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https://github.com/Z3Prover/z3
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fix regression for simplifying tails with quantifiers, add some more handling for quantified tails
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
692593baaa
commit
2d1a6bf270
10 changed files with 888 additions and 627 deletions
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@ -2637,12 +2637,13 @@ proof * ast_manager::mk_unit_resolution(unsigned num_proofs, proof * const * pro
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ptr_buffer<expr> args;
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args.append(num_proofs, (expr**) proofs);
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expr * fact;
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expr const * f1 = get_fact(proofs[0]);
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expr const * f2 = get_fact(proofs[1]);
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expr * f1 = get_fact(proofs[0]);
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expr * f2 = get_fact(proofs[1]);
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if (num_proofs == 2 && is_complement(f1, f2)) {
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fact = mk_false();
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}
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else {
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CTRACE("mk_unit_resolution_bug", !is_or(f1), tout << mk_pp(f1, *this) << " " << mk_pp(f2, *this) << "\n";);
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SASSERT(is_or(f1));
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ptr_buffer<expr> new_lits;
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app const * cls = to_app(f1);
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@ -463,7 +463,7 @@ namespace datalog {
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if (r->has_quantifiers()) {
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res = r;
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return false;
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return true;
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}
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start:
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@ -191,6 +191,11 @@ namespace datalog {
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scoped_coarse_proof(ast_manager& m): scoped_proof_mode(m, PGM_COARSE) {}
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};
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class scoped_fine_proof : public scoped_proof_mode {
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public:
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scoped_fine_proof(ast_manager& m): scoped_proof_mode(m, PGM_FINE) {}
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};
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class scoped_no_proof : public scoped_proof_mode {
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public:
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scoped_no_proof(ast_manager& m): scoped_proof_mode(m, PGM_DISABLED) {}
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102
src/muz_qe/expr_safe_replace.cpp
Normal file
102
src/muz_qe/expr_safe_replace.cpp
Normal file
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@ -0,0 +1,102 @@
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/*++
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Copyright (c) 2012 Microsoft Corporation
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Module Name:
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expr_safe_replace.cpp
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Abstract:
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Version of expr_replace/expr_substitution that is safe for quantifiers.
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Author:
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Nikolaj Bjorner (nbjorner) 2012-11-30
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Revision History:
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--*/
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#include "expr_safe_replace.h"
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#include "rewriter.h"
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void expr_safe_replace::insert(expr* src, expr* dst) {
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m_src.push_back(src);
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m_dst.push_back(dst);
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m_subst.insert(src, dst);
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}
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void expr_safe_replace::operator()(expr* e, expr_ref& res) {
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obj_map<expr,expr*> cache;
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ptr_vector<expr> todo, args;
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expr_ref_vector refs(m);
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todo.push_back(e);
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expr* a, *b, *d;
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todo.push_back(e);
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while (!todo.empty()) {
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a = todo.back();
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if (cache.contains(a)) {
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todo.pop_back();
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}
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else if (m_subst.find(a, b)) {
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cache.insert(a, b);
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todo.pop_back();
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}
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else if (is_var(a)) {
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cache.insert(a, a);
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todo.pop_back();
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}
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else if (is_app(a)) {
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app* c = to_app(a);
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unsigned n = c->get_num_args();
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args.reset();
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for (unsigned i = 0; i < n; ++i) {
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if (cache.find(c->get_arg(i), d)) {
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args.push_back(d);
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}
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else {
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todo.push_back(c->get_arg(i));
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}
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}
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if (args.size() == n) {
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b = m.mk_app(c->get_decl(), args.size(), args.c_ptr());
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refs.push_back(b);
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cache.insert(a, b);
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todo.pop_back();
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}
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}
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else {
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SASSERT(is_quantifier(a));
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quantifier* q = to_quantifier(a);
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expr_safe_replace replace(m);
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var_shifter shift(m);
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expr_ref new_body(m), src(m), dst(m), tmp(m);
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expr_ref_vector pats(m), nopats(m);
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unsigned num_decls = q->get_num_decls();
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for (unsigned i = 0; i < m_src.size(); ++i) {
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shift(m_src[i].get(), num_decls, src);
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shift(m_dst[i].get(), num_decls, dst);
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replace.insert(src, dst);
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}
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unsigned np = q->get_num_patterns();
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for (unsigned i = 0; i < np; ++i) {
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replace(q->get_pattern(i), tmp);
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pats.push_back(tmp);
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}
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np = q->get_num_no_patterns();
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for (unsigned i = 0; i < np; ++i) {
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replace(q->get_no_pattern(i), tmp);
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nopats.push_back(tmp);
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}
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replace(q->get_expr(), new_body);
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b = m.update_quantifier(q, pats.size(), pats.c_ptr(), nopats.size(), nopats.c_ptr(), new_body);
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refs.push_back(b);
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cache.insert(a, b);
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todo.pop_back();
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}
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}
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res = cache.find(e);
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}
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43
src/muz_qe/expr_safe_replace.h
Normal file
43
src/muz_qe/expr_safe_replace.h
Normal file
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@ -0,0 +1,43 @@
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/*++
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Copyright (c) 2012 Microsoft Corporation
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Module Name:
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expr_safe_replace.h
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Abstract:
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Version of expr_replace/expr_substitution that is safe for quantifiers.
