mirrors/z3
3
0
Fork 0
mirror of https://github.com/Z3Prover/z3 synced 2025-04-06 09:34:08 +00:00
Code Activity

Merge branch 'unstable' into contrib

Browse source
This commit is contained in:
Leonardo de Moura 2013-01-13 09:51:22 -08:00
parent 1235b3ea24 7312f49f88
commit 4879b8db7a
53 changed files with 8472 additions and 691 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

10
examples/c++/example.cpp
View file

@ -337,6 +337,15 @@ void ite_example() {
std::cout << "term: " << ite << "\n";
}
void ite_example2() {
std::cout << "if-then-else example2\n";
context c;
expr b = c.bool_const("b");
expr x = c.int_const("x");
expr y = c.int_const("y");
std::cout << (ite(b, x, y) > 0) << "\n";
}
/**
\brief Small example using quantifiers.
*/
@ -889,6 +898,7 @@ int main() {
error_example(); std::cout << "\n";
numeral_example(); std::cout << "\n";
ite_example(); std::cout << "\n";
ite_example2(); std::cout << "\n";
quantifier_example(); std::cout << "\n";
unsat_core_example1(); std::cout << "\n";
unsat_core_example2(); std::cout << "\n";

5
scripts/mk_project.py
View file

@ -15,6 +15,7 @@ def init_project_def():
add_lib('sat', ['util'])
add_lib('nlsat', ['polynomial', 'sat'])
add_lib('interval', ['util'], 'math/interval')
add_lib('realclosure', ['interval'], 'math/realclosure')
add_lib('subpaving', ['interval'], 'math/subpaving')
add_lib('ast', ['util', 'polynomial'])
add_lib('rewriter', ['ast', 'polynomial'], 'ast/rewriter')
@ -58,8 +59,8 @@ def init_project_def():
add_lib('ufbv_tactic', ['normal_forms', 'core_tactics', 'macros', 'smt_tactic', 'rewriter'], 'tactic/ufbv')
add_lib('portfolio', ['smtlogic_tactics', 'ufbv_tactic', 'fpa', 'aig_tactic', 'muz_qe', 'sls_tactic', 'subpaving_tactic'], 'tactic/portfolio')
add_lib('smtparser', ['portfolio'], 'parsers/smt')
API_files = ['z3_api.h', 'z3_algebraic.h', 'z3_polynomial.h']
add_lib('api', ['portfolio', 'user_plugin', 'smtparser'],
API_files = ['z3_api.h', 'z3_algebraic.h', 'z3_polynomial.h', 'z3_rcf.h']
add_lib('api', ['portfolio', 'user_plugin', 'smtparser', 'realclosure'],
includes2install=['z3.h', 'z3_v1.h', 'z3_macros.h'] + API_files)
add_exe('shell', ['api', 'sat', 'extra_cmds'], exe_name='z3')
add_exe('test', ['api', 'fuzzing'], exe_name='test-z3', install=False)

5
scripts/mk_util.py
View file

@ -1320,11 +1320,13 @@ def mk_config():
check_ar()
CXX = find_cxx_compiler()
CC = find_c_compiler()
SLIBEXTRAFLAGS = ''
if GMP:
test_gmp(CXX)
ARITH = "gmp"
CPPFLAGS = '%s -D_MP_GMP' % CPPFLAGS
LDFLAGS = '%s -lgmp' % LDFLAGS
SLIBEXTRAFLAGS = '%s -lgmp' % SLIBEXTRAFLAGS
else:
CPPFLAGS = '%s -D_MP_INTERNAL' % CPPFLAGS
CXXFLAGS = '%s -c' % CXXFLAGS
@ -1332,10 +1334,9 @@ def mk_config():
if HAS_OMP:
CXXFLAGS = '%s -fopenmp -mfpmath=sse' % CXXFLAGS
LDFLAGS = '%s -fopenmp' % LDFLAGS
SLIBEXTRAFLAGS = '-fopenmp'
SLIBEXTRAFLAGS = '%s -fopenmp' % SLIBEXTRAFLAGS
else:
CXXFLAGS = '%s -D_NO_OMP_' % CXXFLAGS
SLIBEXTRAFLAGS = ''
if DEBUG_MODE:
CXXFLAGS = '%s -g -Wall' % CXXFLAGS
else:

21
src/api/api_context.cpp
View file

@ -25,6 +25,7 @@ Revision History:
#include"api_log_macros.h"
#include"api_util.h"
#include"reg_decl_plugins.h"
#include"realclosure.h"
// The install_tactics procedure is automatically generated
void install_tactics(tactic_manager & ctx);
@ -138,6 +139,8 @@ namespace api {
if (m_interruptable)
(*m_interruptable)();
m().set_cancel(true);
if (m_rcf_manager.get() == 0)
m_rcf_manager->set_cancel(true);
}
}
@ -391,6 +394,19 @@ namespace api {
m_smtlib_parser_sorts.reset();
}
}
// ------------------------
//
// RCF manager
//
// -----------------------
realclosure::manager & context::rcfm() {
if (m_rcf_manager.get() == 0) {
m_rcf_manager = alloc(realclosure::manager, m_rcf_qm);
}
return *(m_rcf_manager.get());
}
};
@ -476,8 +492,11 @@ extern "C" {
}
void Z3_API Z3_enable_trace(Z3_string tag) {
memory::initialize(UINT_MAX);
LOG_Z3_enable_trace(tag);
enable_trace(tag);
// Tag is a string that was probably not allocated by Z3. Create a copy using symbol.
symbol tag_sym(tag);
enable_trace(tag_sym.bare_str());
}
void Z3_API Z3_disable_trace(Z3_string tag) {

19
src/api/api_context.h
View file

@ -38,6 +38,10 @@ namespace smtlib {
class parser;
};
namespace realclosure {
class manager;
};
namespace api {
Z3_search_failure mk_Z3_search_failure(smt::failure f);
@ -83,7 +87,6 @@ namespace api {
event_handler * m_interruptable; // Reference to an object that can be interrupted by Z3_interrupt
pmanager m_pmanager;
public:
// Scoped obj for setting m_interruptable
class set_interruptable {
@ -175,8 +178,22 @@ namespace api {
// Polynomial manager & caches
//
// -----------------------
private:
pmanager m_pmanager;
public:
polynomial::manager & pm() { return m_pmanager.pm(); }
// ------------------------
//
// RCF manager
//
// -----------------------
private:
unsynch_mpq_manager m_rcf_qm;
scoped_ptr<realclosure::manager> m_rcf_manager;
public:
realclosure::manager & rcfm();
// ------------------------
//
// Solver interface for backward compatibility

293
src/api/api_rcf.cpp Normal file
View file

@ -0,0 +1,293 @@
/*++
Copyright (c) 2013 Microsoft Corporation
Module Name:
api_rcf.cpp
Abstract:
Additional APIs for handling elements of the Z3 real closed field that contains:
- transcendental extensions
- infinitesimal extensions
- algebraic extensions
Author:
Leonardo de Moura (leonardo) 2012-01-05
Notes:
--*/
#include<iostream>
#include"z3.h"
#include"api_log_macros.h"
#include"api_context.h"
#include"realclosure.h"
static rcmanager & rcfm(Z3_context c) {
return mk_c(c)->rcfm();
}
static void reset_rcf_cancel(Z3_context c) {
rcfm(c).reset_cancel();
}
static Z3_rcf_num from_rcnumeral(rcnumeral a) {
return reinterpret_cast<Z3_rcf_num>(a.c_ptr());
}
static rcnumeral to_rcnumeral(Z3_rcf_num a) {
return rcnumeral::mk(a);
}
extern "C" {
void Z3_API Z3_rcf_del(Z3_context c, Z3_rcf_num a) {
Z3_TRY;
LOG_Z3_rcf_del(c, a);
RESET_ERROR_CODE();
rcnumeral _a = to_rcnumeral(a);
rcfm(c).del(_a);
Z3_CATCH;
}
Z3_rcf_num Z3_API Z3_rcf_mk_rational(Z3_context c, Z3_string val) {
Z3_TRY;
LOG_Z3_rcf_mk_rational(c, val);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
scoped_mpq q(rcfm(c).qm());
rcfm(c).qm().set(q, val);
rcnumeral r;
rcfm(c).set(r, q);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_mk_small_int(Z3_context c, int val) {
Z3_TRY;
LOG_Z3_rcf_mk_small_int(c, val);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
rcfm(c).set(r, val);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_mk_pi(Z3_context c) {
Z3_TRY;
LOG_Z3_rcf_mk_pi(c);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
rcfm(c).mk_pi(r);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_mk_e(Z3_context c) {
Z3_TRY;
LOG_Z3_rcf_mk_e(c);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
rcfm(c).mk_e(r);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_mk_infinitesimal(Z3_context c, Z3_string name) {
Z3_TRY;
LOG_Z3_rcf_mk_infinitesimal(c, name);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
rcfm(c).mk_infinitesimal(name, r);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
unsigned Z3_API Z3_rcf_mk_roots(Z3_context c, unsigned n, Z3_rcf_num const a[], Z3_rcf_num roots[]) {
Z3_TRY;
LOG_Z3_rcf_mk_roots(c, n, a, roots);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral_vector av;
unsigned rz = 0;
for (unsigned i = 0; i < n; i++) {
if (!rcfm(c).is_zero(to_rcnumeral(a[i])))
rz = i + 1;
av.push_back(to_rcnumeral(a[i]));
}
if (rz == 0) {
// it is the zero polynomial
SET_ERROR_CODE(Z3_INVALID_ARG);
return 0;
}
av.shrink(rz);
rcnumeral_vector rs;
rcfm(c).isolate_roots(av.size(), av.c_ptr(), rs);
unsigned num_roots = rs.size();
for (unsigned i = 0; i < num_roots; i++) {
roots[i] = from_rcnumeral(rs[i]);
}
RETURN_Z3_rcf_mk_roots num_roots;
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_add(Z3_context c, Z3_rcf_num a, Z3_rcf_num b) {
Z3_TRY;
LOG_Z3_rcf_add(c, a, b);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
rcfm(c).add(to_rcnumeral(a), to_rcnumeral(b), r);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_sub(Z3_context c, Z3_rcf_num a, Z3_rcf_num b) {
Z3_TRY;
LOG_Z3_rcf_sub(c, a, b);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
rcfm(c).sub(to_rcnumeral(a), to_rcnumeral(b), r);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_mul(Z3_context c, Z3_rcf_num a, Z3_rcf_num b) {
Z3_TRY;
LOG_Z3_rcf_mul(c, a, b);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
rcfm(c).mul(to_rcnumeral(a), to_rcnumeral(b), r);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_div(Z3_context c, Z3_rcf_num a, Z3_rcf_num b) {
Z3_TRY;
LOG_Z3_rcf_div(c, a, b);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
rcfm(c).div(to_rcnumeral(a), to_rcnumeral(b), r);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_neg(Z3_context c, Z3_rcf_num a) {
Z3_TRY;
LOG_Z3_rcf_neg(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
rcfm(c).neg(to_rcnumeral(a), r);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_inv(Z3_context c, Z3_rcf_num a) {
Z3_TRY;
LOG_Z3_rcf_inv(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
rcfm(c).inv(to_rcnumeral(a), r);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
Z3_rcf_num Z3_API Z3_rcf_power(Z3_context c, Z3_rcf_num a, unsigned k) {
Z3_TRY;
LOG_Z3_rcf_power(c, a, k);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
rcnumeral r;
rcfm(c).power(to_rcnumeral(a), k, r);
RETURN_Z3(from_rcnumeral(r));
Z3_CATCH_RETURN(0);
}
Z3_bool Z3_API Z3_rcf_lt(Z3_context c, Z3_rcf_num a, Z3_rcf_num b) {
Z3_TRY;
LOG_Z3_rcf_lt(c, a, b);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).lt(to_rcnumeral(a), to_rcnumeral(b));
Z3_CATCH_RETURN(Z3_FALSE);
}
Z3_bool Z3_API Z3_rcf_gt(Z3_context c, Z3_rcf_num a, Z3_rcf_num b) {
Z3_TRY;
LOG_Z3_rcf_gt(c, a, b);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).gt(to_rcnumeral(a), to_rcnumeral(b));
Z3_CATCH_RETURN(Z3_FALSE);
}
Z3_bool Z3_API Z3_rcf_le(Z3_context c, Z3_rcf_num a, Z3_rcf_num b) {
Z3_TRY;
LOG_Z3_rcf_le(c, a, b);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).le(to_rcnumeral(a), to_rcnumeral(b));
Z3_CATCH_RETURN(Z3_FALSE);
}
Z3_bool Z3_API Z3_rcf_ge(Z3_context c, Z3_rcf_num a, Z3_rcf_num b) {
Z3_TRY;
LOG_Z3_rcf_ge(c, a, b);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).ge(to_rcnumeral(a), to_rcnumeral(b));
Z3_CATCH_RETURN(Z3_FALSE);
}
Z3_bool Z3_API Z3_rcf_eq(Z3_context c, Z3_rcf_num a, Z3_rcf_num b) {
Z3_TRY;
LOG_Z3_rcf_eq(c, a, b);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).eq(to_rcnumeral(a), to_rcnumeral(b));
Z3_CATCH_RETURN(Z3_FALSE);
}
Z3_bool Z3_API Z3_rcf_neq(Z3_context c, Z3_rcf_num a, Z3_rcf_num b) {
Z3_TRY;
LOG_Z3_rcf_neq(c, a, b);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
return rcfm(c).eq(to_rcnumeral(a), to_rcnumeral(b));
Z3_CATCH_RETURN(Z3_FALSE);
}
Z3_string Z3_API Z3_rcf_num_to_string(Z3_context c, Z3_rcf_num a) {
Z3_TRY;
LOG_Z3_rcf_num_to_string(c, a);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
std::ostringstream buffer;
rcfm(c).display(buffer, to_rcnumeral(a));
return mk_c(c)->mk_external_string(buffer.str());
Z3_CATCH_RETURN("");
}
Z3_string Z3_API Z3_rcf_num_to_decimal_string(Z3_context c, Z3_rcf_num a, unsigned prec) {
Z3_TRY;
LOG_Z3_rcf_num_to_decimal_string(c, a, prec);
RESET_ERROR_CODE();
reset_rcf_cancel(c);
std::ostringstream buffer;
rcfm(c).display_decimal(buffer, to_rcnumeral(a), prec);
return mk_c(c)->mk_external_string(buffer.str());
Z3_CATCH_RETURN("");
}
};

1
src/api/api_util.h
View file

@ -37,6 +37,7 @@ namespace api {
public:
object():m_ref_count(0) {}
virtual ~object() {}
unsigned ref_count() const { return m_ref_count; }
void inc_ref() { m_ref_count++; }
void dec_ref() { SASSERT(m_ref_count > 0); m_ref_count--; if (m_ref_count == 0) dealloc(this); }
};

13
src/api/c++/z3++.h
View file

@ -620,6 +620,19 @@ namespace z3 {
return expr(a.ctx(), r);
}
/**
\brief Create the if-then-else expression <tt>ite(c, t, e)</tt>
\pre c.is_bool()
*/
friend expr ite(expr const & c, expr const & t, expr const & e) {
check_context(c, t); check_context(c, e);
assert(c.is_bool());
Z3_ast r = Z3_mk_ite(c.ctx(), c, t, e);
c.check_error();
return expr(c.ctx(), r);
}
friend expr operator==(expr const & a, expr const & b) {
check_context(a, b);
Z3_ast r = Z3_mk_eq(a.ctx(), a, b);

8
src/api/dotnet/AST.cs
View file

@ -149,6 +149,14 @@ namespace Microsoft.Z3
}
}
/// <summary>
/// Indicates whether the AST is an application
/// </summary>
public bool IsApp
{
get { return this.ASTKind == Z3_ast_kind.Z3_APP_AST; }
}
/// <summary>
/// Indicates whether the AST is a BoundVariable
/// </summary>

2
src/api/dotnet/Expr.cs
View file

@ -215,7 +215,7 @@ namespace Microsoft.Z3
/// </summary>
public bool IsConst
{
get { return IsExpr && NumArgs == 0 && FuncDecl.DomainSize == 0; }
get { return IsApp && NumArgs == 0 && FuncDecl.DomainSize == 0; }
}
#endregion

8
src/api/java/AST.java
View file

@ -138,6 +138,14 @@ public class AST extends Z3Object
}
}
/**
* Indicates whether the AST is an application
**/
public boolean IsApp() throws Z3Exception
{
return this.ASTKind() == Z3_ast_kind.Z3_APP_AST;
}
/**
* Indicates whether the AST is a BoundVariable
**/

2
src/api/java/Expr.java
View file

@ -204,7 +204,7 @@ public class Expr extends AST
**/
public boolean IsConst() throws Z3Exception
{
return IsExpr() && NumArgs() == 0 && FuncDecl().DomainSize() == 0;
return IsApp() && NumArgs() == 0 && FuncDecl().DomainSize() == 0;
}
/**

