToIpf &tr = translation; - hash_map &trc = expect_clause ? tr.first : tr.second; - std::pair foo(proof,Iproof::node()); - std::pair::iterator, bool> bar = trc.insert(foo); - Iproof::node &res = bar.first->second; - if(!bar.second) return res; - - // Try the locality rule first - - int frame = get_locality(proof); - if(frame != -1){ - ast e = from_ast(conc(proof)); - if(frame >= frames) frame = frames - 1; - std::vector foo; - if(expect_clause) - get_Z3_lits(conc(proof),foo); - else - foo.push_back(e); - AstSet &hyps = get_hyps(proof); - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it) - foo.push_back(mk_not(*it)); - res = iproof->make_assumption(frame,foo); - return res; - } - - // If the proof is not local, break it down by proof rule - - pfrule dk = pr(proof); - unsigned nprems = num_prems(proof); - if(dk == PR_UNIT_RESOLUTION){ - res = translate_ur(proof); - } - else if(dk == PR_LEMMA){ - ast contra = prem(proof,0); // this is a proof of false from some hyps - res = translate_main(contra); - if(!expect_clause){ - std::vector foo; // the negations of the hyps form a clause - foo.push_back(from_ast(conc(proof))); - AstSet &hyps = get_hyps(proof); - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it) - foo.push_back(mk_not(*it)); - res = iproof->make_contra(res,foo); - } - } - else { - std::vector lits; - ast con = conc(proof); - if(expect_clause) - get_Z3_lits(con, lits); - else - lits.push_back(from_ast(con)); - - // pattern match some idioms - if(dk == PR_MODUS_PONENS && pr(prem(proof,0)) == PR_QUANT_INST){ - if(get_locality_rec(prem(proof,1)) == INT_MAX) { - res = iproof->make_axiom(lits); - return res; - } - } - if(dk == PR_MODUS_PONENS && expect_clause && op(con) == Or && op(conc(prem(proof,0))) == Or){ - Iproof::node clause = translate_main(prem(proof,0),true); - res = RewriteClause(clause,prem(proof,1)); - return res; - } - -#if 0 - if(dk == PR_MODUS_PONENS && expect_clause && op(con) == Or) - std::cout << "foo!\n"; -#endif - - // no idea why this shows up - if(dk == PR_MODUS_PONENS_OEQ){ - if(conc(prem(proof,0)) == con){ - res = translate_main(prem(proof,0),expect_clause); - return res; - } - if(expect_clause && op(con) == Or){ // skolemization does this - Iproof::node clause = translate_main(prem(proof,0),true); - res = RewriteClause(clause,prem(proof,1)); - return res; - } - } - -#if 0 - if(1 && dk == PR_TRANSITIVITY && pr(prem(proof,1)) == PR_COMMUTATIVITY){ - Iproof::node clause = translate_main(prem(proof,0),true); - res = make(commute,clause,conc(prem(proof,0))); // HACK -- we depend on Iproof::node being same as ast. - return res; - } - - if(1 && dk == PR_TRANSITIVITY && pr(prem(proof,0)) == PR_COMMUTATIVITY){ - Iproof::node clause = translate_main(prem(proof,1),true); - res = make(commute,clause,conc(prem(proof,1))); // HACK -- we depend on Iproof::node being same as ast. - return res; - } -#endif - - if(dk == PR_TRANSITIVITY && is_eq_propagate(prem(proof,1))){ - try { - res = CombineEqPropagate(proof); - return res; - } - catch(const CannotCombineEqPropagate &){ - } - } - - /* this is the symmetry rule for ~=, that is, takes x ~= y and yields y ~= x. - the proof idiom uses commutativity, monotonicity and mp, but we replace it here - with symmtrey and resolution, that is, we prove y = x |- x = y, then resolve - with the proof of ~(x=y) to get ~y=x. */ - if(dk == PR_MODUS_PONENS && pr(prem(proof,1)) == PR_MONOTONICITY && pr(prem(prem(proof,1),0)) == PR_COMMUTATIVITY && num_prems(prem(proof,1)) == 1){ - Iproof::node ante = translate_main(prem(proof,0),false); - ast eq0 = arg(conc(prem(prem(proof,1),0)),0); - ast eq1 = arg(conc(prem(prem(proof,1),0)),1); - Iproof::node eq1hy = iproof->make_hypothesis(eq1); - Iproof::node eq0pf = iproof->make_symmetry(eq0,eq1,eq1hy); - std::vector clause; // just a dummy - res = iproof->make_resolution(eq0,clause,ante,eq0pf); - return res; - } - - /* This idiom takes ~P and Q=P, yielding ~Q. It uses a "rewrite" - (Q=false) = ~Q. We eliminate the rewrite by using symmetry, - congruence and modus ponens. */ - - if(dk == PR_MODUS_PONENS && pr(prem(proof,1)) == PR_REWRITE && pr(prem(proof,0)) == PR_TRANSITIVITY && pr(prem(prem(proof,0),1)) == PR_IFF_FALSE){ - if(op(con) == Not && arg(con,0) == arg(conc(prem(proof,0)),0)){ - Iproof::node ante1 = translate_main(prem(prem(proof,0),0),false); - Iproof::node ante2 = translate_main(prem(prem(prem(proof,0),1),0),false); - ast ante1_con = conc(prem(prem(proof,0),0)); - ast eq0 = arg(ante1_con,0); - ast eq1 = arg(ante1_con,1); - ast symm_con = make(Iff,eq1,eq0); - Iproof::node ante1s = iproof->make_symmetry(symm_con,ante1_con,ante1); - ast cong_con = make(Iff,make(Not,eq1),make(Not,eq0)); - Iproof::node ante1sc = iproof->make_congruence(symm_con,cong_con,ante1s); - res = iproof->make_mp(cong_con,ante2,ante1sc); - return res; - } - } - - - // translate all the premises - std::vector args(nprems); - for(unsigned i = 0; i < nprems; i++) - args[i] = translate_main(prem(proof,i),false); - - for(unsigned i = 0; i < nprems; i++) - if(sym(args[i]) == commute - && !(dk == PR_TRANSITIVITY || dk == PR_MODUS_PONENS || dk == PR_SYMMETRY || (dk == PR_MONOTONICITY && op(arg(con,0)) == Not))) - throw_unsupported(proof); - - switch(dk){ - case PR_TRANSITIVITY: { - if(sym(args[0]) == commute || sym(args[1]) == commute) - res = make_commuted_transitivity(proof,args); - else { - // assume the premises are x = y, y = z - ast x = arg(conc(prem(proof,0)),0); - ast y = arg(conc(prem(proof,0)),1); - ast z = arg(conc(prem(proof,1)),1); - res = iproof->make_transitivity(x,y,z,args[0],args[1]); - } - break; - } - case PR_TRANSITIVITY_STAR: { - // assume the premises are x = y, y = z, z = u, u = v, .. - - ast x = arg(conc(prem(proof,0)),0); - ast y = arg(conc(prem(proof,0)),1); - ast z = arg(conc(prem(proof,1)),1); - res = iproof->make_transitivity(x,y,z,args[0],args[1]); - - for (unsigned i = 2; i < nprems; ++i) { - y = z; - z = arg(conc(prem(proof,i)),1); - res = iproof->make_transitivity(x,y,z,res,args[i]); - } - break; - } - case PR_QUANT_INTRO: - case PR_MONOTONICITY: - { - std::vector eqs; eqs.resize(args.size()); - for(unsigned i = 0; i < args.size(); i++) - eqs[i] = conc(prem(proof,i)); - if(op(arg(con,0)) == Not && sym(args[0]) == commute) - res = make_commuted_monotonicity(proof,args); - else - res = iproof->make_congruence(eqs,con,args); - break; - } - case PR_REFLEXIVITY: { - res = iproof->make_reflexivity(con); - break; - } - case PR_SYMMETRY: { - if(sym(args[0]) == commute) - res = make_commuted_symmetry(proof,args); - else - res = iproof->make_symmetry(con,conc(prem(proof,0)),args[0]); - break; - } - case PR_MODUS_PONENS: { - if(sym(args[1]) == commute) - res = make_commuted_modus_ponens(proof,args); - else - res = iproof->make_mp(conc(prem(proof,1)),args[0],args[1]); - break; - } - case PR_TH_LEMMA: { - switch(get_theory_lemma_theory(proof)){ - case ArithTheory: - switch(get_theory_lemma_kind(proof)){ - case FarkasKind: { - std::vector farkas_coeffs, prem_cons; - get_farkas_coeffs(proof,farkas_coeffs); - if(nprems == 0) {// axiom, not rule - int nargs = num_args(con); - if(farkas_coeffs.size() != (unsigned)nargs){ - pfgoto(proof); - throw_unsupported(proof); - } - for(int i = 0; i < nargs; i++){ - ast lit = mk_not(arg(con,i)); - prem_cons.push_back(lit); - args.push_back(iproof->make_hypothesis(lit)); - } - } - else { // rule version (proves false) - prem_cons.resize(nprems); - for(unsigned i = 0; i < nprems; i++) - prem_cons[i] = conc(prem(proof,i)); - } - res = iproof->make_farkas(con,args,prem_cons,farkas_coeffs); - break; - } - case Leq2EqKind: { - // conc should be (or x = y (not (leq x y)) (not(leq y z)) ) - ast xeqy = arg(conc(proof),0); - ast x = arg(xeqy,0); - ast y = arg(xeqy,1); - res = iproof->make_leq2eq(x,y,arg(arg(conc(proof),1),0),arg(arg(conc(proof),2),0)); - break; - } - case Eq2LeqKind: { - // conc should be (or (not (= x y)) (leq x y)) - ast xeqy = arg(arg(conc(proof),0),0); - ast xleqy = arg(conc(proof),1); - ast x = arg(xeqy,0); - ast y = arg(xeqy,1); - res = iproof->make_eq2leq(x,y,xleqy); - break; - } - case GCDTestKind: { - std::vector farkas_coeffs; - get_broken_gcd_test_coeffs(proof,farkas_coeffs); - if(farkas_coeffs.size() != nprems){ - pfgoto(proof); - throw_unsupported(proof); - } - std::vector my_prems; my_prems.resize(2); - std::vector my_prem_cons; my_prem_cons.resize(2); - std::vector my_farkas_coeffs; my_farkas_coeffs.resize(2); - my_prems[0] = GCDtoDivRule(proof, true, farkas_coeffs, args, my_prem_cons[0]); - my_prems[1] = GCDtoDivRule(proof, false, farkas_coeffs, args, my_prem_cons[1]); - ast con = mk_false(); - my_farkas_coeffs[0] = my_farkas_coeffs[1] = make_int("1"); - res = iproof->make_farkas(con,my_prems,my_prem_cons,my_farkas_coeffs); - break; - } - case AssignBoundsKind: { - if(args.size() > 0) - res = AssignBoundsRule2Farkas(proof, conc(proof), args); - else - res = AssignBounds2Farkas(proof,conc(proof)); - break; - } - case GomoryCutKind: { - if(args.size() > 0) - res = GomoryCutRule2Farkas(proof, conc(proof), args); - else - throw_unsupported(proof); - break; - } - case EqPropagateKind: { - std::vector prems(nprems); - for(unsigned i = 0; i < nprems; i++) - prems[i] = prem(proof,i); - res = EqPropagate(con,prems,args); - break; - } - case ArithMysteryKind: { - // Z3 hasn't told us what kind of lemma this is -- maybe we can guess - std::vector prems(nprems); - for(unsigned i = 0; i < nprems; i++) - prems[i] = prem(proof,i); - res = ArithMysteryRule(con,prems,args); - break; - } - default: - throw_unsupported(proof); - } - break; - case ArrayTheory: {// nothing fancy for this - ast store_array; - if(get_store_array(con,store_array)) - res = iproof->make_axiom(lits,ast_scope(store_array)); - else - res = iproof->make_axiom(lits); // for array extensionality axiom - break; - } - default: - throw_unsupported(proof); - } - break; - } - case PR_HYPOTHESIS: { - res = iproof->make_hypothesis(conc(proof)); - break; - } - case PR_QUANT_INST: { - res = iproof->make_axiom(lits); - break; - } - case PR_DEF_AXIOM: { // this should only happen for formulas resulting from quantifier instantiation - res = iproof->make_axiom(lits); - break; - } - case PR_IFF_TRUE: { // turns p into p <-> true, noop for us - res = args[0]; - break; - } - case PR_IFF_FALSE: { // turns ~p into p <-> false, noop for us - if(is_local(con)) - res = args[0]; - else - throw_unsupported(proof); - break; - } - case PR_COMMUTATIVITY: { - ast comm_equiv = make(op(con),arg(con,0),arg(con,0)); - ast pf = iproof->make_reflexivity(comm_equiv); - res = make(commute,pf,comm_equiv); - break; - } - case PR_NOT_OR_ELIM: - case PR_AND_ELIM: { - std::vector rule_ax, res_conc; - ast piv = conc(prem(proof,0)); - rule_ax.push_back(make(Not,piv)); - rule_ax.push_back(con); - ast pf = iproof->make_axiom(rule_ax); - res_conc.push_back(con); - res = iproof->make_resolution(piv,res_conc,pf,args[0]); - break; - } - default: - IF_VERBOSE(0, verbose_stream() << "Unsupported proof rule: " << expr_ref((expr*)proof.raw(), *proof.mgr()) << "\n";); - // pfgoto(proof); - // SASSERT(0 && "translate_main: unsupported proof rule"); - throw_unsupported(proof); - } - } - - return res; - } - - void clear_translation(){ - translation.first.clear(); - translation.second.clear(); - } - - // We actually compute the interpolant here and then produce a proof consisting of just a lemma - - iz3proof::node translate(ast proof, iz3proof &dst) override { - std::vector itps; - scan_skolems(proof); - for(int i = 0; i < frames -1; i++){ -#ifdef NEW_LOCALITY - rng = range_downward(i); - locality.clear(); -#endif - iproof = iz3proof_itp::create(this,range_downward(i),weak_mode()); - try { - Iproof::node ipf = translate_main(proof); - ast itp = iproof->interpolate(ipf); - itps.push_back(itp); - delete iproof; - clear_translation(); - } - catch (const iz3proof_itp::proof_error &) { - delete iproof; - clear_translation(); - throw iz3proof::proof_error(); - } - catch (const unsupported &exc) { - delete iproof; - clear_translation(); - throw exc; - } - } - // Very simple proof -- lemma of the empty clause with computed interpolation - iz3proof::node Ipf = dst.make_lemma(std::vector(),itps); // builds result in dst - return Ipf; - } - - iz3translation_full(iz3mgr &mgr, - iz3secondary *_secondary, - const std::vector > &cnsts, - const std::vector &parents, - const std::vector &theory) - : iz3translation(mgr, cnsts, parents, theory) - { - frames = cnsts.size(); - traced_lit = ast(); - type boolbooldom[2] = {bool_type(),bool_type()}; - commute = function("@commute",2,boolbooldom,bool_type()); - m().inc_ref(commute); - } - - ~iz3translation_full() override { - m().dec_ref(commute); - } -}; - - - - -#ifdef IZ3_TRANSLATE_FULL - -iz3translation *iz3translation::create(iz3mgr &mgr, - iz3secondary *secondary, - const std::vector > &cnsts, - const std::vector &parents, - const std::vector &theory){ - return new iz3translation_full(mgr,secondary,cnsts,parents,theory); -} - - -#if 1 - -// This is just to make sure certain methods are compiled, so we can call then from the debugger. - -void iz3translation_full_trace_lit(iz3translation_full *p, iz3mgr::ast lit, iz3mgr::ast proof){ - p->trace_lit(lit, proof); -} - -void iz3translation_full_show_step(iz3translation_full *p, iz3mgr::ast proof){ - p->show_step(proof); -} - -void iz3translation_full_show_marked(iz3translation_full *p, iz3mgr::ast proof){ - p->show_marked(proof); -} - -void iz3translation_full_show_lit(iz3translation_full *p, iz3mgr::ast lit){ - p->show_lit(lit); -} - -void iz3translation_full_show_z3_lit(iz3translation_full *p, iz3mgr::ast a){ - p->show_z3_lit(a); -} - -void iz3translation_full_pfgoto(iz3translation_full *p, iz3mgr::ast proof){ - p->pfgoto(proof); -} - - -void iz3translation_full_pfback(iz3translation_full *p ){ - p->pfback(); -} - -void iz3translation_full_pffwd(iz3translation_full *p ){ - p->pffwd(); -} - -void iz3translation_full_pfprem(iz3translation_full *p, int i){ - p->pfprem(i); -} - -void iz3translation_full_expand(iz3translation_full *p, int i){ - p->expand(i); -} - -void iz3translation_full_symbols_out_of_scope(iz3translation_full *p, int i, const iz3mgr::ast &t){ - p->symbols_out_of_scope(i,t); -} - -void iz3translation_full_conc_symbols_out_of_scope(iz3translation_full *p, int i, const iz3mgr::ast &t){ - p->conc_symbols_out_of_scope(i,t); -} - -struct stdio_fixer { - stdio_fixer(){ - std::cout.rdbuf()->pubsetbuf(nullptr,0); - } - -} my_stdio_fixer; - -#endif - -#endif - - diff --git a/src/interp/iz3translate.h b/src/interp/iz3translate.h deleted file mode 100755 index d80c3b3fe..000000000 --- a/src/interp/iz3translate.h +++ /dev/null @@ -1,63 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3translate.h - - Abstract: - - Interface for proof translations from Z3 proofs to interpolatable - proofs. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - - -#ifndef IZ3TRANSLATION_H -#define IZ3TRANSLATION_H - -#include "interp/iz3proof.h" -#include "interp/iz3secondary.h" - -// This is a interface class for translation from Z3 proof terms to -// an interpolatable proof - -class iz3translation : public iz3base { - public: - virtual iz3proof::node translate(ast, iz3proof &) = 0; - virtual ast quantify(ast e, const range &rng){return e;} - virtual ~iz3translation(){} - - /** This is thrown when the proof cannot be translated. */ - struct unsupported: public iz3_exception { - raw_ast* m_ast; - unsupported(ast const& a): iz3_exception("unsupported"), m_ast(a.raw()) { } - }; - - static iz3translation *create(iz3mgr &mgr, - iz3secondary *secondary, - const std::vector > &frames, - const std::vector &parents, - const std::vector &theory); - - protected: - iz3translation(iz3mgr &mgr, - const std::vector > &_cnsts, - const std::vector &_parents, - const std::vector &_theory) - : iz3base(mgr,_cnsts,_parents,_theory) {} -}; - -// To use a secondary prover, define IZ3_TRANSLATE_DIRECT instead of this -#define IZ3_TRANSLATE_FULL - -#endif - - - diff --git a/src/interp/iz3translate_direct.cpp b/src/interp/iz3translate_direct.cpp deleted file mode 100644 index 9efb1a383..000000000 --- a/src/interp/iz3translate_direct.cpp +++ /dev/null @@ -1,1717 +0,0 @@ -/*++ - Copyright (c) 2011 Microsoft Corporation - - Module Name: - - iz3translate_direct.cpp - - Abstract: - - Translate a Z3 proof into the interpolating proof calculus. - Translation is direct, without transformations on the target proof - representation. - - Author: - - Ken McMillan (kenmcmil) - - Revision History: - - --*/ - - -#ifdef _WINDOWS -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#pragma warning(disable:4101) -#pragma warning(disable:4390) -#endif - -#include "interp/iz3translate.h" -#include "interp/iz3proof.h" -#include "interp/iz3profiling.h" -#include "interp/iz3interp.h" - -#include -#include -#include -#include -#include -#include -#include - -//using std::vector; -using namespace stl_ext; - -/* This can introduce an address dependency if the range type of hash_map has - a destructor. Since the code in this file is not used and only here for - historical comparisons, we allow this non-determinism. -*/ -namespace stl_ext { - template - class hash { - public: - size_t operator()(const T *p) const { - return (size_t) p; - } - }; -} - -static int lemma_count = 0; -#if 0 -static int nll_lemma_count = 0; -#endif -#define SHOW_LEMMA_COUNT -1 - -// One half of a resolution. We need this to distinguish -// between resolving as a clause and as a unit clause. -// if pivot == conclusion(proof) it is unit. - -struct Z3_resolvent { - iz3base::ast proof; - bool is_unit; - iz3base::ast pivot; - Z3_resolvent(const iz3base::ast &_proof, bool _is_unit, const iz3base::ast &_pivot){ - proof = _proof; - is_unit = _is_unit; - pivot = _pivot; - } -}; - -namespace hash_space { - template <> - class hash { - public: - size_t operator()(const Z3_resolvent &p) const { - return (p.proof.hash() + p.pivot.hash()); - } - }; -} - - -bool operator==(const Z3_resolvent &x, const Z3_resolvent &y) { - return x.proof == y.proof && x.pivot == y.pivot; -} - - - -typedef std::vector ResolventAppSet; - -struct non_local_lits { - ResolventAppSet proofs; // the proof nodes being raised - non_local_lits(ResolventAppSet &_proofs){ - proofs.swap(_proofs); - } -}; - -namespace hash_space { - template <> - class hash { - public: - size_t operator()(const non_local_lits &p) const { - size_t h = 0; - for(ResolventAppSet::const_iterator it = p.proofs.begin(), en = p.proofs.end(); it != en; ++it) - h += (size_t)*it; - return h; - } - }; -} - - -bool operator==(const non_local_lits &x, const non_local_lits &y) { - ResolventAppSet::const_iterator itx = x.proofs.begin(); - ResolventAppSet::const_iterator ity = y.proofs.begin(); - while(true){ - if(ity == y.proofs.end()) return itx == x.proofs.end(); - if(itx == x.proofs.end()) return ity == y.proofs.end(); - if(*itx != *ity) return false; - ++itx; ++ity; - } -} - - -/* This translator goes directly from Z3 proofs to interpolatable - proofs without an intermediate representation as an iz3proof. */ - -class iz3translation_direct : public iz3translation { -public: - - typedef ast Zproof; // type of non-interpolating proofs - typedef iz3proof Iproof; // type of interpolating proofs - - /* Here we have lots of hash tables for memoizing various methods and - other such global data structures. - */ - - typedef hash_map AstToInt; - AstToInt locality; // memoizes locality of Z3 proof terms - - typedef std::pair EquivEntry; - typedef hash_map EquivTab; - EquivTab equivs; // maps non-local terms to equivalent local terms, with proof - - typedef hash_set AstHashSet; - AstHashSet equivs_visited; // proofs already checked for equivalences - - - typedef std::pair, hash_map > AstToIpf; - AstToIpf translation; // Zproof nodes to Iproof nodes - - AstHashSet antes_added; // Z3 proof terms whose antecedents have been added to the list - std::vector > antes; // list of antecedent/frame pairs - std::vector local_antes; // list of local antecedents - - Iproof *iproof; // the interpolating proof we are constructing - - int frames; // number of frames - - typedef std::set AstSet; - typedef hash_map AstToAstSet; - AstToAstSet hyp_map; // map proof terms to hypothesis set - - struct LocVar { // localization vars - ast var; // a fresh variable - ast term; // term it represents - int frame; // frame in which it's defined - LocVar(ast v, ast t, int f){var=v;term=t;frame=f;} - }; - - std::vector localization_vars; // localization vars in order of creation - typedef hash_map AstToAst; - AstToAst localization_map; // maps terms to their localization vars - - typedef hash_map AstToBool; - - - - iz3secondary *secondary; // the secondary prover - - // Unique table for sets of non-local resolutions - hash_map non_local_lits_unique; - - // Unique table for resolvents - hash_map Z3_resolvent_unique; - - // Translation memo for case of non-local resolutions - hash_map non_local_translation; - -public: - - -#define from_ast(x) (x) - - // determine locality of a proof