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Author:
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Nikolaj Bjorner (nbjorner) 2012-11-30
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Revision History:
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--*/
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#ifndef __EXPR_SAFE_REPLACE_H__
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#define __EXPR_SAFE_REPLACE_H__
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#include "ast.h"
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class expr_safe_replace {
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ast_manager& m;
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expr_ref_vector m_src;
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expr_ref_vector m_dst;
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obj_map<expr, expr*> m_subst;
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public:
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expr_safe_replace(ast_manager& m): m(m), m_src(m), m_dst(m) {}
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void insert(expr* src, expr* dst);
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void operator()(expr_ref& e) { (*this)(e.get(), e); }
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void operator()(expr* src, expr_ref& e);
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};
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#endif /* __EXPR_SAFE_REPLACE_H__ */
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@ -27,6 +27,9 @@ Revision History:
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#include "ast_smt_pp.h"
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#include "expr_abstract.h"
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#include "dl_mk_extract_quantifiers.h"
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#include "qe_lite.h"
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#include "well_sorted.h"
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#include "expr_safe_replace.h"
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namespace pdr {
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@ -49,6 +52,12 @@ namespace pdr {
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}
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}
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quantifier_model_checker::~quantifier_model_checker() {
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obj_map<func_decl,expr*>::iterator it = m_reachable.begin(), end = m_reachable.end();
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for (; it != end; ++it) {
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m.dec_ref(it->m_value);
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}
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}
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void quantifier_model_checker::generalize_binding(expr_ref_vector const& binding, vector<expr_ref_vector>& bindings) {
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expr_ref_vector new_binding(m);
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@ -193,13 +202,12 @@ namespace pdr {
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bool quantifier_model_checker::find_instantiations_proof_based(quantifier_ref_vector const& qs, unsigned level) {
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bool found_instance = false;
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TRACE("pdr", tout << mk_pp(m_A,m) << "\n";);
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datalog::scoped_coarse_proof _scp(m);
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datalog::scoped_fine_proof _scp(m);
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expr_ref_vector fmls(m);
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front_end_params fparams;
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fparams.m_proof_mode = PGM_COARSE;
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fparams.m_proof_mode = PGM_FINE;
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fparams.m_mbqi = true;
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fmls.push_back(m_A.get());
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@ -209,15 +217,20 @@ namespace pdr {
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for (unsigned i = 0; i < fmls.size(); ++i) {
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tout << mk_pp(fmls[i].get(), m) << "\n";
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});
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smt::kernel solver(m, fparams);
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for (unsigned i = 0; i < fmls.size(); ++i) {
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solver.assert_expr(fmls[i].get());
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}
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lbool result = solver.check();
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if (result != l_false) {
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TRACE("pdr", tout << result << "\n";);
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return found_instance;
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if (result != l_false) {
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return false;
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}
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m_rules_model_check = false;
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map<symbol, quantifier*, symbol_hash_proc, symbol_eq_proc> qid_map;
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quantifier* q;
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for (unsigned i = 0; i < qs.size(); ++i) {
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@ -234,8 +247,7 @@ namespace pdr {
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for (unsigned i = 0; i < collector.size(); ++i) {
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symbol qid = quants[i]->get_qid();
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if (!qid_map.find(qid, q)) {
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TRACE("pdr", tout << "Could not find quantifier "
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<< mk_pp(quants[i], m) << "\n";);
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TRACE("pdr", tout << "Could not find quantifier " << mk_pp(quants[i], m) << "\n";);
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continue;
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}
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expr_ref_vector const& binding = collector.bindings()[i];
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@ -256,8 +268,43 @@ namespace pdr {
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return found_instance;
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}
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/**
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Given node:
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For under-approximations:
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m_reachable: set of reachable states, per predicate
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rules: P(x) :- B[x,y] & Fa z . Q(y,z)
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Q(y,z) :- C[y,z,u] & Fa w . R(u,w)
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qis: Fa z . Q(y,z)
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M: model satisfying P(x) & B[x,y]
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B'[x,y]: body with reachable states substituted for predicates.
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Q'[y,z]: reachable states substituted for Q.
