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z3-z3-4.12.6.src.tactic.arith.probe_arith.cpp Maven / Gradle / Ivy
/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
probe_arith.cpp
Abstract:
Some probes for arithmetic problems.
Author:
Leonardo de Moura (leonardo) 2012-03-01.
Revision History:
--*/
#include "tactic/probe.h"
#include "ast/expr2polynomial.h"
#include "ast/for_each_expr.h"
#include "ast/arith_decl_plugin.h"
#include "tactic/goal_util.h"
namespace {
class arith_degree_probe : public probe {
struct proc {
ast_manager & m;
unsynch_mpq_manager m_qm;
polynomial::manager m_pm;
default_expr2polynomial m_expr2poly;
arith_util m_util;
unsigned m_max_degree;
unsigned long long m_acc_degree;
unsigned m_counter;
proc(ast_manager & _m):m(_m), m_pm(m.limit(), m_qm), m_expr2poly(m, m_pm), m_util(m) {
m_max_degree = 0;
m_acc_degree = 0;
m_counter = 0;
}
void updt_degree(polynomial_ref const & p) {
unsigned deg = m_pm.total_degree(p);
if (deg > m_max_degree)
m_max_degree = deg;
m_acc_degree += deg;
m_counter++;
}
void process(app * n) {
expr * lhs = n->get_arg(0);
expr * rhs = n->get_arg(1);
polynomial_ref p1(m_pm);
polynomial_ref p2(m_pm);
scoped_mpz d1(m_qm);
scoped_mpz d2(m_qm);
m_expr2poly.to_polynomial(lhs, p1, d1);
m_expr2poly.to_polynomial(rhs, p2, d2);
updt_degree(p1);
updt_degree(p2);
}
void operator()(var * n) {}
void operator()(quantifier * n) {}
void operator()(app * n) {
if (m_util.is_le(n) || m_util.is_lt(n) || m_util.is_gt(n) || m_util.is_ge(n))
process(n);
if (m.is_eq(n) && m_util.is_int_real(n->get_arg(0)))
process(n);
}
};
bool m_avg;
public:
arith_degree_probe(bool avg):m_avg(avg) {}
result operator()(goal const & g) override {
proc p(g.m());
for_each_expr_at(p, g);
if (m_avg)
return p.m_counter == 0 ? 0.0 : static_cast(p.m_acc_degree)/static_cast(p.m_counter);
else
return p.m_max_degree;
}
};
class arith_bw_probe : public probe {
struct proc {
ast_manager & m;
arith_util m_util;
unsigned m_max_bw;
unsigned long long m_acc_bw;
unsigned m_counter;
proc(ast_manager & _m):m(_m), m_util(m) {
m_max_bw = 0;
m_acc_bw = 0;
m_counter = 0;
}
void operator()(var * n) {}
void operator()(quantifier * n) {}
void operator()(app * n) {
rational val;
if (m_util.is_numeral(n, val)) {
unsigned bw = val.bitsize();
if (bw > m_max_bw)
m_max_bw = bw;
m_acc_bw += bw;
m_counter++;
}
}
};
bool m_avg;
public:
arith_bw_probe(bool avg):m_avg(avg) {}
result operator()(goal const & g) override {
proc p(g.m());
for_each_expr_at(p, g);
if (m_avg)
return p.m_counter == 0 ? 0.0 : static_cast(p.m_acc_bw)/static_cast(p.m_counter);
else
return p.m_max_bw;
}
};
struct has_nlmul {
struct found {};
ast_manager& m;
arith_util a;
has_nlmul(ast_manager& m):m(m), a(m) {}
void throw_found(expr* e) {
TRACE("probe", tout << expr_ref(e, m) << ": " << sort_ref(e->get_sort(), m) << "\n";);
throw found();
}
void operator()(var *) { }
void operator()(quantifier *) { }
void operator()(app * n) {
family_id fid = n->get_family_id();
if (fid == a.get_family_id()) {
switch (n->get_decl_kind()) {
case OP_MUL:
if (n->get_num_args() != 2 || !a.is_numeral(n->get_arg(0)))
throw_found(n);
break;
case OP_IDIV: case OP_DIV: case OP_REM: case OP_MOD:
if (!a.is_numeral(n->get_arg(1)))
throw_found(n);
break;
case OP_POWER:
throw_found(n);
default:
break;
}
}
}
};
}
probe * mk_arith_avg_degree_probe() {
return alloc(arith_degree_probe, true);
}
probe * mk_arith_max_degree_probe() {
return alloc(arith_degree_probe, false);
}
probe * mk_arith_avg_bw_probe() {
return alloc(arith_bw_probe, true);
}
probe * mk_arith_max_bw_probe() {