term - // return frame of derivation if local, or -1 if not - // result INT_MAX means the proof term is a tautology - // memoized in hash_map "locality" - - int get_locality_rec(ast proof){ - std::pair foo(proof,INT_MAX); - std::pair bar = locality.insert(foo); - int &res = bar.first->second; - if(!bar.second) return res; - if(pr(proof) == PR_ASSERTED){ - ast ass = conc(proof); - res = frame_of_assertion(ass); - } - else { - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - int bar = get_locality_rec(arg); - if(res == INT_MAX || res == bar) res = bar; - else if(bar != INT_MAX) res = -1; - } - } - return res; - } - - - int get_locality(ast proof){ - // if(lia_z3_axioms_only) return -1; - int res = get_locality_rec(proof); - if(res != -1){ - ast con = conc(proof); - range rng = ast_scope(con); - - // hack: if a clause contains "true", it reduces to "true", - // which means we won't compute the range correctly. we handle - // this case by computing the ranges of the literals separately - - if(is_true(con)){ - std::vector lits; - get_Z3_lits(conc(proof),lits); - for(unsigned i = 0; i < lits.size(); i++) - rng = range_glb(rng,ast_scope(lits[i])); - } - - if(!range_is_empty(rng)){ - AstSet &hyps = get_hyps(proof); - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it){ - ast hyp = *it; - rng = range_glb(rng,ast_scope(hyp)); - } - } - - if(res == INT_MAX){ - if(range_is_empty(rng)) - res = -1; - else res = range_max(rng); - } - else { - if(!in_range(res,rng)) - res = -1; - } - } - return res; - } - - AstSet &get_hyps(ast proof){ - std::pair foo(proof,AstSet()); - std::pair bar = hyp_map.insert(foo); - AstSet &res = bar.first->second; - if(!bar.second) return res; - pfrule dk = pr(proof); - if(dk == PR_HYPOTHESIS){ - ast con = conc(proof); - res.insert(con); - } - else { - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - AstSet &arg_hyps = get_hyps(arg); - res.insert(arg_hyps.begin(),arg_hyps.end()); - } - if(dk == PR_LEMMA){ - ast con = conc(proof); - res.erase(mk_not(con)); - if(is_or(con)){ - int clause_size = num_args(con); - for(int i = 0; i < clause_size; i++){ - ast neglit = mk_not(arg(con,i)); - res.erase(neglit); - } - } - } - } -#if 0 - AstSet::iterator it = res.begin(), en = res.end(); - if(it != en){ - AstSet::iterator old = it; - ++it; - for(; it != en; ++it, ++old) - if(!(*old < *it)) - std::cout << "foo!"; - } -#endif - return res; - } - - - // Find all the judgements of the form p <-> q, where - // p is local and q is non-local, recording them in "equivs" - // the map equivs_visited is used to record the already visited proof terms - - void find_equivs(ast proof){ - if(equivs_visited.find(proof) != equivs_visited.end()) - return; - equivs_visited.insert(proof); - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++) // do all the sub_terms - find_equivs(prem(proof,i)); - ast con = conc(proof); // get the conclusion - if(is_iff(con)){ - ast iff = con; - for(int i = 0; i < 2; i++) - if(!is_local(arg(iff,i)) && is_local(arg(iff,1-i))){ - std::pair > foo(arg(iff,i),std::pair(arg(iff,1-i),proof)); - equivs.insert(foo); - } - } - } - - // get the lits of a Z3 clause as secondary prover terms - void get_Z3_lits(ast t, std::vector &lits){ - opr dk = op(t); - if(dk == False) - return; // false = empty clause - if(dk == Or){ - unsigned nargs = num_args(t); - lits.resize(nargs); - for(unsigned i = 0; i < nargs; i++) // do all the sub_terms - lits[i] = arg(t,i); - } - else { - lits.push_back(t); - } - } - - // resolve two clauses represented as vectors of lits. replace first clause - void resolve(ast pivot, std::vector &cls1, std::vector &cls2){ - ast neg_pivot = mk_not(pivot); - for(unsigned i = 0; i < cls1.size(); i++){ - if(cls1[i] == pivot){ - cls1[i] = cls1.back(); - cls1.pop_back(); - bool found_pivot2 = false; - for(unsigned j = 0; j < cls2.size(); j++){ - if(cls2[j] == neg_pivot) - found_pivot2 = true; - else - cls1.push_back(cls2[j]); - } - (void)found_pivot2; - assert(found_pivot2); - return; - } - } - assert(0 && "resolve failed"); - } - - // get lits resulting from unit resolution up to and including "position" - // TODO: this is quadratic -- fix it - void do_unit_resolution(ast proof, int position, std::vector &lits){ - ast orig_clause = conc(prem(proof,0)); - get_Z3_lits(orig_clause,lits); - for(int i = 1; i <= position; i++){ - std::vector unit(1); - unit[0] = conc(prem(proof,i)); - resolve(mk_not(unit[0]),lits,unit); - } - } - - - // clear the localization variables - void clear_localization(){ - localization_vars.clear(); - localization_map.clear(); - } - - // create a fresh variable for localization - ast fresh_localization_var(ast term, int frame){ - std::ostringstream s; - s << "%" << (localization_vars.size()); - ast var = make_var(s.str().c_str(),get_type(term)); - sym_range(sym(var)) = range_full(); // make this variable global - localization_vars.push_back(LocVar(var,term,frame)); - return var; - } - - - // "localize" a term to a given frame range by - // creating new symbols to represent non-local subterms - - ast localize_term(ast e, const range &rng){ - if(ranges_intersect(ast_scope(e),rng)) - return e; // this term occurs in range, so it's O.K. - AstToAst::iterator it = localization_map.find(e); - if(it != localization_map.end()) - return it->second; - - // if is is non-local, we must first localize the arguments to - // the range of its function symbol - - int nargs = num_args(e); - if(nargs > 0 /* && (!is_local(e) || flo <= hi || fhi >= lo) */){ - range frng = rng; - if(op(e) == Uninterpreted){ - symb f = sym(e); - range srng = sym_range(f); - if(ranges_intersect(srng,rng)) // localize to desired range if possible - frng = range_glb(srng,rng); - } - std::vector largs(nargs); - for(int i = 0; i < nargs; i++){ - largs[i] = localize_term(arg(e,i),frng); - frng = range_glb(frng,ast_scope(largs[i])); - } - e = clone(e,largs); - assert(is_local(e)); - } - - - if(ranges_intersect(ast_scope(e),rng)) - return e; // this term occurs in range, so it's O.K. - - // choose a frame for the constraint that is close to range - int frame = range_near(ast_scope(e),rng); - - ast new_var = fresh_localization_var(e,frame); - localization_map[e] = new_var; - ast cnst = make(Equal,new_var,e); - antes.push_back(std::pair(cnst,frame)); - return new_var; - } - - // some patterm matching functions - - // match logical or with nargs arguments - // assumes AIG form - bool match_or(ast e, ast *args, int nargs){ - if(op(e) != Or) return false; - int n = num_args(e); - if(n != nargs) return false; - for(int i = 0; i < nargs; i++) - args[i] = arg(e,i); - return true; - } - - // match operator f with exactly nargs arguments - bool match_op(ast e, opr f, ast *args, int nargs){ - if(op(e) != f) return false; - int n = num_args(e); - if(n != nargs) return false; - for(int i = 0; i < nargs; i++) - args[i] = arg(e,i); - return true; - } - - // see if the given formula can be interpreted as - // an axiom instance (e.g., an array axiom instance). - // if so, add it to "antes" in an appropriate frame. - // this may require "localization" - - void get_axiom_instance(ast e){ - - // "store" axiom - // (or (= w q) (= (select (store a1 w y) q) (select a1 q))) - // std::cout << "ax: "; show(e); - ast lits[2],eq_ops_l[2],eq_ops_r[2],sel_ops[2], sto_ops[3], sel_ops2[2] ; - if(match_or(e,lits,2)) - if(match_op(lits[0],Equal,eq_ops_l,2)) - if(match_op(lits[1],Equal,eq_ops_r,2)) - for(int i = 0; i < 2; i++){ // try the second equality both ways - if(match_op(eq_ops_r[0],Select,sel_ops,2)) - if(match_op(sel_ops[0],Store,sto_ops,3)) - if(match_op(eq_ops_r[1],Select,sel_ops2,2)) - for(int j = 0; j < 2; j++){ // try the first equality both ways - if(eq_ops_l[0] == sto_ops[1] - && eq_ops_l[1] == sel_ops[1] - && eq_ops_l[1] == sel_ops2[1] - && sto_ops[0] == sel_ops2[0]) - if(is_local(sel_ops[0])) // store term must be local - { - ast sto = sel_ops[0]; - ast addr = localize_term(eq_ops_l[1],ast_scope(sto)); - ast res = make(Or, - make(Equal,eq_ops_l[0],addr), - make(Equal, - make(Select,sto,addr), - make(Select,sel_ops2[0],addr))); - int frame = range_min(ast_scope(res)); - antes.push_back(std::pair(res,frame)); - return; - } - std::swap(eq_ops_l[0],eq_ops_l[1]); - } - std::swap(eq_ops_r[0],eq_ops_r[1]); - } - } - - // a quantifier instantation looks like (~ forall x. P) \/ P[z/x] - // we need to find a time frame for P, then localize P[z/x] in this frame - - void get_quantifier_instance(ast e){ - ast disjs[2]; - if(match_or(e,disjs,2)){ - if(is_local(disjs[0])){ - ast res = localize_term(disjs[1], ast_scope(disjs[0])); - int frame = range_min(ast_scope(res)); - antes.push_back(std::pair(res,frame)); - return; - } - } - } - - ast get_judgement(ast proof){ - ast con = from_ast(conc(proof)); - AstSet &hyps = get_hyps(proof); - std::vector hyps_vec; - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it) - hyps_vec.push_back(*it); - if(hyps_vec.size() == 0) return con; - con = make(Or,mk_not(make(And,hyps_vec)),con); - return con; - } - - // add the premises of a proof term to the "antes" list - - void add_antes(ast proof){ - if(antes_added.find(proof) != antes_added.end()) return; - antes_added.insert(proof); - int frame = get_locality(proof); - if(frame != -1) - if(1){ - ast e = get_judgement(proof); - if(frame >= frames) frame = frames-1; // can happen if there are no symbols - antes.push_back(std::pair(e,frame)); - return; - } - pfrule dk = pr(proof); - if(dk == PR_ASSERTED){ - ast ass = conc(proof); - frame = frame_of_assertion(ass); - if(frame >= frames) frame = frames-1; // can happen if a theory fact - antes.push_back(std::pair(ass,frame)); - return; - } - if(dk == PR_TH_LEMMA && num_prems(proof) == 0){ - get_axiom_instance(conc(proof)); - } - if(dk == PR_QUANT_INST && num_prems(proof) == 0){ - get_quantifier_instance(conc(proof)); - } - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - add_antes(arg); - } - } - - - // add quantifiers over the localization vars - // to an interpolant for frames lo-hi - - ast add_quants(ast e, int lo, int hi){ - for(int i = localization_vars.size() - 1; i >= 0; i--){ - LocVar &lv = localization_vars[i]; - opr quantifier = (lv.frame >= lo && lv.frame <= hi) ? Exists : Forall; - e = apply_quant(quantifier,lv.var,e); - } - return e; - } - - int get_lits_locality(std::vector &lits){ - range rng = range_full(); - for(std::vector::iterator it = lits.begin(), en = lits.end(); it != en; ++it){ - ast lit = *it; - rng = range_glb(rng,ast_scope(lit)); - } - if(range_is_empty(rng)) return -1; - int hi = range_max(rng); - if(hi >= frames) return frames - 1; - return hi; - } - - - struct invalid_lemma: public iz3_exception { - invalid_lemma(): iz3_exception("invalid_lemma") {} - }; - - - - - // prove a lemma (clause) using current antes list - // return proof of the lemma - // use the secondary prover - - int prove_lemma(std::vector &lits){ - - - // first try localization - if(antes.size() == 0){ - int local_frame = get_lits_locality(lits); - if(local_frame != -1) - return iproof->make_assumption(local_frame,lits); // no proof needed for purely local fact - } - - // group the assumptions by frame - std::vector preds(frames); - for(unsigned i = 0; i < preds.size(); i++) - preds[i] = mk_true(); - for(unsigned i = 0; i < antes.size(); i++){ - int frame = antes[i].second; - preds[frame] = mk_and(preds[frame],antes[i].first); // conjoin it to frame - } - - for(unsigned i = 0; i < lits.size(); i++){ - int frame; - if(!weak_mode()){ - frame = range_max(ast_scope(lits[i])); - if(frame >= frames) frame = frames-1; // could happen if contains no symbols - } - else { - frame = range_min(ast_scope(lits[i])); - if(frame < 0){ - frame = range_max(ast_scope(lits[i])); // could happen if contains no symbols - if(frame >= frames) frame = frames-1; - } - } - preds[frame] = mk_and(preds[frame],mk_not(lits[i])); - } - - - std::vector itps; // holds interpolants - - -#if 1 - ++lemma_count; - // std::cout << "lemma: " << lemma_count << std::endl; - if(lemma_count == SHOW_LEMMA_COUNT){ - for(unsigned i = 0; i < lits.size(); i++) - show_lit(lits[i]); - std::cerr << "lemma written to file lemma.smt:\n"; - iz3base foo(*this,preds,std::vector(),std::vector()); - foo.print("lemma.smt"); - throw invalid_lemma(); - } -#endif - -#if 0 - std::cout << "\nLemma:\n"; - for(unsigned i = 0; i < lits.size(); i++) - show_lit(lits[i]); -#endif - - // interpolate using secondary prover - profiling::timer_start("secondary prover"); - int sat = secondary->interpolate(preds,itps); - profiling::timer_stop("secondary prover"); - - std::cout << "lemma done" << std::endl; - - // if sat, lemma isn't valid, something is wrong - if(sat){ -#if 1 - std::cerr << "invalid lemma written to file invalid_lemma.smt:\n"; - iz3base foo(*this,preds,std::vector(),std::vector()); - foo.print("invalid_lemma.smt"); -#endif - throw iz3_incompleteness(); - } - assert(sat == 0); // if sat, lemma doesn't hold! - - // quantifiy the localization vars - for(unsigned i = 0; i < itps.size(); i++) - itps[i] = add_quants(itps[i],0,i); - - // Make a lemma, storing interpolants - Iproof::node res = iproof->make_lemma(lits,itps); - -#if 0 - std::cout << "Lemma interps\n"; - for(unsigned i = 0; i < itps.size(); i++) - show(itps[i]); -#endif - - // Reset state for the next lemma - antes.clear(); - antes_added.clear(); - clear_localization(); // use a fresh localization for each lemma - - return res; - } - - // sanity check: make sure that any non-local lit is really resolved - // with something in the non_local_lits set - - void check_non_local(ast lit, non_local_lits *nll){ - if(nll) - for(ResolventAppSet::iterator it = nll->proofs.begin(), en = nll->proofs.end(); it != en; ++it){ - ast con = (*it)->pivot; - if(con == mk_not(lit)) return; - } - assert(0 && "bug in non-local resolution handling"); - } - - - void get_local_conclusion_lits(ast proof, bool expect_clause, AstSet &lits){ - std::vector reslits; - if(expect_clause) - get_Z3_lits(conc(proof),reslits); - else reslits.push_back(conc(proof)); - for(unsigned i = 0; i < reslits.size(); i++) - if(is_local(reslits[i])) - lits.insert(reslits[i]); - AstSet &pfhyps = get_hyps(proof); - for(AstSet::iterator hit = pfhyps.begin(), hen = pfhyps.end(); hit != hen; ++hit) - if(is_local(*hit)) - lits.insert(mk_not(*hit)); - } - - - void collect_resolvent_lits(Z3_resolvent *res, const AstSet &hyps, std::vector &lits){ - if(!res->is_unit){ - std::vector reslits; - get_Z3_lits(conc(res->proof),reslits); - for(unsigned i = 0; i < reslits.size(); i++) - if(reslits[i] != res->pivot) - lits.push_back(reslits[i]); - } - AstSet &pfhyps = get_hyps(res->proof); - for(AstSet::iterator hit = pfhyps.begin(), hen = pfhyps.end(); hit != hen; ++hit) - if(hyps.find(*hit) == hyps.end()) - lits.push_back(mk_not(*hit)); - } - - void filter_resolvent_lits(non_local_lits *nll, std::vector &lits){ - std::vector orig_lits; orig_lits.swap(lits); - std::set pivs; - for(ResolventAppSet::iterator it = nll->proofs.begin(), en = nll->proofs.end(); it != en; ++it){ - Z3_resolvent *res = *it; - pivs.insert(res->pivot); - pivs.insert(mk_not(res->pivot)); - } - for(unsigned i = 0; i < orig_lits.size(); i++) - if(pivs.find(orig_lits[i]) == pivs.end()) - lits.push_back(orig_lits[i]); - } - - void collect_all_resolvent_lits(non_local_lits *nll, std::vector &lits){ - if(nll){ - std::vector orig_lits; orig_lits.swap(lits); - std::set pivs; - for(ResolventAppSet::iterator it = nll->proofs.begin(), en = nll->proofs.end(); it != en; ++it){ - Z3_resolvent *res = *it; - pivs.insert(res->pivot); - pivs.insert(mk_not(res->pivot)); - } - for(ResolventAppSet::iterator it = nll->proofs.begin(), en = nll->proofs.end(); it != en; ++it){ - Z3_resolvent *res = *it; - { - std::vector reslits; - if(!res->is_unit) get_Z3_lits(conc(res->proof),reslits); - else reslits.push_back(conc(res->proof)); - for(unsigned i = 0; i < reslits.size(); i++) -#if 0 - if(reslits[i] != res->pivot && pivs.find(reslits[i]) == pivs.end()) -#endif - if(is_local(reslits[i])) - lits.push_back(reslits[i]); - } - } - for(unsigned i = 0; i < orig_lits.size(); i++) - if(pivs.find(orig_lits[i]) == pivs.end()) - lits.push_back(orig_lits[i]); - } - } - - void collect_proof_clause(ast proof, bool expect_clause, std::vector &lits){ - if(expect_clause) - get_Z3_lits(conc(proof),lits); - else - lits.push_back(from_ast(conc(proof))); - AstSet &hyps = get_hyps(proof); - for(AstSet::iterator hit = hyps.begin(), hen = hyps.end(); hit != hen; ++hit) - lits.push_back(mk_not(*hit)); - } - - - // turn a bunch of literals into a lemma, replacing - // non-local lits with their local equivalents - // adds the accumulated antecedents (antes) as - // proof obligations of the lemma - - Iproof::node fix_lemma(std::vector &con_lits, AstSet &hyps, non_local_lits *nll){ - std::vector lits(con_lits); - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it) - lits.push_back(mk_not(*it)); - if(nll){ - for(ResolventAppSet::iterator it = nll->proofs.begin(), en = nll->proofs.end(); it != en; ++it){ - Z3_resolvent *res = *it; - collect_resolvent_lits(res,hyps,lits); - add_antes(res->proof); - } - filter_resolvent_lits(nll,lits); - } - for(unsigned int i = 0; i < lits.size(); i++){ - EquivTab::iterator it = equivs.find(lits[i]); - if(it != equivs.end()){ - lits[i] = it->second.first; // replace with local equivalent - add_antes(it->second.second); // collect the premises that prove this - } - else { - if(!is_local(lits[i])){ - check_non_local(lits[i],nll); - lits[i] = mk_false(); - } - } - } - // TODO: should check here that derivation is local? - Iproof::node res = prove_lemma(lits); - return res; - } - - int num_lits(ast ast){ - opr dk = op(ast); - if(dk == False) - return 0; - if(dk == Or){ - unsigned nargs = num_args(ast); - int n = 0; - for(unsigned i = 0; i < nargs; i++) // do all the sub_terms - n += num_lits(arg(ast,i)); - return n; - } - else - return 1; - } - - struct non_lit_local_ante: public iz3_exception { - non_lit_local_ante(): iz3_exception("non_lit_local_ante") {} - }; - - bool local_antes_simple; - - bool add_local_antes(ast proof, AstSet &hyps, bool expect_clause = false){ - if(antes_added.find(proof) != antes_added.end()) return true; - antes_added.insert(proof); - ast con = from_ast(conc(proof)); - pfrule dk = pr(proof); - if(is_local(con) || equivs.find(con) != equivs.end()){ - if(!expect_clause || num_lits(conc(proof)) == 1){ - AstSet &this_hyps = get_hyps(proof); - if(std::includes(hyps.begin(),hyps.end(),this_hyps.begin(),this_hyps.end())){ - // if(hyps.find(con) == hyps.end()) -#if 0 - if(/* lemma_count == SHOW_LEMMA_COUNT - 1 && */ !is_literal_or_lit_iff(conc(proof))){ - std::cout << "\nnon-lit local ante\n"; - show_step(proof); - show(conc(proof)); - throw non_lit_local_ante(); - } -#endif - local_antes.push_back(proof); - return true; - } - else - ; //std::cout << "bar!\n"; - } - } - if(dk == PR_ASSERTED - //|| dk == PR_HYPOTHESIS - //|| dk == PR_TH_LEMMA - || dk == PR_QUANT_INST - //|| dk == PR_UNIT_RESOLUTION - //|| dk == PR_LEMMA - ) - return false; - if(dk == PR_HYPOTHESIS && hyps.find(con) != hyps.end()) - ; //std::cout << "blif!\n"; - if(dk == PR_HYPOTHESIS - || dk == PR_LEMMA) - ; //std::cout << "foo!\n"; - if(dk == PR_TH_LEMMA && num_prems(proof) == 0){ - // Check if this is an axiom instance - get_axiom_instance(conc(proof)); - } - - // #define SIMPLE_PROOFS -#ifdef SIMPLE_PROOFS - if(!(dk == PR_TRANSITIVITY - || dk == PR_MONOTONICITY)) - local_antes_simple = false; -#endif - - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - try { - if(!add_local_antes(arg, hyps, dk == PR_UNIT_RESOLUTION && i == 0)) - return false; - } - catch (const non_lit_local_ante &) { - std::cout << "\n"; - show_step(proof); - show(conc(proof)); - throw non_lit_local_ante(); - } - } - return true; - } - - std::vector lit_trace; - hash_set marked_proofs; - - bool proof_has_lit(const ast &proof, const ast &lit){ - AstSet &hyps = get_hyps(proof); - if(hyps.find(mk_not(lit)) != hyps.end()) - return true; - std::vector lits; - ast con = conc(proof); - get_Z3_lits(con, lits); - for(unsigned i = 0; i < lits.size(); i++) - if(lits[i] == lit) - return true; - return false; - } - - - void trace_lit_rec(const ast &lit, const ast &proof, AstHashSet &memo){ - if(memo.find(proof) == memo.end()){ - memo.insert(proof); - AstSet &hyps = get_hyps(proof); - std::vector lits; - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it) - lits.push_back(mk_not(*it)); - ast con = conc(proof); - get_Z3_lits(con, lits); - for(unsigned i = 0; i < lits.size(); i++){ - if(lits[i] == lit){ - print_expr(std::cout,proof); - std::cout << "\n"; - marked_proofs.insert(proof); - pfrule dk = pr(proof); - if(dk == PR_UNIT_RESOLUTION || dk == PR_LEMMA){ - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - trace_lit_rec(lit,arg,memo); - } - } - else - lit_trace.push_back(proof); - } - } - } - } - - ast traced_lit; - - int trace_lit(const ast &lit, const ast &proof){ - marked_proofs.clear(); - lit_trace.clear(); - traced_lit = lit; - AstHashSet memo; - trace_lit_rec(lit,proof,memo); - return lit_trace.size(); - } - - bool is_literal_or_lit_iff(const ast &lit){ - if(my_is_literal(lit)) return true; - if(op(lit) == Iff){ - return my_is_literal(arg(lit,0)) && my_is_literal(arg(lit,1)); - } - return false; - } - - bool my_is_literal(const ast &lit){ - ast abslit = is_not(lit) ? arg(lit,0) : lit; - int f = op(abslit); - return !