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S'[x]: Ex y . B'[x,y] & Fa z . Q'[y, z]
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Method:
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1. M |= Fa z . Q'[y, z] => done
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Weaker variant:
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Check B[x,y] & Fa z . Q'[y, z] for consistency.
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2. Otherwise, extract instantiations.
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3. Update reachable (for next round):
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Q'[y,z] := Q'[y,z] \/ C'[y,z,u] & Fa w . R'(u,w)
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*/
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/**
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For over-approximations:
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- pt - predicate transformer for rule:
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P(x) :- Body1(x,y) || Body2(x,z) & (Fa u . Q(u,x,z)).
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@ -267,22 +314,201 @@ namespace pdr {
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- A := node.state(x) && Body2(x,y)
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- Bs := array of Bs of the form:
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. Fa u . Q(u, P_x, P_y) - instantiate quantifier to P variables.
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. B := inv(Q_0,Q_1,Q_2)
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. B := inv(u, P_x, P_y) := B[u/Q_0, P_x/Q_1, P_y/Q_2]
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. B := Fa u . inv(u, P_x, P_y)
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*/
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void quantifier_model_checker::update_reachable(func_decl* f, expr* e) {
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expr* e_old;
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m.inc_ref(e);
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if (m_reachable.find(f, e_old)) {
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m.dec_ref(e_old);
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}
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m_reachable.insert(f, e);
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}
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expr_ref quantifier_model_checker::get_reachable(func_decl* p) {
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expr* e = 0;
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if (!m_reachable.find(p, e)) {
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e = m_ctx.get_pred_transformer(p).initial_state();
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update_reachable(p, e);
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}
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return expr_ref(e, m);
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}
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void quantifier_model_checker::add_over_approximations(quantifier_ref_vector& qis, model_node& n) {
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add_approximations(qis, n, true);
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}
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void quantifier_model_checker::add_under_approximations(quantifier_ref_vector& qis, model_node& n) {
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add_approximations(qis, n, false);
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}
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void quantifier_model_checker::add_approximations(quantifier_ref_vector& qis, model_node& n, bool is_over) {
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pred_transformer& pt = n.pt();
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manager& pm = pt.get_pdr_manager();
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unsigned level = n.level();
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expr_ref_vector Bs(m);
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expr_ref B(m), v(m);
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quantifier_ref q(m);
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datalog::scoped_no_proof _no_proof(m);
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scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
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for (unsigned j = 0; j < qis.size(); ++j) {
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q = qis[j].get();
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app_ref_vector& inst = pt.get_inst(m_current_rule);
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TRACE("pdr",
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tout << "q:\n" << mk_pp(q, m) << "\n";
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tout << "level: " << level << "\n";
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model_smt2_pp(tout, m, n.get_model(), 0);
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m_current_rule->display(m_ctx.get_context(), tout << "rule:\n");
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);
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var_subst vs(m, false);
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vs(q, inst.size(), (expr*const*)inst.c_ptr(), B);
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q = to_quantifier(B);
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TRACE("pdr", tout << "q instantiated:\n" << mk_pp(q, m) << "\n";);
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app* a = to_app(q->get_expr());
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func_decl* f = a->get_decl();
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pred_transformer& pt2 = m_ctx.get_pred_transformer(f);
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if (is_over) {
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B = pt2.get_formulas(level - 1, false);
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}
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else {
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B = get_reachable(f);
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SASSERT(is_well_sorted(m, B));
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}
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TRACE("pdr", tout << "B:\n" << mk_pp(B, m) << "\n";);
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expr_safe_replace sub(m);
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for (unsigned i = 0; i < a->get_num_args(); ++i) {
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v = m.mk_const(pm.o2n(pt2.sig(i),0));
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sub.insert(v, a->get_arg(i));
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}
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sub(B);
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TRACE("pdr", tout << "B substituted:\n" << mk_pp(B, m) << "\n";);
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datalog::flatten_and(B, Bs);
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for (unsigned i = 0; i < Bs.size(); ++i) {
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m_Bs.push_back(m.update_quantifier(q, Bs[i].get()));
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}
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}
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}
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/**
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\brief compute strongest post-conditions for each predicate transformer.