153
src/api/python/z3rcf.py Normal file
View file

@ -0,0 +1,153 @@
############################################
# Copyright (c) 2013 Microsoft Corporation
#
# Z3 Python interface for Z3 Real Closed Fields
# that may contain
# - computable transcendentals
# - infinitesimals
# - algebraic extensions
#
# Author: Leonardo de Moura (leonardo)
############################################
from z3 import *
from z3core import *
from z3printer import *
from fractions import Fraction
def _to_rcfnum(num, ctx=None):
if isinstance(num, RCFNum):
return num
else:
return RCFNum(num, ctx)
def Pi(ctx=None):
ctx = z3._get_ctx(ctx)
return RCFNum(Z3_rcf_mk_pi(ctx.ref()), ctx)
def E(ctx=None):
ctx = z3._get_ctx(ctx)
return RCFNum(Z3_rcf_mk_e(ctx.ref()), ctx)
def MkInfinitesimal(name="eps", ctx=None):
ctx = z3._get_ctx(ctx)
return RCFNum(Z3_rcf_mk_infinitesimal(ctx.ref(), name), ctx)
def MkRoots(p, ctx=None):
ctx = z3._get_ctx(ctx)
num = len(p)
_tmp = []
_as = (RCFNumObj * num)()
_rs = (RCFNumObj * num)()
for i in range(num):
_a = _to_rcfnum(p[i], ctx)
_tmp.append(_a) # prevent GC
_as[i] = _a.num
nr = Z3_rcf_mk_roots(ctx.ref(), num, _as, _rs)
r = []
for i in range(nr):
r.append(RCFNum(_rs[i], ctx))
return r
class RCFNum:
def __init__(self, num, ctx=None):
# TODO: add support for converting AST numeral values into RCFNum
if isinstance(num, RCFNumObj):
self.num = num
self.ctx = z3._get_ctx(ctx)
else:
self.ctx = z3._get_ctx(ctx)
self.num = Z3_rcf_mk_rational(self.ctx_ref(), str(num))
def __del__(self):
Z3_rcf_del(self.ctx_ref(), self.num)
def ctx_ref(self):
return self.ctx.ref()
def __repr__(self):
return Z3_rcf_num_to_string(self.ctx_ref(), self.num)
def __add__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_add(self.ctx_ref(), self.num, v.num), self.ctx)
def __radd__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_add(self.ctx_ref(), v.num, self.num), self.ctx)
def __mul__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_mul(self.ctx_ref(), self.num, v.num), self.ctx)
def __rmul__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_mul(self.ctx_ref(), v.num, self.num), self.ctx)
def __sub__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_sub(self.ctx_ref(), self.num, v.num), self.ctx)
def __rsub__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_sub(self.ctx_ref(), v.num, self.num), self.ctx)
def __div__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_div(self.ctx_ref(), self.num, v.num), self.ctx)
def __rdiv__(self, other):
v = _to_rcfnum(other, self.ctx)
return RCFNum(Z3_rcf_div(self.ctx_ref(), v.num, self.num), self.ctx)
def __neg__(self):
return self.__rsub__(0)
def power(self, k):
return RCFNum(Z3_rcf_power(self.ctx_ref(), self.num, k), self.ctx)
def __pow__(self, k):
return self.power(k)
def decimal(self, prec=5):
return Z3_rcf_num_to_decimal_string(self.ctx_ref(), self.num, prec)
def __lt__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_lt(self.ctx_ref(), self.num, v.num)
def __rlt__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_lt(self.ctx_ref(), v.num, self.num)
def __gt__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_gt(self.ctx_ref(), self.num, v.num)
def __rgt__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_gt(self.ctx_ref(), v.num, self.num)
def __le__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_le(self.ctx_ref(), self.num, v.num)
def __rle__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_le(self.ctx_ref(), v.num, self.num)
def __ge__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_ge(self.ctx_ref(), self.num, v.num)
def __rge__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_ge(self.ctx_ref(), v.num, self.num)
def __eq__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_eq(self.ctx_ref(), self.num, v.num)
def __ne__(self, other):
v = _to_rcfnum(other, self.ctx)
return Z3_rcf_neq(self.ctx_ref(), self.num, v.num)

3
src/api/python/z3types.py
View file

@ -106,3 +106,6 @@ class FuncEntryObj(ctypes.c_void_p):
def __init__(self, e): self._as_parameter_ = e
def from_param(obj): return obj
class RCFNumObj(ctypes.c_void_p):
def __init__(self, e): self._as_parameter_ = e
def from_param(obj): return obj

1
src/api/z3.h
View file

@ -26,6 +26,7 @@ Notes:
#include"z3_api.h"
#include"z3_algebraic.h"
#include"z3_polynomial.h"
#include"z3_rcf.h"
#undef __in
#undef __out

2
src/api/z3_api.h
View file

@ -47,6 +47,7 @@ DEFINE_TYPE(Z3_func_interp);
#define Z3_func_interp_opt Z3_func_interp
DEFINE_TYPE(Z3_func_entry);
DEFINE_TYPE(Z3_fixedpoint);
DEFINE_TYPE(Z3_rcf_num);
DEFINE_VOID(Z3_theory_data);
#endif
@ -1190,6 +1191,7 @@ typedef enum
def_Type('FUNC_ENTRY', 'Z3_func_entry', 'FuncEntryObj')
def_Type('FIXEDPOINT', 'Z3_fixedpoint', 'FixedpointObj')
def_Type('PARAM_DESCRS', 'Z3_param_descrs', 'ParamDescrs')
def_Type('RCF_NUM', 'Z3_rcf_num', 'RCFNumObj')
*/
#ifdef Conly

191
src/api/z3_rcf.h Normal file
View file

@ -0,0 +1,191 @@
/*++
Copyright (c) 2013 Microsoft Corporation
Module Name:
z3_rcf.h
Abstract:
Additional APIs for handling elements of the Z3 real closed field that contains:
- transcendental extensions
- infinitesimal extensions
- algebraic extensions
Author:
Leonardo de Moura (leonardo) 2012-01-05
Notes:
--*/
#ifndef _Z3_RCF_H_
#define _Z3_RCF_H_
#ifdef __cplusplus
extern "C" {
#endif // __cplusplus
/**
\brief Delete a RCF numeral created using the RCF API.
def_API('Z3_rcf_del', VOID, (_in(CONTEXT), _in(RCF_NUM)))
*/
void Z3_API Z3_rcf_del(__in Z3_context c, __in Z3_rcf_num a);
/**
\brief Return a RCF rational using the given string.
def_API('Z3_rcf_mk_rational', RCF_NUM, (_in(CONTEXT), _in(STRING)))
*/
Z3_rcf_num Z3_API Z3_rcf_mk_rational(__in Z3_context c, __in Z3_string val);
/**
\brief Return a RCF small integer.
def_API('Z3_rcf_mk_small_int', RCF_NUM, (_in(CONTEXT), _in(INT)))
*/
Z3_rcf_num Z3_API Z3_rcf_mk_small_int(__in Z3_context c, __in int val);
/**
\brief Return Pi
def_API('Z3_rcf_mk_pi', RCF_NUM, (_in(CONTEXT),))
*/
Z3_rcf_num Z3_API Z3_rcf_mk_pi(__in Z3_context c);
/**
\brief Return e (Euler's constant)
def_API('Z3_rcf_mk_e', RCF_NUM, (_in(CONTEXT),))
*/
Z3_rcf_num Z3_API Z3_rcf_mk_e(__in Z3_context c);
/**
\brief Return a new infinitesimal that is smaller than all elements in the Z3 field.
def_API('Z3_rcf_mk_infinitesimal', RCF_NUM, (_in(CONTEXT), _in(STRING)))
*/
Z3_rcf_num Z3_API Z3_rcf_mk_infinitesimal(__in Z3_context c, __in Z3_string name);
/**
\brief Store in roots the roots of the polynomial <tt>a[n-1]*x^{n-1} + ... + a[0]</tt>.
The output vector \c roots must have size \c n.
It returns the number of roots of the polynomial.
\pre The input polynomial is not the zero polynomial.
def_API('Z3_rcf_mk_roots', UINT, (_in(CONTEXT), _in(UINT), _in_array(1, RCF_NUM), _out_array(1, RCF_NUM)))
*/
unsigned Z3_API Z3_rcf_mk_roots(__in Z3_context c, __in unsigned n, __in_ecount(n) Z3_rcf_num const a[], __out_ecount(n) Z3_rcf_num roots[]);
/**
\brief Return the value a + b.
def_API('Z3_rcf_add', RCF_NUM, (_in(CONTEXT), _in(RCF_NUM), _in(RCF_NUM)))
*/
Z3_rcf_num Z3_API Z3_rcf_add(__in Z3_context c, __in Z3_rcf_num a, __in Z3_rcf_num b);
/**
\brief Return the value a - b.
def_API('Z3_rcf_sub', RCF_NUM, (_in(CONTEXT), _in(RCF_NUM), _in(RCF_NUM)))
*/
Z3_rcf_num Z3_API Z3_rcf_sub(__in Z3_context c, __in Z3_rcf_num a, __in Z3_rcf_num b);
/**
\brief Return the value a * b.
def_API('Z3_rcf_mul', RCF_NUM, (_in(CONTEXT), _in(RCF_NUM), _in(RCF_NUM)))
*/
Z3_rcf_num Z3_API Z3_rcf_mul(__in Z3_context c, __in Z3_rcf_num a, __in Z3_rcf_num b);
/**
\brief Return the value a / b.
def_API('Z3_rcf_div', RCF_NUM, (_in(CONTEXT), _in(RCF_NUM), _in(RCF_NUM)))
*/
Z3_rcf_num Z3_API Z3_rcf_div(__in Z3_context c, __in Z3_rcf_num a, __in Z3_rcf_num b);
/**
\brief Return the value -a
def_API('Z3_rcf_neg', RCF_NUM, (_in(CONTEXT), _in(RCF_NUM)))
*/
Z3_rcf_num Z3_API Z3_rcf_neg(__in Z3_context c, __in Z3_rcf_num a);
/**
\brief Return the value 1/a
def_API('Z3_rcf_inv', RCF_NUM, (_in(CONTEXT), _in(RCF_NUM)))
*/
Z3_rcf_num Z3_API Z3_rcf_inv(__in Z3_context c, __in Z3_rcf_num a);
/**
\brief Return the value a^k
def_API('Z3_rcf_power', RCF_NUM, (_in(CONTEXT), _in(RCF_NUM), _in(UINT)))
*/
Z3_rcf_num Z3_API Z3_rcf_power(__in Z3_context c, __in Z3_rcf_num a, __in unsigned k);
/**
\brief Return Z3_TRUE if a < b
def_API('Z3_rcf_lt', BOOL, (_in(CONTEXT), _in(RCF_NUM), _in(RCF_NUM)))
*/
Z3_bool Z3_API Z3_rcf_lt(__in Z3_context c, __in Z3_rcf_num a, __in Z3_rcf_num b);
/**
\brief Return Z3_TRUE if a > b
def_API('Z3_rcf_gt', BOOL, (_in(CONTEXT), _in(RCF_NUM), _in(RCF_NUM)))
*/
Z3_bool Z3_API Z3_rcf_gt(__in Z3_context c, __in Z3_rcf_num a, __in Z3_rcf_num b);
/**
\brief Return Z3_TRUE if a <= b
def_API('Z3_rcf_le', BOOL, (_in(CONTEXT), _in(RCF_NUM), _in(RCF_NUM)))
*/
Z3_bool Z3_API Z3_rcf_le(__in Z3_context c, __in Z3_rcf_num a, __in Z3_rcf_num b);
/**
\brief Return Z3_TRUE if a >= b
def_API('Z3_rcf_ge', BOOL, (_in(CONTEXT), _in(RCF_NUM), _in(RCF_NUM)))
*/
Z3_bool Z3_API Z3_rcf_ge(__in Z3_context c, __in Z3_rcf_num a, __in Z3_rcf_num b);
/**
\brief Return Z3_TRUE if a == b
def_API('Z3_rcf_eq', BOOL, (_in(CONTEXT), _in(RCF_NUM), _in(RCF_NUM)))
*/
Z3_bool Z3_API Z3_rcf_eq(__in Z3_context c, __in Z3_rcf_num a, __in Z3_rcf_num b);
/**
\brief Return Z3_TRUE if a != b
def_API('Z3_rcf_neq', BOOL, (_in(CONTEXT), _in(RCF_NUM), _in(RCF_NUM)))
*/
Z3_bool Z3_API Z3_rcf_neq(__in Z3_context c, __in Z3_rcf_num a, __in Z3_rcf_num b);
/**
\brief Convert the RCF numeral into a string.
def_API('Z3_rcf_num_to_string', STRING, (_in(CONTEXT), _in(RCF_NUM)))
*/
Z3_string Z3_API Z3_rcf_num_to_string(__in Z3_context c, __in Z3_rcf_num a);
/**
\brief Convert the RCF numeral into a string in decimal notation.
def_API('Z3_rcf_num_to_decimal_string', STRING, (_in(CONTEXT), _in(RCF_NUM), _in(UINT)))
*/
Z3_string Z3_API Z3_rcf_num_to_decimal_string(__in Z3_context c, __in Z3_rcf_num a, __in unsigned prec);
#ifdef __cplusplus
};
#endif // __cplusplus
#endif

33
src/math/interval/interval.h
View file

@ -105,10 +105,11 @@ struct interval_deps {
template<typename C>
class interval_manager {
public:
typedef typename C::numeral_manager numeral_manager;
typedef typename numeral_manager::numeral numeral;
typedef typename C::interval interval;
private:
C m_c;
numeral m_result_lower;
numeral m_result_upper;
@ -199,6 +200,11 @@ public:
bool eq(interval const & a, interval const & b) const;
/**
\brief Return true if all values in 'a' are less than all values in 'b'.
*/
bool before(interval const & a, interval const & b) const;
/**
\brief Set lower bound to -oo.
*/
@ -350,4 +356,29 @@ public:
void e(unsigned k, interval & r);
};
template<typename Manager>
class _scoped_interval {
public:
typedef typename Manager::interval interval;
private:
Manager & m_manager;
interval m_interval;
public:
_scoped_interval(Manager & m):m_manager(m) {}
~_scoped_interval() { m_manager.del(m_interval); }
Manager & m() const { return m_manager; }
operator interval const &() const { return m_interval; }
operator interval&() { return m_interval; }
interval const & get() const { return m_interval; }
interval & get() { return m_interval; }
interval * operator->() {
return &m_interval;
}
interval const * operator->() const {
return &m_interval;
}
};
#endif

7
src/math/interval/interval_def.h
View file

@ -687,6 +687,13 @@ bool interval_manager<C>::eq(interval const & a, interval const & b) const {
upper_is_open(a) == upper_is_open(b);
}
template<typename C>
bool interval_manager<C>::before(interval const & a, interval const & b) const {
if (upper_is_inf(a) || lower_is_inf(b))
return false;
return m().lt(upper(a), lower(b)) || (upper_is_open(a) && m().eq(upper(a), lower(b)));
}
template<typename C>
void interval_manager<C>::neg_jst(interval const & a, interval_deps & b_deps) {
if (lower_is_inf(a)) {