(f == And || f == Or || f == Iff); - } - - void print_lit(const ast &lit){ - ast abslit = is_not(lit) ? arg(lit,0) : lit; - if(!is_literal_or_lit_iff(lit)){ - if(is_not(lit)) std::cout << "~"; - std::cout << "["; - print_expr(std::cout,abslit); - std::cout << "]"; - } - else - print_expr(std::cout,lit); - } - - void show_lit(const ast &lit){ - print_lit(lit); - std::cout << "\n"; - } - - void print_z3_lit(const ast &a){ - print_lit(from_ast(a)); - } - - void show_z3_lit(const ast &a){ - print_z3_lit(a); - std::cout << "\n"; - } - - - void show_con(const ast &proof, bool brief){ - if(!traced_lit.null() && proof_has_lit(proof,traced_lit)) - std::cout << "(*) "; - ast con = conc(proof); - AstSet &hyps = get_hyps(proof); - int count = 0; - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it){ - if(brief && ++count > 5){ - std::cout << "... "; - break; - } - print_lit(*it); - std::cout << " "; - } - std::cout << "|- "; - std::vector lits; - get_Z3_lits(con,lits); - for(unsigned i = 0; i < lits.size(); i++){ - print_lit(lits[i]); - std::cout << " "; - } - std::cout << "\n"; - } - - void show_step(const ast &proof){ - std::cout << "\n"; - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - std::cout << "(" << i << ") "; - ast arg = prem(proof,i); - show_con(arg,true); - } - std::cout << "|------ "; - std::cout << string_of_symbol(sym(proof)) << "\n"; - show_con(proof,false); - } - - void show_marked( const ast &proof){ - std::cout << "\n"; - unsigned nprems = num_prems(proof); - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - if(!traced_lit.null() && proof_has_lit(arg,traced_lit)){ - std::cout << "(" << i << ") "; - show_con(arg,true); - } - } - } - - std::vector pfhist; - int pfhist_pos; - - void pfgoto(const ast &proof){ - if(pfhist.size() == 0) - pfhist_pos = 0; - else pfhist_pos++; - pfhist.resize(pfhist_pos); - pfhist.push_back(proof); - show_step(proof); - } - - void show_nll(non_local_lits *nll){ - if(!nll)return; - for(ResolventAppSet::iterator it = nll->proofs.begin(), en = nll->proofs.end(); it != en; ++it){ - Z3_resolvent *res = *it; - show_step(res->proof); - std::cout << "Pivot: "; - show(res->pivot); - std::cout << std::endl; - } - } - - void pfback(){ - if(pfhist_pos > 0){ - pfhist_pos--; - show_step(pfhist[pfhist_pos]); - } - } - - void pffwd(){ - if(pfhist_pos < ((int)pfhist.size()) - 1){ - pfhist_pos++; - show_step(pfhist[pfhist_pos]); - } - } - - void pfprem(int i){ - if(pfhist.size() > 0){ - ast proof = pfhist[pfhist_pos]; - unsigned nprems = num_prems(proof); - if(i >= 0 && i < (int)nprems) - pfgoto(prem(proof,i)); - } - } - - int extract_th_lemma_common(std::vector &lits, non_local_lits *nll, bool lemma_nll = true){ - std::vector la = local_antes; - local_antes.clear(); // clear antecedents for next lemma - antes_added.clear(); - // std::vector lits; - AstSet hyps; // no hyps - for(unsigned i = 0; i < la.size(); i++) - lits.push_back(mk_not(from_ast(conc(la[i])))); - // lits.push_back(from_ast(conc(proof))); - Iproof::node res =fix_lemma(lits,hyps, lemma_nll ? nll : nullptr); - for(unsigned i = 0; i < la.size(); i++){ - Iproof::node q = translate_main(la[i],nll,false); - ast pnode = from_ast(conc(la[i])); - assert(is_local(pnode) || equivs.find(pnode) != equivs.end()); - Iproof::node neg = res; - Iproof::node pos = q; - if(is_not(pnode)){ - pnode = mk_not(pnode); - std::swap(neg,pos); - } - try { - res = iproof->make_resolution(pnode,neg,pos); - } - catch (const iz3proof::proof_error &){ - std::cout << "\nresolution error in theory lemma\n"; - std::cout << "lits:\n"; - for(unsigned j = 0; j < lits.size(); j++) - show_lit(lits[j]); - std::cout << "\nstep:\n"; - show_step(la[i]); - throw invalid_lemma(); - } - } - return res; - } - - Iproof::node extract_simple_proof(const ast &proof, hash_set &leaves){ - if(leaves.find(proof) != leaves.end()) - return iproof->make_hypothesis(conc(proof)); - ast con = from_ast(conc(proof)); - pfrule dk = pr(proof); - unsigned nprems = num_prems(proof); - std::vector args(nprems); - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - args[i] = extract_simple_proof(arg,leaves); - } - - switch(dk){ - case PR_TRANSITIVITY: - return iproof->make_transitivity(con,args[0],args[1]); - case PR_MONOTONICITY: - return iproof->make_congruence(con,args); - case PR_REFLEXIVITY: - return iproof->make_reflexivity(con); - case PR_SYMMETRY: - return iproof->make_symmetry(con,args[0]); - } - assert(0 && "extract_simple_proof: unknown op"); - return 0; - } - - int extract_th_lemma_simple(const ast &proof, std::vector &lits){ - std::vector la = local_antes; - local_antes.clear(); // clear antecedents for next lemma - antes_added.clear(); - - hash_set leaves; - for(unsigned i = 0; i < la.size(); i++) - leaves.insert(la[i]); - - Iproof::node ipf = extract_simple_proof(proof,leaves); - ast con = from_ast(conc(proof)); - Iproof::node hyp = iproof->make_hypothesis(mk_not(con)); - ipf = iproof->make_eqcontra(ipf,hyp); - - // std::vector lits; - AstSet hyps; // no hyps - for(unsigned i = 0; i < la.size(); i++) - lits.push_back(mk_not(from_ast(conc(la[i])))); - // lits.push_back(from_ast(conc(proof))); - - Iproof::node res = iproof->make_contra(ipf,lits); - - for(unsigned i = 0; i < la.size(); i++){ - Iproof::node q = translate_main(la[i],nullptr,false); - ast pnode = from_ast(conc(la[i])); - assert(is_local(pnode) || equivs.find(pnode) != equivs.end()); - Iproof::node neg = res; - Iproof::node pos = q; - if(is_not(pnode)){ - pnode = mk_not(pnode); - std::swap(neg,pos); - } - try { - res = iproof->make_resolution(pnode,neg,pos); - } - catch (const iz3proof::proof_error &){ - std::cout << "\nresolution error in theory lemma\n"; - std::cout << "lits:\n"; - for(unsigned j = 0; j < lits.size(); j++) - show_lit(lits[j]); - std::cout << "\nstep:\n"; - show_step(la[i]); - throw invalid_lemma(); - } - } - return res; - } - - // #define NEW_EXTRACT_TH_LEMMA - - void get_local_hyps(const ast &proof, std::set &res){ - std::set hyps = get_hyps(proof); - for(std::set::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it){ - ast hyp = *it; - if(is_local(hyp)) - res.insert(hyp); - } - } - - int extract_th_lemma(ast proof, std::vector &lits, non_local_lits *nll){ - pfrule dk = pr(proof); - unsigned nprems = num_prems(proof); -#ifdef NEW_EXTRACT_TH_LEMMA - if(nprems == 0 && !nll) -#else - if(nprems == 0) -#endif - return 0; - if(nprems == 0 && dk == PR_TH_LEMMA) - // Check if this is an axiom instance - get_axiom_instance(conc(proof)); - - local_antes_simple = true; - for(unsigned i = 0; i < nprems; i++){ - ast arg = prem(proof,i); - if(!add_local_antes(arg,get_hyps(proof))){ - local_antes.clear(); // clear antecedents for next lemma - antes_added.clear(); - antes.clear(); - return 0; - } - } -#ifdef NEW_EXTRACT_TH_LEMMA - bool lemma_nll = nprems > 1; - if(nll && !lemma_nll){ - lemma_nll = false; - // std::cout << "lemma count = " << nll_lemma_count << "\n"; - for(ResolventAppSet::iterator it = nll->proofs.begin(), en = nll->proofs.end(); it != en; ++it){ - Z3_resolvent *res = *it; - ast arg = res->proof; - std::set loc_hyps; get_local_hyps(arg,loc_hyps); - if(!add_local_antes(arg,loc_hyps)){ - local_antes.clear(); // clear antecedents for next lemma - antes_added.clear(); - antes.clear(); - return 0; - } - } - collect_all_resolvent_lits(nll,lits); - } - int my_count = nll_lemma_count++; - int res; - try { - res = extract_th_lemma_common(lits,nll,lemma_nll); - } -#if 1 - catch (const invalid_lemma &) { - std::cout << "\n\nlemma: " << my_count; - std::cout << "\n\nproof node: \n"; - show_step(proof); - std::cout << "\n\nnon-local: \n"; - show_nll(nll); - pfgoto(nll->proofs[0]->proof); - show(conc(pfhist.back())); - pfprem(1); - show(conc(pfhist.back())); - pfprem(0); - show(conc(pfhist.back())); - pfprem(0); - show(conc(pfhist.back())); - pfprem(0); - show(conc(pfhist.back())); - std::cout << "\n\nliterals: \n"; - for(int i = 0; i < lits.size(); i++) - show_lit(lits[i]); - throw invalid_lemma(); - } -#endif - - return res; -#else -#ifdef SIMPLE_PROOFS - if(local_antes_simple && !nll) - return extract_th_lemma_simple(proof, lits); -#endif - return extract_th_lemma_common(lits,nll); -#endif - } - - int extract_th_lemma_ur(ast proof, int position, std::vector &lits, non_local_lits *nll){ - for(int i = 0; i <= position; i++){ - ast arg = prem(proof,i); - if(!add_local_antes(arg,get_hyps(proof),i==0)){ - local_antes.clear(); // clear antecedents for next lemma - antes_added.clear(); - antes.clear(); - return 0; - } - } - return extract_th_lemma_common(lits,nll); - } - - // see if any of the pushed resolvents are resolutions - // push the current proof into the latest such - int push_into_resolvent(ast proof, std::vector &lits, non_local_lits *nll, bool expect_clause){ - if(!nll) return 0; - if(num_args(proof) > 1) return 0; - ResolventAppSet resos = nll->proofs; - int pos = resos.size()-1; - for( ResolventAppSet::reverse_iterator it = resos.rbegin(), en = resos.rend(); it != en; ++it, --pos){ - Z3_resolvent *reso = *it; - ast ante = reso->proof; - ast pivot = reso->pivot; - bool is_unit = reso->is_unit; - pfrule dk = pr(ante); - bool pushable = dk == PR_UNIT_RESOLUTION || dk == PR_LEMMA; - if(!pushable && num_args(ante) > 1){ -#if 0 - if (!is_local(conc(ante))) - std::cout << "non-local "; - std::cout << "pushable!