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(or at least something sufficient to change the set of current counter-examples)
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*/
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void quantifier_model_checker::weaken_under_approximation() {
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datalog::rule_set::decl2rules::iterator it = m_rules.begin_grouped_rules(), end = m_rules.end_grouped_rules();
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for (; it != end; ++it) {
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func_decl* p = it->m_key;
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datalog::rule_vector& rules = *it->m_value;
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expr_ref_vector bodies(m);
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for (unsigned i = 0; i < rules.size(); ++i) {
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bodies.push_back(strongest_post_condition(*rules[i]));
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}
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update_reachable(p, m.mk_or(bodies.size(), bodies.c_ptr()));
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}
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}
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expr_ref quantifier_model_checker::strongest_post_condition(datalog::rule& r) {
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pred_transformer& pt = m_ctx.get_pred_transformer(r.get_decl());
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manager& pm = pt.get_pdr_manager();
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quantifier_ref_vector* qis = 0;
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m_quantifiers.find(&r, qis);
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expr_ref_vector body(m), inst(m);
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expr_ref fml(m), v(m);
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app* a;
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func_decl* p;
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svector<symbol> names;
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unsigned ut_size = r.get_uninterpreted_tail_size();
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unsigned t_size = r.get_tail_size();
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var_subst vs(m, false);
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sort_ref_vector vars(m);
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r.get_vars(vars);
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if (qis) {
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quantifier_ref_vector const& qi = *qis;
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for (unsigned i = 0; i < qi.size(); ++i) {
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fml = qi[i]->get_expr();
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a = to_app(fml);
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p = a->get_decl();
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expr* p_reach = get_reachable(p);
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pred_transformer& pt2 = m_ctx.get_pred_transformer(p);
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expr_safe_replace sub(m);
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for (unsigned j = 0; j < a->get_num_args(); ++j) {
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||||
v = m.mk_const(pm.o2n(pt2.sig(j),0));
|
||||
sub.insert(v, a->get_arg(j));
|
||||
}
|
||||
sub(p_reach, fml);
|
||||
body.push_back(m.update_quantifier(qi[i], fml));
|
||||
}
|
||||
}
|
||||
a = r.get_head();
|
||||
for (unsigned i = 0; i < a->get_num_args(); ++i) {
|
||||
v = m.mk_var(vars.size()+i, m.get_sort(a->get_arg(i)));
|
||||
body.push_back(m.mk_eq(v, a->get_arg(i)));
|
||||
}
|
||||
for (unsigned i = 0; i < ut_size; ++i) {
|
||||
a = r.get_tail(i);
|
||||
p = a->get_decl();
|
||||
pred_transformer& pt2 = m_ctx.get_pred_transformer(p);
|
||||
expr* p_reach = get_reachable(p);
|
||||
expr_safe_replace sub(m);
|
||||
for (unsigned i = 0; i < a->get_num_args(); ++i) {
|
||||
v = m.mk_const(pm.o2n(pt2.sig(i),0));
|
||||
sub.insert(v, a->get_arg(i));
|
||||
}
|
||||
sub(p_reach, fml);
|
||||
body.push_back(fml);
|
||||
}
|
||||
for (unsigned i = ut_size; i < t_size; ++i) {
|
||||
body.push_back(r.get_tail(i));
|
||||
}
|
||||