421
src/math/realclosure/mpz_matrix.cpp Normal file
View file

@ -0,0 +1,421 @@
/*++
Copyright (c) 2013 Microsoft Corporation
Module Name:
mpz_matrix.h
Abstract:
Matrix with integer coefficients. This is not a general purpose
module for handling matrices with integer coefficients. Instead,
it is a custom package that only contains operations needed to
implement Sign Determination (Algorithm 10.11) in the Book:
"Algorithms in real algebraic geometry", Basu, Pollack, Roy
Design choices:
- Dense representation. The matrices in Alg 10.11 are small and dense.
- Integer coefficients instead of rational coefficients (it only complicates the solver a little bit).
Remark: in Algorithm 10.11, the coefficients of the input matrices are always in {-1, 0, 1}.
During solving, bigger coefficients are produced, but they are usually very small. It may be
an overkill to use mpz instead of int. We use mpz just to be safe.
Remark: We do not use rational arithmetic. The solver is slightly more complicated with integers, but is saves space.
Author:
Leonardo (leonardo) 2013-01-07
Notes:
--*/
#include"mpz_matrix.h"
#include"buffer.h"
mpz_matrix_manager::mpz_matrix_manager(unsynch_mpz_manager & nm, small_object_allocator & a):
m_nm(nm),
m_allocator(a) {
}
mpz_matrix_manager::~mpz_matrix_manager() {
}
void mpz_matrix_manager::mk(unsigned m, unsigned n, mpz_matrix & A) {
SASSERT(m > 0 && n > 0);
del(A);
A.m = m;
A.n = n;
void * mem = m_allocator.allocate(sizeof(mpz)*m*n);
A.a_ij = new (mem) mpz[m*n];
}
void mpz_matrix_manager::del(mpz_matrix & A) {
if (A.a_ij != 0) {
for (unsigned i = 0; i < A.m; i++)
for (unsigned j = 0; j < A.n; j++)
nm().del(A(i,j));
unsigned sz = sizeof(mpz) * A.m * A.n;
m_allocator.deallocate(sz, A.a_ij);
A.m = 0;
A.n = 0;
A.a_ij = 0;
}
}
void mpz_matrix_manager::set(mpz_matrix & A, mpz_matrix const & B) {
if (&A == &B)
return;
if (A.m != B.m || A.n != B.n) {
del(A);
mk(B.m, B.n, A);
}
SASSERT(A.m == B.m && A.n == B.n);
for (unsigned i = 0; i < B.m; i++)
for (unsigned j = 0; j < B.n; j++)
nm().set(A(i, j), B(i, j));
}
void mpz_matrix_manager::tensor_product(mpz_matrix const & A, mpz_matrix const & B, mpz_matrix & C) {
scoped_mpz_matrix _C(*this);
mk(A.m * B.m, A.n * B.n, _C);
for (unsigned i = 0; i < _C.m(); i++)
for (unsigned j = 0; j < _C.n(); j++)
nm().mul(A(i / B.m, j / B.n),
B(i % B.m, j % B.n),
_C(i, j));
C.swap(_C);
}
void mpz_matrix_manager::swap_rows(mpz_matrix & A, unsigned i, unsigned j) {
if (i != j) {
for (unsigned k = 0; k < A.n; k++)
::swap(A(i, k), A(j, k));
}
}
// If b_i == 0, then method just divides the given row by its GCD
// If b_i != 0
// If the GCD of the row divides *b_i
// divide the row and *b_i by the GCD
// Else
// If int_solver == true ==> return false (the system is unsolvable)
bool mpz_matrix_manager::normalize_row(mpz * A_i, unsigned n, mpz * b_i, bool int_solver) {
scoped_mpz g(nm());
bool first = true;
for (unsigned j = 0; j < n; j++) {
if (nm().is_zero(A_i[j]))
continue;
if (first) {
nm().set(g, A_i[j]);
nm().abs(g);
first = false;
}
else {
nm().gcd(g, A_i[j], g);
}
if (nm().is_one(g))
return true;
}
if (first)
return true; // zero row
if (!nm().is_one(g)) {
if (b_i) {
if (nm().divides(g, *b_i)) {
for (unsigned j = 0; j < n; j++) {
nm().div(A_i[j], g, A_i[j]);
}
nm().div(*b_i, g, *b_i);
}
else {
if (int_solver)
return false; // system does not have an integer solution
}
}
else {
for (unsigned j = 0; j < n; j++) {
nm().div(A_i[j], g, A_i[j]);
}
}
}
return true;
}
/*
Given a matrix of the form
k2
|
V
X X ... X X ... X
0 X ... X X ... X
... ... X X ... X
k1=> 0 0 ... 0 X ... X
0 0 ... 0 X ... X
... ... 0 X ... X
0 0 ... 0 X ... X
It will "zero" the elements a_{k1+1, k2} ... a_{m, k2} by addining multiples of the row k1 to multiples of the
rows k1+1, ..., m
The resultant matrix will look like
k2
|
V
X X ... X X ... X
0 X ... X X ... X
... ... X X ... X
k1=> 0 0 ... 0 X ... X
0 0 ... 0 0 ... X
... ... 0 0 ... X
0 0 ... 0 0 ... X
If b != 0, then the transformations are also applied to b.
If int_solver == true and b != 0, then the method returns false if when
performing the transformations it detected that it is impossible to
solve the integer system of equations A x = b.
*/
bool mpz_matrix_manager::eliminate(mpz_matrix & A, mpz * b, unsigned k1, unsigned k2, bool int_solver) {
// check if first k2-1 positions of row k1 are 0
DEBUG_CODE(for (unsigned j = 0; j < k2; j++) { SASSERT(nm().is_zero(A(k1, j))); });
mpz & a_kk = A(k1, k2);
SASSERT(!nm().is_zero(a_kk));
scoped_mpz t1(nm()), t2(nm());
scoped_mpz a_ik_prime(nm()), a_kk_prime(nm()), lcm_a_kk_a_ik(nm());
// for all rows below pivot
for (unsigned i = k1+1; i < A.m; i++) {
// check if first k-1 positions of row k are 0
DEBUG_CODE(for (unsigned j = 0; j < k2; j++) { SASSERT(nm().is_zero(A(i, j))); });
mpz & a_ik = A(i, k2);
if (!nm().is_zero(a_ik)) {
// a_ik' = lcm(a_kk, a_ik)/a_kk
// a_kk' = lcm(a_kk, a_ik)/a_ik
nm().lcm(a_kk, a_ik, lcm_a_kk_a_ik);
nm().div(lcm_a_kk_a_ik, a_kk, a_ik_prime);
nm().div(lcm_a_kk_a_ik, a_ik, a_kk_prime);
for (unsigned j = k2+1; j < A.n; j++) {
// a_ij <- a_kk' * a_ij - a_ik' * a_kj
nm().mul(a_ik_prime, A(k1, j), t1);
nm().mul(a_kk_prime, A(i, j), t2);
nm().sub(t2, t1, A(i, j));
}
if (b) {
// b_i <- a_kk' * b_i - a_ik' * b_k
nm().mul(a_ik_prime, b[k1], t1);
nm().mul(a_kk_prime, b[i], t2);
nm().sub(t2, t1, b[i]);
}
// a_ik <- 0
nm().set(A(i, k2), 0);
// normalize row i
if (!normalize_row(A.row(i), A.n, b ? &(b[i]) : 0, int_solver))
return false;
}
SASSERT(nm().is_zero(A(i, k2)));
}
return true;
}
bool mpz_matrix_manager::solve_core(mpz_matrix const & _A, mpz * b, bool int_solver) {
SASSERT(_A.n == _A.m);
scoped_mpz_matrix A(*this);
set(A, _A);
for (unsigned k = 0; k < A.m(); k++) {
TRACE("mpz_matrix",
tout << "k: " << k << "\n" << A;
tout << "b:";
for (unsigned i = 0; i < A.m(); i++) {
tout << " ";
nm().display(tout, b[i]);
}
tout << "\n";);
// find pivot
unsigned i = k;
for (; i < A.m(); i++) {
if (!nm().is_zero(A(i, k)))
break;
}
if (i == A.m())
return false; // matrix is singular
// swap rows k and i
swap_rows(A, k, i);
swap(b[k], b[i]);
//
if (!eliminate(A, b, k, k, int_solver))
return false;
}
// Back substitution
unsigned k = A.m();
while (k > 0) {
--k;
DEBUG_CODE(for (unsigned j = 0; j < A.n(); j++) { SASSERT(j == k || nm().is_zero(A(k, j))); });
SASSERT(!nm().is_zero(A(k, k)));
if (nm().divides(A(k, k), b[k])) {
nm().div(b[k], A(k, k), b[k]);
nm().set(A(k, k), 1);
}
else {
if (int_solver)
return false; // no integer solution
if (nm().is_neg(A(k, k))) {
nm().neg(A(k, k));
nm().neg(b[k]);
}
}
if (!int_solver) {
// REMARK:
// For the sign determination algorithm, we only use int_solver == true.
//
// TODO: implement backward substitution when int_solver == false
// In this case, A(k, k) may not be 1.
NOT_IMPLEMENTED_YET();
}
SASSERT(!int_solver || nm().is_one(A(k, k)));
// back substitute
unsigned i = k;
while (i > 0) {
--i;
// Assuming int_solver == true
SASSERT(int_solver); // See comment above
// b_i <- b_i - a_ik * b_k
nm().submul(b[i], A(i, k), b[k], b[i]);
nm().set(A(i, k), 0);
}
}
return true;
}
bool mpz_matrix_manager::solve(mpz_matrix const & A, mpz * b, mpz const * c) {
for (unsigned i = 0; i < A.n; i++)
nm().set(b[i], c[i]);
return solve_core(A, b, true);
}
bool mpz_matrix_manager::solve(mpz_matrix const & A, int * b, int const * c) {
scoped_mpz_matrix _b(*this);
mk(A.n, 1, _b);
for (unsigned i = 0; i < A.n; i++)
nm().set(_b(i,0), c[i]);
bool r = solve_core(A, _b.A.a_ij, true);
if (r) {
for (unsigned i = 0; i < A.n; i++)
b[i] = _b.get_int(i, 0);
}
return r;
}
void mpz_matrix_manager::filter_cols(mpz_matrix const & A, unsigned num_cols, unsigned const * cols, mpz_matrix & B) {
SASSERT(num_cols <= A.n);
// Check pre-condition:
// - All elements in cols are smaller than A.n
// - cols is sorted
// - cols does not contain repeated elements
DEBUG_CODE({
for (unsigned i = 0; i < num_cols; i ++) {
SASSERT(cols[i] < A.n);
SASSERT(i == 0 || cols[i-1] < cols[i]);
}
});
if (num_cols == A.n) {
// keep everything
set(B, A);
}
else {
SASSERT(num_cols < A.n);
scoped_mpz_matrix C(*this);
mk(A.m, num_cols, C);
for (unsigned i = 0; i < A.m; i++)
for (unsigned j = 0; j < num_cols; j++)
nm().set(C(i, j), A(i, cols[j]));
B.swap(C);
}
}
void mpz_matrix_manager::permute_rows(mpz_matrix const & A, unsigned const * p, mpz_matrix & B) {
// Check if p is really a permutation
DEBUG_CODE({
buffer<bool> seen;
seen.resize(A.m, false);
for (unsigned i = 0; i < A.m; i++) {
SASSERT(p[i] < A.m);
SASSERT(!seen[p[i]]);
seen[p[i]] = true;
}
});
scoped_mpz_matrix C(*this);
mk(A.m, A.n, C);
for (unsigned i = 0; i < A.m; i++)
for (unsigned j = 0; j < A.n; j++)
nm().set(C(i, j), A(p[i], j));
B.swap(C);
}
unsigned mpz_matrix_manager::linear_independent_rows(mpz_matrix const & _A, unsigned * r, mpz_matrix & B) {
unsigned r_sz = 0;
scoped_mpz_matrix A(*this);
scoped_mpz g(nm());
scoped_mpz t1(nm()), t2(nm());
scoped_mpz a_ik_prime(nm()), a_kk_prime(nm()), lcm_a_kk_a_ik(nm());
set(A, _A);
sbuffer<unsigned, 128> rows;
rows.resize(A.m(), 0);
for (unsigned i = 0; i < A.m(); i++)
rows[i] = i;
for (unsigned k1 = 0, k2 = 0; k1 < A.m(); k1++) {
TRACE("mpz_matrix", tout << "k1: " << k1 << ", k2: " << k2 << "\n" << A;);
// find pivot
unsigned pivot = UINT_MAX;
for (unsigned i = k1; i < A.m(); i++) {
if (!nm().is_zero(A(i, k2))) {
if (pivot == UINT_MAX) {
pivot = i;
}
else {
if (rows[i] < rows[pivot])
pivot = i;
}
}
}
if (pivot == UINT_MAX)
continue;
// swap rows k and pivot
swap_rows(A, k1, pivot);
std::swap(rows[k1], rows[pivot]);
//
r[r_sz] = rows[k1];
r_sz++;
if (r_sz >= A.n())
break;
eliminate(A, 0, k1, k2, false);
k2++;
}
std::sort(r, r + r_sz);
// Copy linear independent rows to B
mpz_matrix & C = A;
mk(r_sz, _A.n, C);
for (unsigned i = 0; i < r_sz; i++ ) {
for (unsigned j = 0; j < _A.n; j++) {
nm().set(C(i, j), _A(r[i], j));
}
}
B.swap(C);
return r_sz;
}
void mpz_matrix_manager::display(std::ostream & out, mpz_matrix const & A, unsigned cell_width) const {
out << A.m << " x " << A.n << " Matrix\n";
for (unsigned i = 0; i < A.m; i++) {
for (unsigned j = 0; j < A.n; j++) {
if (j > 0)
out << " ";
std::string s = nm().to_string(A(i, j));
if (s.size() < cell_width) {
unsigned space = cell_width - static_cast<unsigned>(s.size());
for (unsigned k = 0; k < space; k++)
out << " ";
}
out << s;
}
out << "\n";
}
}

156
src/math/realclosure/mpz_matrix.h Normal file
View file

@ -0,0 +1,156 @@
/*++
Copyright (c) 2013 Microsoft Corporation
Module Name:
mpz_matrix.h
Abstract:
Matrix with integer coefficients. This is not a general purpose
module for handling matrices with integer coefficients. Instead,
it is a custom package that only contains operations needed to
implement Sign Determination (Algorithm 10.11) in the Book:
"Algorithms in real algebraic geometry", Basu, Pollack, Roy
Design choices:
- Dense representation. The matrices in Alg 10.11 are small and dense.
- Integer coefficients instead of rational coefficients (it only complicates the solver a little bit).
Remark: in Algorithm 10.11, the coefficients of the input matrices are always in {-1, 0, 1}.
During solving, bigger coefficients are produced, but they are usually very small. It may be
an overkill to use mpz instead of int. We use mpz just to be safe.
Remark: We do not use rational arithmetic. The solver is slightly more complicated with integers, but is saves space.
Author:
Leonardo (leonardo) 2013-01-07
Notes:
--*/
#ifndef _MPZ_MATRIX_H_
#define _MPZ_MATRIX_H_
#include"mpz.h"
/**
\brief A mxn matrix.
Remark: Algorithm 10.11 only uses square matrices, but supporting
arbitrary matrices does not increase the complexity of this module.
*/
class mpz_matrix {
friend class mpz_matrix_manager;
friend class scoped_mpz_matrix;
unsigned m;
unsigned n;
mpz * a_ij;
public:
mpz_matrix():m(0), n(0), a_ij(0) {}
mpz const & operator()(unsigned i, unsigned j) const {
SASSERT(i < m);
SASSERT(j < n);
return a_ij[i*n + j]; }
mpz & operator()(unsigned i, unsigned j) { SASSERT(i < m); SASSERT(j < n); return a_ij[i*n + j]; }
void swap(mpz_matrix & B) { std::swap(m, B.m); std::swap(n, B.n); std::swap(a_ij, B.a_ij); }
mpz * row(unsigned i) const { SASSERT(i < m); return a_ij + i*n; }
};
class mpz_matrix_manager {
unsynch_mpz_manager & m_nm;
small_object_allocator & m_allocator;
static void swap_rows(mpz_matrix & A, unsigned i, unsigned j);
bool normalize_row(mpz * A_i, unsigned n, mpz * b_i, bool int_solver);
bool eliminate(mpz_matrix & A, mpz * b, unsigned k1, unsigned k2, bool int_solver);
bool solve_core(mpz_matrix const & A, mpz * b, bool int_solver);
public:
mpz_matrix_manager(unsynch_mpz_manager & nm, small_object_allocator & a);
~mpz_matrix_manager();
unsynch_mpz_manager & nm() const { return m_nm; }
void mk(unsigned m, unsigned n, mpz_matrix & A);
void del(mpz_matrix & r);
void set(mpz_matrix & A, mpz_matrix const & B);
void tensor_product(mpz_matrix const & A, mpz_matrix const & B, mpz_matrix & C);
/**
\brief Solve A*b = c
Return false if the system does not have an integer solution.
\pre A is a square matrix
\pre b and c are vectors of size A.n (== A.m)
*/
bool solve(mpz_matrix const & A, mpz * b, mpz const * c);
/**
\brief Solve A*b = c
Return false if the system does not have an integer solution.
\pre A is a square matrix
\pre b and c are vectors of size A.n (== A.m)
*/
bool solve(mpz_matrix const & A, int * b, int const * c);
/**
\brief Store in B that contains the subset cols of columns of A.
\pre num_cols <= A.n
\pre Forall i < num_cols, cols[i] < A.n
\pre Forall 0 < i < num_cols, cols[i-1] < cols[i]
*/
void filter_cols(mpz_matrix const & A, unsigned num_cols, unsigned const * cols, mpz_matrix & B);
/**
\brief Store in B the matrix obtained after applying the given permutation to the rows of A.
*/
void permute_rows(mpz_matrix const & A, unsigned const * p, mpz_matrix & B);
/**
\brief Store in r the row (ids) of A that are linear independent.
\remark If there is an option between rows i and j,
this method will give preference to the row that occurs first.
\remark The vector r must have at least A.n() capacity
The numer of linear independent rows is returned.
Store the new matrix in B.
*/
unsigned linear_independent_rows(mpz_matrix const & A, unsigned * r, mpz_matrix & B);
// method for debugging purposes
void display(std::ostream & out, mpz_matrix const & A, unsigned cell_width=4) const;
};
class scoped_mpz_matrix {
friend class mpz_matrix_manager;
mpz_matrix_manager & m_manager;
mpz_matrix A;
public:
scoped_mpz_matrix(mpz_matrix_manager & m):m_manager(m) {}
scoped_mpz_matrix(mpz_matrix const & B, mpz_matrix_manager & m):m_manager(m) { m_manager.set(A, B); }
~scoped_mpz_matrix() { m_manager.del(A); }
mpz_matrix_manager & mm() const { return m_manager; }
unsynch_mpz_manager & nm() const { return mm().nm(); }
unsigned m() const { return A.m; }
unsigned n() const { return A.n; }
mpz * row(unsigned i) const { return A.row(i); }
operator mpz_matrix const &() const { return A; }
operator mpz_matrix &() { return A; }
mpz_matrix const & get() const { return A; }
mpz_matrix & get() { return A; }
void swap(mpz_matrix & B) { A.swap(B); }
void set(unsigned i, unsigned j, mpz const & v) { nm().set(A(i, j), v); }
void set(unsigned i, unsigned j, int v) { nm().set(A(i, j), v); }
mpz const & operator()(unsigned i, unsigned j) const { return A(i, j); }
mpz & operator()(unsigned i, unsigned j) { return A(i, j); }
int get_int(unsigned i, unsigned j) const { SASSERT(nm().is_int(A(i, j))); return nm().get_int(A(i, j)); }
};
inline std::ostream & operator<<(std::ostream & out, scoped_mpz_matrix const & m) {
m.mm().display(out, m);
return out;
}
#endif