\n"; -#endif - pushable = true; - } - if(pushable){ - // remove the resolvent from list and add new clause as resolvent - resos.erase((++it).base()); - for(; pos < (int)resos.size(); pos++){ - Z3_resolvent *r = resos[pos]; - resos[pos] = find_resolvent(r->proof,r->is_unit,mk_not(pivot)); - } - resos.push_back(find_resolvent(proof,!expect_clause,mk_not(pivot))); - non_local_lits *new_nll = find_nll(resos); - try { - int res = translate_main(ante,new_nll,!is_unit); - return res; - } - catch (const invalid_lemma &) { - std::cout << "\n\npushing: \n"; - std::cout << "nproof node: \n"; - show_step(proof); - std::cout << "\n\nold non-local: \n"; - show_nll(nll); - std::cout << "\n\nnew non-local: \n"; - show_nll(new_nll); - throw invalid_lemma(); - } - } - } - return 0; // no pushed resolvents are resolution steps - } - - non_local_lits *find_nll(ResolventAppSet &proofs){ - if(proofs.empty()) - return (non_local_lits *)nullptr; - std::pair foo(non_local_lits(proofs),(non_local_lits *)nullptr); - std::pair::iterator,bool> bar = - non_local_lits_unique.insert(foo); - non_local_lits *&res = bar.first->second; - if(bar.second) - res = new non_local_lits(bar.first->first); - return res; - } - - Z3_resolvent *find_resolvent(ast proof, bool unit, ast pivot){ - std::pair foo(Z3_resolvent(proof,unit,pivot),(Z3_resolvent *)nullptr); - std::pair::iterator,bool> bar = - Z3_resolvent_unique.insert(foo); - Z3_resolvent *&res = bar.first->second; - if(bar.second) - res = new Z3_resolvent(bar.first->first); - return res; - } - - // translate a unit resolution at position pos of given app - int translate_ur(ast proof, int position, non_local_lits *nll){ - ast ante = prem(proof,position); - if(position <= 0) - return translate_main(ante, nll); - ast pnode = conc(ante); - ast pnode_abs = !is_not(pnode) ? pnode : mk_not(pnode); - if(is_local(pnode) || equivs.find(pnode) != equivs.end()){ - Iproof::node neg = translate_ur(proof,position-1,nll); - Iproof::node pos = translate_main(ante, nll, false); - if(is_not(pnode)){ - pnode = mk_not(pnode); - std::swap(neg,pos); - } - try { - return iproof->make_resolution(pnode,neg,pos); - } - catch (const iz3proof::proof_error &){ - std::cout << "resolution error in unit_resolution, position" << position << "\n"; - show_step(proof); - throw invalid_lemma(); - } - } - else { - // non-local pivot we have no local equivalent for - if(true){ - // try pushing the non-local resolution up - pfrule dk = pr(ante); - non_local_lits *old_nll = nll; - if(dk == PR_HYPOTHESIS) - ; //std::cout << "non-local hyp!\n"; // resolving with a hyp is a no-op - else { - ResolventAppSet new_proofs; - if(nll) new_proofs = nll->proofs; - Z3_resolvent *reso = find_resolvent(ante,true,pnode); - new_proofs.push_back(reso); - nll = find_nll(new_proofs); - } - try { - return translate_ur(proof,position-1,nll); - } - catch (const invalid_lemma &) { - if(old_nll != nll){ - std::cout << "\n\nadded_nll: \n"; - std::cout << "nproof node: \n"; - show_step(proof); - std::cout << "\n\new non-local step: \n"; - show_step(nll->proofs.back()->proof); - } - throw invalid_lemma(); - } - - } - else { - // just make a lemma - std::vector lits; - do_unit_resolution(proof,position,lits); - int res; - if(!(res = extract_th_lemma_ur(proof,position,lits,nll))){ - for(int i = 0; i <= position; i++){ - z3pf p = prem(proof,i); - add_antes(p); - } - res = fix_lemma(lits,get_hyps(proof),nll); - } - return res; - } - } - } - - non_local_lits *update_nll(ast proof, bool expect_clause, non_local_lits *nll){ - std::vector lits; - collect_proof_clause(proof,expect_clause,lits); - AstSet litset; - litset.insert(lits.begin(),lits.end()); - ResolventAppSet to_keep; - for(int i = nll->proofs.size()-1; i >= 0; --i){ - ast traced_lit = (nll->proofs[i])->pivot; - ast traced_lit_neg = mk_not(traced_lit); - if(litset.find(traced_lit) != litset.end() || litset.find(traced_lit_neg) != litset.end()){ - to_keep.push_back(nll->proofs[i]); - std::vector reslits; - AstSet dummy; - collect_resolvent_lits(nll->proofs[i],dummy,reslits); - litset.insert(reslits.begin(),reslits.end()); - } - } - if(to_keep.size() == nll->proofs.size()) return nll; - ResolventAppSet new_proofs; - for(int i = to_keep.size() - 1; i >= 0; --i) - new_proofs.push_back(to_keep[i]); - return find_nll(new_proofs); - } - - // translate a Z3 proof term into a secondary prover proof term - - Iproof::node translate_main(ast proof, non_local_lits *nll, bool expect_clause = true){ - non_local_lits *old_nll = nll; - if(nll) nll = update_nll(proof,expect_clause,nll); - AstToIpf &tr = nll ? non_local_translation[nll] : translation; - hash_map &trc = expect_clause ? tr.first : tr.second; - std::pair foo(proof,INT_MAX); - std::pair bar = trc.insert(foo); - int &res = bar.first->second; - if(!bar.second) return res; - - - try { - int frame = get_locality(proof); - if(frame != -1){ - ast e = from_ast(conc(proof)); - if(frame >= frames) frame = frames - 1; - std::vector foo; - if(expect_clause) - get_Z3_lits(conc(proof),foo); - else - foo.push_back(e); - AstSet &hyps = get_hyps(proof); - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it) - foo.push_back(mk_not(*it)); - res = iproof->make_assumption(frame,foo); - return res; - } - - pfrule dk = pr(proof); - unsigned nprems = num_prems(proof); - if(dk == PR_UNIT_RESOLUTION){ - res = translate_ur(proof, nprems - 1, nll); - } - else if(dk == PR_LEMMA){ - ast contra = prem(proof,0); // this is a proof of false from some hyps - res = translate_main(contra, nll); - if(!expect_clause){ - std::vector foo; // the negations of the hyps form a clause - foo.push_back(from_ast(conc(proof))); - AstSet &hyps = get_hyps(proof); - for(AstSet::iterator it = hyps.begin(), en = hyps.end(); it != en; ++it) - foo.push_back(mk_not(*it)); - res = iproof->make_contra(res,foo); - } - } - else { - std::vector lits; - ast con = conc(proof); - if(expect_clause) - get_Z3_lits(con, lits); - else - lits.push_back(from_ast(con)); -#ifdef NEW_EXTRACT_TH_LEMMA - if(!(res = push_into_resolvent(proof,lits,nll,expect_clause))){ - if(!(res = extract_th_lemma(proof,lits,nll))){ -#else - if(!(res = extract_th_lemma(proof,lits,nll))){ - if(!(res = push_into_resolvent(proof,lits,nll,expect_clause))){ -#endif - // std::cout << "extract theory lemma failed\n"; - add_antes(proof); - res = fix_lemma(lits,get_hyps(proof),nll); - } - } - } -#ifdef CHECK_PROOFS - - if(0){ - AstSet zpf_con_lits, ipf_con_lits; - get_local_conclusion_lits(proof, expect_clause, zpf_con_lits); - if(nll){ - for(unsigned i = 0; i < nll->proofs.size(); i++) - get_local_conclusion_lits(nll->proofs[i]->proof,!nll->proofs[i]->is_unit,zpf_con_lits); - } - std::vector ipf_con; - iproof->get_conclusion(res,ipf_con); - for(unsigned i = 0; i < ipf_con.size(); i++) - ipf_con_lits.insert(ipf_con[i]); - if(!(ipf_con_lits == zpf_con_lits)){ - std::cout << "proof error:\n"; - std::cout << "expected lits:\n"; - for(AstSet::iterator hit = zpf_con_lits.begin(), hen = zpf_con_lits.end(); hit != hen; ++hit) - show_lit(*hit); - std::cout << "got lits:\n"; - for(AstSet::iterator hit = ipf_con_lits.begin(), hen = ipf_con_lits.end(); hit != hen; ++hit) - show_lit(*hit); - std::cout << "\nproof step:"; - show_step(proof); - std::cout << "\n"; - throw invalid_lemma(); - } - } -#endif - - return res; - } - - catch (const invalid_lemma &) { - if(old_nll != nll){ - std::cout << "\n\nupdated nll: \n"; - std::cout << "nproof node: \n"; - show_step(proof); - std::cout << "\n\new non-local: \n"; - show_nll(nll); - } - throw invalid_lemma(); - } - - } - - // Proof translation is in two stages: - // 1) Translate ast proof term to Zproof - // 2) Translate Zproof to Iproof - - Iproof::node translate(ast proof, Iproof &dst) override { - iproof = &dst; - Iproof::node Ipf = translate_main(proof,nullptr); // builds result in dst - return Ipf; - } - - iz3translation_direct(iz3mgr &mgr, - iz3secondary *_secondary, - const std::vector > &cnsts, - const std::vector &parents, - const std::vector &theory) - : iz3translation(mgr, cnsts, parents, theory) - { - secondary = _secondary; - frames = cnsts.size(); - traced_lit = ast(); - } - - ~iz3translation_direct() override { - for(hash_map::iterator - it = non_local_lits_unique.begin(), - en = non_local_lits_unique.end(); - it != en; - ++it) - delete it->second; - - for(hash_map::iterator - it = Z3_resolvent_unique.begin(), - en = Z3_resolvent_unique.end(); - it != en; - ++it) - delete it->second; - } - }; - - - - -#ifdef IZ3_TRANSLATE_DIRECT - - iz3translation *iz3translation::create(iz3mgr &mgr, - iz3secondary *secondary, - const std::vector > &cnsts, - const std::vector &parents, - const std::vector &theory){ - return new iz3translation_direct(mgr,secondary,cnsts,parents,theory); - } - - -#if 1 - - void iz3translation_direct_trace_lit(iz3translation_direct *p, iz3mgr::ast lit, iz3mgr::ast proof){ - p->trace_lit(lit, proof); - } - - void iz3translation_direct_show_step(iz3translation_direct *p, iz3mgr::ast proof){ - p->show_step(proof); - } - - void iz3translation_direct_show_marked(iz3translation_direct *p, iz3mgr::ast proof){ - p->show_marked(proof); - } - - void iz3translation_direct_show_lit(iz3translation_direct *p, iz3mgr::ast lit){ - p->show_lit(lit); - } - - void iz3translation_direct_show_z3_lit(iz3translation_direct *p, iz3mgr::ast a){ - p->show_z3_lit(a); - } - - void iz3translation_direct_pfgoto(iz3translation_direct *p, iz3mgr::ast proof){ - p->pfgoto(proof); - } - - void iz3translation_direct_show_nll(iz3translation_direct *p, non_local_lits *nll){ - p->show_nll(nll); - } - - void iz3translation_direct_pfback(iz3translation_direct *p ){ - p->pfback(); - } - - void iz3translation_direct_pffwd(iz3translation_direct *p ){ - p->pffwd(); - } - - void iz3translation_direct_pfprem(iz3translation_direct *p, int i){ - p->pfprem(i); - } - - - struct stdio_fixer { - stdio_fixer(){ - std::cout.rdbuf()->pubsetbuf(0,0); - } - - } my_stdio_fixer; - -#endif - -#endif - - diff --git a/src/muz/base/dl_context.cpp b/src/muz/base/dl_context.cpp index 54c07da28..cc14de5ce 100644 --- a/src/muz/base/dl_context.cpp +++ b/src/muz/base/dl_context.cpp @@ -188,7 +188,7 @@ namespace datalog { if (m_trail.get_num_scopes() == 0) { throw default_exception("there are no backtracking points to pop to"); } - if (m_engine.get() && get_engine() != DUALITY_ENGINE) { + if (m_engine.get()) { throw default_exception("pop operation is only supported by duality engine"); } m_trail.pop_scope(1); @@ -601,11 +601,6 @@ namespace datalog { m_rule_properties.check_existential_tail(); m_rule_properties.check_for_negated_predicates(); break; - case DUALITY_ENGINE: - m_rule_properties.collect(r); - m_rule_properties.check_existential_tail(); - m_rule_properties.check_for_negated_predicates(); - break; case CLP_ENGINE: m_rule_properties.collect(r); m_rule_properties.check_existential_tail(); @@ -828,9 +823,6 @@ namespace datalog { else if (e == symbol("clp")) { m_engine_type = CLP_ENGINE; } - else if (e == symbol("duality")) { - m_engine_type = DUALITY_ENGINE; - } else if (e == symbol("ddnf")) { m_engine_type = DDNF_ENGINE; } @@ -875,11 +867,6 @@ namespace datalog { case DDNF_ENGINE: flush_add_rules(); break; - case DUALITY_ENGINE: - // this lets us use duality with SAS 2013 abstraction - if(quantify_arrays()) - flush_add_rules(); - break; default: UNREACHABLE(); } diff --git a/src/muz/base/dl_engine_base.h b/src/muz/base/dl_engine_base.h index 576ed7f6b..b9ac6e7b5 100644 --- a/src/muz/base/dl_engine_base.h +++ b/src/muz/base/dl_engine_base.h @@ -32,7 +32,6 @@ namespace datalog { QBMC_ENGINE, TAB_ENGINE, CLP_ENGINE, - DUALITY_ENGINE, DDNF_ENGINE, LAST_ENGINE }; diff --git a/src/muz/duality/CMakeLists.txt b/src/muz/duality/CMakeLists.txt deleted file mode 100644 index f005b88b1..000000000 --- a/src/muz/duality/CMakeLists.txt +++ /dev/null @@ -1,8 +0,0 @@ -z3_add_component(duality_intf - SOURCES - duality_dl_interface.cpp - COMPONENT_DEPENDENCIES - duality - muz - transforms -) diff --git a/src/muz/duality/duality_dl_interface.cpp b/src/muz/duality/duality_dl_interface.cpp deleted file mode 100644 index 60ed1755c..000000000 --- a/src/muz/duality/duality_dl_interface.cpp +++ /dev/null @@ -1,623 +0,0 @@ -/*++ - Copyright (c) 2013 Microsoft Corporation - - Module Name: - - duality_dl_interface.cpp - - Abstract: - - SMT2 interface for Duality - - Author: - - Krystof Hoder (t-khoder) 2011-9-22. - Modified by Ken McMIllan (kenmcmil) 2013-4-18. - - Revision History: - - --*/ - -#include "muz/base/dl_context.h" -#include "muz/transforms/dl_mk_coi_filter.h" -#include "muz/transforms/dl_mk_interp_tail_simplifier.h" -#include "muz/transforms/dl_mk_subsumption_checker.h" -#include "muz/transforms/dl_mk_rule_inliner.h" -#include "muz/base/dl_rule.h" -#include "muz/base/dl_rule_transformer.h" -#include "parsers/smt2/smt2parser.h" -#include "muz/duality/duality_dl_interface.h" -#include "muz/base/dl_rule_set.h" -#include "muz/transforms/dl_mk_slice.h" -#include "muz/transforms/dl_mk_unfold.h" -#include "muz/transforms/dl_mk_coalesce.h" -#include "ast/expr_abstract.h" -#include "model/model_smt2_pp.h" -#include "model/model_v2_pp.h" -#include "muz/base/fixedpoint_params.hpp" -#include "ast/used_vars.h" -#include "ast/func_decl_dependencies.h" -#include "muz/transforms/dl_transforms.h" - -// template class symbol_table; - -#ifdef WIN32 -#pragma warning(disable:4996) -#pragma warning(disable:4800) -#pragma warning(disable:4267) -#pragma warning(disable:4101) -#endif - -#include "duality/duality.h" -#include "duality/duality_profiling.h" - -// using namespace Duality; - -namespace Duality { - - enum DualityStatus {StatusModel, StatusRefutation, StatusUnknown, StatusNull}; - - class duality_data { - public: - context ctx; - RPFP::LogicSolver *ls; - RPFP *rpfp; - - DualityStatus status; - std::vector clauses; - std::vector > clause_labels; - hash_map map; // edges to clauses - Solver *old_rs; - Solver::Counterexample cex; - - duality_data(ast_manager &_m) : ctx(_m,config(params_ref())) { - ls = nullptr; - rpfp = nullptr; - status = StatusNull; - old_rs = nullptr; - } - ~duality_data(){ - if(old_rs) - dealloc(old_rs); - if(rpfp) - dealloc(rpfp); - if(ls) - dealloc(ls); - } - }; - - - dl_interface::dl_interface(datalog::context& dl_ctx) : - engine_base(dl_ctx.get_manager(), "duality"), - m_ctx(dl_ctx) - - { - _d = nullptr; - // dl_ctx.get_manager().toggle_proof_mode(PGM_FINE); - } - - - dl_interface::~dl_interface() { - if(_d) - dealloc(_d); - } - - - // - // Check if the new rules are weaker so that we can - // re-use existing context. - // -#if 0 - void dl_interface::check_reset() { - // TODO - datalog::rule_ref_vector const& new_rules = m_ctx.get_rules().get_rules(); - datalog::rule_ref_vector const& old_rules = m_old_rules.get_rules(); - bool is_subsumed = !old_rules.empty(); - for (unsigned i = 0; is_subsumed && i < new_rules.size(); ++i) { - is_subsumed = false; - for (unsigned j = 0; !is_subsumed && j < old_rules.size(); ++j) { - if (m_ctx.check_subsumes(*old_rules[j], *new_rules[i])) { - is_subsumed = true; - } - } - if (!is_subsumed) { - TRACE("pdr", new_rules[i]->display(m_ctx, tout << "Fresh rule ");); - m_context->reset(); - } - } - m_old_rules.reset(); - m_old_rules.add_rules(new_rules.size(), new_rules.c_ptr()); - } -#endif - - - lbool dl_interface::query(::expr * query) { - - // we restore the initial state in the datalog context - m_ctx.ensure_opened(); - - // if there is old data, get the cex and dispose (later) - duality_data *old_data = _d; - Solver *old_rs = nullptr; - if(old_data){ - old_rs = old_data->old_rs; - old_rs->GetCounterexample().swap(old_data->cex); - } - - scoped_proof generate_proofs_please(m_ctx.get_manager()); - - // make a new problem and solver - _d = alloc(duality_data,m_ctx.get_manager()); - _d->ctx.set("mbqi",m_ctx.get_params().duality_mbqi()); - _d->ls = alloc(RPFP::iZ3LogicSolver,_d->ctx); - _d->rpfp = alloc(RPFP,_d->ls); - - - - expr_ref_vector rules(m_ctx.get_manager()); - svector< ::symbol> names; - unsigned_vector bounds; - // m_ctx.get_rules_as_formulas(rules, names); - - - // If using SAS 2013 abstractiion, we need to perform some transforms - expr_ref query_ref(m_ctx.get_manager()); - if(m_ctx.quantify_arrays()){ - datalog::rule_manager& rm = m_ctx.get_rule_manager(); - rm.mk_query(query, m_ctx.get_rules()); - apply_default_transformation(m_ctx); - datalog::rule_set &rs = m_ctx.get_rules(); - if(m_ctx.get_rules().get_output_predicates().empty()) - query_ref = m_ctx.get_manager().mk_false(); - else { - func_decl_ref query_pred(m_ctx.get_manager()); - query_pred = m_ctx.get_rules().get_output_predicate(); - ptr_vector sorts; - unsigned nargs = query_pred.get()->get_arity(); - expr_ref_vector vars(m_ctx.get_manager()); - for(unsigned i = 0; i < nargs; i++){ - ::sort *s = query_pred.get()->get_domain(i); - vars.push_back(m_ctx.get_manager().mk_var(nargs-1-i,s)); - } - query_ref = m_ctx.get_manager().mk_app(query_pred.get(),nargs,vars.c_ptr()); - query = query_ref.get(); - } - unsigned nrules = rs.get_num_rules(); - for(unsigned i = 0; i < nrules; i++){ - expr_ref f(m_ctx.get_manager()); - rm.to_formula(*rs.get_rule(i), f); - rules.push_back(f); - } - } - else - m_ctx.get_raw_rule_formulas(rules, names, bounds); - - // get all the rules as clauses - std::vector &clauses = _d->clauses; - clauses.clear(); - for (unsigned i = 0; i < rules.size(); ++i) { - expr e(_d->ctx,rules[i].get()); - clauses.push_back(e); - } - - std::vector b_sorts; - std::vector b_names; - used_vars uv; - uv.process(query); - unsigned nuv = uv.get_max_found_var_idx_plus_1(); - for(int i = nuv-1; i >= 0; i--){ // var indices are backward - ::sort * s = uv.get(i); - if(!s) - s = _d->ctx.m().mk_bool_sort(); // missing var, whatever - b_sorts.push_back(sort(_d->ctx,s)); - b_names.push_back(symbol(_d->ctx,::symbol(i))); // names? - } - -#if 0 - // turn the query into a clause - expr q(_d->ctx,m_ctx.bind_variables(query,false)); - - std::vector b_sorts; - std::vector b_names; - if (q.is_quantifier() && !q.is_quantifier_forall()) { - int bound = q.get_quantifier_num_bound(); - for(int j = 0; j < bound; j++){ - b_sorts.push_back(q.get_quantifier_bound_sort(j)); - b_names.push_back(q.get_quantifier_bound_name(j)); - } - q = q.arg(0); - } -#else - expr q(_d->ctx,query); -#endif - - expr qc = implies(q,_d->ctx.bool_val(false)); - qc = _d->ctx.make_quant(Forall,b_sorts,b_names,qc); - clauses.push_back(qc); - bounds.push_back(UINT_MAX); - - // get the background axioms - unsigned num_asserts = m_ctx.get_num_assertions(); - for (unsigned i = 0; i < num_asserts; ++i) { - expr e(_d->ctx,m_ctx.get_assertion(i)); - _d->rpfp->AssertAxiom(e); - } - - // make sure each predicate is the head of at least one clause - func_decl_set heads; - for(unsigned i = 0; i < clauses.size(); i++){ - expr cl = clauses[i]; - - while(true){ - if(cl.is_app()){ - decl_kind k = cl.decl().get_decl_kind(); - if(k == Implies) - cl = cl.arg(1); - else { - heads.insert(cl.decl()); - break; - } - } - else if(cl.is_quantifier()) - cl = cl.body(); - else break; - } - } - ast_ref_vector const &pinned = m_ctx.get_pinned(); - for(unsigned i = 0; i < pinned.size(); i++){ - ::ast *fa = pinned[i]; - if(is_func_decl(fa)){ - ::func_decl *fd = to_func_decl(fa); - if (m_ctx.is_predicate(fd)) { - func_decl f(_d->ctx, fd); - if (!heads.contains(fd)) { - int arity = f.arity(); - std::vector args; - args.reserve(arity); - for (int j = 0; j < arity; j++) - args.push_back(_d->ctx.fresh_func_decl("X", f.domain(j))()); - expr c = implies(_d->ctx.bool_val(false), f(args)); - c = _d->ctx.make_quant(Forall, args, c); - clauses.push_back(c); - bounds.push_back(UINT_MAX); - } - } - } - } - unsigned rb = m_ctx.get_params().duality_recursion_bound(); - std::vector std_bounds; - for(unsigned i = 0; i < bounds.size(); i++){ - unsigned b = bounds[i]; - if (b == UINT_MAX) b = rb; - std_bounds.push_back(b); - } - - // creates 1-1 map between clauses and rpfp edges - _d->rpfp->FromClauses(clauses,&std_bounds); - - // populate the edge-to-clause map - for(unsigned i = 0; i < _d->rpfp->edges.size(); ++i) - _d->map[_d->rpfp->edges[i]] = i; - - // create a solver object - - Solver *rs = Solver::Create("duality", _d->rpfp); - - if(old_rs) - rs->LearnFrom(old_rs); // new solver gets hints from old solver - - // set its options - IF_VERBOSE(1, rs->SetOption("report","1");); - rs->SetOption("full_expand",m_ctx.get_params().duality_full_expand() ? "1" : "0"); - rs->SetOption("no_conj",m_ctx.get_params().duality_no_conj() ? "1" : "0"); - rs->SetOption("feasible_edges",m_ctx.get_params().duality_feasible_edges() ? "1" : "0"); - rs->SetOption("use_underapprox",m_ctx.get_params().duality_use_underapprox() ? "1" : "0"); - rs->SetOption("stratified_inlining",m_ctx.get_params().duality_stratified_inlining() ? "1" : "0"); - rs->SetOption("batch_expand",m_ctx.get_params().duality_batch_expand() ? "1" : "0"); - rs->SetOption("conjecture_file",m_ctx.get_params().duality_conjecture_file()); - rs->SetOption("enable_restarts",m_ctx.get_params().duality_enable_restarts() ? "1" : "0"); -#if 0 - if(rb != UINT_MAX){ - std::ostringstream os; os << rb; - rs->SetOption("recursion_bound", os.str()); - } -#endif - - // Solve! - bool ans; - try { - ans = rs->Solve(); - } - catch (Duality::solver::cancel_exception &exn){ - throw default_exception(Z3_CANCELED_MSG); - } - catch (Duality::Solver::Incompleteness &exn){ - throw default_exception("incompleteness"); - } - - // profile! - - if(m_ctx.get_params().duality_profile()) - print_profile(std::cout); - - // save the result and counterexample if there is one - _d->status = ans ? StatusModel : StatusRefutation; - _d->cex.swap(rs->GetCounterexample()); // take ownership of cex - _d->old_rs = rs; // save this for later hints - - if(old_data){ - dealloc(old_data); // this deallocates the old solver if there is one - } - - // dealloc(rs); this is now owned by data - - // true means the RPFP problem is SAT, so the query is UNSAT - // but we return undef if the UNSAT result is bounded - if(ans){ - if(rs->IsResultRecursionBounded()){ -#if 0 - m_ctx.set_status(datalog::BOUNDED); - return l_undef; -#else - return l_false; -#endif - } - return l_false; - } - return l_true; - } - - expr_ref dl_interface::get_cover_delta(int level, ::func_decl* pred_orig) { - SASSERT(false); - return expr_ref(m_ctx.get_manager()); - } - - void dl_interface::add_cover(int level, ::func_decl* pred, ::expr* property) { - SASSERT(false); - } - - unsigned dl_interface::get_num_levels(::func_decl* pred) { - SASSERT(false); - return 0; - } - - void dl_interface::collect_statistics(::statistics& st) const { - } - - void dl_interface::reset_statistics() { - } - - static hash_set *local_func_decls; - - static void print_proof(dl_interface *d, std::ostream& out, RPFP *tree, RPFP::Node *root) { - context &ctx = d->dd()->ctx; - RPFP::Node &node = *root; - RPFP::Edge &edge = *node.Outgoing; - - // first, prove the children (that are actually used) - - for(unsigned i = 0; i < edge.Children.size(); i++){ - if(!tree->Empty(edge.Children[i])){ - print_proof(d,out,tree,edge.Children[i]); - } - } - - // print the label and the proved fact - - out << "(step s!" << node.number; - out << " (" << node.Name.name(); - for(unsigned i = 0; i < edge.F.IndParams.size(); i++) - out << " " << tree->Eval(&edge,edge.F.IndParams[i]); - out << ")\n"; - - // print the rule number - - out << " rule!" << node.Outgoing->map->number; - - // print the substitution - - out << " (subst\n"; - RPFP::Edge *orig_edge = edge.map; - int orig_clause = d->dd()->map[orig_edge]; - expr &t = d->dd()->clauses[orig_clause]; - if (t.is_quantifier() && t.is_quantifier_forall()) { - int bound = t.get_quantifier_num_bound(); - std::vector sorts; - std::vector names; - hash_map subst; - for(int j = 0; j < bound; j++){ - sort the_sort = t.get_quantifier_bound_sort(j); - symbol name = t.get_quantifier_bound_name(j); - expr skolem = ctx.constant(symbol(ctx,name),sort(ctx,the_sort)); - out << " (= " << skolem << " " << tree->Eval(&edge,skolem) << ")\n"; - expr local_skolem = tree->Localize(&edge,skolem); - (*local_func_decls).insert(local_skolem.decl()); - } - } - out << " )\n"; - - out << " (labels"; - std::vector labels; - tree->GetLabels(&edge,labels); - for(unsigned j = 0; j < labels.size(); j++){ - out << " " << labels[j]; - } - - out << " )\n"; - - // reference the proofs of all the children, in syntactic order - // "true" means the child is not needed - - out << " (ref "; - for(unsigned i = 0; i < edge.Children.size(); i++){ - if(!tree->Empty(edge.Children[i])) - out << " s!" << edge.Children[i]->number; - else - out << " true"; - } - out << " )"; - out << ")\n"; - } - - - void dl_interface::display_certificate(std::ostream& out) const { - ((dl_interface *)this)->display_certificate_non_const(out); - } - - void dl_interface::display_certificate_non_const(std::ostream& out) { - if(_d->status == StatusModel){ - ast_manager &m = m_ctx.get_manager(); - model_ref md = get_model(); - out << "(fixedpoint \n"; - model_smt2_pp(out, m, *md.get(), 0); - out << ")\n"; - } - else if(_d->status == StatusRefutation){ - out << "(derivation\n"; - // negation of the query is the last clause -- prove it - hash_set locals; - local_func_decls = &locals; - print_proof(this,out,_d->cex.get_tree(),_d->cex.get_root()); - out << ")\n"; - out << "(model \n\""; - ::model mod(m_ctx.get_manager()); - model orig_model = _d->cex.get_tree()->dualModel; - for(unsigned i = 0; i < orig_model.num_consts(); i++){ - func_decl cnst = orig_model.get_const_decl(i); - if (locals.find(cnst) == locals.end()) { - expr thing = orig_model.get_const_interp(cnst); - mod.register_decl(to_func_decl(cnst.raw()), to_expr(thing.raw())); - } - } - for(unsigned i = 0; i < orig_model.num_funcs(); i++){ - func_decl cnst = orig_model.get_func_decl(i); - if (locals.find(cnst) == locals.end()) { - func_interp thing = orig_model.get_func_interp(cnst); - ::func_interp *thing_raw = thing; - mod.register_decl(to_func_decl(cnst.raw()), thing_raw->copy()); - } - } - model_v2_pp(out,mod); - out << "\")\n"; - } - } - - expr_ref dl_interface::get_answer() { - SASSERT(false); - return expr_ref(m_ctx.get_manager()); - } - - void dl_interface::cancel() { -#if 0 - if(_d && _d->ls) - _d->ls->cancel(); -#else - // HACK: duality can't cancel at all times, we just exit here - std::cout << "(error \"duality canceled\")\nunknown\n"; - abort(); -#endif - } - - void dl_interface::cleanup() { - } - - void dl_interface::updt_params() { - } - - model_ref dl_interface::get_model() { - ast_manager &m = m_ctx.get_manager(); - model_ref md(alloc(::model, m)); - std::vector &nodes = _d->rpfp->nodes; - expr_ref_vector conjs(m); - for (unsigned i = 0; i < nodes.size(); ++i) { - RPFP::Node *node = nodes[i]; - func_decl &pred = node->Name; - expr_ref prop(m); - prop = to_expr(node->Annotation.Formula); - std::vector ¶ms = node->Annotation.IndParams; - expr_ref q(m); - expr_ref_vector sig_vars(m); - for (unsigned j = 0; j < params.size(); ++j) - sig_vars.push_back(params[params.size()-j-1]); // TODO: why backwards? - expr_abstract(m, 0, sig_vars.size(), sig_vars.c_ptr(), prop, q); - if (params.empty()) { - md->register_decl(pred, q); - } - else { - ::func_interp* fi = alloc(::func_interp, m, params.size()); - fi->set_else(q); - md->register_decl(pred, fi); - } - } - return md; - } - - static proof_ref extract_proof(dl_interface *d, RPFP *tree, RPFP::Node *root) { - context &ctx = d->dd()->ctx; - ast_manager &mgr = ctx.m(); - RPFP::Node &node = *root; - RPFP::Edge &edge = *node.Outgoing; - RPFP::Edge *orig_edge = edge.map; - - // first, prove the children (that are actually used) - - proof_ref_vector prems(mgr); - ::vector substs; - int orig_clause = d->dd()->map[orig_edge]; - expr &t = d->dd()->clauses[orig_clause]; - prems.push_back(mgr.mk_asserted(ctx.uncook(t))); - - substs.push_back(expr_ref_vector(mgr)); - if (t.is_quantifier() && t.is_quantifier_forall()) { - int bound = t.get_quantifier_num_bound(); - std::vector sorts; - std::vector names; - hash_map subst; - for(int j = 0; j < bound; j++){ - sort the_sort = t.get_quantifier_bound_sort(j); - symbol name = t.get_quantifier_bound_name(j); - expr skolem = ctx.constant(symbol(ctx,name),sort(ctx,the_sort)); - expr val = tree->Eval(&edge,skolem); - expr_ref thing(ctx.uncook(val),mgr); - substs[0].push_back(thing); - expr local_skolem = tree->Localize(&edge,skolem); - (*local_func_decls).insert(local_skolem.decl()); - } - } - - svector > pos; - for(unsigned i = 0; i < edge.Children.size(); i++){ - if(!tree->Empty(edge.Children[i])){ - pos.push_back(std::pair(i+1,0)); - proof_ref prem = extract_proof(d,tree,edge.Children[i]); - prems.push_back(prem); - substs.push_back(expr_ref_vector(mgr)); - } - } - - func_decl f = node.Name; - std::vector args; - for(unsigned i = 0; i < edge.F.IndParams.size(); i++) - args.push_back(tree->Eval(&edge,edge.F.IndParams[i])); - expr conc = f(args); - - - ::vector< ::proof *> pprems; - for(unsigned i = 0; i < prems.size(); i++) - pprems.push_back(prems[i].get()); - - proof_ref res(mgr.mk_hyper_resolve(pprems.size(),&pprems[0], ctx.uncook(conc), pos, substs),mgr); - return res; - - } - - proof_ref dl_interface::get_proof() { - if(_d->status == StatusRefutation){ - hash_set locals; - local_func_decls = &locals; - return extract_proof(this,_d->cex.get_tree(),_d->cex.get_root()); - } - else - return proof_ref(m_ctx.get_manager()); - } -} diff --git a/src/muz/duality/duality_dl_interface.h b/src/muz/duality/duality_dl_interface.h deleted file mode 100644 index 8178618ae..000000000 --- a/src/muz/duality/duality_dl_interface.h +++ /dev/null @@ -1,80 +0,0 @@ -/*++ - Copyright (c) 2013 Microsoft Corporation - - Module Name: - - duality_dl_interface.h - - Abstract: - - SMT2 interface for Duality - - Author: - - Krystof Hoder (t-khoder) 2011-9-22. - Modified by Ken McMIllan (kenmcmil) 2013-4-18. - - Revision History: - - --*/ - -#ifndef DUALITY_DL_INTERFACE_H_ -#define DUALITY_DL_INTERFACE_H_ - -#include "util/lbool.h" -#include "muz/base/dl_rule.h" -#include "muz/base/dl_rule_set.h" -#include "muz/base/dl_engine_base.h" -#include "util/statistics.h" - -namespace datalog { - class context; -} - -namespace Duality { - - class duality_data; - - class dl_interface : public datalog::engine_base { - duality_data *_d; - datalog::context &m_ctx; - - public: - dl_interface(datalog::context& ctx); - ~dl_interface() override; - - lbool query(expr* query) override; - - void cancel() override; - - void cleanup() override; - - void display_certificate(std::ostream& out) const override; - - void collect_statistics(statistics& st) const override; - - void reset_statistics() override; - - expr_ref get_answer() override; - - unsigned get_num_levels(func_decl* pred) override; - - expr_ref get_cover_delta(int level, func_decl* pred) override; - - void add_cover(int level, func_decl* pred, expr* property) override; - - void updt_params() override; - - model_ref get_model() override; - - proof_ref get_proof() override; - - duality_data *dd(){return _d;} - - private: - void display_certificate_non_const(std::ostream& out); - }; -} - - -#endif diff --git a/src/muz/fp/CMakeLists.txt b/src/muz/fp/CMakeLists.txt index 0c5f5e915..41262813a 100644 --- a/src/muz/fp/CMakeLists.txt +++ b/src/muz/fp/CMakeLists.txt @@ -8,7 +8,6 @@ z3_add_component(fp bmc clp ddnf - duality_intf muz pdr rel diff --git a/src/muz/fp/dl_register_engine.cpp b/src/muz/fp/dl_register_engine.cpp index 267bfc390..a2270d774 100644 --- a/src/muz/fp/dl_register_engine.cpp +++ b/src/muz/fp/dl_register_engine.cpp @@ -23,7 +23,6 @@ Revision History: #include "muz/rel/rel_context.h" #include "muz/pdr/pdr_dl_interface.h" #include "muz/ddnf/ddnf.h" -#include "muz/duality/duality_dl_interface.h" #include "muz/spacer/spacer_dl_interface.h" namespace datalog { @@ -45,8 +44,6 @@ namespace datalog { return alloc(tab, *m_ctx); case CLP_ENGINE: return alloc(clp, *m_ctx); - case DUALITY_ENGINE: - return alloc(Duality::dl_interface, *m_ctx); case DDNF_ENGINE: return alloc(ddnf, *m_ctx); case LAST_ENGINE: diff --git a/src/smt/smt_internalizer.cpp b/src/smt/smt_internalizer.cpp index c6672c2b8..dc7c32cc1 100644 --- a/src/smt/smt_internalizer.cpp +++ b/src/smt/smt_internalizer.cpp @@ -611,7 +611,6 @@ namespace smt { case OP_XOR: UNREACHABLE(); case OP_OEQ: - case OP_INTERP: UNREACHABLE(); default: break;