fml = m.mk_and(body.size(), body.c_ptr());
|
||||
vars.reverse();
|
||||
for (unsigned i = 0; i < vars.size(); ++i) {
|
||||
names.push_back(symbol(i));
|
||||
}
|
||||
if (!vars.empty()) {
|
||||
fml = m.mk_exists(vars.size(), vars.c_ptr(), names.c_ptr(), fml);
|
||||
SASSERT(is_well_sorted(m, fml));
|
||||
}
|
||||
|
||||
for (unsigned i = 0; i < r.get_head()->get_num_args(); ++i) {
|
||||
inst.push_back(m.mk_const(pm.o2n(pt.sig(i),0)));
|
||||
}
|
||||
vs(fml, inst.size(), inst.c_ptr(), fml);
|
||||
SASSERT(is_well_sorted(m, fml));
|
||||
if (!vars.empty()) {
|
||||
fml = to_quantifier(fml)->get_expr();
|
||||
uint_set empty_index_set;
|
||||
qe_lite qe(m);
|
||||
qe(empty_index_set, false, fml);
|
||||
fml = m.mk_exists(vars.size(), vars.c_ptr(), names.c_ptr(), fml);
|
||||
SASSERT(is_well_sorted(m, fml));
|
||||
m_ctx.get_context().get_rewriter()(fml);
|
||||
}
|
||||
SASSERT(is_well_sorted(m, fml));
|
||||
|
||||
IF_VERBOSE(0, verbose_stream() << "instantiate to\n:" << mk_pp(fml, m) << "\n";);
|
||||
return fml;
|
||||
}
|
||||
|
||||
|
||||
void quantifier_model_checker::model_check_node(model_node& node) {
|
||||
TRACE("pdr", node.display(tout, 0););
|
||||
pred_transformer& pt = node.pt();
|
||||
manager& pm = pt.get_pdr_manager();
|
||||
expr_ref A(m), B(m), C(m), v(m);
|
||||
expr_ref_vector As(m), Bs(m);
|
||||
expr_ref A(m), C(m);
|
||||
expr_ref_vector As(m);
|
||||
m_Bs.reset();
|
||||
//
|
||||
// nodes from leaves that are repeated
|
||||
|
|
@ -307,8 +533,6 @@ namespace pdr {
|
|||
if (level == 0) {
|
||||
return;
|
||||
}
|
||||
unsigned previous_level = level - 1;
|
||||
|
||||
|
||||
As.push_back(pt.get_propagation_formula(m_ctx.get_pred_transformers(), level));
|
||||
As.push_back(node.state());
|
||||
|
|
@ -316,48 +540,8 @@ namespace pdr {
|
|||
m_A = pm.mk_and(As);
|
||||
|
||||
// Add quantifiers:
|
||||
|
||||
{
|
||||
datalog::scoped_no_proof _no_proof(m);
|
||||
quantifier_ref q(m);
|
||||
scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
|
||||
for (unsigned j = 0; j < qis->size(); ++j) {
|
||||
q = (*qis)[j].get();
|
||||
app_ref_vector& inst = pt.get_inst(m_current_rule);
|
||||
TRACE("pdr",
|
||||
tout << "q:\n" << mk_pp(q, m) << "\n";
|
||||
tout << "level: " << level << "\n";
|
||||
model_smt2_pp(tout, m, node.get_model(), 0);
|
||||
m_current_rule->display(m_ctx.get_context(), tout << "rule:\n");
|
||||
|
||||
);
|
||||
|
||||
var_subst vs(m, false);
|
||||
vs(q, inst.size(), (expr*const*)inst.c_ptr(), B);
|
||||
q = to_quantifier(B);
|
||||
TRACE("pdr", tout << "q instantiated:\n" << mk_pp(q, m) << "\n";);
|
||||
|
||||
app* a = to_app(q->get_expr());
|
||||
func_decl* f = a->get_decl();
|
||||
pred_transformer& pt2 = m_ctx.get_pred_transformer(f);
|
||||
B = pt2.get_formulas(previous_level, false);
|
||||
TRACE("pdr", tout << "B:\n" << mk_pp(B, m) << "\n";);
|
||||
|
||||
|
||||
expr_substitution sub(m);
|
||||
for (unsigned i = 0; i < a->get_num_args(); ++i) {
|
||||
v = m.mk_const(pm.o2n(pt2.sig(i),0));
|
||||
sub.insert(v, a->get_arg(i));
|
||||
}
|
||||
rep->set_substitution(&sub);
|
||||
(*rep)(B);
|
||||
TRACE("pdr", tout << "B substituted:\n" << mk_pp(B, m) << "\n";);
|
||||
datalog::flatten_and(B, Bs);
|
||||
for (unsigned i = 0; i < Bs.size(); ++i) {
|
||||
m_Bs.push_back(m.update_quantifier(q, Bs[i].get()));
|
||||
}
|
||||
}
|
||||
}
|
||||
// add_over_approximations(*qis, node);
|
||||
add_under_approximations(*qis, node);
|
||||
|
||||
TRACE("pdr",
|
||||
tout << "A:\n" << mk_pp(m_A, m) << "\n";
|
||||
|
|
@ -384,13 +568,17 @@ namespace pdr {
|
|||
bool quantifier_model_checker::model_check(model_node& root) {
|
||||
m_instantiations.reset();
|
||||
m_instantiated_rules.reset();
|
||||
m_rules_model_check = true;
|
||||
ptr_vector<model_node> nodes;
|
||||
get_nodes(root, nodes);
|
||||
for (unsigned i = nodes.size(); i > 0; ) {
|
||||
--i;
|
||||
model_check_node(*nodes[i]);
|
||||
}
|
||||
return m_instantiations.empty();
|
||||
if (!m_rules_model_check) {
|
||||
weaken_under_approximation();
|
||||
}
|
||||
return m_rules_model_check;
|
||||
}
|
||||
|
||||
void quantifier_model_checker::refine() {
|
||||
|
|
@ -446,136 +634,3 @@ namespace pdr {
|
|||
}
|
||||
};
|
||||
|
||||
|
||||
#if 0
|
||||
//
|
||||
// Build:
|
||||
//
|
||||
// A & forall x . B1 & forall y . B2 & ...
|
||||
// =
|
||||
// not exists x y . (!A or !B1 or !B2 or ...)
|
||||
//
|
||||
// Find an instance that satisfies formula.
|
||||
// (or find all instances?)