8
src/math/realclosure/rcf.pyg Normal file
View file

@ -0,0 +1,8 @@
def_module_params('rcf',
description='real closed fields',
export=True,
params=(('use_prem', BOOL, True, "use pseudo-remainder instead of remainder when computing GCDs and Sturm-Tarski sequences"),
('clean_denominators', BOOL, True, "clean denominators before root isolation"),
('initial_precision', UINT, 24, "a value k that is the initial interval size (as 1/2^k) when creating transcendentals and approximated division"),
('inf_precision', UINT, 24, "a value k that is the initial interval size (i.e., (0, 1/2^l)) used as an approximation for infinitesimal values"),
('max_precision', UINT, 64, "during sign determination we switch from interval arithmetic to complete methods when the interval size is less than 1/2^k, where k is the max_precision")))

5937
src/math/realclosure/realclosure.cpp Normal file
View file

File diff suppressed because it is too large Load diff

406
src/math/realclosure/realclosure.h Normal file
View file

@ -0,0 +1,406 @@
/*++
Copyright (c) 2013 Microsoft Corporation
Module Name:
realclosure.h
Abstract:
Package for computing with elements of the realclosure of a field containing
- all rationals
- extended with computable transcendental real numbers (e.g., pi and e)
- infinitesimals
Author:
Leonardo (leonardo) 2013-01-02
Notes:
--*/
#ifndef _REALCLOSURE_H_
#define _REALCLOSURE_H_
#include"mpq.h"
#include"params.h"
#include"scoped_numeral.h"
#include"scoped_numeral_vector.h"
#include"interval.h"
#include"z3_exception.h"
namespace realclosure {
class num;
typedef interval_manager<im_default_config> mpqi_manager;
typedef default_exception exception;
class mk_interval {
public:
virtual void operator()(unsigned k, mpqi_manager & im, mpqi_manager::interval & r) = 0;
};
class manager {
public:
struct imp;
private:
friend class save_interval_ctx;
imp * m_imp;
public:
manager(unsynch_mpq_manager & m, params_ref const & p = params_ref(), small_object_allocator * a = 0);
~manager();
typedef num numeral;
typedef svector<numeral> numeral_vector;
typedef _scoped_numeral<manager> scoped_numeral;
typedef _scoped_numeral_vector<manager> scoped_numeral_vector;
static void get_param_descrs(param_descrs & r);
static void collect_param_descrs(param_descrs & r) { get_param_descrs(r); }
void set_cancel(bool f);
void cancel() { set_cancel(true); }
void reset_cancel() { set_cancel(false); }
void updt_params(params_ref const & p);
unsynch_mpq_manager & qm() const;
void del(numeral & a);
/**
\brief Add a new infinitesimal to the current field. The new infinitesimal is smaller than any positive element in the field.
*/
void mk_infinitesimal(char const * name, numeral & r);
void mk_infinitesimal(numeral & r);
/**
\brief Add a new transcendental real value to the field.
The functor \c mk_interval is used to compute approximations of the transcendental value.
This procedure should be used with care, if the value is not really transcendental with respect to the current
field, computations with the new numeral may not terminate.
Example: we extended the field with Pi. Pi is transcendental with respect to a field that contains only algebraic real numbers.
So, this step is fine. Let us call the resultant field F.
Then, we extend the field F with 1 - Pi. 1 - Pi is transcendental with respect to algebraic real numbers, but it is NOT transcendental
with respect to F, since F contains Pi.
*/
void mk_transcendental(char const * name, mk_interval & proc, numeral & r);
void mk_transcendental(mk_interval & proc, numeral & r);
/**
\brief r <- pi
*/
void mk_pi(numeral & r);
/**
\brief r <- e (Euler's constant)
*/
void mk_e(numeral & r);
/**
\brief Isolate the roots of the univariate polynomial as[0] + as[1]*x + ... + as[n-1]*x^{n-1}
The roots are stored in \c roots.
*/
void isolate_roots(unsigned n, numeral const * as, numeral_vector & roots);
/**
\brief a <- 0
*/
void reset(numeral & a);
/**
\brief Return the sign of a.
*/
int sign(numeral const & a);
/**
\brief Return true if a is zero.
*/
bool is_zero(numeral const & a);
/**
\brief Return true if a is positive.
*/
bool is_pos(numeral const & a);
/**
\brief Return true if a is negative.
*/
bool is_neg(numeral const & a);
/**
\brief Return true if a is an integer.
*/
bool is_int(numeral const & a);
/**
\brief Return true if the representation of \c a depends on
infinitesimal extensions.
*/
bool depends_on_infinitesimals(numeral const & a);
/**
\brief a <- n
*/
void set(numeral & a, int n);
void set(numeral & a, mpz const & n);
void set(numeral & a, mpq const & n);
void set(numeral & a, numeral const & n);
void swap(numeral & a, numeral & b);
/**
\brief Return a^{1/k}
Throws an exception if (a is negative and k is even) or (k is zero).
*/
void root(numeral const & a, unsigned k, numeral & b);
/**
\brief Return a^k
Throws an exception if 0^0.
*/
void power(numeral const & a, unsigned k, numeral & b);
/**
\brief c <- a + b
*/
void add(numeral const & a, numeral const & b, numeral & c);
void add(numeral const & a, mpz const & b, numeral & c);
/**
\brief c <- a - b
*/
void sub(numeral const & a, numeral const & b, numeral & c);
/**
\brief c <- a * b
*/
void mul(numeral const & a, numeral const & b, numeral & c);
/**
\brief a <- -a
*/
void neg(numeral & a);
/**
\brief b <- -a
*/
void neg(numeral const & a, numeral & b);
/**
\brief a <- 1/a if a != 0
*/
void inv(numeral & a);
/**
\brief b <- 1/a if a != 0
*/
void inv(numeral const & a, numeral & b);
/**
\brief c <- a/b if b != 0
*/
void div(numeral const & a, numeral const & b, numeral & c);
/**
Return -1 if a < b
Return 0 if a == b
Return 1 if a > b
*/
int compare(numeral const & a, numeral const & b);
/**
\brief a == b
*/
bool eq(numeral const & a, numeral const & b);
bool eq(numeral const & a, mpq const & b);
bool eq(numeral const & a, mpz const & b);
/**
\brief a != b
*/
bool neq(numeral const & a, numeral const & b) { return !eq(a, b); }
bool neq(numeral const & a, mpq const & b) { return !eq(a, b); }
bool neq(numeral const & a, mpz const & b) { return !eq(a, b); }
/**
\brief a < b
*/
bool lt(numeral const & a, numeral const & b);
bool lt(numeral const & a, mpq const & b);
bool lt(numeral const & a, mpz const & b);
/**
\brief a > b
*/
bool gt(numeral const & a, numeral const & b) { return lt(b, a); }
bool gt(numeral const & a, mpq const & b);
bool gt(numeral const & a, mpz const & b);
/**
\brief a <= b
*/
bool le(numeral const & a, numeral const & b) { return !gt(a, b); }
bool le(numeral const & a, mpq const & b) { return !gt(a, b); }
bool le(numeral const & a, mpz const & b) { return !gt(a, b); }
/**
\brief a >= b
*/
bool ge(numeral const & a, numeral const & b) { return !lt(a, b); }
bool ge(numeral const & a, mpq const & b) { return !lt(a, b); }
bool ge(numeral const & a, mpz const & b) { return !lt(a, b); }
void display(std::ostream & out, numeral const & a) const;
/**
\brief Display a real number in decimal notation.
A question mark is added based on the precision requested.
This procedure throws an exception if the \c a is not a real.
*/
void display_decimal(std::ostream & out, numeral const & a, unsigned precision = 10) const;
void display_interval(std::ostream & out, numeral const & a) const;
void clean_denominators(numeral const & a, numeral & p, numeral & q);
};
struct value;
class num {
friend class manager;
friend struct manager::imp;
value * m_value;
public:
num():m_value(0) {}
// Low level functions for implementing the C API
void * c_ptr() { return m_value; }
static num mk(void * ptr) { num r; r.m_value = reinterpret_cast<value*>(ptr); return r; }
};
};
typedef realclosure::manager rcmanager;
typedef rcmanager::numeral rcnumeral;
typedef rcmanager::numeral_vector rcnumeral_vector;
typedef rcmanager::scoped_numeral scoped_rcnumeral;
typedef rcmanager::scoped_numeral_vector scoped_rcnumeral_vector;
#define RCF_MK_COMPARISON_CORE(EXTERNAL, INTERNAL, TYPE) \
inline bool EXTERNAL(scoped_rcnumeral const & a, TYPE const & b) { \
rcmanager & m = a.m(); \
scoped_rcnumeral _b(m); \
m.set(_b, b); \
return m.INTERNAL(a, _b); \
}
#define RCF_MK_COMPARISON(EXTERNAL, INTERNAL) \
RCF_MK_COMPARISON_CORE(EXTERNAL, INTERNAL, int) \
RCF_MK_COMPARISON_CORE(EXTERNAL, INTERNAL, mpz) \
RCF_MK_COMPARISON_CORE(EXTERNAL, INTERNAL, mpq)
RCF_MK_COMPARISON(operator==, eq);
RCF_MK_COMPARISON(operator!=, neq);
RCF_MK_COMPARISON(operator<, lt);
RCF_MK_COMPARISON(operator<=, le);
RCF_MK_COMPARISON(operator>, gt);
RCF_MK_COMPARISON(operator>=, ge);
#undef RCF_MK_COMPARISON
#undef RCF_MK_COMPARISON_CORE
#define RCF_MK_BINARY_CORE(EXTERNAL, INTERNAL, TYPE) \
inline scoped_rcnumeral EXTERNAL(scoped_rcnumeral const & a, TYPE const & b) { \
rcmanager & m = a.m(); \
scoped_rcnumeral _b(m); \
m.set(_b, b); \
scoped_rcnumeral r(m); \
m.INTERNAL(a, _b, r); \
return r; \
}
#define RCF_MK_BINARY(EXTERNAL, INTERNAL) \
RCF_MK_BINARY_CORE(EXTERNAL, INTERNAL, int) \
RCF_MK_BINARY_CORE(EXTERNAL, INTERNAL, mpz) \
RCF_MK_BINARY_CORE(EXTERNAL, INTERNAL, mpq)
RCF_MK_BINARY(operator+, add)
RCF_MK_BINARY(operator-, sub)
RCF_MK_BINARY(operator*, mul)
RCF_MK_BINARY(operator/, div)
#undef RCF_MK_BINARY
#undef RCF_MK_BINARY_CORE
inline scoped_rcnumeral root(scoped_rcnumeral const & a, unsigned k) {
scoped_rcnumeral r(a.m());
a.m().root(a, k, r);
return r;
}
inline scoped_rcnumeral power(scoped_rcnumeral const & a, unsigned k) {
scoped_rcnumeral r(a.m());
a.m().power(a, k, r);
return r;
}
inline scoped_rcnumeral operator^(scoped_rcnumeral const & a, unsigned k) {
return power(a, k);
}
inline bool is_int(scoped_rcnumeral const & a) {
return a.m().is_int(a);
}
struct rc_sym_pp {
rcmanager & m;
rcnumeral const & n;
rc_sym_pp(rcmanager & _m, rcnumeral const & _n):m(_m), n(_n) {}
rc_sym_pp(scoped_rcnumeral const & _n):m(_n.m()), n(_n.get()) {}
};
inline rc_sym_pp sym_pp(scoped_rcnumeral const & _n) {
return rc_sym_pp(_n);
}
inline std::ostream & operator<<(std::ostream & out, rc_sym_pp const & n) {
n.m.display(out, n.n);
return out;
}
struct rc_decimal_pp {
rcmanager & m;
rcnumeral const & n;
unsigned prec;
rc_decimal_pp(rcmanager & _m, rcnumeral const & _n, unsigned p):m(_m), n(_n), prec(p) {}
rc_decimal_pp(scoped_rcnumeral const & _n, unsigned p):m(_n.m()), n(_n.get()), prec(p) {}
};
inline std::ostream & operator<<(std::ostream & out, rc_decimal_pp const & n) {
n.m.display_decimal(out, n.n, n.prec);
return out;
}
inline rc_decimal_pp decimal_pp(scoped_rcnumeral const & n, unsigned prec = 10) {
return rc_decimal_pp(n, prec);
}
struct rc_interval_pp {
rcmanager & m;
rcnumeral const & n;
rc_interval_pp(rcmanager & _m, rcnumeral const & _n):m(_m), n(_n) {}
rc_interval_pp(scoped_rcnumeral const & _n):m(_n.m()), n(_n.get()) {}
};
inline std::ostream & operator<<(std::ostream & out, rc_interval_pp const & n) {
n.m.display_interval(out, n.n);
return out;
}
inline rc_interval_pp interval_pp(scoped_rcnumeral const & n) {
return rc_interval_pp(n);
}
#endif

2
src/muz_qe/dl_bmc_engine.cpp
View file

@ -459,7 +459,7 @@ namespace datalog {
void setup() {
b.m_fparams.m_model = true;
b.m_fparams.m_model_compact = true;
b.m_fparams.m_mbqi = true;
// b.m_fparams.m_mbqi = true;
b.m_fparams.m_relevancy_lvl = 2;
}

370
src/muz_qe/dl_mk_extract_quantifiers.cpp
View file

@ -19,6 +19,12 @@ Revision History:
#include"dl_mk_extract_quantifiers.h"
#include"ast_pp.h"
#include"dl_bmc_engine.h"
#include"smt_quantifier.h"
#include"smt_context.h"
#include"for_each_expr.h"
#include "expr_abstract.h"
namespace datalog {
@ -27,24 +33,16 @@ namespace datalog {
rule_transformer::plugin(101, false),
m_ctx(ctx),
m(ctx.get_manager()),
rm(ctx.get_rule_manager())
rm(ctx.get_rule_manager()),
m_query_pred(m)
{}
mk_extract_quantifiers::~mk_extract_quantifiers() {
for (unsigned i = 0; i < m_refs.size(); ++i) {
dealloc(m_refs[i]);
}
m_quantifiers.reset();
m_refs.reset();
reset();
}
app_ref mk_extract_quantifiers::ensure_app(expr* e) {
if (is_app(e)) {
return app_ref(to_app(e), m);
}
else {
return app_ref(m.mk_eq(e, m.mk_true()), m);
}
void mk_extract_quantifiers::set_query(func_decl* q) {
m_query_pred = q;
}
void mk_extract_quantifiers::ensure_predicate(expr* e, unsigned& max_var, app_ref_vector& tail) {
@ -67,85 +65,305 @@ namespace datalog {
tail.push_back(m.mk_app(a->get_decl(), args.size(), args.c_ptr()));
}
class mk_extract_quantifiers::collect_insts {
ast_manager& m;
ptr_vector<expr> m_binding;
vector<expr_ref_vector> m_bindings;
ptr_vector<quantifier> m_quantifiers;
public:
collect_insts(ast_manager& m): m(m) { }
void operator()(expr* n) {
expr* not_q_or_i, *e1, *e2, *e3;
if (m.is_quant_inst(n, not_q_or_i, m_binding)) {
VERIFY(m.is_or(not_q_or_i, e1, e2));
VERIFY(m.is_not(e1, e3));
SASSERT(is_quantifier(e3));
m_quantifiers.push_back(to_quantifier(e3));
m_bindings.push_back(expr_ref_vector(m,m_binding.size(), m_binding.c_ptr()));
m_binding.reset();
}
else if ((m.is_rewrite(n, e1, e2) ||
(m.is_rewrite_star(n) &&
(e3 = to_app(n)->get_arg(to_app(n)->get_num_args()-1),
e1 = to_app(e3)->get_arg(0),
e2 = to_app(e3)->get_arg(1),
true))) &&
is_quantifier(e1) && m.is_false(e2)) {
quantifier* q = to_quantifier(e1);
m_quantifiers.push_back(q);
m_bindings.push_back(expr_ref_vector(m));
expr_ref_vector& b = m_bindings.back();
for (unsigned i = 0; i < q->get_num_decls(); ++i) {
b.push_back(m.mk_fresh_const("V", q->get_decl_sort(i)));
}
}
}
void reset() {
m_quantifiers.reset();
m_bindings.reset();
}
unsigned size() const { return m_quantifiers.size(); }
ptr_vector<quantifier> const& quantifiers() const { return m_quantifiers; }
vector<expr_ref_vector> const& bindings() const { return m_bindings; }
};
/*
* forall y . P1(x,y) &
* forall y . P2(x,y) &
* Body[x] &
* ~H[x]
* forall y . y != binding1 => ~ P1(x,y)
* forall y . y != binding2 => ~ P2(x,y)
*/
void mk_extract_quantifiers::extract(rule& r, rule_set& new_rules) {
app_ref_vector tail(m);
quantifier_ref_vector quantifiers(m);
unsigned utsz = r.get_uninterpreted_tail_size();
unsigned tsz = r.get_tail_size();
var_counter vc(true);
unsigned max_var = vc.get_max_var(r);
for (unsigned i = 0; i < utsz; ++i) {
tail.push_back(r.get_tail(i));
if (r.is_neg_tail(i)) {
new_rules.add_rule(&r);
return;
expr_ref_vector conjs(m);
quantifier_ref_vector qs(m);
for (unsigned i = utsz; i < r.get_tail_size(); ++i) {
conjs.push_back(r.get_tail(i));
}
datalog::flatten_and(conjs);
for (unsigned j = 0; j < conjs.size(); ++j) {
expr* e = conjs[j].get();
quantifier* q;
if (rule_manager::is_forall(m, e, q)) {
qs.push_back(q);
conjs[j] = conjs.back();
conjs.pop_back();
--j;
}
}
var_subst vs(m, true);
for (unsigned i = utsz; i < tsz; ++i) {
app* t = r.get_tail(i);
expr_ref_vector conjs(m);
datalog::flatten_and(t, conjs);
expr_ref qe(m);
quantifier* q = 0;
for (unsigned j = 0; j < conjs.size(); ++j) {
expr* e = conjs[j].get();
if (rule_manager::is_forall(m, e, q)) {
quantifiers.push_back(q);
expr_ref_vector sub(m);
ptr_vector<sort> fv;
unsigned num_decls = q->get_num_decls();
get_free_vars(q, fv);
for (unsigned k = 0; k < fv.size(); ++k) {
unsigned idx = fv.size()-k-1;
if (!fv[idx]) {
fv[idx] = m.mk_bool_sort();
}
sub.push_back(m.mk_var(idx, fv[idx]));
}
for (unsigned k = 0; k < num_decls; ++k) {
sub.push_back(m.mk_var(num_decls+max_var-k, q->get_decl_sort(k)));
}
max_var += num_decls;
vs(q->get_expr(), sub.size(), sub.c_ptr(), qe);
ensure_predicate(qe, max_var, tail);
}
else {
tail.push_back(ensure_app(e));
}
}
}
if (quantifiers.empty()) {
if (qs.empty()) {
new_rules.add_rule(&r);
}
else {
rule_ref new_rule(rm);
TRACE("dl",
tout << mk_pp(r.get_head(), m) << " :- \n";
for (unsigned i = 0; i < tail.size(); ++i) {
tout << " " << mk_pp(tail[i].get(), m) << "\n";
});
new_rule = rm.mk(r.get_head(), tail.size(), tail.c_ptr(), 0, r.name(), false);
quantifier_ref_vector* qs = alloc(quantifier_ref_vector, quantifiers);
m_refs.push_back(qs);
new_rules.add_rule(new_rule);
m_quantifiers.insert(new_rule, qs);
expr_ref fml(m);
expr_ref_vector bindings(m);
obj_map<quantifier, expr_ref_vector*> insts;
for (unsigned i = 0; i < qs.size(); ++i) {
insts.insert(qs[i].get(), alloc(expr_ref_vector, m));
}
unsigned max_inst = 10; // TODO configuration.
for (unsigned i = 0; i < max_inst; ++i) {
app_ref_vector sub(m);
rule2formula(r, insts, fml, sub);
bool new_binding = find_instantiations_proof_based(fml, sub, insts, bindings);
if (!new_binding) {
break;
}
}
expr_ref_vector fmls(m);
for (unsigned i = 0; i < utsz; ++i) {
fmls.push_back(r.get_tail(i));
}
fmls.append(bindings);
fmls.append(conjs);
fml = m.mk_implies(m.mk_and(fmls.size(), fmls.c_ptr()), r.get_head());
TRACE("dl", tout << "new rule\n" << mk_pp(fml, m) << "\n";);
rule_ref_vector rules(rm);
rm.mk_rule(fml, rules, r.name());
for (unsigned i = 0; i < rules.size(); ++i) {
new_rules.add_rule(rules[i].get());
m_quantifiers.insert(rules[i].get(), alloc(quantifier_ref_vector, qs));
}
obj_map<quantifier, expr_ref_vector*>::iterator it = insts.begin(), end = insts.end();
for (; it != end; ++it) {
dealloc(it->m_value);
}
}
}
void mk_extract_quantifiers::rule2formula(
rule& r,
obj_map<quantifier, expr_ref_vector*> const& insts,
expr_ref& fml,
app_ref_vector& sub)
{
expr_ref body(m);
expr_ref_vector fmls(m);
ptr_vector<sort> sorts;
var_subst vs(m, false);
obj_map<quantifier, expr_ref_vector*>::iterator it = insts.begin(), end = insts.end();
for (; it != end; ++it) {
quantifier* q = it->m_key;
expr_ref_vector& eqs = *it->m_value;
expr_ref_vector disj(m);
disj.append(eqs);
disj.push_back(m.mk_not(q->get_expr()));
body = m.mk_or(disj.size(), disj.c_ptr());
fml = m.update_quantifier(q, body);
fmls.push_back(fml);
}
fml = m.mk_or(fmls.size(), fmls.c_ptr());
fmls.reset();
fmls.push_back(fml);
for (unsigned i = 0; i < r.get_tail_size(); ++i) {
SASSERT(!r.is_neg_tail(i));
fmls.push_back(r.get_tail(i));
}
fmls.push_back(m.mk_not(r.get_head()));
fml = m.mk_and(fmls.size(), fmls.c_ptr());
get_free_vars(fml, sorts);
for (unsigned i = 0; i < sorts.size(); ++i) {
if (!sorts[i]) {
sorts[i] = m.mk_bool_sort();
}
sub.push_back(m.mk_const(symbol(i), sorts[i]));
}
vs(fml, sub.size(), (expr*const*)sub.c_ptr(), fml);
}
bool mk_extract_quantifiers::find_instantiations_proof_based(
expr* fml,
app_ref_vector const& var_inst,
obj_map<quantifier, expr_ref_vector*>& insts,
expr_ref_vector& bindings)
{
datalog::scoped_fine_proof _scp(m);
smt_params fparams;
fparams.m_mbqi = true; // false
fparams.m_soft_timeout = 1000;
smt::kernel solver(m, fparams);
solver.assert_expr(fml);
IF_VERBOSE(1, verbose_stream() << "check\n";);
lbool result = solver.check();
IF_VERBOSE(1, verbose_stream() << "checked\n";);
TRACE("dl", tout << result << "\n";);
if (result != l_false) {
return false;
}
map<symbol, quantifier*, symbol_hash_proc, symbol_eq_proc> qid_map;
quantifier* q;
obj_map<quantifier, expr_ref_vector*>::iterator it = insts.begin(), end = insts.end();
for (; it != end; ++it) {
q = it->m_key;
qid_map.insert(q->get_qid(), q);
}
proof* p = solver.get_proof();
TRACE("dl", tout << mk_pp(p, m) << "\n";);
collect_insts collector(m);
for_each_expr(collector, p);
ptr_vector<quantifier> const& quants = collector.quantifiers();
for (unsigned i = 0; i < collector.size(); ++i) {
symbol qid = quants[i]->get_qid();
if (!qid_map.find(qid, q)) {
TRACE("dl", tout << "Could not find quantifier " << mk_pp(quants[i], m) << "\n";);
continue;
}
expr_ref_vector const& binding = collector.bindings()[i];
TRACE("dl", tout << "Instantiating:\n" << mk_pp(quants[i], m) << "\n";
for (unsigned j = 0; j < binding.size(); ++j) {
tout << mk_pp(binding[j], m) << " ";
}
tout << "\n";);
expr_ref_vector instantiation(m);
for (unsigned j = 0; j < binding.size(); ++j) {
instantiation.push_back(binding[j]);
}
add_binding(var_inst, bindings, q, instantiation, insts);
}
return collector.size() > 0;
}
void mk_extract_quantifiers::add_binding(
app_ref_vector const& var_inst,
expr_ref_vector& bindings,
quantifier* q,
expr_ref_vector const& instantiation,
obj_map<quantifier, expr_ref_vector*>& insts)
{
if (instantiation.size() == q->get_num_decls()) {
// Full binding.
apply_binding(var_inst, bindings, q, instantiation, insts);
}
}
void mk_extract_quantifiers::apply_binding(
app_ref_vector const& var_inst,
expr_ref_vector& bindings,
quantifier* q,
expr_ref_vector const& instantiation,
obj_map<quantifier, expr_ref_vector*>& insts)
{
datalog::scoped_no_proof _scp(m);
expr_ref e(m);
expr_ref_vector eqs(m);
var_subst vs(m, false);
inv_var_shifter invsh(m);
vs(q->get_expr(), instantiation.size(), instantiation.c_ptr(), e);
invsh(e, q->get_num_decls(), e);
expr_ref_vector inst(m);
inst.append(var_inst.size(), (expr*const*)var_inst.c_ptr());
inst.reverse();
expr_abstract(m, 0, inst.size(), inst.c_ptr(), e, e);
bindings.push_back(e);
for (unsigned i = 0; i < instantiation.size(); ++i) {
e = instantiation[i];
e = m.mk_eq(m.mk_var(i, q->get_decl_sort(i)), e);
eqs.push_back(e);
}
e = m.mk_and(eqs.size(), eqs.c_ptr());
insts.find(q)->push_back(e);
TRACE("dl", tout << mk_pp(q, m) << "\n";
tout << "instantiation: ";
for (unsigned i = 0; i < instantiation.size(); ++i) {
tout << mk_pp(instantiation[i], m) << " ";
}
tout << "\n";
tout << "inst: ";
for (unsigned i = 0; i < var_inst.size(); ++i) {
tout << mk_pp(var_inst[i], m) << " ";
}
tout << "\n";
tout << mk_pp(bindings.back(), m) << "\n";
tout << "eqs: " << mk_pp(e, m) << "\n";
);
}
void mk_extract_quantifiers::reset() {
obj_map<rule const, quantifier_ref_vector*>::iterator it = m_quantifiers.begin(),
end = m_quantifiers.end();
for (; it != end; ++it) {
dealloc(it->m_value);
}
m_has_quantifiers = false;
m_quantifiers.reset();
}
rule_set * mk_extract_quantifiers::operator()(rule_set const & source, model_converter_ref& mc, proof_converter_ref& pc) {
m_quantifiers.reset();
rule_set* rules = alloc(rule_set, m_ctx);
reset();
rule_set::iterator it = source.begin(), end = source.end();
for (; !m_has_quantifiers && it != end; ++it) {
m_has_quantifiers = (*it)->has_quantifiers();
}
if (!m_has_quantifiers) {
return 0;
}
rule_set* rules = alloc(rule_set, m_ctx);
it = source.begin();
for (; it != end; ++it) {
extract(**it, *rules);
}
if (m_quantifiers.empty()) {
dealloc(rules);
rules = 0;
}
return rules;
return rules;
}
};

52
src/muz_qe/dl_mk_extract_quantifiers.h
View file

@ -7,7 +7,8 @@ Module Name:
Abstract:
Remove universal quantifiers over interpreted predicates in the body.
Replace universal quantifiers over interpreted predicates in the body
by instantiations mined using bounded model checking search.
Author:
@ -22,6 +23,7 @@ Revision History:
#include"dl_context.h"
#include"dl_rule_set.h"
#include"dl_rule_transformer.h"
#include"obj_pair_hashtable.h"
namespace datalog {
@ -29,15 +31,41 @@ namespace datalog {
\brief Extract universal quantifiers from rules.
*/
class mk_extract_quantifiers : public rule_transformer::plugin {
context& m_ctx;
ast_manager& m;
rule_manager& rm;
ptr_vector<quantifier_ref_vector> m_refs;
class collect_insts;
context& m_ctx;
ast_manager& m;
rule_manager& rm;
func_decl_ref m_query_pred;
bool m_has_quantifiers;
obj_map<rule const, quantifier_ref_vector*> m_quantifiers;
void reset();
void extract(rule& r, rule_set& new_rules);
app_ref ensure_app(expr* e);
void rule2formula(
rule& r,
obj_map<quantifier, expr_ref_vector*> const& insts,
expr_ref& fml,
app_ref_vector& sub);
void add_binding(
app_ref_vector const& var_inst,
expr_ref_vector& bindings,
quantifier* q,
expr_ref_vector const& instantiation,
obj_map<quantifier, expr_ref_vector*>& insts);
void apply_binding(
app_ref_vector const& var_inst,
expr_ref_vector& bindings,
quantifier* q,
expr_ref_vector const& instantiation,
obj_map<quantifier, expr_ref_vector*>& insts);
public:
/**
@ -46,15 +74,23 @@ namespace datalog {
mk_extract_quantifiers(context & ctx);
virtual ~mk_extract_quantifiers();
void set_query(func_decl* q);
rule_set * operator()(rule_set const & source, model_converter_ref& mc, proof_converter_ref& pc);
bool has_quantifiers() { return m_has_quantifiers; }
obj_map<rule const, quantifier_ref_vector*>& quantifiers() { return m_quantifiers; }
bool has_quantifiers() const { return !m_quantifiers.empty(); }
void ensure_predicate(expr* e, unsigned& max_var, app_ref_vector& tail);
bool find_instantiations_proof_based(
expr* fml,
app_ref_vector const& var_inst,
obj_map<quantifier, expr_ref_vector*>& insts,
expr_ref_vector& bindings);
};
};

366
src/muz_qe/dl_mk_extract_quantifiers2.cpp
View file

@ -1,366 +0,0 @@
/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
dl_mk_extract_quantifiers2.cpp
Abstract:
Remove universal quantifiers over interpreted predicates in the body.
Author:
Nikolaj Bjorner (nbjorner) 2012-11-21
Revision History:
--*/
#include"dl_mk_extract_quantifiers2.h"
#include"ast_pp.h"
#include"dl_bmc_engine.h"
#include"smt_quantifier.h"
#include"smt_context.h"
namespace datalog {
mk_extract_quantifiers2::mk_extract_quantifiers2(context & ctx) :
rule_transformer::plugin(101, false),
m_ctx(ctx),
m(ctx.get_manager()),
rm(ctx.get_rule_manager()),
m_query_pred(m),
m_quantifiers(m),
m_refs(m)
{}
mk_extract_quantifiers2::~mk_extract_quantifiers2() {
reset();
}
void mk_extract_quantifiers2::set_query(func_decl* q) {
m_query_pred = q;
}
bool mk_extract_quantifiers2::matches_signature(func_decl* head, expr_ref_vector const& binding) {
unsigned sz = head->get_arity();
if (sz != binding.size()) {
return false;
}
for (unsigned i = 0; i < sz; ++i) {
if (head->get_domain(i) != m.get_sort(binding[sz-i-1])) {
return false;
}
}
return true;
}
bool mk_extract_quantifiers2::matches_quantifier(quantifier* q, expr_ref_vector const& binding) {
unsigned sz = q->get_num_decls();
if (sz != binding.size()) {
return false;
}
for (unsigned i = 0; i < sz; ++i) {
if (q->get_decl_sort(i) != m.get_sort(binding[sz-i-1])) {
return false;
}
}
return true;
}
bool mk_extract_quantifiers2::mk_abstract_expr(expr_ref& term) {
if (!is_app(term)) {
return false;
}
expr* r;
if (m_map.find(term, r)) {
term = r;
return true;
}
if (to_app(term)->get_family_id() == null_family_id) {
return false;
}
expr_ref_vector args(m);
expr_ref tmp(m);
for (unsigned i = 0; i < to_app(term)->get_num_args(); ++i) {
tmp = to_app(term)->get_arg(i);
if (!mk_abstract_expr(tmp)) {
return false;
}
args.push_back(tmp);
}
tmp = m.mk_app(to_app(term)->get_decl(), args.size(), args.c_ptr());
m_refs.push_back(tmp);
m_map.insert(term, tmp);
term = tmp;
return true;
}
bool mk_extract_quantifiers2::mk_abstract_binding(expr_ref_vector const& binding, expr_ref_vector& result) {
for (unsigned i = 0; i < binding.size(); ++i) {
expr_ref tmp(m);
tmp = binding[i];
if (!mk_abstract_expr(tmp)) {
return false;
}
result.push_back(tmp);
}
return true;
}
void mk_extract_quantifiers2::mk_abstraction_map(rule& r, expr_ref_vector const& binding) {
m_map.reset();
unsigned sz = binding.size();
SASSERT(sz == r.get_decl()->get_arity());
for (unsigned i = 0; i < sz; ++i) {
m_map.insert(binding[sz-i-1], r.get_head()->get_arg(i));
SASSERT(m.get_sort(binding[sz-i-1]) == m.get_sort(r.get_head()->get_arg(i)));
}
// todo: also make bindings for variables in rule body.
}
void mk_extract_quantifiers2::match_bindings(unsigned i, unsigned j, unsigned k) {
expr_ref_vector resb(m);
rule* r = m_qrules[i];
quantifier* q = m_quantifiers[i].get();
expr_ref_vector const& ruleb = m_rule_bindings[i][j];
expr_ref_vector const& quantb = m_quantifier_bindings[i][k];
mk_abstraction_map(*r, ruleb);
if (!mk_abstract_binding(quantb, resb)) {
return;
}
expr_ref inst(m), tmp(m);
var_shifter shift(m);
for (unsigned l = 0; l < resb.size(); ++l) {
tmp = resb[l].get();
shift(tmp, q->get_num_decls(), tmp);
resb[l] = tmp;
}
instantiate(m, q, resb.c_ptr(), inst);
if (!m_seen.contains(r)) {
m_seen.insert(r, alloc(obj_hashtable<expr>));
}
obj_hashtable<expr>& seen = *m_seen.find(r);
if (seen.contains(inst)) {
return;
}
seen.insert(inst);
m_refs.push_back(inst);
if (!m_quantifier_instantiations.contains(r, q)) {
m_quantifier_instantiations.insert(r, q, alloc(expr_ref_vector, m));
}
expr_ref_vector* vec = 0;
VERIFY(m_quantifier_instantiations.find(r, q, vec));
vec->push_back(inst);
TRACE("dl", tout << "matched: " << mk_pp(q, m) << "\n" << mk_pp(inst, m) << "\n";);
}
app_ref mk_extract_quantifiers2::ensure_app(expr* e) {
if (is_app(e)) {
return app_ref(to_app(e), m);
}
else {
return app_ref(m.mk_eq(e, m.mk_true()), m);
}
}
void mk_extract_quantifiers2::extract(rule& r, rule_set& new_rules) {
unsigned utsz = r.get_uninterpreted_tail_size();
unsigned tsz = r.get_tail_size();
bool has_quantifier = false;
expr_ref_vector conjs(m);
for (unsigned i = utsz; i < tsz; ++i) {
conjs.push_back(r.get_tail(i));
}
datalog::flatten_and(conjs);
for (unsigned j = 0; j < conjs.size(); ++j) {
expr* e = conjs[j].get();
quantifier* q;
if (rule_manager::is_forall(m, e, q)) {
m_quantifiers.push_back(q);
m_qrules.push_back(&r);
m_rule_bindings.push_back(vector<expr_ref_vector>());
m_quantifier_bindings.push_back(vector<expr_ref_vector>());
has_quantifier = true;
}
}
if (!has_quantifier) {
new_rules.add_rule(&r);
}
}
void mk_extract_quantifiers2::apply(rule& r, rule_set& new_rules) {
expr_ref_vector tail(m), conjs(m);
expr_ref fml(m);
unsigned utsz = r.get_uninterpreted_tail_size();
unsigned tsz = r.get_tail_size();
for (unsigned i = 0; i < utsz; ++i) {
SASSERT(!r.is_neg_tail(i));
tail.push_back(r.get_tail(i));
}
bool has_quantifier = false;
for (unsigned i = utsz; i < tsz; ++i) {
conjs.push_back(r.get_tail(i));
}
datalog::flatten_and(conjs);
for (unsigned j = 0; j < conjs.size(); ++j) {
expr* e = conjs[j].get();
quantifier* q;
if (rule_manager::is_forall(m, e, q)) {
expr_ref_vector* ls;
if (m_quantifier_instantiations.find(&r,q,ls)) {
tail.append(*ls);
}
has_quantifier = true;
}
else {
tail.push_back(e);
}
}
if (has_quantifier) {
fml = m.mk_implies(m.mk_and(tail.size(), tail.c_ptr()), r.get_head());
rule_ref_vector rules(rm);
rm.mk_rule(fml, rules, r.name());
for (unsigned i = 0; i < rules.size(); ++i) {
new_rules.add_rule(rules[i].get());
}
}
}
#if 0
class mk_extract_quantifiers2::instance_plugin : public smt::quantifier_instance_plugin {
mk_extract_quantifiers2& ex;
ast_manager& m;
expr_ref_vector m_refs;
obj_hashtable<expr> m_bindings;
public:
instance_plugin(mk_extract_quantifiers2& ex): ex(ex), m(ex.m), m_refs(m) {}
virtual void operator()(quantifier* q, unsigned num_bindings, smt::enode*const* bindings) {
expr_ref_vector binding(m);
ptr_vector<sort> sorts;
for (unsigned i = 0; i < num_bindings; ++i) {
binding.push_back(bindings[i]->get_owner());
sorts.push_back(m.get_sort(binding[i].get()));
}
func_decl* f = m.mk_func_decl(symbol("T"), sorts.size(), sorts.c_ptr(), m.mk_bool_sort());
expr_ref tup(m);
tup = m.mk_app(f, binding.size(), binding.c_ptr());
if (!m_bindings.contains(tup)) {
m_bindings.insert(tup);
m_refs.push_back(tup);
ex.m_bindings.push_back(binding);
TRACE("dl", tout << "insert\n" << mk_pp(q, m) << "\n" << mk_pp(tup, m) << "\n";);
}
}
};
#endif
void mk_extract_quantifiers2::reset() {
{
obj_pair_map<rule,quantifier, expr_ref_vector*>::iterator
it = m_quantifier_instantiations.begin(),
end = m_quantifier_instantiations.end();
for (; it != end; ++it) {
dealloc(it->get_value());
}
}
{
obj_map<rule,obj_hashtable<expr>*>::iterator
it = m_seen.begin(),
end = m_seen.end();
for (; it != end; ++it) {
dealloc(it->m_value);
}
}
m_quantifier_instantiations.reset();
m_seen.reset();
m_has_quantifiers = false;
m_quantifiers.reset();
m_qrules.reset();
m_bindings.reset();
m_rule_bindings.reset();
m_quantifier_bindings.reset();
m_refs.reset();
}
rule_set * mk_extract_quantifiers2::operator()(rule_set const & source, model_converter_ref& mc, proof_converter_ref& pc) {
reset();
rule_set::iterator it = source.begin(), end = source.end();
for (; !m_has_quantifiers && it != end; ++it) {
m_has_quantifiers = (*it)->has_quantifiers();
}
if (!m_has_quantifiers) {
return 0;
}
rule_set* rules = alloc(rule_set, m_ctx);
it = source.begin();
for (; it != end; ++it) {
extract(**it, *rules);
}
bmc bmc(m_ctx);
expr_ref_vector fmls(m);
bmc.compile(source, fmls, 0); // TBD: use cancel_eh to terminate without base-case.
bmc.compile(source, fmls, 1);
bmc.compile(source, fmls, 2);
// bmc.compile(source, fmls, 3);
expr_ref query = bmc.compile_query(m_query_pred, 2);
fmls.push_back(query);
smt_params fparams;
fparams.m_relevancy_lvl = 0;
fparams.m_model = true;
fparams.m_model_compact = true;
fparams.m_mbqi = true;
smt::kernel solver(m, fparams);
TRACE("dl",
for (unsigned i = 0; i < fmls.size(); ++i) {
tout << mk_pp(fmls[i].get(), m) << "\n";
});
for (unsigned i = 0; i < fmls.size(); ++i) {
solver.assert_expr(fmls[i].get());
}
#if 0
smt::context& ctx = solver.get_context();
smt::quantifier_manager* qm = ctx.get_quantifier_manager();
qm->get_plugin()->set_instance_plugin(alloc(instance_plugin, *this));
#endif
solver.check();
for (unsigned i = 0; i < m_bindings.size(); ++i) {
expr_ref_vector& binding = m_bindings[i];
for (unsigned j = 0; j < m_qrules.size(); ++j) {
rule* r = m_qrules[j];
if (matches_signature(r->get_decl(), binding)) {
m_rule_bindings[j].push_back(binding);
}
else if (matches_quantifier(m_quantifiers[j].get(), binding)) {
m_quantifier_bindings[j].push_back(binding);
}
}
}
for (unsigned i = 0; i < m_qrules.size(); ++i) {
for (unsigned j = 0; j < m_rule_bindings[i].size(); ++j) {
for (unsigned k = 0; k < m_quantifier_bindings[i].size(); ++k) {
match_bindings(i, j, k);
}
}
}
it = source.begin();
for (; it != end; ++it) {
apply(**it, *rules);
}
return rules;
}
};

91
src/muz_qe/dl_mk_extract_quantifiers2.h
View file

@ -1,91 +0,0 @@
/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
dl_mk_extract_quantifiers2.h
Abstract:
Replace universal quantifiers over interpreted predicates in the body
by instantiations mined using bounded model checking search.
Author:
Nikolaj Bjorner (nbjorner) 2012-11-21
Revision History:
--*/
#ifndef _DL_MK_EXTRACT_QUANTIFIERS2_H_
#define _DL_MK_EXTRACT_QUANTIFIERS2_H_
#include"dl_context.h"
#include"dl_rule_set.h"
#include"dl_rule_transformer.h"
#include"obj_pair_hashtable.h"
namespace datalog {
/**
\brief Extract universal quantifiers from rules.
*/
class mk_extract_quantifiers2 : public rule_transformer::plugin {
context& m_ctx;
ast_manager& m;
rule_manager& rm;
func_decl_ref m_query_pred;
quantifier_ref_vector m_quantifiers;
ptr_vector<rule> m_qrules;
vector<expr_ref_vector>m_bindings;
vector<vector<expr_ref_vector> > m_rule_bindings;
vector<vector<expr_ref_vector> > m_quantifier_bindings;
obj_pair_map<rule,quantifier, expr_ref_vector*> m_quantifier_instantiations;
obj_map<rule, obj_hashtable<expr>*> m_seen;
bool m_has_quantifiers;
obj_map<expr,expr*> m_map;
expr_ref_vector m_refs;
class instance_plugin;
void reset();
void extract(rule& r, rule_set& new_rules);
void apply(rule& r, rule_set& new_rules);
app_ref ensure_app(expr* e);
bool matches_signature(func_decl* head, expr_ref_vector const& binding);
bool matches_quantifier(quantifier* q, expr_ref_vector const& binding);
void match_bindings(unsigned i, unsigned j, unsigned k);
bool mk_abstract_expr(expr_ref& term);
bool mk_abstract_binding(expr_ref_vector const& binding, expr_ref_vector& result);
void mk_abstraction_map(rule& r, expr_ref_vector const& binding);
public:
/**
\brief Create rule transformer that extracts universal quantifiers (over recursive predicates).
*/
mk_extract_quantifiers2(context & ctx);
virtual ~mk_extract_quantifiers2();
void set_query(func_decl* q);
rule_set * operator()(rule_set const & source, model_converter_ref& mc, proof_converter_ref& pc);
bool has_quantifiers() { return m_has_quantifiers; }
};
};
#endif /* _DL_MK_EXTRACT_QUANTIFIERS2_H_ */

4
src/muz_qe/pdr_context.cpp
View file

@ -33,7 +33,6 @@ Notes:
#include "pdr_prop_solver.h"
#include "pdr_context.h"
#include "pdr_generalizers.h"
#include "datatype_decl_plugin.h"
#include "for_each_expr.h"
#include "dl_rule_set.h"
#include "unit_subsumption_tactic.h"
@ -1682,7 +1681,8 @@ namespace pdr {
case l_false: {
core_generalizer::cores cores;
cores.push_back(std::make_pair(cube, uses_level));
TRACE("pdr", tout << "cube:\n";
for (unsigned j = 0; j < cube.size(); ++j) tout << mk_pp(cube[j].get(), m) << "\n";);
for (unsigned i = 0; !cores.empty() && i < m_core_generalizers.size(); ++i) {
core_generalizer::cores new_cores;
for (unsigned j = 0; j < cores.size(); ++j) {

5
src/muz_qe/pdr_dl_interface.cpp
View file

@ -177,8 +177,9 @@ lbool dl_interface::query(expr * query) {
while (true) {
result = m_context->solve();
if (result == l_true && extract_quantifiers->has_quantifiers()) {
if (quantifier_mc.check()) {
return l_true;
result = quantifier_mc.check();
if (result != l_false) {
return result;
}
// else continue
}

5
src/muz_qe/pdr_farkas_learner.cpp
View file

@ -398,6 +398,11 @@ namespace pdr {
for (unsigned i = 0; i < r->size(); ++i) {
lemmas.push_back(r->form(i));
}
TRACE("farkas_simplify_lemmas",
tout << "simplified:\n";
for (unsigned i = 0; i < lemmas.size(); ++i) {
tout << mk_pp(lemmas[i].get(), m) << "\n";
});
}

39
src/muz_qe/pdr_prop_solver.cpp
View file

@ -46,7 +46,6 @@ namespace pdr {
expr_ref_vector m_assumptions;
obj_map<app,expr *> m_proxies2expr;
obj_map<expr, app*> m_expr2proxies;
obj_hashtable<expr> m_implies;
unsigned m_num_proxies;
app * mk_proxy(expr* literal) {
@ -72,7 +71,6 @@ namespace pdr {
expr_ref implies(m.mk_or(m.mk_not(res), literal), m);
s.m_ctx->assert_expr(implies);
m_assumptions.push_back(implies);
m_implies.insert(implies);
TRACE("pdr_verbose", tout << "name asserted " << mk_pp(implies, m) << "\n";);
return res;
}
@ -92,6 +90,19 @@ namespace pdr {
m_assumptions.append(conjs);
}
expr* apply_accessor(
ptr_vector<func_decl> const& acc,
unsigned j,
func_decl* f,
expr* c) {
if (is_app(c) && to_app(c)->get_decl() == f) {
return to_app(c)->get_arg(j);
}
else {
return m.mk_app(acc[j], c);
}
}
void expand_literals(expr_ref_vector& conjs) {
arith_util arith(m);
datatype_util dt(m);
@ -100,6 +111,12 @@ namespace pdr {
rational r;
unsigned bv_size;
TRACE("pdr",
tout << "begin expand\n";
for (unsigned i = 0; i < conjs.size(); ++i) {
tout << mk_pp(conjs[i].get(), m) << "\n";
});
for (unsigned i = 0; i < conjs.size(); ++i) {
expr* e = conjs[i].get();
if (m.is_eq(e, e1, e2) && arith.is_int_real(e1)) {
@ -117,10 +134,10 @@ namespace pdr {
(m.is_eq(e, val, c) && is_app(val) && dt.is_constructor(to_app(val)))){
func_decl* f = to_app(val)->get_decl();
func_decl* r = dt.get_constructor_recognizer(f);
conjs[i] = m.mk_app(r,c);
conjs[i] = m.mk_app(r, c);
ptr_vector<func_decl> const& acc = *dt.get_constructor_accessors(f);
for (unsigned i = 0; i < acc.size(); ++i) {
conjs.push_back(m.mk_eq(m.mk_app(acc[i], c), to_app(val)->get_arg(i)));
for (unsigned j = 0; j < acc.size(); ++j) {
conjs.push_back(m.mk_eq(apply_accessor(acc, j, f, c), to_app(val)->get_arg(j)));
}
}
else if ((m.is_eq(e, c, val) && bv.is_numeral(val, r, bv_size)) ||
@ -142,6 +159,11 @@ namespace pdr {
}
}
}
TRACE("pdr",
tout << "end expand\n";
for (unsigned i = 0; i < conjs.size(); ++i) {
tout << mk_pp(conjs[i].get(), m) << "\n";
});
}
public:
@ -190,12 +212,7 @@ namespace pdr {
expr_ref e(m);
for (unsigned i = 0; i < es.size(); ++i) {
e = es[i].get();
if (m_implies.contains(e)) {
e = m.mk_true();
}
else {
rep(e);
}
rep(e);
es[i] = e;
if (m.is_true(e)) {
es[i] = es.back();

45
src/muz_qe/pdr_quantifiers.cpp
View file

@ -154,13 +154,10 @@ namespace pdr {
// As & not Body_i is satisfiable
// then instantiate with model for parameters to Body_i
bool quantifier_model_checker::find_instantiations(quantifier_ref_vector const& qs, unsigned level) {
return
find_instantiations_proof_based(qs, level); // ||
// find_instantiations_qe_based(qs, level);
void quantifier_model_checker::find_instantiations(quantifier_ref_vector const& qs, unsigned level) {
find_instantiations_proof_based(qs, level);
}
class collect_insts {
ast_manager& m;
ptr_vector<expr> m_binding;
@ -207,7 +204,7 @@ namespace pdr {
};
bool quantifier_model_checker::find_instantiations_proof_based(quantifier_ref_vector const& qs, unsigned level) {
void quantifier_model_checker::find_instantiations_proof_based(quantifier_ref_vector const& qs, unsigned level) {
bool found_instance = false;
datalog::scoped_fine_proof _scp(m);
@ -233,10 +230,13 @@ namespace pdr {
TRACE("pdr", tout << result << "\n";);
if (result != l_false) {
return false;
if (m_rules_model_check != l_false) {
m_rules_model_check = result;
}
if (result != l_false) {
return;
}
m_rules_model_check = false;
map<symbol, quantifier*, symbol_hash_proc, symbol_eq_proc> qid_map;
quantifier* q;
@ -272,7 +272,12 @@ namespace pdr {
add_binding(q, new_binding);
found_instance = true;
}
return found_instance;
if (found_instance) {
m_rules_model_check = l_false;
}
else if (m_rules_model_check != l_false) {
m_rules_model_check = l_undef;
}
}
@ -445,7 +450,7 @@ namespace pdr {
qe_lite qe(m);
r.get_vars(vars);
#if 1
if (qis) {
quantifier_ref_vector const& qi = *qis;
for (unsigned i = 0; i < qi.size(); ++i) {
@ -471,7 +476,7 @@ namespace pdr {
body.push_back(m.update_quantifier(q, fml));
}
}
#endif
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)));
@ -584,17 +589,17 @@ namespace pdr {
find_instantiations(*qis, level);
}
bool quantifier_model_checker::model_check(model_node& root) {
lbool quantifier_model_checker::model_check(model_node& root) {
m_instantiations.reset();
m_instantiated_rules.reset();
m_rules_model_check = true;
m_rules_model_check = l_true;
ptr_vector<model_node> nodes;
get_nodes(root, nodes);
for (unsigned i = nodes.size(); i > 0; ) {
--i;
model_check_node(*nodes[i]);
}
if (!m_rules_model_check) {
if (m_rules_model_check == l_false) {
weaken_under_approximation();
}
return m_rules_model_check;
@ -644,12 +649,12 @@ namespace pdr {
TRACE("pdr", m_rules.display(tout););
}
bool quantifier_model_checker::check() {
if (model_check(m_ctx.get_root())) {
return true;
lbool quantifier_model_checker::check() {
lbool result = model_check(m_ctx.get_root());
if (result == l_false) {
refine();
}
refine();
return false;
return result;
}
};

15
src/muz_qe/pdr_quantifiers.h
View file

@ -21,6 +21,7 @@ Revision History:
#define _PDR_QUANTIFIERS_H_
#include "ast.h"
#include "lbool.h"
#include "dl_rule.h"
#include "obj_pair_hashtable.h"
@ -46,7 +47,7 @@ namespace pdr {
pred_transformer* m_current_pt;
datalog::rule const* m_current_rule;
model_node* m_current_node;
bool m_rules_model_check;
lbool m_rules_model_check;
app_ref_vector m_instantiations;
ptr_vector<datalog::rule const> m_instantiated_rules;
@ -54,13 +55,9 @@ namespace pdr {
void weaken_under_approximation();
bool find_instantiations(quantifier_ref_vector const& qs, unsigned level);
void find_instantiations(quantifier_ref_vector const& qs, unsigned level);
bool find_instantiations_model_based(quantifier_ref_vector const& qs, unsigned level);
bool find_instantiations_proof_based(quantifier_ref_vector const& qs, unsigned level);
bool find_instantiations_qe_based(quantifier_ref_vector const& qs, unsigned level);
void find_instantiations_proof_based(quantifier_ref_vector const& qs, unsigned level);
void add_binding(quantifier* q, expr_ref_vector& binding);
@ -80,7 +77,7 @@ namespace pdr {
'false' and a set of instantiations that contradict the current model.
*/
bool model_check(model_node& root);
lbool model_check(model_node& root);
void add_over_approximations(quantifier_ref_vector& qis, model_node& n);
@ -113,7 +110,7 @@ namespace pdr {
~quantifier_model_checker();
bool check();
lbool check();
};
};

20
src/muz_qe/pdr_smt_context_manager.cpp
View file

@ -20,6 +20,7 @@ Revision History:
#include "pdr_smt_context_manager.h"
#include "has_free_vars.h"
#include "ast_pp.h"
#include "ast_smt_pp.h"
#include <sstream>
#include "smt_params.h"
@ -78,6 +79,25 @@ namespace pdr {
if (!m.is_true(m_pred)) {
assumptions.push_back(m_pred);
}
TRACE("pdr_check",
{
ast_smt_pp pp(m);
for (unsigned i = 0; i < m_context.size(); ++i) {
pp.add_assumption(m_context.get_formulas()[i]);
}
for (unsigned i = 0; i < assumptions.size(); ++i) {
pp.add_assumption(assumptions[i].get());
}
pp.display_smt2(tout, m.mk_true());
static unsigned lemma_id = 0;
std::ostringstream strm;
strm << "pdr-lemma-" << lemma_id << ".smt2";
std::ofstream out(strm.str().c_str());
pp.display_smt2(out, m.mk_true());
out.close();
lemma_id++;
});
lbool result = m_context.check(assumptions.size(), assumptions.c_ptr());
if (!m.is_true(m_pred)) {
assumptions.pop_back();

41
src/muz_qe/proof_utils.cpp
View file

@ -223,7 +223,7 @@ public:
found_false = true;
break;
}
// SASSERT(m.get_fact(tmp) == m.get_fact(m.get_parent(p, i)));
SASSERT(m.get_fact(tmp) == m.get_fact(m.get_parent(p, i)));
parents.push_back(tmp);
if (is_closed(tmp) && !m_units.contains(m.get_fact(tmp))) {
m_units.insert(m.get_fact(tmp), tmp);
@ -235,6 +235,7 @@ public:
break;
}
tmp = m.get_parent(p, 0);
expr* old_clause = m.get_fact(tmp);
elim(tmp);
parents[0] = tmp;
expr* clause = m.get_fact(tmp);
@ -244,6 +245,31 @@ public:
pop();
break;
}
//
// case where clause is a literal in the old clause.
//
if (is_literal_in_clause(clause, old_clause)) {
bool found = false;
for (unsigned i = 1; !found && i < parents.size(); ++i) {
if (m.is_complement(clause, m.get_fact(parents[i].get()))) {
parents[1] = parents[i].get();
parents.resize(2);
result = m.mk_unit_resolution(parents.size(), parents.c_ptr());
m_refs.push_back(result);
add_hypotheses(result);
found = true;
}
}
if (!found) {
result = parents[0].get();
}
pop();
break;
}
//
// case where new clause is a subset of old clause.
// the literals in clause should be a subset of literals in old_clause.
//
get_literals(clause);
for (unsigned i = 1; i < parents.size(); ++i) {
bool found = false;
@ -309,6 +335,19 @@ public:
m_cache.insert(p, result);
p = result;
}
bool is_literal_in_clause(expr* fml, expr* clause) {
if (!m.is_or(clause)) {
return false;
}
app* cl = to_app(clause);
for (unsigned i = 0; i < cl->get_num_args(); ++i) {
if (cl->get_arg(i) == fml) {
return true;
}
}
return false;
}
};
void proof_utils::reduce_hypotheses(proof_ref& pr) {

34
src/nlsat/nlsat_explain.cpp
View file

@ -42,7 +42,8 @@ namespace nlsat {
bool m_simplify_cores;
bool m_full_dimensional;
bool m_minimize_cores;
bool m_factor;
struct todo_set {
polynomial::cache & m_cache;
polynomial_ref_vector m_set;
@ -568,21 +569,22 @@ namespace nlsat {
elim_vanishing(p);
if (is_const(p))
return;
#if 1
TRACE("nlsat_explain", tout << "adding factors of\n"; display(tout, p); tout << "\n";);
factor(p, m_factors);
polynomial_ref f(m_pm);
for (unsigned i = 0; i < m_factors.size(); i++) {
f = m_factors.get(i);
elim_vanishing(f);
if (!is_const(f)) {
TRACE("nlsat_explain", tout << "adding factor:\n"; display(tout, f); tout << "\n";);
m_todo.insert(f);
if (m_factor) {
TRACE("nlsat_explain", tout << "adding factors of\n"; display(tout, p); tout << "\n";);
factor(p, m_factors);
polynomial_ref f(m_pm);
for (unsigned i = 0; i < m_factors.size(); i++) {
f = m_factors.get(i);
elim_vanishing(f);
if (!is_const(f)) {
TRACE("nlsat_explain", tout << "adding factor:\n"; display(tout, f); tout << "\n";);
m_todo.insert(f);
}
}
}
#else
m_todo.insert(normalize(p));
#endif
else {
m_todo.insert(p);
}
}
/**
@ -1344,6 +1346,10 @@ namespace nlsat {
m_imp->m_minimize_cores = f;
}
void explain::set_factor(bool f) {
m_imp->m_factor = f;
}
void explain::operator()(unsigned n, literal const * ls, scoped_literal_vector & result) {
(*m_imp)(n, ls, result);
}

1
src/nlsat/nlsat_explain.h
View file

@ -40,6 +40,7 @@ namespace nlsat {
void set_simplify_cores(bool f);
void set_full_dimensional(bool f);
void set_minimize_cores(bool f);
void set_factor(bool f);
/**
\brief Given a set of literals ls[0], ... ls[n-1] s.t.

4
src/nlsat/nlsat_params.pyg
View file

@ -10,5 +10,7 @@ def_module_params('nlsat',
('randomize', BOOL, True, "randomize selection of a witness in nlsat."),
('max_conflicts', UINT, UINT_MAX, "maximum number of conflicts."),
('shuffle_vars', BOOL, False, "use a random variable order."),
('seed', UINT, 0, "random seed.")))
('seed', UINT, 0, "random seed."),
('factor', BOOL, True, "factor polynomials produced during conflict resolution.")
))

1
src/nlsat/nlsat_solver.cpp
View file

@ -212,6 +212,7 @@ namespace nlsat {
m_ism.set_seed(m_random_seed);
m_explain.set_simplify_cores(m_simplify_cores);
m_explain.set_minimize_cores(min_cores);
m_explain.set_factor(p.factor());
m_am.updt_params(p.p);
}

7
src/smt/smt_kernel.cpp
View file

@ -69,10 +69,6 @@ namespace smt {
return m_kernel.get_asserted_formulas();
}
bool reduce() {
return m_kernel.reduce_assertions();
}
void push() {
TRACE("smt_kernel", tout << "push()\n";);
m_kernel.push();
@ -221,9 +217,6 @@ namespace smt {
return m_imp->get_formulas();
}
bool kernel::reduce() {
return m_imp->reduce();
}
void kernel::push() {
m_imp->push();

9
src/smt/smt_kernel.h
View file

@ -84,15 +84,6 @@ namespace smt {
*/
expr * const * get_formulas() const;
/**
\brief Reduce the set of asserted formulas using preprocessors.
Return true if an inconsistency is detected.
\remark This is mainly used by dl_smt_relation. This method
seens to be misplaced. This is not the right place.
*/
bool reduce();
/**
\brief Create a backtracking point (aka scope level).
*/

20
src/tactic/fpa/fpa2bv_converter.cpp
View file

@ -237,15 +237,14 @@ void fpa2bv_converter::mk_pzero(func_decl *f, expr_ref & result) {
void fpa2bv_converter::add_core(unsigned sbits, unsigned ebits, expr_ref & rm,
expr_ref & c_sgn, expr_ref & c_sig, expr_ref & c_exp, expr_ref & d_sgn, expr_ref & d_sig, expr_ref & d_exp,
expr_ref & res_sgn, expr_ref & res_sig, expr_ref & res_exp)
{
{
// c/d are now such that c_exp >= d_exp.
expr_ref exp_delta(m);
exp_delta = m_bv_util.mk_bv_sub(c_exp, d_exp);
dbg_decouple("fpa2bv_add_exp_delta", exp_delta);
// cap the delta
// cap the delta
expr_ref cap(m);
cap = m_bv_util.mk_numeral(sbits+2, ebits);
m_simp.mk_ite(m_bv_util.mk_ule(cap, exp_delta), cap, exp_delta, exp_delta);
@ -404,8 +403,7 @@ void fpa2bv_converter::mk_add(func_decl * f, unsigned num, expr * const * args,
// Actual addition.
unsigned ebits = m_util.get_ebits(f->get_range());
unsigned sbits = m_util.get_sbits(f->get_range());
SASSERT(ebits <= sbits);
unsigned sbits = m_util.get_sbits(f->get_range());
expr_ref a_sgn(m), a_sig(m), a_exp(m), b_sgn(m), b_sig(m), b_exp(m);
unpack(x, a_sgn, a_sig, a_exp, true);
@ -1636,7 +1634,6 @@ void fpa2bv_converter::unpack(expr * e, expr_ref & sgn, expr_ref & sig, expr_ref
mk_unbias(denormal_exp, denormal_exp);
if (normalize) {
SASSERT(ebits <= sbits);
expr_ref is_sig_zero(m), shift(m), lz(m);
m_simp.mk_eq(m_bv_util.mk_numeral(0, sbits-1), sig, is_sig_zero);
mk_leading_zeros(sig, ebits, lz);
@ -1644,9 +1641,14 @@ void fpa2bv_converter::unpack(expr * e, expr_ref & sgn, expr_ref & sig, expr_ref
SASSERT(is_well_sorted(m, is_sig_zero));
SASSERT(is_well_sorted(m, lz));
SASSERT(is_well_sorted(m, shift));
denormal_sig = m_bv_util.mk_bv_shl(denormal_sig, m_bv_util.mk_zero_extend(sbits-ebits, shift));
// CMW: The book says we don't need this, but it feels wrong not to do that.
//denormal_exp = m_bv_util.mk_bv_sub(denormal_exp, shift);
if (ebits > sbits) {
expr_ref q(m);
q = m_bv_util.mk_zero_extend(sbits-ebits, shift);
denormal_sig = m_bv_util.mk_bv_shl(denormal_sig, q);
}
else {
denormal_sig = m_bv_util.mk_bv_shl(denormal_sig, shift);
}
}
SASSERT(is_well_sorted(m, normal_sig));

8
src/test/algebraic.cpp
View file

@ -176,11 +176,11 @@ static void tst1() {
display_anums(std::cout, rs1);
}
void tst_refine_mpbq() {
void tst_refine_mpbq(int n, int d) {
unsynch_mpq_manager qm;
mpbq_manager bqm(qm);
scoped_mpq q1(qm);
qm.set(q1, 5, 7);
qm.set(q1, n, d);
scoped_mpbq l(bqm);
scoped_mpbq u(bqm);
std::cout << "using refine upper...\n";
@ -207,6 +207,10 @@ void tst_refine_mpbq() {
}
}
void tst_refine_mpbq() {
tst_refine_mpbq(5, 7);
}
void tst_mpbq_root() {
unsynch_mpq_manager qm;
mpbq_manager bqm(qm);

1
src/test/main.cpp
View file

@ -206,6 +206,7 @@ int main(int argc, char ** argv) {
TST(mpff);
TST(horn_subsume_model_converter);
TST(model2expr);
TST(rcf);
}
void initialize_mam() {}