return alloc(arith_bw_probe, false);
}
namespace {
struct is_non_qflira_functor {
struct found {};
ast_manager & m;
arith_util u;
bool m_int;
bool m_real;
is_non_qflira_functor(ast_manager & _m, bool _int, bool _real):m(_m), u(m), m_int(_int), m_real(_real) {}
void operator()(var *) { throw found(); }
void operator()(quantifier *) { throw found(); }
bool compatible_sort(app * n) const {
if (m.is_bool(n))
return true;
if (m_int && u.is_int(n))
return true;
if (m_real && u.is_real(n))
return true;
return false;
}
void operator()(app * n) {
if (!compatible_sort(n))
throw found();
family_id fid = n->get_family_id();
if (fid == m.get_basic_family_id())
return;
if (fid == u.get_family_id()) {
switch (n->get_decl_kind()) {
case OP_LE: case OP_GE: case OP_LT: case OP_GT:
case OP_ADD: case OP_NUM:
return;
case OP_MUL:
if (n->get_num_args() != 2)
throw found();
if (!u.is_numeral(n->get_arg(0)))
throw found();
return;
case OP_TO_REAL:
if (!m_real)
throw found();
break;
default:
throw found();
}
return;
}
if (is_uninterp_const(n))
return;
throw found();
}
};
struct is_non_qfauflira_functor {
struct found {};
ast_manager & m;
arith_util m_arith_util;
array_util m_array_util;
bool m_int;
bool m_real;
is_non_qfauflira_functor(ast_manager & _m, bool _int, bool _real) :
m(_m), m_arith_util(_m), m_array_util(_m), m_int(_int), m_real(_real) {}
void operator()(var *) { throw found(); }
void operator()(quantifier *) { throw found(); }
bool compatible_sort(app * n) const {
if (m.is_bool(n))
return true;
if (m_int && m_arith_util.is_int(n))
return true;
if (m_real && m_arith_util.is_real(n))
return true;
if (m_array_util.is_array(n))
return true;
return false;
}
void operator()(app * n) {
if (!compatible_sort(n))
throw found();
family_id fid = n->get_family_id();
if (fid == m.get_basic_family_id())
return;
if (fid == m_arith_util.get_family_id()) {
switch (n->get_decl_kind()) {
case OP_LE: case OP_GE: case OP_LT: case OP_GT:
case OP_ADD: case OP_NUM:
return;
case OP_MUL:
if (n->get_num_args() != 2)
throw found();
if (!m_arith_util.is_numeral(n->get_arg(0)))
throw found();
return;
case OP_TO_REAL:
if (!m_real)
throw found();
break;
default:
throw found();
}
return;
}
if (is_uninterp(n))
return;
throw found();
}
};
static bool is_qflia(goal const & g) {
is_non_qflira_functor p(g.m(), true, false);
return !test(g, p);
}
static bool is_qfauflia(goal const & g) {
is_non_qfauflira_functor p(g.m(), true, false);
return !test(g, p);
}
class is_qflia_probe : public probe {
public:
result operator()(goal const & g) override {
return is_qflia(g);
}
};
class is_qfauflia_probe : public probe {
public:
result operator()(goal const & g) override {
return is_qfauflia(g);
}
};
static bool is_qflra(goal const & g) {
is_non_qflira_functor p(g.m(), false, true);
return !test(g, p);
}
class is_qflra_probe : public probe {
public:
result operator()(goal const & g) override {
return is_qflra(g);
}
};
static bool is_qflira(goal const & g) {
is_non_qflira_functor p(g.m(), true, true);
return !test(g, p);
}
class is_qflira_probe : public probe {
public:
result operator()(goal const & g) override {
return is_qflira(g);
}
};
static bool is_lp(goal const & g) {
ast_manager & m = g.m();
arith_util u(m);
unsigned sz = g.size();
for (unsigned i = 0; i < sz; i++) {
expr * f = g.form(i);
bool sign = false;
while (m.is_not(f, f))
sign = !sign;
if (m.is_eq(f) && !sign) {
if (to_app(f)->get_arg(0)->get_sort()->get_family_id() != u.get_family_id())
return false;
continue;
}
if (u.is_le(f) || u.is_ge(f) || u.is_lt(f) || u.is_gt(f))
continue;
return false;