|
||||
//
|
||||
bool quantifier_model_checker::find_instantiations_qe_based(quantifier_ref_vector const& qs, unsigned level) {
|
||||
expr_ref_vector fmls(m), conjs(m), fresh_vars(m);
|
||||
app_ref_vector all_vars(m);
|
||||
expr_ref C(m);
|
||||
qe::def_vector defs(m);
|
||||
front_end_params fparams;
|
||||
qe::expr_quant_elim qe(m, fparams);
|
||||
for (unsigned i = 0; i < m_Bs.size(); ++i) {
|
||||
quantifier* q = qs[i];
|
||||
unsigned num_decls = q->get_num_decls();
|
||||
unsigned offset = all_vars.size();
|
||||
for (unsigned j = 0; j < num_decls; ++j) {
|
||||
all_vars.push_back(m.mk_fresh_const("V",q->get_decl_sort(j)));
|
||||
}
|
||||
var_subst varsubst(m, false);
|
||||
varsubst(m_Bs[i].get(), num_decls, (expr**)(all_vars.c_ptr() + offset), C);
|
||||
fmls.push_back(C);
|
||||
}
|
||||
conjs.push_back(m_A);
|
||||
conjs.push_back(m.mk_not(m.mk_and(fmls.size(), fmls.c_ptr())));
|
||||
// add previous instances.
|
||||
expr* r = m.mk_and(m_Bs.size(), m_Bs.c_ptr());
|
||||
m_trail.push_back(r);
|
||||
expr* inst;
|
||||
if (!m_bound.find(m_current_rule, r, inst)) {
|
||||
TRACE("pdr", tout << "did not find: " << mk_pp(r, m) << "\n";);
|
||||
m_trail.push_back(r);Newton Sanches
|
||||
inst = m.mk_true();
|
||||
m_bound.insert(m_current_rule, r, inst);
|
||||
}
|
||||
else {
|
||||
TRACE("pdr", tout << "blocking: " << mk_pp(inst, m) << "\n";);
|
||||
conjs.push_back(inst);
|
||||
}
|
||||
C = m.mk_and(conjs.size(), conjs.c_ptr());
|
||||
lbool result = qe.first_elim(all_vars.size(), all_vars.c_ptr(), C, defs);
|
||||
TRACE("pdr", tout << mk_pp(C.get(), m) << "\n" << result << "\n";);
|
||||
if (result != l_true) {
|
||||
return false;
|
||||
}
|
||||
inst = m.mk_and(inst, m.mk_not(C));
|
||||
m_trail.push_back(inst);
|
||||
m_bound.insert(m_current_rule, r, inst);
|
||||
TRACE("pdr",
|
||||
tout << "Instantiating\n";
|
||||
for (unsigned i = 0; i < defs.size(); ++i) {
|
||||
tout << defs.var(i)->get_name() << " " << mk_pp(defs.def(i), m) << "\n";
|
||||
}
|
||||
);
|
||||
expr_substitution sub(m);
|
||||
for (unsigned i = 0; i < defs.size(); ++i) {
|
||||
sub.insert(m.mk_const(defs.var(i)), defs.def(i));
|
||||
}
|
||||
scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
|
||||
rep->set_substitution(&sub);
|
||||
for (unsigned i = 0; i < all_vars.size(); ++i) {
|
||||
expr_ref tmp(all_vars[i].get(), m);
|
||||
(*rep)(tmp);
|
||||
all_vars[i] = to_app(tmp);
|
||||
}
|
||||
unsigned offset = 0;
|
||||
for (unsigned i = 0; i < m_Bs.size(); ++i) {
|
||||
quantifier* q = qs[i];
|
||||
unsigned num_decls = q->get_num_decls();
|
||||
expr_ref_vector new_binding(m);
|
||||
for (unsigned j = 0; j < num_decls; ++j) {
|
||||
new_binding.push_back(all_vars[offset+j].get());
|
||||
}
|
||||
offset += num_decls;
|
||||
add_binding(q, new_binding);
|
||||
}
|
||||
return true;
|
||||
}
|
||||
|
||||
bool quantifier_model_checker::find_instantiations_model_based(quantifier_ref_vector const& qs, unsigned level) {
|
||||
bool found_instance = false;
|
||||
expr_ref C(m);
|
||||
front_end_params fparams;
|
||||
smt::kernel solver(m, fparams);
|
||||
solver.assert_expr(m_A);
|
||||
for (unsigned i = 0; i < m_Bs.size(); ++i) {
|
||||
expr_ref_vector fresh_vars(m);
|
||||
quantifier* q = qs[i];
|
||||
for (unsigned j = 0; j < q->get_num_decls(); ++j) {
|
||||
fresh_vars.push_back(m.mk_fresh_const("V",q->get_decl_sort(j)));
|
||||
}
|
||||
var_subst varsubst(m, false);
|
||||
varsubst(m_Bs[i].get(), fresh_vars.size(), fresh_vars.c_ptr(), C);
|
||||
TRACE("pdr", tout << "updated propagation formula: " << mk_pp(C,m) << "\n";);
|
||||
|
||||
solver.push();
|
||||
// TBD: what to do with the different tags when unfolding the same predicate twice?