175
src/test/rcf.cpp Normal file
View file

@ -0,0 +1,175 @@
/*++
Copyright (c) 2013 Microsoft Corporation
Module Name:
rcf.cpp
Abstract:
Testing RCF module
Author:
Leonardo (leonardo) 2013-01-04
Notes:
--*/
#include"realclosure.h"
#include"mpz_matrix.h"
static void tst1() {
unsynch_mpq_manager qm;
rcmanager m(qm);
scoped_rcnumeral a(m);
#if 0
a = 10;
std::cout << sym_pp(a) << std::endl;
std::cout << sym_pp(eps) << std::endl;
std::cout << interval_pp(a) << std::endl;
std::cout << interval_pp(eps) << std::endl;
#endif
scoped_rcnumeral eps(m);
m.mk_infinitesimal("eps", eps);
mpq aux;
qm.set(aux, 1, 3);
m.set(a, aux);
#if 0
std::cout << interval_pp(a) << std::endl;
std::cout << decimal_pp(eps, 4) << std::endl;
std::cout << decimal_pp(a) << std::endl;
std::cout << a + eps << std::endl;
std::cout << a * eps << std::endl;
std::cout << (a + eps)*eps - eps << std::endl;
#endif
std::cout << interval_pp(a - eps*2) << std::endl;
std::cout << interval_pp(eps + 1) << std::endl;
scoped_rcnumeral t(m);
t = (a - eps*2) / (eps + 1);
std::cout << t << std::endl;
std::cout << t * (eps + 1) << std::endl;
a = 10;
std::cout << (a + eps > a) << std::endl;
scoped_rcnumeral pi(m);
m.mk_pi(pi);
std::cout << pi + 1 << std::endl;
std::cout << decimal_pp(pi) << std::endl;
std::cout << decimal_pp(pi + 1) << std::endl;
scoped_rcnumeral e(m);
m.mk_e(e);
t = e + (pi + 1)*2;
std::cout << t << std::endl;
std::cout << decimal_pp(t, 10) << std::endl;
std::cout << (eps + 1 > 1) << std::endl;
std::cout << interval_pp((a + eps)/(a - eps)) << std::endl;
}
static void tst2() {
enable_trace("mpz_matrix");
unsynch_mpq_manager nm;
small_object_allocator allocator;
mpz_matrix_manager mm(nm, allocator);
scoped_mpz_matrix A(mm);
mm.mk(3, 3, A);
// Matrix
// 1 1 1
// 0 1 -1
// 0 1 1
A.set(0, 0, 1); A.set(0, 1, 1); A.set(0, 2, 1);
A.set(1, 0, 0); A.set(1, 1, 1); A.set(1, 2, -1);
A.set(2, 0, 0); A.set(2, 1, 1); A.set(2, 2, 1);
std::cout << A;
{
int b[3];
int c[3] = { 10, -2, 8 };
std::cout << "solve: " << mm.solve(A, b, c) << "\n";
for (unsigned i = 0; i < 3; i++) std::cout << b[i] << " ";
std::cout << "\n";
}
scoped_mpz_matrix A2(mm);
mm.tensor_product(A, A, A2);
std::cout << A2;
scoped_mpz_matrix B(mm);
unsigned cols[] = { 1, 3, 7, 8 };
mm.filter_cols(A2, 4, cols, B);
std::cout << B;
scoped_mpz_matrix C(mm);
unsigned perm[] = { 8, 7, 6, 5, 4, 3, 2, 1, 0 };
mm.permute_rows(B, perm, C);
std::cout << C;
}
static void tst_solve(unsigned n, int _A[], int _b[], int _c[], bool solved) {
unsynch_mpq_manager nm;
small_object_allocator allocator;
mpz_matrix_manager mm(nm, allocator);
scoped_mpz_matrix A(mm);
mm.mk(n, n, A);
for (unsigned i = 0; i < n; i++)
for (unsigned j = 0; j < n; j++)
A.set(i, j, _A[i*n + j]);
svector<int> b;
b.resize(n, 0);
if (mm.solve(A, b.c_ptr(), _c)) {
SASSERT(solved);
for (unsigned i = 0; i < n; i++) {
SASSERT(b[i] == _b[i]);
}
}
else {
SASSERT(!solved);
}
}
static void tst_lin_indep(unsigned m, unsigned n, int _A[], unsigned ex_sz, unsigned ex_r[]) {
unsynch_mpq_manager nm;
small_object_allocator allocator;
mpz_matrix_manager mm(nm, allocator);
scoped_mpz_matrix A(mm);
mm.mk(m, n, A);
for (unsigned i = 0; i < m; i++)
for (unsigned j = 0; j < n; j++)
A.set(i, j, _A[i*n + j]);
unsigned_vector r;
r.resize(A.n());
scoped_mpz_matrix B(mm);
mm.linear_independent_rows(A, r.c_ptr(), B);
SASSERT(r.size() == ex_sz);
for (unsigned i = 0; i < ex_sz; i++) {
SASSERT(r[i] == ex_r[i]);
}
}
static void tst_denominators() {
unsynch_mpq_manager qm;
rcmanager m(qm);
scoped_rcnumeral a(m);
scoped_rcnumeral t(m);
scoped_rcnumeral eps(m);
m.mk_pi(a);
m.inv(a);
m.mk_infinitesimal("eps", eps);
t = (a - eps*2) / (a*eps + 1);
// t = t + a * 2;
scoped_rcnumeral n(m), d(m);
std::cout << t << "\n";
m.clean_denominators(t, n, d);
std::cout << "---->\n" << n << "\n" << d << "\n";
}
void tst_rcf() {
enable_trace("rcf_clean");
enable_trace("rcf_clean_bug");
tst_denominators();
return;
tst1();
tst2();
{ int A[] = {0, 1, 1, 1, 0, 1, 1, 1, -1}; int c[] = {10, 4, -4}; int b[] = {-2, 4, 6}; tst_solve(3, A, b, c, true); }
{ int A[] = {1, 1, 1, 0, 1, 1, 0, 1, 1}; int c[] = {3, 2, 2}; int b[] = {1, 1, 1}; tst_solve(3, A, b, c, false); }
{ int A[] = {1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, -1}; unsigned r[] = {0, 1, 4}; tst_lin_indep(5, 3, A, 3, r); }
{ int A[] = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, -1}; unsigned r[] = {0, 4}; tst_lin_indep(5, 3, A, 2, r); }
{ int A[] = {1, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 3, 1, 3}; unsigned r[] = {0, 2}; tst_lin_indep(5, 3, A, 2, r); }
}

61
src/util/array.h
View file

@ -40,7 +40,7 @@ private:
array & operator=(array const & source);
void set_data(void * mem, size_t sz) {
void set_data(void * mem, unsigned sz) {
size_t * _mem = static_cast<size_t*>(mem);
*_mem = sz;
_mem ++;
@ -48,16 +48,16 @@ private:
}
template<typename Allocator>
void allocate(Allocator & a, size_t sz) {
void allocate(Allocator & a, unsigned sz) {
size_t * mem = reinterpret_cast<size_t*>(a.allocate(space(sz)));
set_data(mem, sz);
}
void init() {
void init(T const & v) {
iterator it = begin();
iterator e = end();
for (; it != e; ++it) {
new (it) T();
new (it) T(v);
}
}
@ -80,13 +80,13 @@ public:
\brief Store the array in the given chunk of memory (mem).
This chunck should be big enough to store space(sz) bytes.
*/
array(void * mem, size_t sz, T const * vs) {
array(void * mem, unsigned sz, T const * vs) {
DEBUG_CODE(m_data = 0;);
set(mem, sz, vs);
}
// WARNING: the memory allocated will not be automatically freed.
array(void * mem, size_t sz, bool init_mem) {
array(void * mem, unsigned sz, bool init_mem) {
DEBUG_CODE(m_data = 0;);
set_data(mem, sz);
if (init_mem)
@ -95,14 +95,14 @@ public:
// WARNING: the memory allocated will not be automatically freed.
template<typename Allocator>
array(Allocator & a, size_t sz, T const * vs) {
array(Allocator & a, unsigned sz, T const * vs) {
DEBUG_CODE(m_data = 0;);
set(a, sz, vs);
}
// WARNING: the memory allocated will not be automatically freed.
template<typename Allocator>
array(Allocator & a, size_t sz, bool init_mem) {
array(Allocator & a, unsigned sz, bool init_mem) {
DEBUG_CODE(m_data = 0;);
allocate(a, sz);
if (init_mem)
@ -122,39 +122,46 @@ public:
if (m_data) {
if (CallDestructors)
destroy_elements();
a.deallocate(size(), raw_ptr);
a.deallocate(size(), raw_ptr());
m_data = 0;
}
}
void set(void * mem, size_t sz, T const * vs) {
void set(void * mem, unsigned sz, T const * vs) {
SASSERT(m_data == 0);
set_data(mem, sz);
init(vs);
}
template<typename Allocator>
void set(Allocator & a, size_t sz, T const * vs) {
void set(Allocator & a, unsigned sz, T const * vs) {
SASSERT(m_data == 0);
allocate(a, sz);
init(sz, vs);
init(vs);
}
size_t size() const {
template<typename Allocator>
void set(Allocator & a, unsigned sz, T const & v = T()) {
SASSERT(m_data == 0);
allocate(a, sz);
init(v);
}
unsigned size() const {
if (m_data == 0) {
return 0;
}
return reinterpret_cast<size_t *>(m_data)[SIZE_IDX];
return static_cast<unsigned>(reinterpret_cast<size_t *>(m_data)[SIZE_IDX]);
}
bool empty() const { return m_data == 0; }
T & operator[](size_t idx) {
T & operator[](unsigned idx) {
SASSERT(idx < size());
return m_data[idx];
}
T const & operator[](size_t idx) const {
T const & operator[](unsigned idx) const {
SASSERT(idx < size());
return m_data[idx];
}
@ -175,31 +182,37 @@ public:
return m_data + size();
}
T const * c_ptr() const { return m_data; }
T * c_ptr() { return m_data; }
void swap(array & other) {
std::swap(m_data, other.m_data);
}
};
template<typename T>
class ptr_array : public array<T *, false> {
public:
ptr_array() {}
ptr_array(void * mem, size_t sz, T * const * vs):array<T*, false>(mem, sz, vs) {}
ptr_array(void * mem, unsigned sz, T * const * vs):array<T*, false>(mem, sz, vs) {}
template<typename Allocator>
ptr_array(Allocator & a, size_t sz, T * const * vs):array<T*, false>(a, sz, vs) {}
ptr_array(void * mem, size_t sz, bool init_mem):array<T*, false>(mem, sz, init_mem) {}
ptr_array(Allocator & a, unsigned sz, T * const * vs):array<T*, false>(a, sz, vs) {}
ptr_array(void * mem, unsigned sz, bool init_mem):array<T*, false>(mem, sz, init_mem) {}
template<typename Allocator>
ptr_array(Allocator & a, size_t sz, bool init_mem):array<T*, false>(a, sz, init_mem) {}
ptr_array(Allocator & a, unsigned sz, bool init_mem):array<T*, false>(a, sz, init_mem) {}
};
template<typename T>
class sarray : public array<T, false> {
public:
sarray() {}
sarray(void * mem, size_t sz, T const * vs):array<T, false>(mem, sz, vs) {}
sarray(void * mem, unsigned sz, T const * vs):array<T, false>(mem, sz, vs) {}
template<typename Allocator>
sarray(Allocator & a, size_t sz, T const * vs):array<T, false>(a, sz, vs) {}
sarray(void * mem, size_t sz, bool init_mem):array<T, false>(mem, sz, init_mem) {}
sarray(Allocator & a, unsigned sz, T const * vs):array<T, false>(a, sz, vs) {}
sarray(void * mem, unsigned sz, bool init_mem):array<T, false>(mem, sz, init_mem) {}
template<typename Allocator>
sarray(Allocator & a, size_t sz, bool init_mem):array<T, false>(a, sz, init_mem) {}
sarray(Allocator & a, unsigned sz, bool init_mem):array<T, false>(a, sz, init_mem) {}
};
#endif

9
src/util/buffer.h
View file

@ -231,8 +231,13 @@ public:
SASSERT(size() == nsz);
}
private:
buffer& operator=(buffer const&);
buffer & operator=(buffer const & other) {
if (this == &other)
return *this;
reset();
append(other);
return *this;
}
};
template<typename T, unsigned INITIAL_SIZE=16>

16
src/util/mpbq.cpp
View file

@ -855,16 +855,16 @@ void mpbq_manager::approx_div(mpbq const & a, mpbq const & b, mpbq & c, unsigned
unsigned k_prime;
if (m_manager.is_power_of_two(b.m_num, k_prime)) {
// The division is precise, so we ignore k and to_plus_inf
SASSERT(b.m_k == 0); // remark: b.m_num is odd when b.m_k > 0
SASSERT(b.m_k == 0 || k_prime == 0); // remark: b.m_num is odd when b.m_k > 0, since b.m_num is a power of two we have that b.m_k == 0 or b.m_num == 1.
m_manager.set(c.m_num, a.m_num);
if (a.m_k == 0) {
c.m_k = k_prime;
normalize(c);
}
else {
c.m_k = a.m_k + k_prime;
// there is not need to normalize since the least significant bit of a must be 1.
if (b.m_k > 0) {
SASSERT(k_prime == 0);
mpz & pw2 = m_div_tmp1;
m_manager.power(mpz(2), b.m_k, pw2);
m_manager.mul(c.m_num, pw2, c.m_num);
}
c.m_k = a.m_k + k_prime;
normalize(c);
}
else if (m_manager.divides(b.m_num, a.m_num)) {
// result is also precise

16
src/util/mpz.h
View file

@ -251,8 +251,10 @@ class mpz_manager {
}
void mk_big(mpz & a) {
if (a.m_ptr == 0)
if (a.m_ptr == 0) {
a.m_val = 0;
a.m_ptr = allocate();
}
}
#endif
@ -374,7 +376,7 @@ public:
}
// d <- a + b*c
// d <- a - b*c
void submul(mpz const & a, mpz const & b, mpz const & c, mpz & d) {
if (is_one(b)) {
sub(a, c, d);
@ -676,10 +678,18 @@ public:
int64 get_int64(mpz const & a) const;
bool is_uint(mpz const & a) const { return is_uint64(a) && get_uint64(a) < UINT_MAX; }
unsigned get_uint(mpz const & a) const { SASSERT(is_uint(a)); return static_cast<unsigned>(get_uint64(a)); }
bool is_int(mpz const & a) const { return is_int64(a) && INT_MIN < get_int64(a) && get_int64(a) < INT_MAX; }
int get_int(mpz const & a) const { SASSERT(is_int(a)); return static_cast<int>(get_int64(a)); }
double get_double(mpz const & a) const;
std::string to_string(mpz const & a) const;
void display(std::ostream & out, mpz const & a) const;
/**

37
src/util/ref_buffer.h
View file

@ -30,10 +30,10 @@ Revision History:
- void dec_ref(T * obj)
- void inc_ref(T * obj)
*/
template<typename T, typename Ref>
template<typename T, typename Ref, unsigned INITIAL_SIZE=16>
class ref_buffer_core : public Ref {
protected:
ptr_buffer<T> m_buffer;
ptr_buffer<T, INITIAL_SIZE> m_buffer;
void inc_ref(T * o) { Ref::inc_ref(o); }
void dec_ref(T * o) { Ref::dec_ref(o); }
@ -78,11 +78,7 @@ public:
return m_buffer.c_ptr();
}
T const * operator[](unsigned idx) const {
return m_buffer[idx];
}
T * operator[](unsigned idx) {
T * operator[](unsigned idx) const {
return m_buffer[idx];
}
@ -126,6 +122,11 @@ public:
m_buffer.resize(sz, 0);
}
void shrink(unsigned sz) {
SASSERT(sz <= m_buffer.size());
resize(sz);
}
// set pos idx with elem. If idx >= size, then expand.
void setx(unsigned idx, T * elem) {
if (idx >= size()) {
@ -133,19 +134,23 @@ public:
}
set(idx, elem);
}
private:
// prevent abuse:
ref_buffer_core& operator=(ref_buffer_core const & other);
ref_buffer_core & operator=(ref_buffer_core const & other) {
if (this == &other)
return *this;
reset();
append(other);
return *this;
}
};
/**
\brief Buffer of managed references
*/
template<typename T, typename TManager>
class ref_buffer : public ref_buffer_core<T, ref_manager_wrapper<T, TManager> > {
typedef ref_buffer_core<T, ref_manager_wrapper<T, TManager> > super;
template<typename T, typename TManager, unsigned INITIAL_SIZE=16>
class ref_buffer : public ref_buffer_core<T, ref_manager_wrapper<T, TManager>, INITIAL_SIZE> {
typedef ref_buffer_core<T, ref_manager_wrapper<T, TManager>, INITIAL_SIZE> super;
public:
ref_buffer(TManager & m):
super(ref_manager_wrapper<T, TManager>(m)) {
@ -161,8 +166,8 @@ public:
/**
\brief Buffer of unmanaged references
*/
template<typename T>
class sref_buffer : public ref_buffer_core<T, ref_unmanaged_wrapper<T> > {
template<typename T, unsigned INITIAL_SIZE=16>
class sref_buffer : public ref_buffer_core<T, ref_unmanaged_wrapper<T>, INITIAL_SIZE> {
public:
};

4
src/util/util.h
View file

@ -243,6 +243,10 @@ public:
m_ptr = 0;
return tmp;
}
void swap(scoped_ptr & p) {
std::swap(m_ptr, p.m_ptr);
}
};
template<typename T1, typename T2>