}
return true;
}
static bool is_ilp(goal const & g) {
if (!is_qflia(g))
return false;
if (has_term_ite(g))
return false;
return is_lp(g);
}
static bool is_mip(goal const & g) {
if (!is_qflira(g))
return false;
if (has_term_ite(g))
return false;
return is_lp(g);
}
class is_ilp_probe : public probe {
public:
result operator()(goal const & g) override {
return is_ilp(g);
}
};
class is_mip_probe : public probe {
public:
result operator()(goal const & g) override {
return is_mip(g);
}
};
}
probe * mk_is_qflia_probe() {
return alloc(is_qflia_probe);
}
probe * mk_is_qfauflia_probe() {
return alloc(is_qfauflia_probe);
}
probe * mk_is_qflra_probe() {
return alloc(is_qflra_probe);
}
probe * mk_is_qflira_probe() {
return alloc(is_qflira_probe);
}
probe * mk_is_ilp_probe() {
return alloc(is_ilp_probe);
}
probe * mk_is_mip_probe() {
return alloc(is_mip_probe);
}
namespace {
struct is_non_nira_functor {
struct found {};
ast_manager & m;
arith_util u;
bool m_int;
bool m_real;
bool m_quant;
bool m_linear;
is_non_nira_functor(ast_manager & _m, bool _int, bool _real, bool _quant, bool linear):m(_m), u(m), m_int(_int), m_real(_real), m_quant(_quant), m_linear(linear) {}
void throw_found(expr* e) {
TRACE("probe", tout << expr_ref(e, m) << ": " << sort_ref(e->get_sort(), m) << "\n";);
throw found();
}
void operator()(var * x) {
if (!m_quant)
throw_found(x);
sort * s = x->get_sort();
if (m_int && u.is_int(s))
return;
if (m_real && u.is_real(s))
return;
if (m.is_bool(s))
return;
throw_found(x);
}
void operator()(quantifier * q) {
if (!m_quant)
throw_found(q);
}
bool compatible_sort(app * n) const {
if (m.is_bool(n))
return true;
if (m_int && u.is_int(n))
return true;
if (m_real && u.is_real(n))
return true;
return false;
}
void operator()(app * n) {
if (!compatible_sort(n))
throw_found(n);
family_id fid = n->get_family_id();
rational r;
if (fid == m.get_basic_family_id())
return;
if (fid == u.get_family_id()) {
switch (n->get_decl_kind()) {
case OP_LE: case OP_GE: case OP_LT: case OP_GT:
case OP_ADD: case OP_UMINUS: case OP_SUB: case OP_ABS:
case OP_NUM:
return;
case OP_MUL:
if (m_linear) {
if (n->get_num_args() != 2)
throw_found(n);
if (!u.is_numeral(n->get_arg(0)) && !u.is_numeral(n->get_arg(1)))
throw_found(n);
}
return;
case OP_IDIV: case OP_DIV: case OP_REM: case OP_MOD:
if (m_linear && !u.is_numeral(n->get_arg(1)))
throw_found(n);
if (m_linear && u.is_numeral(n->get_arg(1), r) && r.is_zero())
throw_found(n);
if (m_linear && u.is_numeral(n->get_arg(1), r) && !r.is_zero())
return;
if (!is_ground(n->get_arg(0)) || !is_ground(n->get_arg(1)))
throw_found(n);
return;
case OP_IS_INT:
if (m_real)
throw_found(n);
return;
case OP_TO_INT:
case OP_TO_REAL:
return;
case OP_POWER:
if (m_linear)
throw_found(n);
//if (!u.is_numeral(n->get_arg(0), r) || !r.is_unsigned() || r.is_zero())
// throw_found(n);
return;
case OP_IRRATIONAL_ALGEBRAIC_NUM:
if (m_linear || !m_real)
throw_found(n);
return;
default:
throw_found(n);
}
return;
}
if (is_uninterp_const(n))
return;
throw_found(n);
}
};
static bool is_qfnia(goal const & g) {
is_non_nira_functor p(g.m(), true, false, false, false);
return !test(g, p) && test(g);
}
static bool is_qfnra(goal const & g) {
is_non_nira_functor p(g.m(), false, true, false, false);
return !test(g, p) && test(g);
}
static bool is_nia(goal const & g) {
is_non_nira_functor p(g.m(), true, false, true, false);
return !test(g, p) && test(g);
}
static bool is_nra(goal const & g) {
is_non_nira_functor p(g.m(), false, true, true, false);
return !test(g, p) && test(g);
}
static bool is_nira(goal const & g) {
is_non_nira_functor p(g.m(), true, true, true, false);
return !test(g, p) && test(g);
}
static bool is_lra(goal const & g) {
is_non_nira_functor p(g.m(), false, true, true, true);
return !test(g, p);
}
static bool is_lia(goal const & g) {
is_non_nira_functor p(g.m(), true, false, true, true);
return !test(g, p);
}
static bool is_lira(goal const & g) {
is_non_nira_functor p(g.m(), true, true, true, true);
return !test(g, p);
}
struct is_non_qfufnra_functor {
struct found {};
ast_manager & m;
arith_util u;
bool m_has_nonlinear;
is_non_qfufnra_functor(ast_manager & _m):
m(_m), u(m), m_has_nonlinear(false) {}
void throw_found() {
throw found();
}
bool has_nonlinear() const {
return m_has_nonlinear;
}
void operator()(var * x) {
throw_found();
}
void operator()(quantifier *) {
throw_found();
}
void operator()(app * n) {
family_id fid = n->get_family_id();
if (fid == m.get_basic_family_id())
return;
if (fid == u.get_family_id()) {
switch (n->get_decl_kind()) {
case OP_LE: case OP_GE: case OP_LT: case OP_GT:
case OP_ADD: case OP_UMINUS: case OP_SUB: case OP_ABS:
case OP_NUM:
case OP_IRRATIONAL_ALGEBRAIC_NUM:
return;
case OP_MUL:
if (n->get_num_args() == 2 &&
u.is_real(n->get_arg(0)) &&
!u.is_numeral(n->get_arg(0)) &&
!u.is_numeral(n->get_arg(1))) {
m_has_nonlinear = true;
}
return;
case OP_IDIV: case OP_DIV: case OP_REM: case OP_MOD:
if (!u.is_numeral(n->get_arg(1))) {
TRACE("arith", tout << "non-linear " << expr_ref(n, m) << "\n";);
throw_found();
}
return;
case OP_POWER:
if (!u.is_numeral(n->get_arg(1))) {
TRACE("arith", tout << "non-linear " << expr_ref(n, m) << "\n";);
throw_found();
}
m_has_nonlinear = true;
return;
case OP_IS_INT:
case OP_TO_INT:
case OP_TO_REAL:
throw_found();
return;
default:
TRACE("arith", tout << "non-linear " << expr_ref(n, m) << "\n";);
throw_found();
}
}
}
};
class is_qfnia_probe : public probe {
public:
result operator()(goal const & g) override {
return is_qfnia(g);
}
};
class is_qfnra_probe : public probe {
public:
result operator()(goal const & g) override {
return is_qfnra(g);
}
};
class is_nia_probe : public probe {
public:
result operator()(goal const & g) override {
return is_nia(g);
}
};
class is_nra_probe : public probe {
public:
result operator()(goal const & g) override {
return is_nra(g);
}
};
class is_nira_probe : public probe {
public:
result operator()(goal const & g) override {
return is_nira(g);
}
};
class is_lia_probe : public probe {
public:
result operator()(goal const & g) override {
return is_lia(g);
}
};
class is_lra_probe : public probe {
public:
result operator()(goal const & g) override {
return is_lra(g);
}
};
class is_lira_probe : public probe {
public:
result operator()(goal const & g) override {
return is_lira(g);
}
};
static bool is_qfufnra(goal const& g) {
is_non_qfufnra_functor p(g.m());
return !g.proofs_enabled() && !g.unsat_core_enabled() && !test(g, p) && p.has_nonlinear();
}
class is_qfufnra_probe : public probe {
public:
result operator()(goal const & g) override {
return is_qfufnra(g);
}
};
}
probe * mk_is_qfnia_probe() {
return alloc(is_qfnia_probe);
}
probe * mk_is_qfnra_probe() {
return alloc(is_qfnra_probe);
}
probe * mk_is_nia_probe() {
return alloc(is_nia_probe);
}
probe * mk_is_nra_probe() {
return alloc(is_nra_probe);
}
probe * mk_is_nira_probe() {
return alloc(is_nira_probe);
}
probe * mk_is_lia_probe() {
return alloc(is_lia_probe);
}
probe * mk_is_lra_probe() {
return alloc(is_lra_probe);
}
probe * mk_is_lira_probe() {
return alloc(is_lira_probe);
}
probe* mk_is_qfufnra_probe() {
return alloc(is_qfufnra_probe);
}