|
||||
solver.assert_expr(m.mk_not(C));
|
||||
lbool result = solver.check();
|
||||
if (result == l_true) {
|
||||
found_instance = true;
|
||||
model_ref mr;
|
||||
solver.get_model(mr);
|
||||
TRACE("pdr", model_smt2_pp(tout, m, *mr, 0););
|
||||
|
||||
expr_ref_vector insts(m);
|
||||
for (unsigned j = 0; j < fresh_vars.size(); ++j) {
|
||||
expr* interp = mr->get_const_interp(to_app(fresh_vars[j].get())->get_decl());
|
||||
if (interp) {
|
||||
insts.push_back(interp);
|
||||
}
|
||||
else {
|
||||
insts.push_back(fresh_vars[j].get());
|
||||
}
|
||||
TRACE("pdr", tout << mk_pp(insts.back(), m) << "\n";);
|
||||
}
|
||||
add_binding(q, insts);
|
||||
}
|
||||
solver.pop(1);
|
||||
}
|
||||
return found_instance;
|
||||
}
|
||||
|
||||
|
||||
#endif
|
||||
|
||||
|
|
|
|||
|
|
@ -34,23 +34,26 @@ namespace pdr {
|
|||
class pred_transformer;
|
||||
class context;
|
||||
|
||||
|
||||
class quantifier_model_checker {
|
||||
context& m_ctx;
|
||||
ast_manager& m;
|
||||
obj_map<datalog::rule const, quantifier_ref_vector*>& m_quantifiers;
|
||||
datalog::rule_set& m_rules;
|
||||
expr_ref_vector m_trail;
|
||||
|
||||
obj_map<func_decl, expr*> m_reachable; // set of reachable states
|
||||
expr_ref m_A;
|
||||
expr_ref_vector m_Bs;
|
||||
pred_transformer* m_current_pt;
|
||||
datalog::rule const* m_current_rule;
|
||||
model_node* m_current_node;
|
||||
bool m_rules_model_check;
|
||||
app_ref_vector m_instantiations;
|
||||
ptr_vector<datalog::rule const> m_instantiated_rules;
|
||||
|
||||
void model_check_node(model_node& node);
|
||||
|
||||
void weaken_under_approximation();
|
||||
|
||||
bool find_instantiations(quantifier_ref_vector const& qs, unsigned level);
|
||||
|
||||
bool find_instantiations_model_based(quantifier_ref_vector const& qs, unsigned level);
|
||||
|
|
@ -79,6 +82,18 @@ namespace pdr {
|
|||
|
||||
bool model_check(model_node& root);
|
||||
|
||||
void add_over_approximations(quantifier_ref_vector& qis, model_node& n);
|
||||
|
||||
void add_under_approximations(quantifier_ref_vector& qis, model_node& n);
|
||||
|
||||
void add_approximations(quantifier_ref_vector& qis, model_node& n, bool is_over);
|
||||
|
||||
expr_ref get_reachable(func_decl* f);
|
||||
|
||||
void update_reachable(func_decl* f, expr* e);
|
||||
|
||||
expr_ref strongest_post_condition(datalog::rule& r);
|
||||
|
||||
public:
|
||||
quantifier_model_checker(
|
||||
context& ctx,
|
||||
|
|
@ -89,9 +104,14 @@ namespace pdr {
|
|||
m(m),
|
||||
m_quantifiers(quantifiers),
|
||||
m_rules(rules),
|
||||
m_trail(m), m_A(m), m_Bs(m),
|
||||
m_current_pt(0), m_current_rule(0),
|
||||
m_current_node(0), m_instantiations(m) {}
|
||||
m_A(m),
|
||||
m_Bs(m),
|
||||
m_current_pt(0),
|
||||
m_current_rule(0),
|
||||
m_current_node(0),
|
||||
m_instantiations(m) {}
|
||||
|
||||
~quantifier_model_checker();
|
||||
|
||||
bool check();
|
||||
};
|
||||
|
|
|
|||
|
|
@ -74,7 +74,8 @@ public:
|
|||
};
|
||||
|
||||
|
||||
class der2 {
|
||||
namespace eq {
|
||||
class der {
|
||||
ast_manager & m;
|
||||
is_variable_proc* m_is_variable;
|
||||
var_subst m_subst;
|
||||
|
|
@ -492,9 +493,8 @@ class der2 {
|
|||
return false;
|
||||
}
|
||||
|
||||
|
||||
public:
|
||||
der2(ast_manager & m): m(m), m_is_variable(0), m_subst(m), m_new_exprs(m), m_subst_map(m), m_new_args(m), m_rewriter(m) {}
|
||||
public:
|
||||
der(ast_manager & m): m(m), m_is_variable(0), m_subst(m), m_new_exprs(m), m_subst_map(m), m_new_args(m), m_rewriter(m) {}
|
||||
|
||||
void set_is_variable_proc(is_variable_proc& proc) { m_is_variable = &proc;}
|
||||
|
||||
|
|
@ -529,7 +529,34 @@ public:
|
|||
}
|
||||
|
||||
ast_manager& get_manager() const { return m; }
|
||||
};
|
||||
};
|
||||
}; // namespace eq
|
||||
|
||||
// ------------------------------------------------------------
|
||||
// basic destructive equality (and disequality) resolution for arrays.
|
||||
|
||||
namespace ar {
|
||||
class der {
|
||||
ast_manager& m;
|
||||
is_variable_proc* m_is_variable;
|
||||
|
||||
bool is_variable(expr * e) const {
|
||||
return (*m_is_variable)(e);
|
||||
}
|
||||
|
||||
public:
|
||||
|
||||
der(ast_manager& m): m(m), m_is_variable(0) {}
|
||||
|
||||
void operator()(expr_ref_vector& fmls) {
|
||||
IF_VERBOSE(1, verbose_stream() << "Todo: eliminate arrays\n";);
|
||||
}
|
||||
|
||||
void set_is_variable_proc(is_variable_proc& proc) { m_is_variable = &proc;}
|
||||
|
||||
};
|
||||
}; // namespace ar
|
||||
|
||||
|
||||
// ------------------------------------------------------------
|
||||
// fm_tactic adapted to eliminate designated de-Brujin indices.
|
||||
|
|
@ -1808,7 +1835,6 @@ namespace fm {
|
|||
|
||||
void set_is_variable_proc(is_variable_proc& proc) { m_is_variable = &proc;}
|
||||
|
||||
|
||||
void operator()(expr_ref_vector& fmls) {
|
||||
init(fmls);
|
||||
init_use_list(fmls);
|
||||
|
|
@ -1873,12 +1899,13 @@ namespace fm {
|
|||
|
||||
class qe_lite::impl {
|
||||
ast_manager& m;
|
||||
der2 m_der;
|
||||
params_ref m_params;
|
||||
eq::der m_der;
|
||||
fm::fm m_fm;
|
||||
ar::der m_array_der;
|
||||
|
||||
public:
|
||||
impl(ast_manager& m): m(m), m_der(m), m_fm(m, m_params) {}
|
||||
impl(ast_manager& m): m(m), m_der(m), m_fm(m, m_params), m_array_der(m) {}
|
||||
|
||||
void operator()(app_ref_vector& vars, expr_ref& fml) {
|
||||
if (vars.empty()) {
|
||||
|
|
@ -1928,10 +1955,16 @@ public:
|
|||
}
|
||||
|
||||
void operator()(uint_set const& index_set, bool index_of_bound, expr_ref& fml) {
|
||||
expr_ref_vector disjs(m);
|
||||
datalog::flatten_or(fml, disjs);
|
||||
for (unsigned i = 0; i < disjs.size(); ++i) {
|
||||
expr_ref_vector conjs(m);
|
||||
conjs.push_back(fml);
|
||||
conjs.push_back(disjs[i].get());
|
||||
(*this)(index_set, index_of_bound, conjs);
|
||||
bool_rewriter(m).mk_and(conjs.size(), conjs.c_ptr(), fml);
|
||||
disjs[i] = fml;
|
||||
}
|
||||
bool_rewriter(m).mk_or(disjs.size(), disjs.c_ptr(), fml);
|
||||
}
|
||||
|
||||
|
||||
|
|
@ -1941,9 +1974,11 @@ public:
|
|||
TRACE("qe_lite", for (unsigned i = 0; i < fmls.size(); ++i) tout << mk_pp(fmls[i].get(), m) << "\n";);
|
||||
IF_VERBOSE(3, for (unsigned i = 0; i < fmls.size(); ++i) verbose_stream() << mk_pp(fmls[i].get(), m) << "\n";);
|
||||
m_der.set_is_variable_proc(is_var);
|
||||
m_der(fmls);
|
||||
m_fm.set_is_variable_proc(is_var);
|
||||
m_array_der.set_is_variable_proc(is_var);
|
||||
m_der(fmls);
|
||||
m_fm(fmls);
|
||||
m_array_der(fmls);
|
||||
TRACE("qe_lite", for (unsigned i = 0; i < fmls.size(); ++i) tout << mk_pp(fmls[i].get(), m) << "\n";);
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
/*++
|
||||
Copyright (c) 2010 Microsoft Corporation
|
||||
Copyright (c) 2012 Microsoft Corporation
|
||||
|
||||
Module Name:
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue