mirror of
https://github.com/Z3Prover/z3
synced 2025-04-11 19:53:34 +00:00
4137 lines
152 KiB
C++
4137 lines
152 KiB
C++
/*++
|
|
Copyright (c) 2012 Microsoft Corporation
|
|
|
|
Module Name:
|
|
|
|
nlsat_solver.cpp
|
|
|
|
Abstract:
|
|
|
|
Nonlinear arithmetic satisfiability procedure. The procedure is
|
|
complete for nonlinear real arithmetic, but it also has limited
|
|
support for integers.
|
|
|
|
Author:
|
|
|
|
Leonardo de Moura (leonardo) 2012-01-02.
|
|
|
|
Revision History:
|
|
|
|
--*/
|
|
#include "util/z3_exception.h"
|
|
#include "util/chashtable.h"
|
|
#include "util/id_gen.h"
|
|
#include "util/map.h"
|
|
#include "util/dependency.h"
|
|
#include "util/permutation.h"
|
|
#include "math/polynomial/algebraic_numbers.h"
|
|
#include "math/polynomial/polynomial_cache.h"
|
|
#include "nlsat/nlsat_solver.h"
|
|
#include "nlsat/nlsat_clause.h"
|
|
#include "nlsat/nlsat_assignment.h"
|
|
#include "nlsat/nlsat_justification.h"
|
|
#include "nlsat/nlsat_evaluator.h"
|
|
#include "nlsat/nlsat_explain.h"
|
|
#include "nlsat/nlsat_params.hpp"
|
|
#include "nlsat/nlsat_simplify.h"
|
|
#include "nlsat/nlsat_simple_checker.h"
|
|
#include "nlsat/nlsat_variable_ordering_strategy.h"
|
|
|
|
#define NLSAT_EXTRA_VERBOSE
|
|
|
|
#ifdef NLSAT_EXTRA_VERBOSE
|
|
#define NLSAT_VERBOSE(CODE) IF_VERBOSE(10, CODE)
|
|
#else
|
|
#define NLSAT_VERBOSE(CODE) ((void)0)
|
|
#endif
|
|
|
|
namespace nlsat {
|
|
|
|
|
|
typedef chashtable<ineq_atom*, ineq_atom::hash_proc, ineq_atom::eq_proc> ineq_atom_table;
|
|
typedef chashtable<root_atom*, root_atom::hash_proc, root_atom::eq_proc> root_atom_table;
|
|
|
|
// for apply_permutation procedure
|
|
void swap(clause * & c1, clause * & c2) noexcept {
|
|
std::swap(c1, c2);
|
|
}
|
|
|
|
struct solver::ctx {
|
|
params_ref m_params;
|
|
reslimit& m_rlimit;
|
|
small_object_allocator m_allocator;
|
|
unsynch_mpq_manager m_qm;
|
|
pmanager m_pm;
|
|
anum_manager m_am;
|
|
bool m_incremental;
|
|
ctx(reslimit& rlim, params_ref const & p, bool incremental):
|
|
m_params(p),
|
|
m_rlimit(rlim),
|
|
m_allocator("nlsat"),
|
|
m_pm(rlim, m_qm, &m_allocator),
|
|
m_am(rlim, m_qm, p, &m_allocator),
|
|
m_incremental(incremental)
|
|
{}
|
|
};
|
|
|
|
struct solver::imp {
|
|
|
|
|
|
struct dconfig {
|
|
typedef imp value_manager;
|
|
typedef small_object_allocator allocator;
|
|
typedef void* value;
|
|
static const bool ref_count = false;
|
|
};
|
|
|
|
typedef dependency_manager<dconfig> assumption_manager;
|
|
typedef assumption_manager::dependency* _assumption_set;
|
|
|
|
typedef obj_ref<assumption_manager::dependency, assumption_manager> assumption_set_ref;
|
|
|
|
|
|
typedef polynomial::cache cache;
|
|
typedef ptr_vector<interval_set> interval_set_vector;
|
|
|
|
|
|
|
|
ctx& m_ctx;
|
|
solver& m_solver;
|
|
reslimit& m_rlimit;
|
|
small_object_allocator& m_allocator;
|
|
bool m_incremental;
|
|
unsynch_mpq_manager& m_qm;
|
|
pmanager& m_pm;
|
|
cache m_cache;
|
|
anum_manager& m_am;
|
|
mutable assumption_manager m_asm;
|
|
assignment m_assignment, m_lo, m_hi; // partial interpretation
|
|
evaluator m_evaluator;
|
|
interval_set_manager & m_ism;
|
|
ineq_atom_table m_ineq_atoms;
|
|
root_atom_table m_root_atoms;
|
|
|
|
|
|
vector<bound_constraint> m_bounds;
|
|
|
|
id_gen m_cid_gen;
|
|
clause_vector m_clauses; // set of clauses
|
|
clause_vector m_learned; // set of learned clauses
|
|
clause_vector m_valids;
|
|
|
|
unsigned m_num_bool_vars;
|
|
atom_vector m_atoms; // bool_var -> atom
|
|
svector<lbool> m_bvalues; // boolean assignment
|
|
unsigned_vector m_levels; // bool_var -> level
|
|
svector<justification> m_justifications;
|
|
vector<clause_vector> m_bwatches; // bool_var (that are not attached to atoms) -> clauses where it is maximal
|
|
bool_vector m_dead; // mark dead boolean variables
|
|
id_gen m_bid_gen;
|
|
|
|
simplify m_simplify;
|
|
|
|
bool_vector m_is_int; // m_is_int[x] is true if variable is integer
|
|
vector<clause_vector> m_watches; // var -> clauses where variable is maximal
|
|
interval_set_vector m_infeasible; // var -> to a set of interval where the variable cannot be assigned to.
|
|
atom_vector m_var2eq; // var -> to asserted equality
|
|
var_vector m_perm; // var -> var permutation of the variables
|
|
var_vector m_inv_perm;
|
|
// m_perm: internal -> external
|
|
// m_inv_perm: external -> internal
|
|
struct perm_display_var_proc : public display_var_proc {
|
|
var_vector & m_perm;
|
|
display_var_proc m_default_display_var;
|
|
display_var_proc const * m_proc; // display external var ids
|
|
perm_display_var_proc(var_vector & perm):
|
|
m_perm(perm),
|
|
m_proc(nullptr) {
|
|
}
|
|
std::ostream& operator()(std::ostream & out, var x) const override {
|
|
if (m_proc == nullptr)
|
|
m_default_display_var(out, x);
|
|
else
|
|
(*m_proc)(out, m_perm[x]);
|
|
return out;
|
|
}
|
|
};
|
|
perm_display_var_proc m_display_var;
|
|
|
|
display_assumption_proc const* m_display_assumption;
|
|
struct display_literal_assumption : public display_assumption_proc {
|
|
imp& i;
|
|
literal_vector const& lits;
|
|
display_literal_assumption(imp& i, literal_vector const& lits): i(i), lits(lits) {}
|
|
std::ostream& operator()(std::ostream& out, assumption a) const override {
|
|
if (lits.begin() <= a && a < lits.end()) {
|
|
out << *((literal const*)a);
|
|
}
|
|
else if (i.m_display_assumption) {
|
|
(*i.m_display_assumption)(out, a);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
};
|
|
struct scoped_display_assumptions {
|
|
imp& i;
|
|
display_assumption_proc const* m_save;
|
|
scoped_display_assumptions(imp& i, display_assumption_proc const& p): i(i), m_save(i.m_display_assumption) {
|
|
i.m_display_assumption = &p;
|
|
}
|
|
~scoped_display_assumptions() {
|
|
i.m_display_assumption = m_save;
|
|
}
|
|
};
|
|
|
|
explain m_explain;
|
|
|
|
bool_var m_bk; // current Boolean variable we are processing
|
|
var m_xk; // current arith variable we are processing
|
|
|
|
unsigned m_scope_lvl;
|
|
|
|
struct bvar_assignment {};
|
|
struct stage {};
|
|
struct trail {
|
|
enum kind { BVAR_ASSIGNMENT, INFEASIBLE_UPDT, NEW_LEVEL, NEW_STAGE, UPDT_EQ };
|
|
kind m_kind;
|
|
union {
|
|
bool_var m_b;
|
|
interval_set * m_old_set;
|
|
atom * m_old_eq;
|
|
};
|
|
trail(bool_var b, bvar_assignment):m_kind(BVAR_ASSIGNMENT), m_b(b) {}
|
|
trail(interval_set * old_set):m_kind(INFEASIBLE_UPDT), m_old_set(old_set) {}
|
|
trail(bool s, stage):m_kind(s ? NEW_STAGE : NEW_LEVEL) {}
|
|
trail(atom * a):m_kind(UPDT_EQ), m_old_eq(a) {}
|
|
};
|
|
svector<trail> m_trail;
|
|
|
|
anum m_zero;
|
|
|
|
// configuration
|
|
unsigned long long m_max_memory;
|
|
unsigned m_lazy; // how lazy the solver is: 0 - satisfy all learned clauses, 1 - process only unit and empty learned clauses, 2 - use only conflict clauses for resolving conflicts
|
|
bool m_simplify_cores;
|
|
bool m_reorder;
|
|
bool m_randomize;
|
|
bool m_random_order;
|
|
unsigned m_random_seed;
|
|
bool m_inline_vars;
|
|
bool m_log_lemmas;
|
|
bool m_check_lemmas;
|
|
unsigned m_max_conflicts;
|
|
unsigned m_lemma_count;
|
|
bool m_simple_check;
|
|
unsigned m_variable_ordering_strategy;
|
|
bool m_set_0_more;
|
|
bool m_cell_sample;
|
|
|
|
struct stats {
|
|
unsigned m_simplifications;
|
|
unsigned m_restarts;
|
|
unsigned m_conflicts;
|
|
unsigned m_propagations;
|
|
unsigned m_decisions;
|
|
unsigned m_stages;
|
|
unsigned m_irrational_assignments; // number of irrational witnesses
|
|
void reset() { memset(this, 0, sizeof(*this)); }
|
|
stats() { reset(); }
|
|
};
|
|
// statistics
|
|
stats m_stats;
|
|
|
|
imp(solver& s, ctx& c):
|
|
m_ctx(c),
|
|
m_solver(s),
|
|
m_rlimit(c.m_rlimit),
|
|
m_allocator(c.m_allocator),
|
|
m_incremental(c.m_incremental),
|
|
m_qm(c.m_qm),
|
|
m_pm(c.m_pm),
|
|
m_cache(m_pm),
|
|
m_am(c.m_am),
|
|
m_asm(*this, m_allocator),
|
|
m_assignment(m_am), m_lo(m_am), m_hi(m_am),
|
|
m_evaluator(s, m_assignment, m_pm, m_allocator),
|
|
m_ism(m_evaluator.ism()),
|
|
m_num_bool_vars(0),
|
|
m_simplify(s, m_atoms, m_clauses, m_learned, m_pm),
|
|
m_display_var(m_perm),
|
|
m_display_assumption(nullptr),
|
|
m_explain(s, m_assignment, m_cache, m_atoms, m_var2eq, m_evaluator, nlsat_params(c.m_params).cell_sample()),
|
|
m_scope_lvl(0),
|
|
m_lemma(s),
|
|
m_lazy_clause(s),
|
|
m_lemma_assumptions(m_asm) {
|
|
updt_params(c.m_params);
|
|
reset_statistics();
|
|
mk_true_bvar();
|
|
m_lemma_count = 0;
|
|
}
|
|
|
|
~imp() {
|
|
clear();
|
|
}
|
|
|
|
void mk_true_bvar() {
|
|
bool_var b = mk_bool_var();
|
|
SASSERT(b == true_bool_var);
|
|
literal true_lit(b, false);
|
|
mk_clause(1, &true_lit, false, nullptr);
|
|
}
|
|
|
|
void updt_params(params_ref const & _p) {
|
|
nlsat_params p(_p);
|
|
m_max_memory = p.max_memory();
|
|
m_lazy = p.lazy();
|
|
m_simplify_cores = p.simplify_conflicts();
|
|
bool min_cores = p.minimize_conflicts();
|
|
m_reorder = p.reorder();
|
|
m_randomize = p.randomize();
|
|
m_max_conflicts = p.max_conflicts();
|
|
m_random_order = p.shuffle_vars();
|
|
m_random_seed = p.seed();
|
|
m_inline_vars = p.inline_vars();
|
|
m_log_lemmas = p.log_lemmas();
|
|
m_check_lemmas = p.check_lemmas();
|
|
m_variable_ordering_strategy = p.variable_ordering_strategy();
|
|
|
|
|
|
m_cell_sample = p.cell_sample();
|
|
|
|
|
|
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);
|
|
}
|
|
|
|
void reset() {
|
|
m_explain.reset();
|
|
m_lemma.reset();
|
|
m_lazy_clause.reset();
|
|
undo_until_size(0);
|
|
del_clauses();
|
|
del_unref_atoms();
|
|
m_cache.reset();
|
|
m_assignment.reset();
|
|
m_lo.reset();
|
|
m_hi.reset();
|
|
}
|
|
|
|
void clear() {
|
|
m_explain.reset();
|
|
m_lemma.reset();
|
|
m_lazy_clause.reset();
|
|
undo_until_size(0);
|
|
del_clauses();
|
|
del_unref_atoms();
|
|
}
|
|
|
|
void checkpoint() {
|
|
if (!m_rlimit.inc()) throw solver_exception(m_rlimit.get_cancel_msg());
|
|
if (memory::get_allocation_size() > m_max_memory) throw solver_exception(Z3_MAX_MEMORY_MSG);
|
|
}
|
|
|
|
// -----------------------
|
|
//
|
|
// Basic
|
|
//
|
|
// -----------------------
|
|
|
|
unsigned num_bool_vars() const {
|
|
return m_num_bool_vars;
|
|
}
|
|
|
|
unsigned num_vars() const {
|
|
return m_is_int.size();
|
|
}
|
|
|
|
bool is_int(var x) const {
|
|
return m_is_int[x];
|
|
}
|
|
|
|
void inc_ref(assumption) {}
|
|
|
|
void dec_ref(assumption) {}
|
|
|
|
void inc_ref(_assumption_set a) {
|
|
if (a != nullptr) m_asm.inc_ref(a);
|
|
}
|
|
|
|
void dec_ref(_assumption_set a) {
|
|
if (a != nullptr) m_asm.dec_ref(a);
|
|
}
|
|
|
|
void inc_ref(bool_var b) {
|
|
if (b == null_bool_var)
|
|
return;
|
|
atom * a = m_atoms[b];
|
|
if (a == nullptr)
|
|
return;
|
|
TRACE("ref", display(tout << "inc: " << b << " " << a->ref_count() << " ", *a) << "\n";);
|
|
a->inc_ref();
|
|
}
|
|
|
|
void inc_ref(literal l) {
|
|
inc_ref(l.var());
|
|
}
|
|
|
|
void dec_ref(bool_var b) {
|
|
if (b == null_bool_var)
|
|
return;
|
|
atom * a = m_atoms[b];
|
|
if (a == nullptr)
|
|
return;
|
|
SASSERT(a->ref_count() > 0);
|
|
a->dec_ref();
|
|
TRACE("ref", display(tout << "dec: " << b << " " << a->ref_count() << " ", *a) << "\n";);
|
|
if (a->ref_count() == 0)
|
|
del(a);
|
|
}
|
|
|
|
void dec_ref(literal l) {
|
|
dec_ref(l.var());
|
|
}
|
|
|
|
bool is_arith_atom(bool_var b) const { return m_atoms[b] != nullptr; }
|
|
|
|
bool is_arith_literal(literal l) const { return is_arith_atom(l.var()); }
|
|
|
|
var max_var(poly const * p) const {
|
|
return m_pm.max_var(p);
|
|
}
|
|
|
|
var max_var(bool_var b) const {
|
|
if (!is_arith_atom(b))
|
|
return null_var;
|
|
else
|
|
return m_atoms[b]->max_var();
|
|
}
|
|
|
|
var max_var(literal l) const {
|
|
return max_var(l.var());
|
|
}
|
|
|
|
/**
|
|
\brief Return the maximum variable occurring in cls.
|
|
*/
|
|
var max_var(unsigned sz, literal const * cls) const {
|
|
var x = null_var;
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
literal l = cls[i];
|
|
if (is_arith_literal(l)) {
|
|
var y = max_var(l);
|
|
if (x == null_var || y > x)
|
|
x = y;
|
|
}
|
|
}
|
|
return x;
|
|
}
|
|
|
|
var max_var(clause const & cls) const {
|
|
return max_var(cls.size(), cls.data());
|
|
}
|
|
|
|
/**
|
|
\brief Return the maximum Boolean variable occurring in cls.
|
|
*/
|
|
bool_var max_bvar(clause const & cls) const {
|
|
bool_var b = null_bool_var;
|
|
for (literal l : cls) {
|
|
if (b == null_bool_var || l.var() > b)
|
|
b = l.var();
|
|
}
|
|
return b;
|
|
}
|
|
|
|
/**
|
|
\brief Return the degree of the maximal variable of the given atom
|
|
*/
|
|
unsigned degree(atom const * a) const {
|
|
if (a->is_ineq_atom()) {
|
|
unsigned max = 0;
|
|
unsigned sz = to_ineq_atom(a)->size();
|
|
var x = a->max_var();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
unsigned d = m_pm.degree(to_ineq_atom(a)->p(i), x);
|
|
if (d > max)
|
|
max = d;
|
|
}
|
|
return max;
|
|
}
|
|
else {
|
|
return m_pm.degree(to_root_atom(a)->p(), a->max_var());
|
|
}
|
|
}
|
|
|
|
/**
|
|
\brief Return the degree of the maximal variable in c
|
|
*/
|
|
unsigned degree(clause const & c) const {
|
|
var x = max_var(c);
|
|
if (x == null_var)
|
|
return 0;
|
|
unsigned max = 0;
|
|
for (literal l : c) {
|
|
atom const * a = m_atoms[l.var()];
|
|
if (a == nullptr)
|
|
continue;
|
|
unsigned d = degree(a);
|
|
if (d > max)
|
|
max = d;
|
|
}
|
|
return max;
|
|
}
|
|
|
|
// -----------------------
|
|
//
|
|
// Variable, Atoms, Clauses & Assumption creation
|
|
//
|
|
// -----------------------
|
|
|
|
bool_var mk_bool_var_core() {
|
|
bool_var b = m_bid_gen.mk();
|
|
m_num_bool_vars++;
|
|
m_atoms .setx(b, nullptr, nullptr);
|
|
m_bvalues .setx(b, l_undef, l_undef);
|
|
m_levels .setx(b, UINT_MAX, UINT_MAX);
|
|
m_justifications.setx(b, null_justification, null_justification);
|
|
m_bwatches .setx(b, clause_vector(), clause_vector());
|
|
m_dead .setx(b, false, true);
|
|
return b;
|
|
}
|
|
|
|
bool_var mk_bool_var() {
|
|
return mk_bool_var_core();
|
|
}
|
|
|
|
var mk_var(bool is_int) {
|
|
var x = m_pm.mk_var();
|
|
register_var(x, is_int);
|
|
return x;
|
|
}
|
|
void register_var(var x, bool is_int) {
|
|
SASSERT(x == num_vars());
|
|
m_is_int. push_back(is_int);
|
|
m_watches. push_back(clause_vector());
|
|
m_infeasible.push_back(nullptr);
|
|
m_var2eq. push_back(nullptr);
|
|
m_perm. push_back(x);
|
|
m_inv_perm. push_back(x);
|
|
SASSERT(m_is_int.size() == m_watches.size());
|
|
SASSERT(m_is_int.size() == m_infeasible.size());
|
|
SASSERT(m_is_int.size() == m_var2eq.size());
|
|
SASSERT(m_is_int.size() == m_perm.size());
|
|
SASSERT(m_is_int.size() == m_inv_perm.size());
|
|
}
|
|
|
|
bool_vector m_found_vars;
|
|
void vars(literal l, var_vector& vs) {
|
|
vs.reset();
|
|
atom * a = m_atoms[l.var()];
|
|
if (a == nullptr) {
|
|
|
|
}
|
|
else if (a->is_ineq_atom()) {
|
|
unsigned sz = to_ineq_atom(a)->size();
|
|
var_vector new_vs;
|
|
for (unsigned j = 0; j < sz; j++) {
|
|
m_found_vars.reset();
|
|
m_pm.vars(to_ineq_atom(a)->p(j), new_vs);
|
|
for (unsigned i = 0; i < new_vs.size(); ++i) {
|
|
if (!m_found_vars.get(new_vs[i], false)) {
|
|
m_found_vars.setx(new_vs[i], true, false);
|
|
vs.push_back(new_vs[i]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
m_pm.vars(to_root_atom(a)->p(), vs);
|
|
//vs.erase(max_var(to_root_atom(a)->p()));
|
|
vs.push_back(to_root_atom(a)->x());
|
|
}
|
|
}
|
|
|
|
void deallocate(ineq_atom * a) {
|
|
unsigned obj_sz = ineq_atom::get_obj_size(a->size());
|
|
a->~ineq_atom();
|
|
m_allocator.deallocate(obj_sz, a);
|
|
}
|
|
|
|
void deallocate(root_atom * a) {
|
|
a->~root_atom();
|
|
m_allocator.deallocate(sizeof(root_atom), a);
|
|
}
|
|
|
|
void del(bool_var b) {
|
|
SASSERT(m_bwatches[b].empty());
|
|
//SASSERT(m_bvalues[b] == l_undef);
|
|
m_num_bool_vars--;
|
|
m_dead[b] = true;
|
|
m_atoms[b] = nullptr;
|
|
m_bvalues[b] = l_undef;
|
|
m_bid_gen.recycle(b);
|
|
}
|
|
|
|
void del(ineq_atom * a) {
|
|
CTRACE("nlsat_solver", a->ref_count() > 0, display(tout, *a) << "\n";);
|
|
// this triggers in too many benign cases:
|
|
// SASSERT(a->ref_count() == 0);
|
|
m_ineq_atoms.erase(a);
|
|
del(a->bvar());
|
|
unsigned sz = a->size();
|
|
for (unsigned i = 0; i < sz; i++)
|
|
m_pm.dec_ref(a->p(i));
|
|
deallocate(a);
|
|
}
|
|
|
|
void del(root_atom * a) {
|
|
SASSERT(a->ref_count() == 0);
|
|
m_root_atoms.erase(a);
|
|
del(a->bvar());
|
|
m_pm.dec_ref(a->p());
|
|
deallocate(a);
|
|
}
|
|
|
|
void del(atom * a) {
|
|
if (a == nullptr)
|
|
return;
|
|
TRACE("nlsat_verbose", display(tout << "del: b" << a->m_bool_var << " " << a->ref_count() << " ", *a) << "\n";);
|
|
if (a->is_ineq_atom())
|
|
del(to_ineq_atom(a));
|
|
else
|
|
del(to_root_atom(a));
|
|
}
|
|
|
|
// Delete atoms with ref_count == 0
|
|
void del_unref_atoms() {
|
|
for (auto* a : m_atoms) {
|
|
del(a);
|
|
}
|
|
}
|
|
|
|
|
|
ineq_atom* mk_ineq_atom(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even, bool& is_new, bool simplify) {
|
|
SASSERT(sz >= 1);
|
|
SASSERT(k == atom::LT || k == atom::GT || k == atom::EQ);
|
|
int sign = 1;
|
|
polynomial_ref p(m_pm);
|
|
ptr_buffer<poly> uniq_ps;
|
|
var max = null_var;
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
p = m_pm.flip_sign_if_lm_neg(ps[i]);
|
|
if (p.get() != ps[i] && !is_even[i]) {
|
|
sign = -sign;
|
|
}
|
|
var curr_max = max_var(p.get());
|
|
if (curr_max > max || max == null_var)
|
|
max = curr_max;
|
|
if (sz == 1 && simplify) {
|
|
if (sign < 0)
|
|
k = atom::flip(k);
|
|
sign = 1;
|
|
polynomial::manager::ineq_type t;
|
|
switch (k) {
|
|
case atom::EQ: t = polynomial::manager::ineq_type::EQ; break;
|
|
case atom::LT: t = polynomial::manager::ineq_type::LT; break;
|
|
case atom::GT: t = polynomial::manager::ineq_type::GT; break;
|
|
default: UNREACHABLE(); break;
|
|
}
|
|
polynomial::var_vector vars;
|
|
m_pm.vars(p, vars);
|
|
bool all_int = all_of(vars, [&](var x) { return is_int(x); });
|
|
if (!all_int)
|
|
t = polynomial::manager::ineq_type::EQ;
|
|
m_pm.gcd_simplify(p, t);
|
|
}
|
|
uniq_ps.push_back(m_cache.mk_unique(p));
|
|
TRACE("nlsat_table_bug", tout << "p: " << p << ", uniq: " << uniq_ps.back() << "\n";);
|
|
//verbose_stream() << "p: " << p.get() << ", uniq: " << uniq_ps.back() << "\n";
|
|
}
|
|
void * mem = m_allocator.allocate(ineq_atom::get_obj_size(sz));
|
|
if (sign < 0)
|
|
k = atom::flip(k);
|
|
ineq_atom * tmp_atom = new (mem) ineq_atom(k, sz, uniq_ps.data(), is_even, max);
|
|
ineq_atom * atom = m_ineq_atoms.insert_if_not_there(tmp_atom);
|
|
CTRACE("nlsat_table_bug", tmp_atom != atom, ineq_atom::hash_proc h;
|
|
tout << "mk_ineq_atom hash: " << h(tmp_atom) << "\n"; display(tout, *tmp_atom, m_display_var) << "\n";);
|
|
CTRACE("nlsat_table_bug", atom->max_var() != max, display(tout << "nonmax: ", *atom, m_display_var) << "\n";);
|
|
SASSERT(atom->max_var() == max);
|
|
is_new = (atom == tmp_atom);
|
|
if (is_new) {
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
m_pm.inc_ref(atom->p(i));
|
|
}
|
|
}
|
|
else {
|
|
deallocate(tmp_atom);
|
|
}
|
|
return atom;
|
|
}
|
|
|
|
bool_var mk_ineq_atom(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even, bool simplify = false) {
|
|
bool is_new = false;
|
|
ineq_atom* atom = mk_ineq_atom(k, sz, ps, is_even, is_new, simplify);
|
|
if (!is_new) {
|
|
return atom->bvar();
|
|
}
|
|
else {
|
|
bool_var b = mk_bool_var_core();
|
|
m_atoms[b] = atom;
|
|
atom->m_bool_var = b;
|
|
TRACE("nlsat_verbose", display(tout << "create: b" << atom->m_bool_var << " ", *atom) << "\n";);
|
|
return b;
|
|
}
|
|
}
|
|
|
|
literal mk_ineq_literal(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even, bool simplify = false) {
|
|
SASSERT(k == atom::LT || k == atom::GT || k == atom::EQ);
|
|
bool is_const = true;
|
|
polynomial::manager::scoped_numeral cnst(m_pm.m());
|
|
m_pm.m().set(cnst, 1);
|
|
for (unsigned i = 0; i < sz; ++i) {
|
|
if (m_pm.is_const(ps[i])) {
|
|
if (m_pm.is_zero(ps[i])) {
|
|
m_pm.m().set(cnst, 0);
|
|
is_const = true;
|
|
break;
|
|
}
|
|
auto const& c = m_pm.coeff(ps[i], 0);
|
|
m_pm.m().mul(cnst, c, cnst);
|
|
if (is_even[i] && m_pm.m().is_neg(c)) {
|
|
m_pm.m().neg(cnst);
|
|
}
|
|
}
|
|
else {
|
|
is_const = false;
|
|
}
|
|
}
|
|
if (is_const) {
|
|
if (m_pm.m().is_pos(cnst) && k == atom::GT) return true_literal;
|
|
if (m_pm.m().is_neg(cnst) && k == atom::LT) return true_literal;
|
|
if (m_pm.m().is_zero(cnst) && k == atom::EQ) return true_literal;
|
|
return false_literal;
|
|
}
|
|
return literal(mk_ineq_atom(k, sz, ps, is_even, simplify), false);
|
|
}
|
|
|
|
bool_var mk_root_atom(atom::kind k, var x, unsigned i, poly * p) {
|
|
polynomial_ref p1(m_pm), uniq_p(m_pm);
|
|
p1 = m_pm.flip_sign_if_lm_neg(p); // flipping the sign of the polynomial will not change its roots.
|
|
uniq_p = m_cache.mk_unique(p1);
|
|
TRACE("nlsat_solver", tout << x << " " << p1 << " " << uniq_p << "\n";);
|
|
SASSERT(i > 0);
|
|
SASSERT(x >= max_var(p));
|
|
SASSERT(k == atom::ROOT_LT || k == atom::ROOT_GT || k == atom::ROOT_EQ || k == atom::ROOT_LE || k == atom::ROOT_GE);
|
|
|
|
void * mem = m_allocator.allocate(sizeof(root_atom));
|
|
root_atom * new_atom = new (mem) root_atom(k, x, i, uniq_p);
|
|
root_atom * old_atom = m_root_atoms.insert_if_not_there(new_atom);
|
|
SASSERT(old_atom->max_var() == x);
|
|
if (old_atom != new_atom) {
|
|
deallocate(new_atom);
|
|
return old_atom->bvar();
|
|
}
|
|
bool_var b = mk_bool_var_core();
|
|
m_atoms[b] = new_atom;
|
|
new_atom->m_bool_var = b;
|
|
m_pm.inc_ref(new_atom->p());
|
|
return b;
|
|
}
|
|
|
|
void attach_clause(clause & cls) {
|
|
var x = max_var(cls);
|
|
if (x != null_var) {
|
|
m_watches[x].push_back(&cls);
|
|
}
|
|
else {
|
|
bool_var b = max_bvar(cls);
|
|
m_bwatches[b].push_back(&cls);
|
|
}
|
|
}
|
|
|
|
void deattach_clause(clause & cls) {
|
|
var x = max_var(cls);
|
|
if (x != null_var) {
|
|
m_watches[x].erase(&cls);
|
|
}
|
|
else {
|
|
bool_var b = max_bvar(cls);
|
|
m_bwatches[b].erase(&cls);
|
|
}
|
|
}
|
|
|
|
void deallocate(clause * cls) {
|
|
size_t obj_sz = clause::get_obj_size(cls->size());
|
|
cls->~clause();
|
|
m_allocator.deallocate(obj_sz, cls);
|
|
}
|
|
|
|
void del_clause(clause * cls) {
|
|
deattach_clause(*cls);
|
|
m_cid_gen.recycle(cls->id());
|
|
unsigned sz = cls->size();
|
|
for (unsigned i = 0; i < sz; i++)
|
|
dec_ref((*cls)[i]);
|
|
_assumption_set a = static_cast<_assumption_set>(cls->assumptions());
|
|
dec_ref(a);
|
|
deallocate(cls);
|
|
}
|
|
|
|
void del_clause(clause * cls, clause_vector& clauses) {
|
|
clauses.erase(cls);
|
|
del_clause(cls);
|
|
}
|
|
|
|
void del_clauses(ptr_vector<clause> & cs) {
|
|
for (clause* cp : cs)
|
|
del_clause(cp);
|
|
cs.reset();
|
|
}
|
|
|
|
void del_clauses() {
|
|
del_clauses(m_clauses);
|
|
del_clauses(m_learned);
|
|
del_clauses(m_valids);
|
|
}
|
|
|
|
// We use a simple heuristic to sort literals
|
|
// - bool literals < arith literals
|
|
// - sort literals based on max_var
|
|
// - sort literal with the same max_var using degree
|
|
// break ties using the fact that ineqs are usually cheaper to process than eqs.
|
|
struct lit_lt {
|
|
imp & m;
|
|
lit_lt(imp & _m):m(_m) {}
|
|
|
|
bool operator()(literal l1, literal l2) const {
|
|
atom * a1 = m.m_atoms[l1.var()];
|
|
atom * a2 = m.m_atoms[l2.var()];
|
|
if (a1 == nullptr && a2 == nullptr)
|
|
return l1.index() < l2.index();
|
|
if (a1 == nullptr)
|
|
return true;
|
|
if (a2 == nullptr)
|
|
return false;
|
|
var x1 = a1->max_var();
|
|
var x2 = a2->max_var();
|
|
if (x1 < x2)
|
|
return true;
|
|
if (x1 > x2)
|
|
return false;
|
|
SASSERT(x1 == x2);
|
|
unsigned d1 = m.degree(a1);
|
|
unsigned d2 = m.degree(a2);
|
|
if (d1 < d2)
|
|
return true;
|
|
if (d1 > d2)
|
|
return false;
|
|
if (!a1->is_eq() && a2->is_eq())
|
|
return true;
|
|
if (a1->is_eq() && !a2->is_eq())
|
|
return false;
|
|
return l1.index() < l2.index();
|
|
}
|
|
};
|
|
|
|
class scoped_bool_vars {
|
|
imp& s;
|
|
svector<bool_var> vec;
|
|
public:
|
|
scoped_bool_vars(imp& s):s(s) {}
|
|
~scoped_bool_vars() {
|
|
for (bool_var v : vec) {
|
|
s.dec_ref(v);
|
|
}
|
|
}
|
|
void push_back(bool_var v) {
|
|
s.inc_ref(v);
|
|
vec.push_back(v);
|
|
}
|
|
bool_var const* begin() const { return vec.begin(); }
|
|
bool_var const* end() const { return vec.end(); }
|
|
bool_var operator[](bool_var v) const { return vec[v]; }
|
|
};
|
|
|
|
void check_lemma(unsigned n, literal const* cls, bool is_valid, assumption_set a) {
|
|
TRACE("nlsat", display(tout << "check lemma: ", n, cls) << "\n";
|
|
display(tout););
|
|
IF_VERBOSE(2, display(verbose_stream() << "check lemma " << (is_valid?"valid: ":"consequence: "), n, cls) << "\n");
|
|
for (clause* c : m_learned) IF_VERBOSE(1, display(verbose_stream() << "lemma: ", *c) << "\n");
|
|
scoped_suspend_rlimit _limit(m_rlimit);
|
|
ctx c(m_rlimit, m_ctx.m_params, m_ctx.m_incremental);
|
|
solver solver2(c);
|
|
imp& checker = *(solver2.m_imp);
|
|
checker.m_check_lemmas = false;
|
|
checker.m_log_lemmas = false;
|
|
checker.m_inline_vars = false;
|
|
|
|
auto pconvert = [&](poly* p) {
|
|
return convert(m_pm, p, checker.m_pm);
|
|
};
|
|
|
|
// need to translate Boolean variables and literals
|
|
scoped_bool_vars tr(checker);
|
|
for (var x = 0; x < m_is_int.size(); ++x) {
|
|
checker.register_var(x, is_int(x));
|
|
}
|
|
bool_var bv = 0;
|
|
tr.push_back(bv);
|
|
for (bool_var b = 1; b < m_atoms.size(); ++b) {
|
|
atom* a = m_atoms[b];
|
|
if (a == nullptr) {
|
|
bv = checker.mk_bool_var();
|
|
}
|
|
else if (a->is_ineq_atom()) {
|
|
ineq_atom& ia = *to_ineq_atom(a);
|
|
unsigned sz = ia.size();
|
|
polynomial_ref_vector ps(checker.m_pm);
|
|
bool_vector is_even;
|
|
for (unsigned i = 0; i < sz; ++i) {
|
|
ps.push_back(pconvert(ia.p(i)));
|
|
is_even.push_back(ia.is_even(i));
|
|
}
|
|
bv = checker.mk_ineq_atom(ia.get_kind(), sz, ps.data(), is_even.data());
|
|
}
|
|
else if (a->is_root_atom()) {
|
|
root_atom& r = *to_root_atom(a);
|
|
if (r.x() >= max_var(r.p())) {
|
|
// permutation may be reverted after check completes,
|
|
// but then root atoms are not used in lemmas.
|
|
bv = checker.mk_root_atom(r.get_kind(), r.x(), r.i(), pconvert(r.p()));
|
|
}
|
|
}
|
|
else {
|
|
UNREACHABLE();
|
|
}
|
|
tr.push_back(bv);
|
|
}
|
|
if (!is_valid) {
|
|
for (clause* c : m_clauses) {
|
|
if (!a && c->assumptions()) {
|
|
continue;
|
|
}
|
|
literal_vector lits;
|
|
for (literal lit : *c) {
|
|
lits.push_back(literal(tr[lit.var()], lit.sign()));
|
|
}
|
|
checker.mk_external_clause(lits.size(), lits.data(), nullptr);
|
|
}
|
|
}
|
|
for (unsigned i = 0; i < n; ++i) {
|
|
literal lit = cls[i];
|
|
literal nlit(tr[lit.var()], !lit.sign());
|
|
checker.mk_external_clause(1, &nlit, nullptr);
|
|
}
|
|
lbool r = checker.check();
|
|
if (r == l_true) {
|
|
for (bool_var b : tr) {
|
|
literal lit(b, false);
|
|
IF_VERBOSE(0, checker.display(verbose_stream(), lit) << " := " << checker.value(lit) << "\n");
|
|
TRACE("nlsat", checker.display(tout, lit) << " := " << checker.value(lit) << "\n";);
|
|
}
|
|
for (clause* c : m_learned) {
|
|
bool found = false;
|
|
for (literal lit: *c) {
|
|
literal tlit(tr[lit.var()], lit.sign());
|
|
found |= checker.value(tlit) == l_true;
|
|
}
|
|
if (!found) {
|
|
IF_VERBOSE(0, display(verbose_stream() << "violdated clause: ", *c) << "\n");
|
|
TRACE("nlsat", display(tout << "violdated clause: ", *c) << "\n";);
|
|
}
|
|
}
|
|
for (clause* c : m_valids) {
|
|
bool found = false;
|
|
for (literal lit: *c) {
|
|
literal tlit(tr[lit.var()], lit.sign());
|
|
found |= checker.value(tlit) == l_true;
|
|
}
|
|
if (!found) {
|
|
IF_VERBOSE(0, display(verbose_stream() << "violdated tautology clause: ", *c) << "\n");
|
|
TRACE("nlsat", display(tout << "violdated tautology clause: ", *c) << "\n";);
|
|
}
|
|
}
|
|
throw default_exception("lemma did not check");
|
|
UNREACHABLE();
|
|
}
|
|
}
|
|
|
|
void log_lemma(std::ostream& out, clause const& cls) {
|
|
log_lemma(out, cls.size(), cls.data(), false);
|
|
}
|
|
|
|
void log_lemma(std::ostream& out, unsigned n, literal const* cls, bool is_valid) {
|
|
++m_lemma_count;
|
|
out << "(set-logic NRA)\n";
|
|
if (is_valid) {
|
|
display_smt2_bool_decls(out);
|
|
display_smt2_arith_decls(out);
|
|
}
|
|
else
|
|
display_smt2(out);
|
|
for (unsigned i = 0; i < n; ++i)
|
|
display_smt2(out << "(assert ", ~cls[i]) << ")\n";
|
|
display(out << "(echo \"#" << m_lemma_count << " ", n, cls) << "\")\n";
|
|
out << "(check-sat)\n(reset)\n";
|
|
|
|
TRACE("nlsat", display(tout << "(echo \"#" << m_lemma_count << " ", n, cls) << "\")\n");
|
|
}
|
|
|
|
clause * mk_clause_core(unsigned num_lits, literal const * lits, bool learned, _assumption_set a) {
|
|
SASSERT(num_lits > 0);
|
|
unsigned cid = m_cid_gen.mk();
|
|
void * mem = m_allocator.allocate(clause::get_obj_size(num_lits));
|
|
clause * cls = new (mem) clause(cid, num_lits, lits, learned, a);
|
|
for (unsigned i = 0; i < num_lits; i++)
|
|
inc_ref(lits[i]);
|
|
inc_ref(a);
|
|
return cls;
|
|
}
|
|
|
|
clause * mk_clause(unsigned num_lits, literal const * lits, bool learned, _assumption_set a) {
|
|
if (num_lits == 0) {
|
|
num_lits = 1;
|
|
lits = &false_literal;
|
|
}
|
|
SASSERT(num_lits > 0);
|
|
clause * cls = mk_clause_core(num_lits, lits, learned, a);
|
|
TRACE("nlsat_sort", display(tout << "mk_clause:\n", *cls) << "\n";);
|
|
std::sort(cls->begin(), cls->end(), lit_lt(*this));
|
|
TRACE("nlsat", display(tout << " after sort:\n", *cls) << "\n";);
|
|
if (learned && m_log_lemmas) {
|
|
log_lemma(verbose_stream(), *cls);
|
|
}
|
|
if (learned && m_check_lemmas && false) {
|
|
check_lemma(cls->size(), cls->data(), false, cls->assumptions());
|
|
}
|
|
if (learned)
|
|
m_learned.push_back(cls);
|
|
else
|
|
m_clauses.push_back(cls);
|
|
attach_clause(*cls);
|
|
return cls;
|
|
}
|
|
|
|
void mk_external_clause(unsigned num_lits, literal const * lits, assumption a) {
|
|
_assumption_set as = nullptr;
|
|
if (a != nullptr)
|
|
as = m_asm.mk_leaf(a);
|
|
if (num_lits == 0) {
|
|
num_lits = 1;
|
|
lits = &false_literal;
|
|
}
|
|
mk_clause(num_lits, lits, false, as);
|
|
}
|
|
|
|
// -----------------------
|
|
//
|
|
// Search
|
|
//
|
|
// -----------------------
|
|
|
|
void save_assign_trail(bool_var b) {
|
|
m_trail.push_back(trail(b, bvar_assignment()));
|
|
}
|
|
|
|
void save_set_updt_trail(interval_set * old_set) {
|
|
m_trail.push_back(trail(old_set));
|
|
}
|
|
|
|
void save_updt_eq_trail(atom * old_eq) {
|
|
m_trail.push_back(trail(old_eq));
|
|
}
|
|
|
|
void save_new_stage_trail() {
|
|
m_trail.push_back(trail(true, stage()));
|
|
}
|
|
|
|
void save_new_level_trail() {
|
|
m_trail.push_back(trail(false, stage()));
|
|
}
|
|
|
|
void undo_bvar_assignment(bool_var b) {
|
|
m_bvalues[b] = l_undef;
|
|
m_levels[b] = UINT_MAX;
|
|
del_jst(m_allocator, m_justifications[b]);
|
|
m_justifications[b] = null_justification;
|
|
if (m_atoms[b] == nullptr && b < m_bk)
|
|
m_bk = b;
|
|
}
|
|
|
|
void undo_set_updt(interval_set * old_set) {
|
|
if (m_xk == null_var)
|
|
return;
|
|
var x = m_xk;
|
|
if (x < m_infeasible.size()) {
|
|
m_ism.dec_ref(m_infeasible[x]);
|
|
m_infeasible[x] = old_set;
|
|
}
|
|
}
|
|
|
|
void undo_new_stage() {
|
|
if (m_xk == 0) {
|
|
m_xk = null_var;
|
|
}
|
|
else if (m_xk != null_var) {
|
|
m_xk--;
|
|
m_assignment.reset(m_xk);
|
|
}
|
|
}
|
|
|
|
void undo_new_level() {
|
|
SASSERT(m_scope_lvl > 0);
|
|
m_scope_lvl--;
|
|
m_evaluator.pop(1);
|
|
}
|
|
|
|
void undo_updt_eq(atom * a) {
|
|
if (m_var2eq.size() > m_xk)
|
|
m_var2eq[m_xk] = a;
|
|
}
|
|
|
|
template<typename Predicate>
|
|
void undo_until(Predicate const & pred) {
|
|
while (pred() && !m_trail.empty()) {
|
|
trail & t = m_trail.back();
|
|
switch (t.m_kind) {
|
|
case trail::BVAR_ASSIGNMENT:
|
|
undo_bvar_assignment(t.m_b);
|
|
break;
|
|
case trail::INFEASIBLE_UPDT:
|
|
undo_set_updt(t.m_old_set);
|
|
break;
|
|
case trail::NEW_STAGE:
|
|
undo_new_stage();
|
|
break;
|
|
case trail::NEW_LEVEL:
|
|
undo_new_level();
|
|
break;
|
|
case trail::UPDT_EQ:
|
|
undo_updt_eq(t.m_old_eq);
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
m_trail.pop_back();
|
|
}
|
|
}
|
|
|
|
struct size_pred {
|
|
svector<trail> & m_trail;
|
|
unsigned m_old_size;
|
|
size_pred(svector<trail> & trail, unsigned old_size):m_trail(trail), m_old_size(old_size) {}
|
|
bool operator()() const { return m_trail.size() > m_old_size; }
|
|
};
|
|
|
|
// Keep undoing until trail has the given size
|
|
void undo_until_size(unsigned old_size) {
|
|
SASSERT(m_trail.size() >= old_size);
|
|
undo_until(size_pred(m_trail, old_size));
|
|
}
|
|
|
|
struct stage_pred {
|
|
var const & m_xk;
|
|
var m_target;
|
|
stage_pred(var const & xk, var target):m_xk(xk), m_target(target) {}
|
|
bool operator()() const { return m_xk != m_target; }
|
|
};
|
|
|
|
// Keep undoing until stage is new_xk
|
|
void undo_until_stage(var new_xk) {
|
|
undo_until(stage_pred(m_xk, new_xk));
|
|
}
|
|
|
|
struct level_pred {
|
|
unsigned const & m_scope_lvl;
|
|
unsigned m_new_lvl;
|
|
level_pred(unsigned const & scope_lvl, unsigned new_lvl):m_scope_lvl(scope_lvl), m_new_lvl(new_lvl) {}
|
|
bool operator()() const { return m_scope_lvl > m_new_lvl; }
|
|
};
|
|
|
|
// Keep undoing until level is new_lvl
|
|
void undo_until_level(unsigned new_lvl) {
|
|
undo_until(level_pred(m_scope_lvl, new_lvl));
|
|
}
|
|
|
|
struct unassigned_pred {
|
|
bool_var m_b;
|
|
svector<lbool> const & m_bvalues;
|
|
unassigned_pred(svector<lbool> const & bvalues, bool_var b):
|
|
m_b(b),
|
|
m_bvalues(bvalues) {}
|
|
bool operator()() const { return m_bvalues[m_b] != l_undef; }
|
|
};
|
|
|
|
// Keep undoing until b is unassigned
|
|
void undo_until_unassigned(bool_var b) {
|
|
undo_until(unassigned_pred(m_bvalues, b));
|
|
SASSERT(m_bvalues[b] == l_undef);
|
|
}
|
|
|
|
struct true_pred {
|
|
bool operator()() const { return true; }
|
|
};
|
|
|
|
void undo_until_empty() {
|
|
undo_until(true_pred());
|
|
}
|
|
|
|
/**
|
|
\brief Create a new scope level
|
|
*/
|
|
void new_level() {
|
|
m_evaluator.push();
|
|
m_scope_lvl++;
|
|
save_new_level_trail();
|
|
}
|
|
|
|
/**
|
|
\brief Return the value of the given literal that was assigned by the search
|
|
engine.
|
|
*/
|
|
lbool assigned_value(literal l) const {
|
|
bool_var b = l.var();
|
|
if (l.sign())
|
|
return ~m_bvalues[b];
|
|
else
|
|
return m_bvalues[b];
|
|
}
|
|
|
|
/**
|
|
\brief Assign literal using the given justification
|
|
*/
|
|
void assign(literal l, justification j) {
|
|
TRACE("nlsat_assign",
|
|
display(tout << "assigning literal: ", l);
|
|
display(tout << " <- ", j););
|
|
|
|
SASSERT(assigned_value(l) == l_undef);
|
|
SASSERT(j != null_justification);
|
|
SASSERT(!j.is_null());
|
|
if (j.is_decision())
|
|
m_stats.m_decisions++;
|
|
else
|
|
m_stats.m_propagations++;
|
|
bool_var b = l.var();
|
|
m_bvalues[b] = to_lbool(!l.sign());
|
|
m_levels[b] = m_scope_lvl;
|
|
m_justifications[b] = j;
|
|
save_assign_trail(b);
|
|
updt_eq(b, j);
|
|
TRACE("nlsat_assign", tout << "b" << b << " -> " << m_bvalues[b] << "\n";);
|
|
}
|
|
|
|
/**
|
|
\brief Create a "case-split"
|
|
*/
|
|
void decide(literal l) {
|
|
new_level();
|
|
assign(l, decided_justification);
|
|
}
|
|
|
|
/**
|
|
\brief Return the value of a literal as defined in Dejan and Leo's paper.
|
|
*/
|
|
lbool value(literal l) {
|
|
lbool val = assigned_value(l);
|
|
if (val != l_undef) {
|
|
TRACE("nlsat_verbose", display(tout << " assigned value " << val << " for ", l) << "\n";);
|
|
return val;
|
|
}
|
|
bool_var b = l.var();
|
|
atom * a = m_atoms[b];
|
|
if (a == nullptr) {
|
|
TRACE("nlsat_verbose", display(tout << " no atom for ", l) << "\n";);
|
|
return l_undef;
|
|
}
|
|
var max = a->max_var();
|
|
if (!m_assignment.is_assigned(max)) {
|
|
TRACE("nlsat_verbose", display(tout << " maximal variable not assigned ", l) << "\n";);
|
|
return l_undef;
|
|
}
|
|
val = to_lbool(m_evaluator.eval(a, l.sign()));
|
|
TRACE("nlsat_verbose", display(tout << " evaluated value " << val << " for ", l) << "\n";);
|
|
TRACE("value_bug", tout << "value of: "; display(tout, l); tout << " := " << val << "\n";
|
|
tout << "xk: " << m_xk << ", a->max_var(): " << a->max_var() << "\n";
|
|
display_assignment(tout););
|
|
return val;
|
|
}
|
|
|
|
/**
|
|
\brief Return true if the given clause is already satisfied in the current partial interpretation.
|
|
*/
|
|
bool is_satisfied(clause const & cls) const {
|
|
for (literal l : cls) {
|
|
if (const_cast<imp*>(this)->value(l) == l_true) {
|
|
TRACE("value_bug:", tout << l << " := true\n";);
|
|
return true;
|
|
}
|
|
}
|
|
return false;
|
|
}
|
|
|
|
/**
|
|
\brief Return true if the given clause is false in the current partial interpretation.
|
|
*/
|
|
bool is_inconsistent(unsigned sz, literal const * cls) {
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
if (value(cls[i]) != l_false) {
|
|
TRACE("is_inconsistent", tout << "literal is not false:\n"; display(tout, cls[i]); tout << "\n";);
|
|
return false;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
/**
|
|
\brief Process a clauses that contains only Boolean literals.
|
|
*/
|
|
bool process_boolean_clause(clause const & cls) {
|
|
SASSERT(m_xk == null_var);
|
|
unsigned num_undef = 0;
|
|
unsigned first_undef = UINT_MAX;
|
|
unsigned sz = cls.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
literal l = cls[i];
|
|
SASSERT(m_atoms[l.var()] == nullptr);
|
|
SASSERT(value(l) != l_true);
|
|
if (value(l) == l_false)
|
|
continue;
|
|
SASSERT(value(l) == l_undef);
|
|
num_undef++;
|
|
if (first_undef == UINT_MAX)
|
|
first_undef = i;
|
|
}
|
|
if (num_undef == 0)
|
|
return false;
|
|
SASSERT(first_undef != UINT_MAX);
|
|
if (num_undef == 1)
|
|
assign(cls[first_undef], mk_clause_jst(&cls)); // unit clause
|
|
else
|
|
decide(cls[first_undef]);
|
|
return true;
|
|
}
|
|
|
|
/**
|
|
\brief assign l to true, because l + (justification of) s is infeasible in RCF in the current interpretation.
|
|
*/
|
|
literal_vector core;
|
|
ptr_vector<clause> clauses;
|
|
void R_propagate(literal l, interval_set const * s, bool include_l = true) {
|
|
m_ism.get_justifications(s, core, clauses);
|
|
if (include_l)
|
|
core.push_back(~l);
|
|
auto j = mk_lazy_jst(m_allocator, core.size(), core.data(), clauses.size(), clauses.data());
|
|
TRACE("nlsat_resolve", display(tout, j); display_eval(tout << "evaluated:", j));
|
|
assign(l, j);
|
|
SASSERT(value(l) == l_true);
|
|
}
|
|
|
|
/**
|
|
\brief m_infeasible[m_xk] <- m_infeasible[m_xk] Union s
|
|
*/
|
|
void updt_infeasible(interval_set const * s) {
|
|
SASSERT(m_xk != null_var);
|
|
interval_set * xk_set = m_infeasible[m_xk];
|
|
save_set_updt_trail(xk_set);
|
|
interval_set_ref new_set(m_ism);
|
|
TRACE("nlsat_inf_set", tout << "updating infeasible set\n"; m_ism.display(tout, xk_set) << "\n"; m_ism.display(tout, s) << "\n";);
|
|
new_set = m_ism.mk_union(s, xk_set);
|
|
TRACE("nlsat_inf_set", tout << "new infeasible set:\n"; m_ism.display(tout, new_set) << "\n";);
|
|
SASSERT(!m_ism.is_full(new_set));
|
|
m_ism.inc_ref(new_set);
|
|
m_infeasible[m_xk] = new_set;
|
|
}
|
|
|
|
/**
|
|
\brief Update m_var2eq mapping.
|
|
*/
|
|
void updt_eq(bool_var b, justification j) {
|
|
if (!m_simplify_cores)
|
|
return;
|
|
if (m_bvalues[b] != l_true)
|
|
return;
|
|
atom * a = m_atoms[b];
|
|
if (a == nullptr || a->get_kind() != atom::EQ || to_ineq_atom(a)->size() > 1 || to_ineq_atom(a)->is_even(0))
|
|
return;
|
|
switch (j.get_kind()) {
|
|
case justification::CLAUSE:
|
|
if (j.get_clause()->assumptions() != nullptr) return;
|
|
break;
|
|
case justification::LAZY:
|
|
if (j.get_lazy()->num_clauses() > 0) return;
|
|
if (j.get_lazy()->num_lits() > 0) return;
|
|
break;
|
|
default:
|
|
break;
|
|
}
|
|
var x = m_xk;
|
|
SASSERT(a->max_var() == x);
|
|
SASSERT(x != null_var);
|
|
if (m_var2eq[x] != 0 && degree(m_var2eq[x]) <= degree(a))
|
|
return; // we only update m_var2eq if the new equality has smaller degree
|
|
TRACE("nlsat_simplify_core", tout << "Saving equality for "; m_display_var(tout, x) << " (x" << x << ") ";
|
|
tout << "scope-lvl: " << scope_lvl() << "\n"; display(tout, literal(b, false)) << "\n";
|
|
display(tout, j);
|
|
);
|
|
save_updt_eq_trail(m_var2eq[x]);
|
|
m_var2eq[x] = a;
|
|
}
|
|
|
|
/**
|
|
\brief Process a clause that contains nonlinear arithmetic literals
|
|
|
|
If satisfy_learned is true, then learned clauses are satisfied even if m_lazy > 0
|
|
*/
|
|
bool process_arith_clause(clause const & cls, bool satisfy_learned) {
|
|
if (!satisfy_learned && m_lazy >= 2 && cls.is_learned()) {
|
|
TRACE("nlsat", tout << "skip learned\n";);
|
|
return true; // ignore lemmas in super lazy mode
|
|
}
|
|
SASSERT(m_xk == max_var(cls));
|
|
unsigned num_undef = 0; // number of undefined literals
|
|
unsigned first_undef = UINT_MAX; // position of the first undefined literal
|
|
interval_set_ref first_undef_set(m_ism); // infeasible region of the first undefined literal
|
|
interval_set * xk_set = m_infeasible[m_xk]; // current set of infeasible interval for current variable
|
|
SASSERT(!m_ism.is_full(xk_set));
|
|
for (unsigned idx = 0; idx < cls.size(); ++idx) {
|
|
literal l = cls[idx];
|
|
checkpoint();
|
|
if (value(l) == l_false)
|
|
continue;
|
|
if (value(l) == l_true)
|
|
return true; // could happen if clause is a tautology
|
|
CTRACE("nlsat", max_var(l) != m_xk || value(l) != l_undef, display(tout);
|
|
tout << "xk: " << m_xk << ", max_var(l): " << max_var(l) << ", l: "; display(tout, l) << "\n";
|
|
display(tout, cls) << "\n";);
|
|
SASSERT(value(l) == l_undef);
|
|
SASSERT(max_var(l) == m_xk);
|
|
bool_var b = l.var();
|
|
atom * a = m_atoms[b];
|
|
SASSERT(a != nullptr);
|
|
interval_set_ref curr_set(m_ism);
|
|
curr_set = m_evaluator.infeasible_intervals(a, l.sign(), &cls);
|
|
TRACE("nlsat_inf_set", tout << "infeasible set for literal: "; display(tout, l); tout << "\n"; m_ism.display(tout, curr_set); tout << "\n";
|
|
display(tout, cls) << "\n";);
|
|
if (m_ism.is_empty(curr_set)) {
|
|
TRACE("nlsat_inf_set", tout << "infeasible set is empty, found literal\n";);
|
|
R_propagate(l, nullptr);
|
|
SASSERT(is_satisfied(cls));
|
|
return true;
|
|
}
|
|
if (m_ism.is_full(curr_set)) {
|
|
TRACE("nlsat_inf_set", tout << "infeasible set is R, skip literal\n";);
|
|
R_propagate(~l, nullptr);
|
|
continue;
|
|
}
|
|
if (m_ism.subset(curr_set, xk_set)) {
|
|
TRACE("nlsat_inf_set", tout << "infeasible set is a subset of current set, found literal\n";);
|
|
R_propagate(l, xk_set);
|
|
return true;
|
|
}
|
|
interval_set_ref tmp(m_ism);
|
|
tmp = m_ism.mk_union(curr_set, xk_set);
|
|
if (m_ism.is_full(tmp)) {
|
|
TRACE("nlsat_inf_set", tout << "infeasible set + current set = R, skip literal\n";
|
|
display(tout, cls) << "\n";
|
|
m_ism.display(tout, tmp); tout << "\n";
|
|
);
|
|
R_propagate(~l, tmp, false);
|
|
continue;
|
|
}
|
|
num_undef++;
|
|
if (first_undef == UINT_MAX) {
|
|
first_undef = idx;
|
|
first_undef_set = curr_set;
|
|
}
|
|
}
|
|
TRACE("nlsat_inf_set", tout << "num_undef: " << num_undef << "\n";);
|
|
if (num_undef == 0)
|
|
return false;
|
|
SASSERT(first_undef != UINT_MAX);
|
|
if (num_undef == 1) {
|
|
// unit clause
|
|
assign(cls[first_undef], mk_clause_jst(&cls));
|
|
updt_infeasible(first_undef_set);
|
|
}
|
|
else if ( satisfy_learned ||
|
|
!cls.is_learned() /* must always satisfy input clauses */ ||
|
|
m_lazy == 0 /* if not in lazy mode, we also satiffy lemmas */) {
|
|
decide(cls[first_undef]);
|
|
updt_infeasible(first_undef_set);
|
|
}
|
|
else {
|
|
TRACE("nlsat_lazy", tout << "skipping clause, satisfy_learned: " << satisfy_learned << ", cls.is_learned(): " << cls.is_learned()
|
|
<< ", lazy: " << m_lazy << "\n";);
|
|
}
|
|
return true;
|
|
}
|
|
|
|
/**
|
|
\brief Try to satisfy the given clause. Return true if succeeded.
|
|
|
|
If satisfy_learned is true, then (arithmetic) learned clauses are satisfied even if m_lazy > 0
|
|
*/
|
|
bool process_clause(clause const & cls, bool satisfy_learned) {
|
|
if (is_satisfied(cls))
|
|
return true;
|
|
if (m_xk == null_var)
|
|
return process_boolean_clause(cls);
|
|
else
|
|
return process_arith_clause(cls, satisfy_learned);
|
|
}
|
|
|
|
/**
|
|
\brief Try to satisfy the given "set" of clauses.
|
|
Return 0, if the set was satisfied, or the violating clause otherwise
|
|
*/
|
|
clause * process_clauses(clause_vector const & cs) {
|
|
for (clause* c : cs) {
|
|
if (!process_clause(*c, false))
|
|
return c;
|
|
}
|
|
return nullptr; // succeeded
|
|
}
|
|
|
|
/**
|
|
\brief Make sure m_bk is the first unassigned pure Boolean variable.
|
|
Set m_bk == null_bool_var if there is no unassigned pure Boolean variable.
|
|
*/
|
|
void peek_next_bool_var() {
|
|
while (m_bk < m_atoms.size()) {
|
|
if (!m_dead[m_bk] && m_atoms[m_bk] == nullptr && m_bvalues[m_bk] == l_undef) {
|
|
return;
|
|
}
|
|
m_bk++;
|
|
}
|
|
m_bk = null_bool_var;
|
|
}
|
|
|
|
/**
|
|
\brief Create a new stage. See Dejan and Leo's paper.
|
|
*/
|
|
void new_stage() {
|
|
m_stats.m_stages++;
|
|
save_new_stage_trail();
|
|
if (m_xk == null_var)
|
|
m_xk = 0;
|
|
else
|
|
m_xk++;
|
|
}
|
|
|
|
/**
|
|
\brief Assign m_xk
|
|
*/
|
|
void select_witness() {
|
|
scoped_anum w(m_am);
|
|
SASSERT(!m_ism.is_full(m_infeasible[m_xk]));
|
|
m_ism.pick_in_complement(m_infeasible[m_xk], is_int(m_xk), w, m_randomize);
|
|
TRACE("nlsat",
|
|
tout << "infeasible intervals: "; m_ism.display(tout, m_infeasible[m_xk]); tout << "\n";
|
|
tout << "assigning "; m_display_var(tout, m_xk) << "(x" << m_xk << ") -> " << w << "\n";);
|
|
TRACE("nlsat_root", tout << "value as root object: "; m_am.display_root(tout, w); tout << "\n";);
|
|
if (!m_am.is_rational(w))
|
|
m_stats.m_irrational_assignments++;
|
|
m_assignment.set_core(m_xk, w);
|
|
}
|
|
|
|
|
|
|
|
bool is_satisfied() {
|
|
if (m_bk == null_bool_var && m_xk >= num_vars()) {
|
|
TRACE("nlsat", tout << "found model\n"; display_assignment(tout););
|
|
fix_patch();
|
|
SASSERT(check_satisfied(m_clauses));
|
|
return true; // all variables were assigned, and all clauses were satisfied.
|
|
}
|
|
else {
|
|
return false;
|
|
}
|
|
}
|
|
|
|
|
|
/**
|
|
\brief main procedure
|
|
*/
|
|
lbool search() {
|
|
TRACE("nlsat", tout << "starting search...\n"; display(tout); tout << "\nvar order:\n"; display_vars(tout););
|
|
TRACE("nlsat_proof", tout << "ASSERTED\n"; display(tout););
|
|
TRACE("nlsat_proof_sk", tout << "ASSERTED\n"; display_abst(tout););
|
|
TRACE("nlsat_mathematica", display_mathematica(tout););
|
|
TRACE("nlsat", display_smt2(tout););
|
|
m_bk = 0;
|
|
m_xk = null_var;
|
|
|
|
while (true) {
|
|
if (should_reorder())
|
|
do_reorder();
|
|
|
|
#if 0
|
|
if (should_gc())
|
|
do_gc();
|
|
#endif
|
|
|
|
if (should_simplify())
|
|
do_simplify();
|
|
|
|
CASSERT("nlsat", check_satisfied());
|
|
if (m_xk == null_var) {
|
|
peek_next_bool_var();
|
|
if (m_bk == null_bool_var)
|
|
new_stage(); // move to arith vars
|
|
}
|
|
else {
|
|
new_stage(); // peek next arith var
|
|
}
|
|
TRACE("nlsat_bug", tout << "xk: x" << m_xk << " bk: b" << m_bk << "\n";);
|
|
if (is_satisfied()) {
|
|
return l_true;
|
|
}
|
|
while (true) {
|
|
TRACE("nlsat_verbose", tout << "processing variable ";
|
|
if (m_xk != null_var) {
|
|
m_display_var(tout, m_xk); tout << " " << m_watches[m_xk].size();
|
|
}
|
|
else {
|
|
tout << m_bwatches[m_bk].size() << " boolean b" << m_bk;
|
|
}
|
|
tout << "\n";);
|
|
checkpoint();
|
|
clause * conflict_clause;
|
|
if (m_xk == null_var)
|
|
conflict_clause = process_clauses(m_bwatches[m_bk]);
|
|
else
|
|
conflict_clause = process_clauses(m_watches[m_xk]);
|
|
if (conflict_clause == nullptr)
|
|
break;
|
|
if (!resolve(*conflict_clause))
|
|
return l_false;
|
|
if (m_stats.m_conflicts >= m_max_conflicts)
|
|
return l_undef;
|
|
log();
|
|
}
|
|
|
|
if (m_xk == null_var) {
|
|
if (m_bvalues[m_bk] == l_undef) {
|
|
decide(literal(m_bk, true));
|
|
m_bk++;
|
|
}
|
|
}
|
|
else {
|
|
select_witness();
|
|
}
|
|
}
|
|
}
|
|
|
|
void gc() {
|
|
if (m_learned.size() <= 4*m_clauses.size())
|
|
return;
|
|
reset_watches();
|
|
reinit_cache();
|
|
unsigned j = 0;
|
|
for (unsigned i = 0; i < m_learned.size(); ++i) {
|
|
auto cls = m_learned[i];
|
|
if (i - j < m_clauses.size() && cls->size() > 1 && !cls->is_active())
|
|
del_clause(cls);
|
|
else {
|
|
m_learned[j++] = cls;
|
|
cls->set_active(false);
|
|
}
|
|
}
|
|
m_learned.shrink(j);
|
|
reattach_arith_clauses(m_clauses);
|
|
reattach_arith_clauses(m_learned);
|
|
}
|
|
|
|
|
|
bool should_gc() {
|
|
return m_learned.size() > 10 * m_clauses.size();
|
|
}
|
|
|
|
void do_gc() {
|
|
undo_to_base();
|
|
gc();
|
|
}
|
|
|
|
void undo_to_base() {
|
|
init_search();
|
|
m_bk = 0;
|
|
m_xk = null_var;
|
|
}
|
|
|
|
unsigned m_restart_threshold = 10000;
|
|
bool should_reorder() {
|
|
return m_stats.m_conflicts > 0 && m_stats.m_conflicts % m_restart_threshold == 0;
|
|
}
|
|
|
|
void do_reorder() {
|
|
undo_to_base();
|
|
m_stats.m_restarts++;
|
|
m_stats.m_conflicts++;
|
|
if (m_reordered)
|
|
restore_order();
|
|
apply_reorder();
|
|
}
|
|
|
|
bool m_did_simplify = false;
|
|
bool should_simplify() {
|
|
return
|
|
!m_did_simplify && m_inline_vars &&
|
|
!m_incremental && m_stats.m_conflicts > 100;
|
|
}
|
|
|
|
void do_simplify() {
|
|
undo_to_base();
|
|
m_did_simplify = true;
|
|
m_simplify();
|
|
}
|
|
|
|
unsigned m_next_conflict = 100;
|
|
void log() {
|
|
if (m_stats.m_conflicts != 1 && m_stats.m_conflicts < m_next_conflict)
|
|
return;
|
|
m_next_conflict += 100;
|
|
IF_VERBOSE(2, verbose_stream() << "(nlsat :conflicts " << m_stats.m_conflicts
|
|
<< " :decisions " << m_stats.m_decisions
|
|
<< " :propagations " << m_stats.m_propagations
|
|
<< " :clauses " << m_clauses.size()
|
|
<< " :learned " << m_learned.size() << ")\n");
|
|
}
|
|
|
|
|
|
lbool search_check() {
|
|
lbool r = l_undef;
|
|
m_stats.m_conflicts = 0;
|
|
m_stats.m_restarts = 0;
|
|
m_next_conflict = 0;
|
|
while (true) {
|
|
r = search();
|
|
if (r != l_true)
|
|
break;
|
|
++m_stats.m_restarts;
|
|
vector<std::pair<var, rational>> bounds;
|
|
|
|
for (var x = 0; x < num_vars(); x++) {
|
|
if (is_int(x) && m_assignment.is_assigned(x) && !m_am.is_int(m_assignment.value(x))) {
|
|
scoped_anum v(m_am), vlo(m_am);
|
|
v = m_assignment.value(x);
|
|
rational lo;
|
|
m_am.int_lt(v, vlo);
|
|
if (!m_am.is_int(vlo))
|
|
continue;
|
|
m_am.to_rational(vlo, lo);
|
|
// derive tight bounds.
|
|
while (true) {
|
|
lo++;
|
|
if (!m_am.gt(v, lo.to_mpq())) {
|
|
lo--;
|
|
break;
|
|
}
|
|
}
|
|
bounds.push_back(std::make_pair(x, lo));
|
|
}
|
|
}
|
|
if (bounds.empty())
|
|
break;
|
|
|
|
gc();
|
|
if (m_stats.m_restarts % 10 == 0) {
|
|
if (m_reordered)
|
|
restore_order();
|
|
apply_reorder();
|
|
}
|
|
|
|
init_search();
|
|
IF_VERBOSE(2, verbose_stream() << "(nlsat-b&b :conflicts " << m_stats.m_conflicts
|
|
<< " :decisions " << m_stats.m_decisions
|
|
<< " :propagations " << m_stats.m_propagations
|
|
<< " :clauses " << m_clauses.size()
|
|
<< " :learned " << m_learned.size() << ")\n");
|
|
for (auto const& b : bounds) {
|
|
var x = b.first;
|
|
rational lo = b.second;
|
|
rational hi = lo + 1; // rational::one();
|
|
bool is_even = false;
|
|
polynomial_ref p(m_pm);
|
|
rational one(1);
|
|
m_lemma.reset();
|
|
p = m_pm.mk_linear(1, &one, &x, -lo);
|
|
poly* p1 = p.get();
|
|
m_lemma.push_back(~mk_ineq_literal(atom::GT, 1, &p1, &is_even));
|
|
p = m_pm.mk_linear(1, &one, &x, -hi);
|
|
poly* p2 = p.get();
|
|
m_lemma.push_back(~mk_ineq_literal(atom::LT, 1, &p2, &is_even));
|
|
|
|
// perform branch and bound
|
|
clause * cls = mk_clause(m_lemma.size(), m_lemma.data(), true, nullptr);
|
|
IF_VERBOSE(4, display(verbose_stream(), *cls) << "\n");
|
|
if (cls) {
|
|
TRACE("nlsat", display(tout << "conflict " << lo << " " << hi, *cls); tout << "\n";);
|
|
}
|
|
}
|
|
}
|
|
return r;
|
|
}
|
|
|
|
bool m_reordered = false;
|
|
bool simple_check() {
|
|
// test_anum();
|
|
literal_vector learned_unit;
|
|
// Simple_Checker checker(m_solver, m_pm, m_am, m_clauses, m_learned, m_atoms, m_is_int.size());
|
|
simple_checker checker(m_pm, m_am, m_clauses, learned_unit, m_atoms, m_is_int.size());
|
|
if (!checker())
|
|
return false;
|
|
for (unsigned i = 0, sz = learned_unit.size(); i < sz; ++i) {
|
|
clause *cla = mk_clause(1, &learned_unit[i], true, nullptr);
|
|
if (m_atoms[learned_unit[i].var()] == nullptr) {
|
|
assign(learned_unit[i], mk_clause_jst(cla));
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
|
|
void run_variable_ordering_strategy() {
|
|
TRACE("reorder", tout << "runing vos: " << m_variable_ordering_strategy << '\n';);
|
|
|
|
unsigned num = num_vars();
|
|
vos_var_info_collector vos_collector(m_pm, m_atoms, num, m_variable_ordering_strategy);
|
|
vos_collector.collect(m_clauses);
|
|
vos_collector.collect(m_learned);
|
|
|
|
var_vector perm;
|
|
vos_collector(perm);
|
|
reorder(perm.size(), perm.data());
|
|
}
|
|
|
|
void apply_reorder() {
|
|
m_reordered = false;
|
|
if (!can_reorder())
|
|
;
|
|
else if (m_random_order) {
|
|
shuffle_vars();
|
|
m_reordered = true;
|
|
}
|
|
else if (m_reorder) {
|
|
heuristic_reorder();
|
|
m_reordered = true;
|
|
}
|
|
}
|
|
|
|
lbool check() {
|
|
|
|
if (m_simple_check) {
|
|
if (!simple_check()) {
|
|
TRACE("simple_check", tout << "real unsat\n";);
|
|
return l_false;
|
|
}
|
|
TRACE("simple_checker_learned",
|
|
tout << "simple check done\n";
|
|
);
|
|
}
|
|
|
|
TRACE("nlsat_smt2", display_smt2(tout););
|
|
TRACE("nlsat_fd", tout << "is_full_dimensional: " << is_full_dimensional() << "\n";);
|
|
init_search();
|
|
m_explain.set_full_dimensional(is_full_dimensional());
|
|
bool reordered = false;
|
|
|
|
|
|
if (!can_reorder()) {
|
|
|
|
}
|
|
else if (m_variable_ordering_strategy > 0) {
|
|
run_variable_ordering_strategy();
|
|
reordered = true;
|
|
}
|
|
else if (m_random_order) {
|
|
shuffle_vars();
|
|
reordered = true;
|
|
}
|
|
else if (m_reorder) {
|
|
heuristic_reorder();
|
|
reordered = true;
|
|
}
|
|
sort_watched_clauses();
|
|
lbool r = search_check();
|
|
CTRACE("nlsat_model", r == l_true, tout << "model before restore order\n"; display_assignment(tout););
|
|
if (reordered) {
|
|
restore_order();
|
|
}
|
|
CTRACE("nlsat_model", r == l_true, tout << "model\n"; display_assignment(tout););
|
|
CTRACE("nlsat", r == l_false, display(tout << "unsat\n"););
|
|
SASSERT(r != l_true || check_satisfied(m_clauses));
|
|
return r;
|
|
}
|
|
|
|
void init_search() {
|
|
undo_until_empty();
|
|
while (m_scope_lvl > 0) {
|
|
undo_new_level();
|
|
}
|
|
m_xk = null_var;
|
|
for (unsigned i = 0; i < m_bvalues.size(); ++i) {
|
|
m_bvalues[i] = l_undef;
|
|
}
|
|
m_assignment.reset();
|
|
}
|
|
|
|
lbool check(literal_vector& assumptions) {
|
|
literal_vector result;
|
|
unsigned sz = assumptions.size();
|
|
literal const* ptr = assumptions.data();
|
|
for (unsigned i = 0; i < sz; ++i) {
|
|
mk_external_clause(1, ptr+i, (assumption)(ptr+i));
|
|
}
|
|
display_literal_assumption dla(*this, assumptions);
|
|
scoped_display_assumptions _scoped_display(*this, dla);
|
|
lbool r = check();
|
|
|
|
if (r == l_false) {
|
|
// collect used literals from m_lemma_assumptions
|
|
vector<assumption, false> deps;
|
|
get_core(deps);
|
|
for (unsigned i = 0; i < deps.size(); ++i) {
|
|
literal const* lp = (literal const*)(deps[i]);
|
|
if (ptr <= lp && lp < ptr + sz) {
|
|
result.push_back(*lp);
|
|
}
|
|
}
|
|
}
|
|
collect(assumptions, m_clauses);
|
|
collect(assumptions, m_learned);
|
|
del_clauses(m_valids);
|
|
if (m_check_lemmas) {
|
|
for (clause* c : m_learned) {
|
|
check_lemma(c->size(), c->data(), false, nullptr);
|
|
}
|
|
}
|
|
|
|
#if 0
|
|
for (clause* c : m_learned) {
|
|
IF_VERBOSE(0, display(verbose_stream() << "KEEP: ", c->size(), c->c_ptr()) << "\n");
|
|
}
|
|
#endif
|
|
assumptions.reset();
|
|
assumptions.append(result);
|
|
return r;
|
|
}
|
|
|
|
void get_core(vector<assumption, false>& deps) {
|
|
m_asm.linearize(m_lemma_assumptions.get(), deps);
|
|
}
|
|
|
|
void collect(literal_vector const& assumptions, clause_vector& clauses) {
|
|
unsigned j = 0;
|
|
for (clause * c : clauses) {
|
|
if (collect(assumptions, *c)) {
|
|
del_clause(c);
|
|
}
|
|
else {
|
|
clauses[j++] = c;
|
|
}
|
|
}
|
|
clauses.shrink(j);
|
|
}
|
|
|
|
bool collect(literal_vector const& assumptions, clause const& c) {
|
|
unsigned sz = assumptions.size();
|
|
literal const* ptr = assumptions.data();
|
|
_assumption_set asms = static_cast<_assumption_set>(c.assumptions());
|
|
if (asms == nullptr) {
|
|
return false;
|
|
}
|
|
vector<assumption, false> deps;
|
|
m_asm.linearize(asms, deps);
|
|
for (auto dep : deps) {
|
|
if (ptr <= dep && dep < ptr + sz) {
|
|
return true;
|
|
}
|
|
}
|
|
return false;
|
|
}
|
|
|
|
// -----------------------
|
|
//
|
|
// Conflict Resolution
|
|
//
|
|
// -----------------------
|
|
svector<char> m_marks; // bool_var -> bool temp mark used during conflict resolution
|
|
unsigned m_num_marks;
|
|
scoped_literal_vector m_lemma;
|
|
scoped_literal_vector m_lazy_clause;
|
|
assumption_set_ref m_lemma_assumptions; // assumption tracking
|
|
|
|
// Conflict resolution invariant: a marked literal is in m_lemma or on the trail stack.
|
|
|
|
bool check_marks() {
|
|
for (unsigned m : m_marks) {
|
|
(void)m;
|
|
SASSERT(m == 0);
|
|
}
|
|
return true;
|
|
}
|
|
|
|
unsigned scope_lvl() const { return m_scope_lvl; }
|
|
|
|
bool is_marked(bool_var b) const { return m_marks.get(b, 0) == 1; }
|
|
|
|
void mark(bool_var b) { m_marks.setx(b, 1, 0); }
|
|
|
|
void reset_mark(bool_var b) { m_marks[b] = 0; }
|
|
|
|
void reset_marks() {
|
|
for (auto const& l : m_lemma) {
|
|
reset_mark(l.var());
|
|
}
|
|
}
|
|
|
|
void process_antecedent(literal antecedent) {
|
|
checkpoint();
|
|
bool_var b = antecedent.var();
|
|
TRACE("nlsat_resolve", display(tout << "resolving antecedent: ", antecedent) << "\n";);
|
|
if (assigned_value(antecedent) == l_undef) {
|
|
checkpoint();
|
|
// antecedent must be false in the current arith interpretation
|
|
SASSERT(value(antecedent) == l_false || m_rlimit.is_canceled());
|
|
if (!is_marked(b)) {
|
|
SASSERT(is_arith_atom(b) && max_var(b) < m_xk); // must be in a previous stage
|
|
TRACE("nlsat_resolve", tout << "literal is unassigned, but it is false in arithmetic interpretation, adding it to lemma\n";);
|
|
mark(b);
|
|
m_lemma.push_back(antecedent);
|
|
}
|
|
return;
|
|
}
|
|
|
|
unsigned b_lvl = m_levels[b];
|
|
TRACE("nlsat_resolve", tout << "b_lvl: " << b_lvl << ", is_marked(b): " << is_marked(b) << ", m_num_marks: " << m_num_marks << "\n";);
|
|
if (!is_marked(b)) {
|
|
mark(b);
|
|
if (b_lvl == scope_lvl() /* same level */ && max_var(b) == m_xk /* same stage */) {
|
|
TRACE("nlsat_resolve", tout << "literal is in the same level and stage, increasing marks\n";);
|
|
m_num_marks++;
|
|
}
|
|
else {
|
|
TRACE("nlsat_resolve", tout << "previous level or stage, adding literal to lemma\n";
|
|
tout << "max_var(b): " << max_var(b) << ", m_xk: " << m_xk << ", lvl: " << b_lvl << ", scope_lvl: " << scope_lvl() << "\n";);
|
|
m_lemma.push_back(antecedent);
|
|
}
|
|
}
|
|
}
|
|
|
|
void resolve_clause(bool_var b, unsigned sz, literal const * c) {
|
|
TRACE("nlsat_proof", tout << "resolving "; if (b != null_bool_var) display_atom(tout, b) << "\n"; display(tout, sz, c); tout << "\n";);
|
|
TRACE("nlsat_proof_sk", tout << "resolving "; if (b != null_bool_var) tout << "b" << b; tout << "\n"; display_abst(tout, sz, c); tout << "\n";);
|
|
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
if (c[i].var() != b)
|
|
process_antecedent(c[i]);
|
|
}
|
|
}
|
|
|
|
void resolve_clause(bool_var b, clause & c) {
|
|
TRACE("nlsat_resolve", tout << "resolving clause "; if (b != null_bool_var) tout << "for b: " << b << "\n"; display(tout, c) << "\n";);
|
|
c.set_active(true);
|
|
resolve_clause(b, c.size(), c.data());
|
|
m_lemma_assumptions = m_asm.mk_join(static_cast<_assumption_set>(c.assumptions()), m_lemma_assumptions);
|
|
}
|
|
|
|
void resolve_lazy_justification(bool_var b, lazy_justification const & jst) {
|
|
TRACE("nlsat_resolve", tout << "resolving lazy_justification for b" << b << "\n";);
|
|
unsigned sz = jst.num_lits();
|
|
|
|
// Dump lemma as Mathematica formula that must be true,
|
|
// if the current interpretation (really) makes the core in jst infeasible.
|
|
TRACE("nlsat_mathematica",
|
|
tout << "assignment lemma\n";
|
|
literal_vector core;
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
core.push_back(~jst.lit(i));
|
|
}
|
|
display_mathematica_lemma(tout, core.size(), core.data(), true););
|
|
|
|
m_lazy_clause.reset();
|
|
m_explain(jst.num_lits(), jst.lits(), m_lazy_clause);
|
|
for (unsigned i = 0; i < sz; i++)
|
|
m_lazy_clause.push_back(~jst.lit(i));
|
|
|
|
// lazy clause is a valid clause
|
|
TRACE("nlsat_mathematica", display_mathematica_lemma(tout, m_lazy_clause.size(), m_lazy_clause.data()););
|
|
TRACE("nlsat_proof_sk", tout << "theory lemma\n"; display_abst(tout, m_lazy_clause.size(), m_lazy_clause.data()); tout << "\n";);
|
|
TRACE("nlsat_resolve",
|
|
tout << "m_xk: " << m_xk << ", "; m_display_var(tout, m_xk) << "\n";
|
|
tout << "new valid clause:\n";
|
|
display(tout, m_lazy_clause.size(), m_lazy_clause.data()) << "\n";);
|
|
|
|
|
|
if (m_log_lemmas)
|
|
log_lemma(verbose_stream(), m_lazy_clause.size(), m_lazy_clause.data(), true);
|
|
|
|
if (m_check_lemmas) {
|
|
check_lemma(m_lazy_clause.size(), m_lazy_clause.data(), true, nullptr);
|
|
m_valids.push_back(mk_clause_core(m_lazy_clause.size(), m_lazy_clause.data(), false, nullptr));
|
|
}
|
|
|
|
#ifdef Z3DEBUG
|
|
{
|
|
unsigned sz = m_lazy_clause.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
literal l = m_lazy_clause[i];
|
|
if (l.var() != b) {
|
|
if (value(l) != l_false)
|
|
display(verbose_stream() << value(l) << " ", 1, &l);
|
|
SASSERT(value(l) == l_false || m_rlimit.is_canceled());
|
|
}
|
|
else {
|
|
SASSERT(value(l) == l_true || m_rlimit.is_canceled());
|
|
SASSERT(!l.sign() || m_bvalues[b] == l_false);
|
|
SASSERT(l.sign() || m_bvalues[b] == l_true);
|
|
}
|
|
}
|
|
}
|
|
#endif
|
|
checkpoint();
|
|
resolve_clause(b, m_lazy_clause.size(), m_lazy_clause.data());
|
|
|
|
for (unsigned i = 0; i < jst.num_clauses(); ++i) {
|
|
clause const& c = jst.clause(i);
|
|
TRACE("nlsat", display(tout << "adding clause assumptions ", c) << "\n";);
|
|
m_lemma_assumptions = m_asm.mk_join(static_cast<_assumption_set>(c.assumptions()), m_lemma_assumptions);
|
|
}
|
|
}
|
|
|
|
/**
|
|
\brief Return true if all literals in ls are from previous stages.
|
|
*/
|
|
bool only_literals_from_previous_stages(unsigned num, literal const * ls) const {
|
|
for (unsigned i = 0; i < num; i++) {
|
|
if (max_var(ls[i]) == m_xk)
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
/**
|
|
\brief Return the maximum scope level in ls.
|
|
|
|
\pre This method assumes value(ls[i]) is l_false for i in [0, num)
|
|
*/
|
|
unsigned max_scope_lvl(unsigned num, literal const * ls) {
|
|
unsigned max = 0;
|
|
for (unsigned i = 0; i < num; i++) {
|
|
literal l = ls[i];
|
|
bool_var b = l.var();
|
|
SASSERT(value(ls[i]) == l_false);
|
|
if (assigned_value(l) == l_false) {
|
|
unsigned lvl = m_levels[b];
|
|
if (lvl > max)
|
|
max = lvl;
|
|
}
|
|
else {
|
|
// l must be a literal from a previous stage that is false in the current interpretation
|
|
SASSERT(assigned_value(l) == l_undef);
|
|
SASSERT(max_var(b) != null_var);
|
|
SASSERT(m_xk != null_var);
|
|
SASSERT(max_var(b) < m_xk);
|
|
}
|
|
}
|
|
return max;
|
|
}
|
|
|
|
/**
|
|
\brief Remove literals of the given lvl (that are in the current stage) from lemma.
|
|
|
|
\pre This method assumes value(ls[i]) is l_false for i in [0, num)
|
|
*/
|
|
void remove_literals_from_lvl(scoped_literal_vector & lemma, unsigned lvl) {
|
|
TRACE("nlsat_resolve", tout << "removing literals from lvl: " << lvl << " and stage " << m_xk << "\n";);
|
|
unsigned sz = lemma.size();
|
|
unsigned j = 0;
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
literal l = lemma[i];
|
|
bool_var b = l.var();
|
|
SASSERT(is_marked(b));
|
|
SASSERT(value(lemma[i]) == l_false);
|
|
if (assigned_value(l) == l_false && m_levels[b] == lvl && max_var(b) == m_xk) {
|
|
m_num_marks++;
|
|
continue;
|
|
}
|
|
lemma.set(j, l);
|
|
j++;
|
|
}
|
|
lemma.shrink(j);
|
|
}
|
|
|
|
/**
|
|
\brief Return true if it is a Boolean lemma.
|
|
*/
|
|
bool is_bool_lemma(unsigned sz, literal const * ls) const {
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
if (m_atoms[ls[i].var()] != nullptr)
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
|
|
/**
|
|
Return the maximal decision level in lemma for literals in the first sz-1 positions that
|
|
are at the same stage. If all these literals are from previous stages,
|
|
we just backtrack the current level.
|
|
*/
|
|
unsigned find_new_level_arith_lemma(unsigned sz, literal const * lemma) {
|
|
SASSERT(!is_bool_lemma(sz, lemma));
|
|
unsigned new_lvl = 0;
|
|
bool found_lvl = false;
|
|
for (unsigned i = 0; i < sz - 1; i++) {
|
|
literal l = lemma[i];
|
|
if (max_var(l) == m_xk) {
|
|
bool_var b = l.var();
|
|
if (!found_lvl) {
|
|
found_lvl = true;
|
|
new_lvl = m_levels[b];
|
|
}
|
|
else {
|
|
if (m_levels[b] > new_lvl)
|
|
new_lvl = m_levels[b];
|
|
}
|
|
}
|
|
}
|
|
SASSERT(!found_lvl || new_lvl < scope_lvl());
|
|
if (!found_lvl) {
|
|
TRACE("nlsat_resolve", tout << "fail to find new lvl, using previous one\n";);
|
|
new_lvl = scope_lvl() - 1;
|
|
}
|
|
return new_lvl;
|
|
}
|
|
|
|
struct scoped_reset_marks {
|
|
imp& i;
|
|
scoped_reset_marks(imp& i):i(i) {}
|
|
~scoped_reset_marks() { if (i.m_num_marks > 0) { i.m_num_marks = 0; for (char& m : i.m_marks) m = 0; } }
|
|
};
|
|
|
|
|
|
/**
|
|
\brief Return true if the conflict was solved.
|
|
*/
|
|
bool resolve(clause & conflict) {
|
|
clause * conflict_clause = &conflict;
|
|
m_lemma_assumptions = nullptr;
|
|
start:
|
|
SASSERT(check_marks());
|
|
TRACE("nlsat_proof", tout << "STARTING RESOLUTION\n";);
|
|
TRACE("nlsat_proof_sk", tout << "STARTING RESOLUTION\n";);
|
|
m_stats.m_conflicts++;
|
|
TRACE("nlsat", tout << "resolve, conflicting clause:\n"; display(tout, *conflict_clause) << "\n";
|
|
tout << "xk: "; if (m_xk != null_var) m_display_var(tout, m_xk); else tout << "<null>"; tout << "\n";
|
|
tout << "scope_lvl: " << scope_lvl() << "\n";
|
|
tout << "current assignment\n"; display_assignment(tout););
|
|
|
|
m_num_marks = 0;
|
|
m_lemma.reset();
|
|
m_lemma_assumptions = nullptr;
|
|
scoped_reset_marks _sr(*this);
|
|
resolve_clause(null_bool_var, *conflict_clause);
|
|
|
|
unsigned top = m_trail.size();
|
|
bool found_decision;
|
|
while (true) {
|
|
found_decision = false;
|
|
while (m_num_marks > 0) {
|
|
checkpoint();
|
|
SASSERT(top > 0);
|
|
trail & t = m_trail[top-1];
|
|
SASSERT(t.m_kind != trail::NEW_STAGE); // we only mark literals that are in the same stage
|
|
if (t.m_kind == trail::BVAR_ASSIGNMENT) {
|
|
bool_var b = t.m_b;
|
|
if (is_marked(b)) {
|
|
TRACE("nlsat_resolve", tout << "found marked: b" << b << "\n"; display_atom(tout, b) << "\n";);
|
|
m_num_marks--;
|
|
reset_mark(b);
|
|
justification jst = m_justifications[b];
|
|
switch (jst.get_kind()) {
|
|
case justification::CLAUSE:
|
|
resolve_clause(b, *(jst.get_clause()));
|
|
break;
|
|
case justification::LAZY:
|
|
resolve_lazy_justification(b, *(jst.get_lazy()));
|
|
break;
|
|
case justification::DECISION:
|
|
SASSERT(m_num_marks == 0);
|
|
found_decision = true;
|
|
TRACE("nlsat_resolve", tout << "found decision\n";);
|
|
m_lemma.push_back(literal(b, m_bvalues[b] == l_true));
|
|
break;
|
|
default:
|
|
UNREACHABLE();
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
top--;
|
|
}
|
|
|
|
// m_lemma is an implicating clause after backtracking current scope level.
|
|
if (found_decision)
|
|
break;
|
|
|
|
// If lemma only contains literals from previous stages, then we can stop.
|
|
// We make progress by returning to a previous stage with additional information (new lemma)
|
|
// that forces us to select a new partial interpretation
|
|
if (only_literals_from_previous_stages(m_lemma.size(), m_lemma.data()))
|
|
break;
|
|
|
|
// Conflict does not depend on the current decision, and it is still in the current stage.
|
|
// We should find
|
|
// - the maximal scope level in the lemma
|
|
// - remove literal assigned in the scope level from m_lemma
|
|
// - backtrack to this level
|
|
// - and continue conflict resolution from there
|
|
// - we must bump m_num_marks for literals removed from m_lemma
|
|
unsigned max_lvl = max_scope_lvl(m_lemma.size(), m_lemma.data());
|
|
TRACE("nlsat_resolve", tout << "conflict does not depend on current decision, backtracking to level: " << max_lvl << "\n";);
|
|
SASSERT(max_lvl < scope_lvl());
|
|
remove_literals_from_lvl(m_lemma, max_lvl);
|
|
undo_until_level(max_lvl);
|
|
top = m_trail.size();
|
|
TRACE("nlsat_resolve", tout << "scope_lvl: " << scope_lvl() << " num marks: " << m_num_marks << "\n";);
|
|
SASSERT(scope_lvl() == max_lvl);
|
|
}
|
|
|
|
TRACE("nlsat_proof", tout << "New lemma\n"; display(tout, m_lemma); tout << "\n=========================\n";);
|
|
TRACE("nlsat_proof_sk", tout << "New lemma\n"; display_abst(tout, m_lemma); tout << "\n=========================\n";);
|
|
|
|
if (m_lemma.empty()) {
|
|
TRACE("nlsat", tout << "empty clause generated\n";);
|
|
return false; // problem is unsat, empty clause was generated
|
|
}
|
|
|
|
reset_marks(); // remove marks from the literals in m_lemmas.
|
|
TRACE("nlsat", tout << "new lemma:\n"; display(tout, m_lemma.size(), m_lemma.data()); tout << "\n";
|
|
tout << "found_decision: " << found_decision << "\n";);
|
|
|
|
if (m_check_lemmas) {
|
|
check_lemma(m_lemma.size(), m_lemma.data(), false, m_lemma_assumptions.get());
|
|
}
|
|
|
|
if (m_log_lemmas)
|
|
log_lemma(verbose_stream(), m_lemma.size(), m_lemma.data(), false);
|
|
|
|
// There are two possibilities:
|
|
// 1) m_lemma contains only literals from previous stages, and they
|
|
// are false in the current interpretation. We make progress
|
|
// by returning to a previous stage with additional information (new clause)
|
|
// that forces us to select a new partial interpretation
|
|
// >>> Return to some previous stage (we may also backjump many decisions and stages).
|
|
//
|
|
// 2) m_lemma contains at most one literal from the current level (the last literal).
|
|
// Moreover, this literal was a decision, but the new lemma forces it to
|
|
// be assigned to a different value.
|
|
// >>> In this case, we remain in the same stage but, we add a new asserted literal
|
|
// in a previous scope level. We may backjump many decisions.
|
|
//
|
|
unsigned sz = m_lemma.size();
|
|
clause * new_cls = nullptr;
|
|
if (!found_decision) {
|
|
// Case 1)
|
|
// We just have to find the maximal variable in m_lemma, and return to that stage
|
|
// Remark: the lemma may contain only boolean literals, in this case new_max_var == null_var;
|
|
var new_max_var = max_var(sz, m_lemma.data());
|
|
TRACE("nlsat_resolve", tout << "backtracking to stage: " << new_max_var << ", curr: " << m_xk << "\n";);
|
|
undo_until_stage(new_max_var);
|
|
SASSERT(m_xk == new_max_var);
|
|
new_cls = mk_clause(sz, m_lemma.data(), true, m_lemma_assumptions.get());
|
|
TRACE("nlsat", tout << "new_level: " << scope_lvl() << "\nnew_stage: " << new_max_var << "\n";
|
|
if (new_max_var != null_var) m_display_var(tout, new_max_var) << "\n";);
|
|
}
|
|
else {
|
|
SASSERT(scope_lvl() >= 1);
|
|
// Case 2)
|
|
if (is_bool_lemma(m_lemma.size(), m_lemma.data())) {
|
|
// boolean lemma, we just backtrack until the last literal is unassigned.
|
|
bool_var max_bool_var = m_lemma[m_lemma.size()-1].var();
|
|
undo_until_unassigned(max_bool_var);
|
|
}
|
|
else {
|
|
// We must find the maximal decision level in literals in the first sz-1 positions that
|
|
// are at the same stage. If all these literals are from previous stages,
|
|
// we just backtrack the current level.
|
|
unsigned new_lvl = find_new_level_arith_lemma(m_lemma.size(), m_lemma.data());
|
|
TRACE("nlsat", tout << "backtracking to new level: " << new_lvl << ", curr: " << m_scope_lvl << "\n";);
|
|
undo_until_level(new_lvl);
|
|
}
|
|
|
|
if (lemma_is_clause(*conflict_clause)) {
|
|
TRACE("nlsat", tout << "found decision literal in conflict clause\n";);
|
|
VERIFY(process_clause(*conflict_clause, true));
|
|
return true;
|
|
}
|
|
new_cls = mk_clause(sz, m_lemma.data(), true, m_lemma_assumptions.get());
|
|
}
|
|
NLSAT_VERBOSE(display(verbose_stream(), *new_cls) << "\n";);
|
|
if (!process_clause(*new_cls, true)) {
|
|
TRACE("nlsat", tout << "new clause triggered another conflict, restarting conflict resolution...\n";
|
|
display(tout, *new_cls) << "\n";
|
|
);
|
|
// we are still in conflict
|
|
conflict_clause = new_cls;
|
|
goto start;
|
|
}
|
|
TRACE("nlsat_resolve_done", display_assignment(tout););
|
|
return true;
|
|
}
|
|
|
|
bool lemma_is_clause(clause const& cls) const {
|
|
bool same = (m_lemma.size() == cls.size());
|
|
for (unsigned i = 0; same && i < m_lemma.size(); ++i) {
|
|
same = m_lemma[i] == cls[i];
|
|
}
|
|
return same;
|
|
}
|
|
|
|
|
|
// -----------------------
|
|
//
|
|
// Debugging
|
|
//
|
|
// -----------------------
|
|
|
|
bool check_watches() const {
|
|
#ifdef Z3DEBUG
|
|
for (var x = 0; x < num_vars(); x++) {
|
|
clause_vector const & cs = m_watches[x];
|
|
unsigned sz = cs.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
SASSERT(max_var(*(cs[i])) == x);
|
|
}
|
|
}
|
|
#endif
|
|
return true;
|
|
}
|
|
|
|
bool check_bwatches() const {
|
|
#ifdef Z3DEBUG
|
|
for (bool_var b = 0; b < m_bwatches.size(); b++) {
|
|
clause_vector const & cs = m_bwatches[b];
|
|
unsigned sz = cs.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
clause const & c = *(cs[i]);
|
|
SASSERT(max_var(c) == null_var);
|
|
SASSERT(max_bvar(c) == b);
|
|
}
|
|
}
|
|
#endif
|
|
return true;
|
|
}
|
|
|
|
bool check_invariant() const {
|
|
SASSERT(check_watches());
|
|
SASSERT(check_bwatches());
|
|
return true;
|
|
}
|
|
|
|
bool check_satisfied(clause_vector const & cs) const {
|
|
unsigned sz = cs.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
clause const & c = *(cs[i]);
|
|
if (!is_satisfied(c)) {
|
|
TRACE("nlsat", tout << "not satisfied\n"; display(tout, c); tout << "\n";);
|
|
return false;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool check_satisfied() const {
|
|
TRACE("nlsat", tout << "bk: b" << m_bk << ", xk: x" << m_xk << "\n"; if (m_xk != null_var) { m_display_var(tout, m_xk); tout << "\n"; });
|
|
unsigned num = m_atoms.size();
|
|
if (m_bk != null_bool_var)
|
|
num = m_bk;
|
|
for (bool_var b = 0; b < num; b++) {
|
|
if (!check_satisfied(m_bwatches[b])) {
|
|
UNREACHABLE();
|
|
return false;
|
|
}
|
|
}
|
|
if (m_xk != null_var) {
|
|
for (var x = 0; x < m_xk; x++) {
|
|
if (!check_satisfied(m_watches[x])) {
|
|
UNREACHABLE();
|
|
return false;
|
|
}
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
// -----------------------
|
|
//
|
|
// Statistics
|
|
//
|
|
// -----------------------
|
|
|
|
void collect_statistics(statistics & st) {
|
|
st.update("nlsat conflicts", m_stats.m_conflicts);
|
|
st.update("nlsat propagations", m_stats.m_propagations);
|
|
st.update("nlsat decisions", m_stats.m_decisions);
|
|
st.update("nlsat restarts", m_stats.m_restarts);
|
|
st.update("nlsat stages", m_stats.m_stages);
|
|
st.update("nlsat simplifications", m_stats.m_simplifications);
|
|
st.update("nlsat irrational assignments", m_stats.m_irrational_assignments);
|
|
}
|
|
|
|
void reset_statistics() {
|
|
m_stats.reset();
|
|
}
|
|
|
|
// -----------------------
|
|
//
|
|
// Variable reordering
|
|
//
|
|
// -----------------------
|
|
|
|
struct var_info_collector {
|
|
pmanager & pm;
|
|
atom_vector const & m_atoms;
|
|
var_vector m_shuffle;
|
|
unsigned_vector m_max_degree;
|
|
unsigned_vector m_num_occs;
|
|
|
|
var_info_collector(pmanager & _pm, atom_vector const & atoms, unsigned num_vars):
|
|
pm(_pm),
|
|
m_atoms(atoms) {
|
|
m_max_degree.resize(num_vars, 0);
|
|
m_num_occs.resize(num_vars, 0);
|
|
}
|
|
|
|
var_vector m_vars;
|
|
void collect(poly * p) {
|
|
m_vars.reset();
|
|
pm.vars(p, m_vars);
|
|
unsigned sz = m_vars.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
var x = m_vars[i];
|
|
unsigned k = pm.degree(p, x);
|
|
m_num_occs[x]++;
|
|
if (k > m_max_degree[x])
|
|
m_max_degree[x] = k;
|
|
}
|
|
}
|
|
|
|
void collect(literal l) {
|
|
bool_var b = l.var();
|
|
atom * a = m_atoms[b];
|
|
if (a == nullptr)
|
|
return;
|
|
if (a->is_ineq_atom()) {
|
|
unsigned sz = to_ineq_atom(a)->size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
collect(to_ineq_atom(a)->p(i));
|
|
}
|
|
}
|
|
else {
|
|
collect(to_root_atom(a)->p());
|
|
}
|
|
}
|
|
|
|
void collect(clause const & c) {
|
|
unsigned sz = c.size();
|
|
for (unsigned i = 0; i < sz; i++)
|
|
collect(c[i]);
|
|
}
|
|
|
|
void collect(clause_vector const & cs) {
|
|
unsigned sz = cs.size();
|
|
for (unsigned i = 0; i < sz; i++)
|
|
collect(*(cs[i]));
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, display_var_proc const & proc) {
|
|
unsigned sz = m_num_occs.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
proc(out, i); out << " -> " << m_max_degree[i] << " : " << m_num_occs[i] << "\n";
|
|
}
|
|
return out;
|
|
}
|
|
};
|
|
|
|
struct reorder_lt {
|
|
var_info_collector const & m_info;
|
|
reorder_lt(var_info_collector const & info):m_info(info) {}
|
|
bool operator()(var x, var y) const {
|
|
// high degree first
|
|
if (m_info.m_max_degree[x] < m_info.m_max_degree[y])
|
|
return false;
|
|
if (m_info.m_max_degree[x] > m_info.m_max_degree[y])
|
|
return true;
|
|
// more constrained first
|
|
if (m_info.m_num_occs[x] < m_info.m_num_occs[y])
|
|
return false;
|
|
if (m_info.m_num_occs[x] > m_info.m_num_occs[y])
|
|
return true;
|
|
return m_info.m_shuffle[x] < m_info.m_shuffle[y];
|
|
}
|
|
};
|
|
|
|
// Order variables by degree and number of occurrences
|
|
void heuristic_reorder() {
|
|
unsigned num = num_vars();
|
|
var_info_collector collector(m_pm, m_atoms, num);
|
|
collector.collect(m_clauses);
|
|
collector.collect(m_learned);
|
|
init_shuffle(collector.m_shuffle);
|
|
TRACE("nlsat_reorder", collector.display(tout, m_display_var););
|
|
var_vector new_order;
|
|
for (var x = 0; x < num; x++)
|
|
new_order.push_back(x);
|
|
|
|
std::sort(new_order.begin(), new_order.end(), reorder_lt(collector));
|
|
TRACE("nlsat_reorder",
|
|
tout << "new order: "; for (unsigned i = 0; i < num; i++) tout << new_order[i] << " "; tout << "\n";);
|
|
var_vector perm;
|
|
perm.resize(num, 0);
|
|
for (var x = 0; x < num; x++) {
|
|
perm[new_order[x]] = x;
|
|
}
|
|
reorder(perm.size(), perm.data());
|
|
SASSERT(check_invariant());
|
|
}
|
|
|
|
void init_shuffle(var_vector& p) {
|
|
unsigned num = num_vars();
|
|
for (var x = 0; x < num; x++)
|
|
p.push_back(x);
|
|
|
|
random_gen r(++m_random_seed);
|
|
shuffle(p.size(), p.data(), r);
|
|
}
|
|
|
|
void shuffle_vars() {
|
|
var_vector p;
|
|
init_shuffle(p);
|
|
reorder(p.size(), p.data());
|
|
}
|
|
|
|
bool can_reorder() const {
|
|
return all_of(m_learned, [&](clause* c) { return !has_root_atom(*c); })
|
|
&& all_of(m_clauses, [&](clause* c) { return !has_root_atom(*c); });
|
|
}
|
|
|
|
/**
|
|
\brief Reorder variables using the giving permutation.
|
|
p maps internal variables to their new positions
|
|
*/
|
|
|
|
|
|
void reorder(unsigned sz, var const * p) {
|
|
|
|
remove_learned_roots();
|
|
SASSERT(can_reorder());
|
|
TRACE("nlsat_reorder", tout << "solver before variable reorder\n"; display(tout);
|
|
display_vars(tout);
|
|
tout << "\npermutation:\n";
|
|
for (unsigned i = 0; i < sz; i++) tout << p[i] << " "; tout << "\n";
|
|
);
|
|
// verbose_stream() << "\npermutation: " << p[0] << " count " << count << " " << m_rlimit.is_canceled() << "\n";
|
|
reinit_cache();
|
|
SASSERT(num_vars() == sz);
|
|
TRACE("nlsat_bool_assignment_bug", tout << "before reset watches\n"; display_bool_assignment(tout););
|
|
reset_watches();
|
|
assignment new_assignment(m_am);
|
|
for (var x = 0; x < num_vars(); x++) {
|
|
if (m_assignment.is_assigned(x))
|
|
new_assignment.set(p[x], m_assignment.value(x));
|
|
}
|
|
var_vector new_inv_perm;
|
|
new_inv_perm.resize(sz);
|
|
// the undo_until_size(0) statement erases the Boolean assignment.
|
|
// undo_until_size(0)
|
|
undo_until_stage(null_var);
|
|
m_cache.reset();
|
|
#ifdef Z3DEBUG
|
|
for (var x = 0; x < num_vars(); x++) {
|
|
SASSERT(m_watches[x].empty());
|
|
}
|
|
#endif
|
|
// update m_perm mapping
|
|
for (unsigned ext_x = 0; ext_x < sz; ext_x++) {
|
|
// p: internal -> new pos
|
|
// m_perm: internal -> external
|
|
// m_inv_perm: external -> internal
|
|
new_inv_perm[ext_x] = p[m_inv_perm[ext_x]];
|
|
m_perm.set(new_inv_perm[ext_x], ext_x);
|
|
}
|
|
bool_vector is_int;
|
|
is_int.swap(m_is_int);
|
|
for (var x = 0; x < sz; x++) {
|
|
m_is_int.setx(p[x], is_int[x], false);
|
|
SASSERT(m_infeasible[x] == 0);
|
|
}
|
|
m_inv_perm.swap(new_inv_perm);
|
|
#ifdef Z3DEBUG
|
|
for (var x = 0; x < num_vars(); x++) {
|
|
SASSERT(x == m_inv_perm[m_perm[x]]);
|
|
SASSERT(m_watches[x].empty());
|
|
}
|
|
#endif
|
|
m_pm.rename(sz, p);
|
|
for (auto& b : m_bounds)
|
|
b.x = p[b.x];
|
|
TRACE("nlsat_bool_assignment_bug", tout << "before reinit cache\n"; display_bool_assignment(tout););
|
|
reinit_cache();
|
|
m_assignment.swap(new_assignment);
|
|
reattach_arith_clauses(m_clauses);
|
|
reattach_arith_clauses(m_learned);
|
|
TRACE("nlsat_reorder", tout << "solver after variable reorder\n"; display(tout); display_vars(tout););
|
|
}
|
|
|
|
|
|
/**
|
|
\brief Restore variable order.
|
|
*/
|
|
void restore_order() {
|
|
// m_perm: internal -> external
|
|
// m_inv_perm: external -> internal
|
|
var_vector p;
|
|
p.append(m_perm);
|
|
reorder(p.size(), p.data());
|
|
#ifdef Z3DEBUG
|
|
for (var x = 0; x < num_vars(); x++) {
|
|
SASSERT(m_perm[x] == x);
|
|
SASSERT(m_inv_perm[x] == x);
|
|
}
|
|
#endif
|
|
}
|
|
|
|
/**
|
|
\brief After variable reordering some lemmas containing root atoms may be ill-formed.
|
|
*/
|
|
void remove_learned_roots() {
|
|
unsigned j = 0;
|
|
for (clause* c : m_learned) {
|
|
if (has_root_atom(*c)) {
|
|
del_clause(c);
|
|
}
|
|
else {
|
|
m_learned[j++] = c;
|
|
}
|
|
}
|
|
m_learned.shrink(j);
|
|
}
|
|
|
|
/**
|
|
\brief Return true if the clause contains an ill formed root atom
|
|
*/
|
|
bool has_root_atom(clause const & c) const {
|
|
for (literal lit : c) {
|
|
bool_var b = lit.var();
|
|
atom * a = m_atoms[b];
|
|
if (a && a->is_root_atom())
|
|
return true;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
/**
|
|
\brief reinsert all polynomials in the unique cache
|
|
*/
|
|
void reinit_cache() {
|
|
reinit_cache(m_clauses);
|
|
reinit_cache(m_learned);
|
|
for (atom* a : m_atoms)
|
|
reinit_cache(a);
|
|
}
|
|
void reinit_cache(clause_vector const & cs) {
|
|
for (clause* c : cs)
|
|
reinit_cache(*c);
|
|
}
|
|
void reinit_cache(clause const & c) {
|
|
for (literal l : c)
|
|
reinit_cache(l);
|
|
}
|
|
void reinit_cache(literal l) {
|
|
bool_var b = l.var();
|
|
reinit_cache(m_atoms[b]);
|
|
}
|
|
void reinit_cache(atom* a) {
|
|
if (a == nullptr) {
|
|
|
|
}
|
|
else if (a->is_ineq_atom()) {
|
|
var max = 0;
|
|
unsigned sz = to_ineq_atom(a)->size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
poly * p = to_ineq_atom(a)->p(i);
|
|
VERIFY(m_cache.mk_unique(p) == p);
|
|
var x = m_pm.max_var(p);
|
|
if (x > max)
|
|
max = x;
|
|
}
|
|
a->m_max_var = max;
|
|
}
|
|
else {
|
|
poly * p = to_root_atom(a)->p();
|
|
VERIFY(m_cache.mk_unique(p) == p);
|
|
a->m_max_var = m_pm.max_var(p);
|
|
}
|
|
}
|
|
|
|
void reset_watches() {
|
|
unsigned num = num_vars();
|
|
for (var x = 0; x < num; x++) {
|
|
m_watches[x].reset();
|
|
}
|
|
}
|
|
|
|
void reattach_arith_clauses(clause_vector const & cs) {
|
|
for (clause* cp : cs) {
|
|
var x = max_var(*cp);
|
|
if (x != null_var)
|
|
m_watches[x].push_back(cp);
|
|
}
|
|
}
|
|
|
|
// -----------------------
|
|
//
|
|
// Solver initialization
|
|
//
|
|
// -----------------------
|
|
|
|
struct degree_lt {
|
|
unsigned_vector & m_degrees;
|
|
degree_lt(unsigned_vector & ds):m_degrees(ds) {}
|
|
bool operator()(unsigned i1, unsigned i2) const {
|
|
if (m_degrees[i1] < m_degrees[i2])
|
|
return true;
|
|
if (m_degrees[i1] > m_degrees[i2])
|
|
return false;
|
|
return i1 < i2;
|
|
}
|
|
};
|
|
|
|
unsigned_vector m_cs_degrees;
|
|
unsigned_vector m_cs_p;
|
|
void sort_clauses_by_degree(unsigned sz, clause ** cs) {
|
|
if (sz <= 1)
|
|
return;
|
|
TRACE("nlsat_reorder_clauses", tout << "before:\n"; for (unsigned i = 0; i < sz; i++) { display(tout, *(cs[i])); tout << "\n"; });
|
|
m_cs_degrees.reset();
|
|
m_cs_p.reset();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
m_cs_p.push_back(i);
|
|
m_cs_degrees.push_back(degree(*(cs[i])));
|
|
}
|
|
std::sort(m_cs_p.begin(), m_cs_p.end(), degree_lt(m_cs_degrees));
|
|
TRACE("nlsat_reorder_clauses", tout << "permutation: "; ::display(tout, m_cs_p.begin(), m_cs_p.end()); tout << "\n";);
|
|
apply_permutation(sz, cs, m_cs_p.data());
|
|
TRACE("nlsat_reorder_clauses", tout << "after:\n"; for (unsigned i = 0; i < sz; i++) { display(tout, *(cs[i])); tout << "\n"; });
|
|
}
|
|
|
|
|
|
struct degree_lit_num_lt {
|
|
unsigned_vector & m_degrees;
|
|
unsigned_vector & m_lit_num;
|
|
degree_lit_num_lt(unsigned_vector & ds, unsigned_vector ln) :
|
|
m_degrees(ds),
|
|
m_lit_num(ln) {
|
|
}
|
|
bool operator()(unsigned i1, unsigned i2) const {
|
|
if (m_lit_num[i1] == 1 && m_lit_num[i2] > 1)
|
|
return true;
|
|
if (m_lit_num[i1] > 1 && m_lit_num[i2] == 1)
|
|
return false;
|
|
if (m_degrees[i1] != m_degrees[i2])
|
|
return m_degrees[i1] < m_degrees[i2];
|
|
if (m_lit_num[i1] != m_lit_num[i2])
|
|
return m_lit_num[i1] < m_lit_num[i2];
|
|
return i1 < i2;
|
|
}
|
|
};
|
|
|
|
unsigned_vector m_dl_degrees;
|
|
unsigned_vector m_dl_lit_num;
|
|
unsigned_vector m_dl_p;
|
|
void sort_clauses_by_degree_lit_num(unsigned sz, clause ** cs) {
|
|
if (sz <= 1)
|
|
return;
|
|
TRACE("nlsat_reorder_clauses", tout << "before:\n"; for (unsigned i = 0; i < sz; i++) { display(tout, *(cs[i])); tout << "\n"; });
|
|
m_dl_degrees.reset();
|
|
m_dl_lit_num.reset();
|
|
m_dl_p.reset();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
m_dl_degrees.push_back(degree(*(cs[i])));
|
|
m_dl_lit_num.push_back(cs[i]->size());
|
|
m_dl_p.push_back(i);
|
|
}
|
|
std::sort(m_dl_p.begin(), m_dl_p.end(), degree_lit_num_lt(m_dl_degrees, m_dl_lit_num));
|
|
TRACE("nlsat_reorder_clauses", tout << "permutation: "; ::display(tout, m_dl_p.begin(), m_dl_p.end()); tout << "\n";);
|
|
apply_permutation(sz, cs, m_dl_p.data());
|
|
TRACE("nlsat_reorder_clauses", tout << "after:\n"; for (unsigned i = 0; i < sz; i++) { display(tout, *(cs[i])); tout << "\n"; });
|
|
}
|
|
|
|
void sort_watched_clauses() {
|
|
unsigned num = num_vars();
|
|
for (unsigned i = 0; i < num; i++) {
|
|
clause_vector & ws = m_watches[i];
|
|
// sort_clauses_by_degree(ws.size(), ws.data());
|
|
if (m_simple_check) {
|
|
sort_clauses_by_degree_lit_num(ws.size(), ws.data());
|
|
}
|
|
else {
|
|
sort_clauses_by_degree(ws.size(), ws.data());
|
|
}
|
|
}
|
|
}
|
|
|
|
// -----------------------
|
|
//
|
|
// Full dimensional
|
|
//
|
|
// A problem is in the full dimensional fragment if it does
|
|
// not contain equalities or non-strict inequalities.
|
|
//
|
|
// -----------------------
|
|
|
|
bool is_full_dimensional(literal l) const {
|
|
atom * a = m_atoms[l.var()];
|
|
if (a == nullptr)
|
|
return true;
|
|
switch (a->get_kind()) {
|
|
case atom::EQ: return l.sign();
|
|
case atom::LT: return !l.sign();
|
|
case atom::GT: return !l.sign();
|
|
case atom::ROOT_EQ: return l.sign();
|
|
case atom::ROOT_LT: return !l.sign();
|
|
case atom::ROOT_GT: return !l.sign();
|
|
case atom::ROOT_LE: return l.sign();
|
|
case atom::ROOT_GE: return l.sign();
|
|
default:
|
|
UNREACHABLE();
|
|
return false;
|
|
}
|
|
}
|
|
|
|
bool is_full_dimensional(clause const & c) const {
|
|
for (literal l : c) {
|
|
if (!is_full_dimensional(l))
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool is_full_dimensional(clause_vector const & cs) const {
|
|
for (clause* c : cs) {
|
|
if (!is_full_dimensional(*c))
|
|
return false;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool is_full_dimensional() const {
|
|
return is_full_dimensional(m_clauses);
|
|
}
|
|
|
|
|
|
// -----------------------
|
|
//
|
|
// Simplification
|
|
//
|
|
// -----------------------
|
|
|
|
// solve simple equalities
|
|
// TBD WU-Reit decomposition?
|
|
|
|
// - elim_unconstrained
|
|
// - solve_eqs
|
|
// - fm
|
|
|
|
/**
|
|
\brief isolate variables in unit equalities.
|
|
Assume a clause is c == v*p + q
|
|
and the context implies p > 0
|
|
|
|
replace v by -q/p
|
|
remove clause c,
|
|
The for other occurrences of v,
|
|
replace v*r + v*v*r' > 0 by
|
|
by p*p*v*r + p*p*v*v*r' > 0
|
|
by p*q*r + q*q*r' > 0
|
|
|
|
The method ignores lemmas and assumes constraints don't use roots.
|
|
*/
|
|
|
|
|
|
|
|
// Eliminated variables are tracked in m_bounds.
|
|
// Each element in m_bounds tracks the eliminated variable and an upper or lower bound
|
|
// that has to be satisfied. Variables that are eliminated through equalities are tracked
|
|
// by non-strict bounds. A satisfiable solution is required to provide an evaluation that
|
|
// is consistent with the bounds. For equalities, the non-strict lower or upper bound can
|
|
// always be assigned as a value to the variable.
|
|
|
|
void fix_patch() {
|
|
m_lo.reset(); m_hi.reset();
|
|
for (auto& b : m_bounds)
|
|
m_assignment.reset(b.x);
|
|
for (unsigned i = m_bounds.size(); i-- > 0; )
|
|
fix_patch(m_bounds[i]);
|
|
}
|
|
|
|
// x is unassigned, lo < x -> x <- lo + 1
|
|
// x is unassigned, x < hi -> x <- hi - 1
|
|
// x is unassigned, lo <= x -> x <- lo
|
|
// x is unassigned, x <= hi -> x <- hi
|
|
// x is assigned above hi, lo is strict lo < x < hi -> set x <- (lo + hi)/2
|
|
// x is assigned below hi, above lo -> no-op
|
|
// x is assigned below lo, hi is strict lo < x < hi -> set x <-> (lo + hi)/2
|
|
// x is assigned above hi, x <= hi -> x <- hi
|
|
// x is assigned blow lo, lo <= x -> x <- lo
|
|
void fix_patch(bound_constraint& b) {
|
|
var x = b.x;
|
|
scoped_anum Av(m_am), Bv(m_am), val(m_am);
|
|
m_pm.eval(b.A, m_assignment, Av);
|
|
m_pm.eval(b.B, m_assignment, Bv);
|
|
m_am.neg(Bv);
|
|
val = Bv / Av;
|
|
// Ax >= B
|
|
// is-lower : A > 0
|
|
// is-upper: A < 0
|
|
// x <- B / A
|
|
bool is_lower = m_am.is_pos(Av);
|
|
TRACE("nlsat",
|
|
m_display_var(tout << "patch v" << x << " ", x) << "\n";
|
|
if (m_assignment.is_assigned(x)) m_am.display(tout << "previous value: ", m_assignment.value(x)); tout << "\n";
|
|
m_am.display(tout << "updated value: ", val); tout << "\n";
|
|
);
|
|
|
|
if (!m_assignment.is_assigned(x)) {
|
|
if (!b.is_strict)
|
|
m_assignment.set_core(x, val);
|
|
else if (is_lower)
|
|
m_assignment.set_core(x, val + 1);
|
|
else
|
|
m_assignment.set_core(x, val - 1);
|
|
}
|
|
else {
|
|
auto& aval = m_assignment.value(x);
|
|
if (is_lower) {
|
|
// lo < value(x), lo < x -> x is unchanged
|
|
if (b.is_strict && m_am.lt(val, aval))
|
|
;
|
|
else if (!b.is_strict && m_am.le(val, aval))
|
|
;
|
|
else if (!b.is_strict)
|
|
m_assignment.set_core(x, val);
|
|
// aval < lo < x, hi is unassigned: x <- lo + 1
|
|
else if (!m_hi.is_assigned(x))
|
|
m_assignment.set_core(x, val + 1);
|
|
// aval < lo < x, hi is assigned: x <- (lo + hi) / 2
|
|
else {
|
|
scoped_anum mid(m_am);
|
|
m_am.add(m_hi.value(x), val, mid);
|
|
mid = mid / 2;
|
|
m_assignment.set_core(x, mid);
|
|
}
|
|
}
|
|
else {
|
|
// dual to lower bounds
|
|
if (b.is_strict && m_am.lt(aval, val))
|
|
;
|
|
else if (!b.is_strict && m_am.le(aval, val))
|
|
;
|
|
else if (!b.is_strict)
|
|
m_assignment.set_core(x, val);
|
|
else if (!m_lo.is_assigned(x))
|
|
m_assignment.set_core(x, val - 1);
|
|
else {
|
|
scoped_anum mid(m_am);
|
|
m_am.add(m_lo.value(x), val, mid);
|
|
mid = mid / 2;
|
|
m_assignment.set_core(x, mid);
|
|
}
|
|
}
|
|
}
|
|
|
|
if (is_lower) {
|
|
if (!m_lo.is_assigned(x) || m_am.lt(m_lo.value(x), val))
|
|
m_lo.set_core(x, val);
|
|
}
|
|
else {
|
|
if (!m_hi.is_assigned(x) || m_am.gt(m_hi.value(x), val))
|
|
m_hi.set_core(x, val);
|
|
}
|
|
}
|
|
|
|
bool is_unit_ineq(clause const& c) const {
|
|
return
|
|
c.size() == 1 &&
|
|
m_atoms[c[0].var()] &&
|
|
m_atoms[c[0].var()]->is_ineq_atom();
|
|
}
|
|
|
|
bool is_unit_eq(clause const& c) const {
|
|
return
|
|
is_unit_ineq(c) &&
|
|
!c[0].sign() &&
|
|
m_atoms[c[0].var()]->is_eq();
|
|
}
|
|
|
|
/**
|
|
\brief determine whether the clause is a comparison v > k or v < k', where k >= 0 or k' <= 0.
|
|
*/
|
|
lbool is_cmp0(clause const& c, var& v) {
|
|
if (!is_unit_ineq(c))
|
|
return l_undef;
|
|
literal lit = c[0];
|
|
ineq_atom const& a = *to_ineq_atom(m_atoms[lit.var()]);
|
|
bool sign = lit.sign();
|
|
poly * p0;
|
|
if (!is_single_poly(a, p0))
|
|
return l_undef;
|
|
if (m_pm.is_var(p0, v)) {
|
|
if (!sign && a.get_kind() == atom::GT) {
|
|
return l_true;
|
|
}
|
|
if (!sign && a.get_kind() == atom::LT) {
|
|
return l_false;
|
|
}
|
|
return l_undef;
|
|
}
|
|
polynomial::scoped_numeral n(m_pm.m());
|
|
if (m_pm.is_var_num(p0, v, n)) {
|
|
// x - k > 0
|
|
if (!sign && a.get_kind() == atom::GT && m_pm.m().is_nonneg(n)) {
|
|
return l_true;
|
|
}
|
|
// x + k < 0
|
|
if (!sign && a.get_kind() == atom::LT && m_pm.m().is_nonpos(n)) {
|
|
return l_false;
|
|
}
|
|
// !(x + k > 0)
|
|
if (sign && a.get_kind() == atom::GT && m_pm.m().is_pos(n)) {
|
|
return l_false;
|
|
}
|
|
// !(x - k < 0)
|
|
if (sign && a.get_kind() == atom::LT && m_pm.m().is_neg(n)) {
|
|
return l_true;
|
|
}
|
|
}
|
|
return l_undef;
|
|
}
|
|
|
|
bool is_single_poly(ineq_atom const& a, poly*& p) {
|
|
unsigned sz = a.size();
|
|
return sz == 1 && a.is_odd(0) && (p = a.p(0), true);
|
|
}
|
|
|
|
bool is_unit(polynomial_ref const& p) {
|
|
if (!m_pm.is_const(p))
|
|
return false;
|
|
auto const& c = m_pm.coeff(p, 0);
|
|
return m_pm.m().is_one(c) || m_pm.m().is_minus_one(c);
|
|
}
|
|
|
|
// -----------------------
|
|
//
|
|
// Pretty printing
|
|
//
|
|
// -----------------------
|
|
|
|
std::ostream& display_num_assignment(std::ostream & out, display_var_proc const & proc) const {
|
|
for (var x = 0; x < num_vars(); x++) {
|
|
if (m_assignment.is_assigned(x)) {
|
|
proc(out, x);
|
|
out << " -> ";
|
|
m_am.display_decimal(out, m_assignment.value(x));
|
|
out << "\n";
|
|
}
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_bool_assignment(std::ostream & out) const {
|
|
unsigned sz = m_atoms.size();
|
|
for (bool_var b = 0; b < sz; b++) {
|
|
if (m_atoms[b] == nullptr && m_bvalues[b] != l_undef) {
|
|
out << "b" << b << " -> " << (m_bvalues[b] == l_true ? "true" : "false") << " @" << m_levels[b] << "\n";
|
|
}
|
|
else if (m_atoms[b] != nullptr && m_bvalues[b] != l_undef) {
|
|
display(out << "b" << b << " ", *m_atoms[b]) << " -> " << (m_bvalues[b] == l_true ? "true" : "false") << " @" << m_levels[b] << "\n";
|
|
}
|
|
}
|
|
TRACE("nlsat_bool_assignment",
|
|
for (bool_var b = 0; b < sz; b++) {
|
|
out << "b" << b << " -> " << m_bvalues[b] << " ";
|
|
if (m_atoms[b]) display(out, *m_atoms[b]);
|
|
out << "\n";
|
|
});
|
|
return out;
|
|
}
|
|
|
|
bool display_mathematica_assignment(std::ostream & out) const {
|
|
bool first = true;
|
|
for (var x = 0; x < num_vars(); x++) {
|
|
if (m_assignment.is_assigned(x)) {
|
|
if (first)
|
|
first = false;
|
|
else
|
|
out << " && ";
|
|
out << "x" << x << " == ";
|
|
m_am.display_mathematica(out, m_assignment.value(x));
|
|
}
|
|
}
|
|
return !first;
|
|
}
|
|
|
|
std::ostream& display_num_assignment(std::ostream & out) const {
|
|
return display_num_assignment(out, m_display_var);
|
|
}
|
|
|
|
std::ostream& display_assignment(std::ostream& out) const {
|
|
display_bool_assignment(out);
|
|
display_num_assignment(out);
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display(std::ostream& out, justification j) const {
|
|
switch (j.get_kind()) {
|
|
case justification::CLAUSE:
|
|
display(out, *j.get_clause()) << "\n";
|
|
break;
|
|
case justification::LAZY: {
|
|
lazy_justification const& lz = *j.get_lazy();
|
|
display_not(out, lz.num_lits(), lz.lits()) << "\n";
|
|
for (unsigned i = 0; i < lz.num_clauses(); ++i) {
|
|
display(out, lz.clause(i)) << "\n";
|
|
}
|
|
break;
|
|
}
|
|
default:
|
|
out << j.get_kind() << "\n";
|
|
break;
|
|
}
|
|
return out;
|
|
}
|
|
|
|
bool m_display_eval = false;
|
|
std::ostream& display_eval(std::ostream& out, justification j) {
|
|
flet<bool> _display(m_display_eval, true);
|
|
return display(out, j);
|
|
}
|
|
|
|
std::ostream& display_ineq(std::ostream & out, ineq_atom const & a, display_var_proc const & proc, bool use_star = false) const {
|
|
unsigned sz = a.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
if (use_star && i > 0)
|
|
out << "*";
|
|
bool is_even = a.is_even(i);
|
|
if (is_even || sz > 1)
|
|
out << "(";
|
|
display_polynomial(out, a.p(i), proc, use_star);
|
|
if (is_even || sz > 1)
|
|
out << ")";
|
|
if (is_even)
|
|
out << "^2";
|
|
}
|
|
switch (a.get_kind()) {
|
|
case atom::LT: out << " < 0"; break;
|
|
case atom::GT: out << " > 0"; break;
|
|
case atom::EQ: out << " = 0"; break;
|
|
default: UNREACHABLE(); break;
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_mathematica(std::ostream & out, ineq_atom const & a) const {
|
|
unsigned sz = a.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
if (i > 0)
|
|
out << "*";
|
|
bool is_even = a.is_even(i);
|
|
if (sz > 1)
|
|
out << "(";
|
|
if (is_even)
|
|
out << "(";
|
|
m_pm.display(out, a.p(i), display_var_proc(), true);
|
|
if (is_even)
|
|
out << "^2)";
|
|
if (sz > 1)
|
|
out << ")";
|
|
}
|
|
switch (a.get_kind()) {
|
|
case atom::LT: out << " < 0"; break;
|
|
case atom::GT: out << " > 0"; break;
|
|
case atom::EQ: out << " == 0"; break;
|
|
default: UNREACHABLE(); break;
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_polynomial_smt2(std::ostream & out, poly const* p, display_var_proc const & proc) const {
|
|
return m_pm.display_smt2(out, p, proc);
|
|
}
|
|
|
|
std::ostream& display_ineq_smt2(std::ostream & out, ineq_atom const & a, display_var_proc const & proc) const {
|
|
switch (a.get_kind()) {
|
|
case atom::LT: out << "(< "; break;
|
|
case atom::GT: out << "(> "; break;
|
|
case atom::EQ: out << "(= "; break;
|
|
default: UNREACHABLE(); break;
|
|
}
|
|
unsigned sz = a.size();
|
|
if (sz > 1)
|
|
out << "(* ";
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
if (i > 0) out << " ";
|
|
if (a.is_even(i)) {
|
|
out << "(* ";
|
|
display_polynomial_smt2(out, a.p(i), proc);
|
|
out << " ";
|
|
display_polynomial_smt2(out, a.p(i), proc);
|
|
out << ")";
|
|
}
|
|
else {
|
|
display_polynomial_smt2(out, a.p(i), proc);
|
|
}
|
|
}
|
|
if (sz > 1)
|
|
out << ")";
|
|
out << " 0)";
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_poly_root(std::ostream& out, char const* y, root_atom const& a, display_var_proc const& proc) const {
|
|
out << "(exists (("; proc(out,a.x()); out << " Real))\n";
|
|
out << "(and (= " << y << " ";
|
|
proc(out, a.x());
|
|
out << ") (= 0 ";
|
|
display_polynomial_smt2(out, a.p(), proc);
|
|
out << ")))\n";
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_binary_smt2(std::ostream& out, poly const* p1, char const* rel, poly const* p2, display_var_proc const& proc) const {
|
|
out << "(" << rel << " ";
|
|
display_polynomial_smt2(out, p1, proc);
|
|
out << " ";
|
|
display_polynomial_smt2(out, p2, proc);
|
|
out << ")";
|
|
return out;
|
|
}
|
|
|
|
|
|
std::ostream& display_linear_root_smt2(std::ostream & out, root_atom const & a, display_var_proc const & proc) const {
|
|
polynomial_ref A(m_pm), B(m_pm), Z(m_pm), Ax(m_pm);
|
|
polynomial::scoped_numeral zero(m_qm);
|
|
m_pm.m().set(zero, 0);
|
|
A = m_pm.derivative(a.p(), a.x());
|
|
B = m_pm.neg(m_pm.substitute(a.p(), a.x(), zero));
|
|
Z = m_pm.mk_zero();
|
|
|
|
Ax = m_pm.mul(m_pm.mk_polynomial(a.x()), A);
|
|
|
|
// x < root[1](ax + b) == (a > 0 => ax + b < 0) & (a < 0 => ax + b > 0)
|
|
// x < root[1](ax + b) == (a > 0 => ax < -b) & (a < 0 => ax > -b)
|
|
|
|
char const* rel1 = "<", *rel2 = ">";
|
|
switch (a.get_kind()) {
|
|
case atom::ROOT_LT: rel1 = "<"; rel2 = ">"; break;
|
|
case atom::ROOT_GT: rel1 = ">"; rel2 = "<"; break;
|
|
case atom::ROOT_LE: rel1 = "<="; rel2 = ">="; break;
|
|
case atom::ROOT_GE: rel1 = ">="; rel2 = "<="; break;
|
|
case atom::ROOT_EQ: rel1 = rel2 = "="; break;
|
|
default: UNREACHABLE(); break;
|
|
}
|
|
|
|
out << "(and ";
|
|
out << "(=> "; display_binary_smt2(out, A, ">", Z, proc); display_binary_smt2(out, Ax, rel1, B, proc); out << ") ";
|
|
out << "(=> "; display_binary_smt2(out, A, "<", Z, proc); display_binary_smt2(out, Ax, rel2, B, proc); out << ") ";
|
|
out << ")";
|
|
|
|
return out;
|
|
}
|
|
|
|
|
|
std::ostream& display_root_smt2(std::ostream& out, root_atom const& a, display_var_proc const& proc) const {
|
|
if (a.i() == 1 && m_pm.degree(a.p(), a.x()) == 1)
|
|
return display_linear_root_smt2(out, a, proc);
|
|
#if 1
|
|
out << "(exists (";
|
|
for (unsigned j = 0; j < a.i(); ++j) {
|
|
std::string y = std::string("y") + std::to_string(j);
|
|
out << "(" << y << " Real) ";
|
|
}
|
|
out << ")\n";
|
|
out << "(and\n";
|
|
for (unsigned j = 0; j < a.i(); ++j) {
|
|
std::string y = std::string("y") + std::to_string(j);
|
|
display_poly_root(out, y.c_str(), a, proc);
|
|
}
|
|
for (unsigned j = 0; j + 1 < a.i(); ++j) {
|
|
std::string y1 = std::string("y") + std::to_string(j);
|
|
std::string y2 = std::string("y") + std::to_string(j+1);
|
|
out << "(< " << y1 << " " << y2 << ")\n";
|
|
}
|
|
|
|
std::string yn = "y" + std::to_string(a.i() - 1);
|
|
|
|
// TODO we need (forall z : z < yn . p(z) => z = y1 or ... z = y_{n-1})
|
|
// to say y1, .., yn are the first n distinct roots.
|
|
//
|
|
out << "(forall ((z Real)) (=> (and (< z " << yn << ") "; display_poly_root(out, "z", a, proc) << ") ";
|
|
if (a.i() == 1) {
|
|
out << "false))\n";
|
|
}
|
|
else {
|
|
out << "(or ";
|
|
for (unsigned j = 0; j + 1 < a.i(); ++j) {
|
|
std::string y1 = std::string("y") + std::to_string(j);
|
|
out << "(= z " << y1 << ") ";
|
|
}
|
|
out << ")))\n";
|
|
}
|
|
switch (a.get_kind()) {
|
|
case atom::ROOT_LT: out << "(< "; proc(out, a.x()); out << " " << yn << ")"; break;
|
|
case atom::ROOT_GT: out << "(> "; proc(out, a.x()); out << " " << yn << ")"; break;
|
|
case atom::ROOT_LE: out << "(<= "; proc(out, a.x()); out << " " << yn << ")"; break;
|
|
case atom::ROOT_GE: out << "(>= "; proc(out, a.x()); out << " " << yn << ")"; break;
|
|
case atom::ROOT_EQ: out << "(= "; proc(out, a.x()); out << " " << yn << ")"; NOT_IMPLEMENTED_YET(); break;
|
|
default: UNREACHABLE(); break;
|
|
}
|
|
out << "))";
|
|
return out;
|
|
#endif
|
|
|
|
|
|
return display_root(out, a, proc);
|
|
}
|
|
|
|
std::ostream& display_root(std::ostream & out, root_atom const & a, display_var_proc const & proc) const {
|
|
proc(out, a.x());
|
|
switch (a.get_kind()) {
|
|
case atom::ROOT_LT: out << " < "; break;
|
|
case atom::ROOT_GT: out << " > "; break;
|
|
case atom::ROOT_LE: out << " <= "; break;
|
|
case atom::ROOT_GE: out << " >= "; break;
|
|
case atom::ROOT_EQ: out << " = "; break;
|
|
default: UNREACHABLE(); break;
|
|
}
|
|
out << "root[" << a.i() << "](";
|
|
display_polynomial(out, a.p(), proc);
|
|
out << ")";
|
|
return out;
|
|
}
|
|
|
|
struct mathematica_var_proc : public display_var_proc {
|
|
var m_x;
|
|
public:
|
|
mathematica_var_proc(var x):m_x(x) {}
|
|
std::ostream& operator()(std::ostream & out, var x) const override {
|
|
if (m_x == x)
|
|
return out << "#1";
|
|
else
|
|
return out << "x" << x;
|
|
}
|
|
};
|
|
|
|
std::ostream& display_mathematica(std::ostream & out, root_atom const & a) const {
|
|
out << "x" << a.x();
|
|
switch (a.get_kind()) {
|
|
case atom::ROOT_LT: out << " < "; break;
|
|
case atom::ROOT_GT: out << " > "; break;
|
|
case atom::ROOT_LE: out << " <= "; break;
|
|
case atom::ROOT_GE: out << " >= "; break;
|
|
case atom::ROOT_EQ: out << " == "; break;
|
|
default: UNREACHABLE(); break;
|
|
}
|
|
out << "Root[";
|
|
display_polynomial(out, a.p(), mathematica_var_proc(a.x()), true);
|
|
out << " &, " << a.i() << "]";
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, atom const & a, display_var_proc const & proc) const {
|
|
if (a.is_ineq_atom())
|
|
return display_ineq(out, static_cast<ineq_atom const &>(a), proc);
|
|
else
|
|
return display_root(out, static_cast<root_atom const &>(a), proc);
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, atom const & a) const {
|
|
return display(out, a, m_display_var);
|
|
}
|
|
|
|
std::ostream& display_mathematica(std::ostream & out, atom const & a) const {
|
|
if (a.is_ineq_atom())
|
|
return display_mathematica(out, static_cast<ineq_atom const &>(a));
|
|
else
|
|
return display_mathematica(out, static_cast<root_atom const &>(a));
|
|
}
|
|
|
|
std::ostream& display_smt2(std::ostream & out, atom const & a, display_var_proc const & proc) const {
|
|
if (a.is_ineq_atom())
|
|
return display_ineq_smt2(out, static_cast<ineq_atom const &>(a), proc);
|
|
else
|
|
return display_root_smt2(out, static_cast<root_atom const &>(a), proc);
|
|
}
|
|
|
|
std::ostream& display_atom(std::ostream & out, bool_var b, display_var_proc const & proc) const {
|
|
if (b == 0)
|
|
out << "true";
|
|
else if (m_atoms[b] == 0)
|
|
out << "b" << b;
|
|
else
|
|
display(out, *(m_atoms[b]), proc);
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_atom(std::ostream & out, bool_var b) const {
|
|
return display_atom(out, b, m_display_var);
|
|
}
|
|
|
|
std::ostream& display_mathematica_atom(std::ostream & out, bool_var b) const {
|
|
if (b == 0)
|
|
out << "(0 < 1)";
|
|
else if (m_atoms[b] == 0)
|
|
out << "b" << b;
|
|
else
|
|
display_mathematica(out, *(m_atoms[b]));
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_smt2_atom(std::ostream & out, bool_var b, display_var_proc const & proc) const {
|
|
if (b == 0)
|
|
out << "true";
|
|
else if (m_atoms[b] == 0)
|
|
out << "b" << b;
|
|
else
|
|
display_smt2(out, *(m_atoms[b]), proc);
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, literal l, display_var_proc const & proc) const {
|
|
if (l.sign()) {
|
|
bool_var b = l.var();
|
|
out << "!";
|
|
if (m_atoms[b] != 0)
|
|
out << "(";
|
|
display_atom(out, b, proc);
|
|
if (m_atoms[b] != 0)
|
|
out << ")";
|
|
}
|
|
else {
|
|
display_atom(out, l.var(), proc);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, literal l) const {
|
|
return display(out, l, m_display_var);
|
|
}
|
|
|
|
std::ostream& display_smt2(std::ostream & out, literal l) const {
|
|
return display_smt2(out, l, m_display_var);
|
|
}
|
|
|
|
std::ostream& display_mathematica(std::ostream & out, literal l) const {
|
|
if (l.sign()) {
|
|
bool_var b = l.var();
|
|
out << "!";
|
|
if (m_atoms[b] != 0)
|
|
out << "(";
|
|
display_mathematica_atom(out, b);
|
|
if (m_atoms[b] != 0)
|
|
out << ")";
|
|
}
|
|
else {
|
|
display_mathematica_atom(out, l.var());
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_smt2(std::ostream & out, literal l, display_var_proc const & proc) const {
|
|
if (l.sign()) {
|
|
bool_var b = l.var();
|
|
out << "(not ";
|
|
display_smt2_atom(out, b, proc);
|
|
out << ")";
|
|
}
|
|
else {
|
|
display_smt2_atom(out, l.var(), proc);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_assumptions(std::ostream & out, _assumption_set s) const {
|
|
if (!m_display_assumption)
|
|
return out;
|
|
vector<assumption, false> deps;
|
|
m_asm.linearize(s, deps);
|
|
bool first = true;
|
|
for (auto dep : deps) {
|
|
if (first) first = false; else out << " ";
|
|
(*m_display_assumption)(out, dep);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, unsigned num, literal const * ls, display_var_proc const & proc) const {
|
|
for (unsigned i = 0; i < num; i++) {
|
|
if (i > 0)
|
|
out << " or ";
|
|
display(out, ls[i], proc);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, unsigned num, literal const * ls) const {
|
|
return display(out, num, ls, m_display_var);
|
|
}
|
|
|
|
std::ostream& display_not(std::ostream & out, unsigned num, literal const * ls, display_var_proc const & proc) const {
|
|
for (unsigned i = 0; i < num; i++) {
|
|
if (i > 0)
|
|
out << " or ";
|
|
display(out, ~ls[i], proc);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_not(std::ostream & out, unsigned num, literal const * ls) const {
|
|
return display_not(out, num, ls, m_display_var);
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, scoped_literal_vector const & cs) {
|
|
return display(out, cs.size(), cs.data(), m_display_var);
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, clause const & c, display_var_proc const & proc) const {
|
|
if (c.assumptions() != nullptr) {
|
|
display_assumptions(out, static_cast<_assumption_set>(c.assumptions()));
|
|
out << " |- ";
|
|
}
|
|
return display(out, c.size(), c.data(), proc);
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, clause const & c) const {
|
|
return display(out, c, m_display_var);
|
|
}
|
|
|
|
|
|
std::ostream& display_polynomial(std::ostream& out, poly* p, display_var_proc const & proc, bool use_star = false) const {
|
|
if (m_display_eval) {
|
|
polynomial_ref q(m_pm);
|
|
q = p;
|
|
for (var x = 0; x < num_vars(); x++)
|
|
if (m_assignment.is_assigned(x)) {
|
|
auto& a = m_assignment.value(x);
|
|
if (!m_am.is_rational(a))
|
|
continue;
|
|
mpq r;
|
|
m_am.to_rational(a, r);
|
|
q = m_pm.substitute(q, 1, &x, &r);
|
|
}
|
|
m_pm.display(out, q, proc, use_star);
|
|
}
|
|
else
|
|
m_pm.display(out, p, proc, use_star);
|
|
return out;
|
|
}
|
|
|
|
// --
|
|
|
|
std::ostream& display_smt2(std::ostream & out, unsigned n, literal const* ls) const {
|
|
return display_smt2(out, n, ls, display_var_proc());
|
|
}
|
|
|
|
|
|
std::ostream& display_smt2(std::ostream & out, unsigned num, literal const * ls, display_var_proc const & proc) const {
|
|
if (num == 0) {
|
|
out << "false";
|
|
}
|
|
else if (num == 1) {
|
|
display_smt2(out, ls[0], proc);
|
|
}
|
|
else {
|
|
out << "(or";
|
|
for (unsigned i = 0; i < num; i++) {
|
|
out << " ";
|
|
display_smt2(out, ls[i], proc);
|
|
}
|
|
out << ")";
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_smt2(std::ostream & out, clause const & c, display_var_proc const & proc = display_var_proc()) const {
|
|
return display_smt2(out, c.size(), c.data(), proc);
|
|
}
|
|
|
|
std::ostream& display_abst(std::ostream & out, literal l) const {
|
|
if (l.sign()) {
|
|
bool_var b = l.var();
|
|
out << "!";
|
|
if (b == true_bool_var)
|
|
out << "true";
|
|
else
|
|
out << "b" << b;
|
|
}
|
|
else {
|
|
out << "b" << l.var();
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_abst(std::ostream & out, unsigned num, literal const * ls) const {
|
|
for (unsigned i = 0; i < num; i++) {
|
|
if (i > 0)
|
|
out << " or ";
|
|
display_abst(out, ls[i]);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_abst(std::ostream & out, scoped_literal_vector const & cs) const {
|
|
return display_abst(out, cs.size(), cs.data());
|
|
}
|
|
|
|
std::ostream& display_abst(std::ostream & out, clause const & c) const {
|
|
return display_abst(out, c.size(), c.data());
|
|
}
|
|
|
|
std::ostream& display_mathematica(std::ostream & out, clause const & c) const {
|
|
out << "(";
|
|
unsigned sz = c.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
if (i > 0)
|
|
out << " || ";
|
|
display_mathematica(out, c[i]);
|
|
}
|
|
out << ")";
|
|
return out;
|
|
}
|
|
|
|
// Debugging support:
|
|
// Display generated lemma in Mathematica format.
|
|
// Mathematica must reduce lemma to True (modulo resource constraints).
|
|
std::ostream& display_mathematica_lemma(std::ostream & out, unsigned num, literal const * ls, bool include_assignment = false) const {
|
|
out << "Resolve[ForAll[{";
|
|
// var definition
|
|
for (unsigned i = 0; i < num_vars(); i++) {
|
|
if (i > 0)
|
|
out << ", ";
|
|
out << "x" << i;
|
|
}
|
|
out << "}, ";
|
|
if (include_assignment) {
|
|
out << "!(";
|
|
if (!display_mathematica_assignment(out))
|
|
out << "0 < 1"; // nothing was printed
|
|
out << ") || ";
|
|
}
|
|
for (unsigned i = 0; i < num; i++) {
|
|
if (i > 0)
|
|
out << " || ";
|
|
display_mathematica(out, ls[i]);
|
|
}
|
|
out << "], Reals]\n"; // end of exists
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, clause_vector const & cs, display_var_proc const & proc) const {
|
|
for (clause* c : cs) {
|
|
display(out, *c, proc) << "\n";
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, clause_vector const & cs) const {
|
|
return display(out, cs, m_display_var);
|
|
}
|
|
|
|
std::ostream& display_mathematica(std::ostream & out, clause_vector const & cs) const {
|
|
unsigned sz = cs.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
if (i > 0) out << ",\n";
|
|
display_mathematica(out << " ", *(cs[i]));
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_abst(std::ostream & out, clause_vector const & cs) const {
|
|
for (clause* c : cs) {
|
|
display_abst(out, *c) << "\n";
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out, display_var_proc const & proc) const {
|
|
display(out, m_clauses, proc);
|
|
if (!m_learned.empty()) {
|
|
display(out << "Lemmas:\n", m_learned, proc);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_mathematica(std::ostream & out) const {
|
|
return display_mathematica(out << "{\n", m_clauses) << "}\n";
|
|
}
|
|
|
|
std::ostream& display_abst(std::ostream & out) const {
|
|
display_abst(out, m_clauses);
|
|
if (!m_learned.empty()) {
|
|
display_abst(out << "Lemmas:\n", m_learned);
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display(std::ostream & out) const {
|
|
display(out, m_display_var);
|
|
display_assignment(out << "assignment:\n");
|
|
return out << "---\n";
|
|
}
|
|
|
|
std::ostream& display_vars(std::ostream & out) const {
|
|
for (unsigned i = 0; i < num_vars(); i++) {
|
|
out << i << " -> "; m_display_var(out, i); out << "\n";
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_smt2_arith_decls(std::ostream & out) const {
|
|
unsigned sz = m_is_int.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
if (is_int(i)) {
|
|
out << "(declare-fun "; m_display_var(out, i) << " () Int)\n";
|
|
}
|
|
else {
|
|
out << "(declare-fun "; m_display_var(out, i) << " () Real)\n";
|
|
}
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_smt2_bool_decls(std::ostream & out) const {
|
|
unsigned sz = m_atoms.size();
|
|
for (unsigned i = 0; i < sz; i++) {
|
|
if (m_atoms[i] == nullptr)
|
|
out << "(declare-fun b" << i << " () Bool)\n";
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& display_smt2(std::ostream & out) const {
|
|
display_smt2_bool_decls(out);
|
|
display_smt2_arith_decls(out);
|
|
out << "(assert (and true\n";
|
|
for (clause* c : m_clauses) {
|
|
display_smt2(out, *c, m_display_var) << "\n";
|
|
}
|
|
out << "))\n" << std::endl;
|
|
return out;
|
|
}
|
|
};
|
|
|
|
solver::solver(reslimit& rlim, params_ref const & p, bool incremental) {
|
|
m_ctx = alloc(ctx, rlim, p, incremental);
|
|
m_imp = alloc(imp, *this, *m_ctx);
|
|
}
|
|
|
|
solver::solver(ctx& ctx) {
|
|
m_ctx = nullptr;
|
|
m_imp = alloc(imp, *this, ctx);
|
|
}
|
|
|
|
solver::~solver() {
|
|
dealloc(m_imp);
|
|
dealloc(m_ctx);
|
|
}
|
|
|
|
lbool solver::check() {
|
|
return m_imp->check();
|
|
}
|
|
|
|
lbool solver::check(literal_vector& assumptions) {
|
|
return m_imp->check(assumptions);
|
|
}
|
|
|
|
void solver::get_core(vector<assumption, false>& assumptions) {
|
|
return m_imp->get_core(assumptions);
|
|
}
|
|
|
|
void solver::reset() {
|
|
m_imp->reset();
|
|
}
|
|
|
|
|
|
void solver::updt_params(params_ref const & p) {
|
|
m_imp->updt_params(p);
|
|
}
|
|
|
|
|
|
void solver::collect_param_descrs(param_descrs & d) {
|
|
algebraic_numbers::manager::collect_param_descrs(d);
|
|
nlsat_params::collect_param_descrs(d);
|
|
}
|
|
|
|
unsynch_mpq_manager & solver::qm() {
|
|
return m_imp->m_qm;
|
|
}
|
|
|
|
anum_manager & solver::am() {
|
|
return m_imp->m_am;
|
|
}
|
|
|
|
pmanager & solver::pm() {
|
|
return m_imp->m_pm;
|
|
}
|
|
|
|
void solver::set_display_var(display_var_proc const & proc) {
|
|
m_imp->m_display_var.m_proc = &proc;
|
|
}
|
|
|
|
void solver::set_display_assumption(display_assumption_proc const& proc) {
|
|
m_imp->m_display_assumption = &proc;
|
|
}
|
|
|
|
|
|
unsigned solver::num_vars() const {
|
|
return m_imp->num_vars();
|
|
}
|
|
|
|
bool solver::is_int(var x) const {
|
|
return m_imp->is_int(x);
|
|
}
|
|
|
|
bool_var solver::mk_bool_var() {
|
|
return m_imp->mk_bool_var();
|
|
}
|
|
|
|
literal solver::mk_true() {
|
|
return literal(0, false);
|
|
}
|
|
|
|
atom * solver::bool_var2atom(bool_var b) {
|
|
return m_imp->m_atoms[b];
|
|
}
|
|
|
|
void solver::vars(literal l, var_vector& vs) {
|
|
m_imp->vars(l, vs);
|
|
}
|
|
|
|
atom_vector const& solver::get_atoms() {
|
|
return m_imp->m_atoms;
|
|
}
|
|
|
|
atom_vector const& solver::get_var2eq() {
|
|
return m_imp->m_var2eq;
|
|
}
|
|
|
|
evaluator& solver::get_evaluator() {
|
|
return m_imp->m_evaluator;
|
|
}
|
|
|
|
explain& solver::get_explain() {
|
|
return m_imp->m_explain;
|
|
}
|
|
|
|
void solver::reorder(unsigned sz, var const* p) {
|
|
m_imp->reorder(sz, p);
|
|
}
|
|
|
|
void solver::restore_order() {
|
|
m_imp->restore_order();
|
|
}
|
|
|
|
void solver::set_rvalues(assignment const& as) {
|
|
m_imp->m_assignment.copy(as);
|
|
}
|
|
|
|
void solver::get_rvalues(assignment& as) {
|
|
as.copy(m_imp->m_assignment);
|
|
}
|
|
|
|
void solver::get_bvalues(svector<bool_var> const& bvars, svector<lbool>& vs) {
|
|
vs.reset();
|
|
for (bool_var b : bvars) {
|
|
vs.reserve(b + 1, l_undef);
|
|
if (!m_imp->m_atoms[b]) {
|
|
vs[b] = m_imp->m_bvalues[b];
|
|
}
|
|
}
|
|
TRACE("nlsat", display(tout););
|
|
}
|
|
|
|
void solver::set_bvalues(svector<lbool> const& vs) {
|
|
TRACE("nlsat", display(tout););
|
|
for (bool_var b = 0; b < vs.size(); ++b) {
|
|
if (vs[b] != l_undef) {
|
|
m_imp->m_bvalues[b] = vs[b];
|
|
SASSERT(!m_imp->m_atoms[b]);
|
|
}
|
|
}
|
|
#if 0
|
|
m_imp->m_bvalues.reset();
|
|
m_imp->m_bvalues.append(vs);
|
|
m_imp->m_bvalues.resize(m_imp->m_atoms.size(), l_undef);
|
|
for (unsigned i = 0; i < m_imp->m_atoms.size(); ++i) {
|
|
atom* a = m_imp->m_atoms[i];
|
|
SASSERT(!a);
|
|
if (a) {
|
|
m_imp->m_bvalues[i] = to_lbool(m_imp->m_evaluator.eval(a, false));
|
|
}
|
|
}
|
|
#endif
|
|
TRACE("nlsat", display(tout););
|
|
}
|
|
|
|
void solver::del_clause(clause* c) {
|
|
m_imp->del_clause(c);
|
|
}
|
|
|
|
var solver::mk_var(bool is_int) {
|
|
return m_imp->mk_var(is_int);
|
|
}
|
|
|
|
bool_var solver::mk_ineq_atom(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even) {
|
|
return m_imp->mk_ineq_atom(k, sz, ps, is_even);
|
|
}
|
|
|
|
literal solver::mk_ineq_literal(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even, bool simplify) {
|
|
return m_imp->mk_ineq_literal(k, sz, ps, is_even, simplify);
|
|
}
|
|
|
|
bool_var solver::mk_root_atom(atom::kind k, var x, unsigned i, poly * p) {
|
|
return m_imp->mk_root_atom(k, x, i, p);
|
|
}
|
|
|
|
void solver::inc_ref(bool_var b) {
|
|
m_imp->inc_ref(b);
|
|
}
|
|
|
|
void solver::dec_ref(bool_var b) {
|
|
m_imp->dec_ref(b);
|
|
}
|
|
|
|
void solver::inc_ref(assumption a) {
|
|
m_imp->inc_ref(static_cast<imp::_assumption_set>(a));
|
|
}
|
|
|
|
void solver::dec_ref(assumption a) {
|
|
m_imp->dec_ref(static_cast<imp::_assumption_set>(a));
|
|
}
|
|
|
|
void solver::mk_clause(unsigned num_lits, literal * lits, assumption a) {
|
|
return m_imp->mk_external_clause(num_lits, lits, a);
|
|
}
|
|
|
|
std::ostream& solver::display(std::ostream & out) const {
|
|
return m_imp->display(out);
|
|
}
|
|
|
|
std::ostream& solver::display(std::ostream & out, literal l) const {
|
|
return m_imp->display(out, l);
|
|
}
|
|
|
|
std::ostream& solver::display(std::ostream & out, unsigned n, literal const* ls) const {
|
|
for (unsigned i = 0; i < n; ++i) {
|
|
display(out, ls[i]);
|
|
out << "; ";
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& solver::display(std::ostream & out, literal_vector const& ls) const {
|
|
return display(out, ls.size(), ls.data());
|
|
}
|
|
|
|
std::ostream& solver::display_smt2(std::ostream & out, literal l) const {
|
|
return m_imp->display_smt2(out, l);
|
|
}
|
|
|
|
std::ostream& solver::display_smt2(std::ostream & out, unsigned n, literal const* ls) const {
|
|
for (unsigned i = 0; i < n; ++i) {
|
|
display_smt2(out, ls[i]);
|
|
out << " ";
|
|
}
|
|
return out;
|
|
}
|
|
|
|
std::ostream& solver::display(std::ostream& out, clause const& c) const {
|
|
return m_imp->display(out, c);
|
|
}
|
|
|
|
std::ostream& solver::display_smt2(std::ostream & out) const {
|
|
return m_imp->display_smt2(out);
|
|
}
|
|
|
|
std::ostream& solver::display_smt2(std::ostream & out, literal_vector const& ls) const {
|
|
return display_smt2(out, ls.size(), ls.data());
|
|
}
|
|
|
|
std::ostream& solver::display(std::ostream & out, var x) const {
|
|
return m_imp->m_display_var(out, x);
|
|
}
|
|
|
|
std::ostream& solver::display(std::ostream & out, atom const& a) const {
|
|
return m_imp->display(out, a, m_imp->m_display_var);
|
|
}
|
|
|
|
display_var_proc const & solver::display_proc() const {
|
|
return m_imp->m_display_var;
|
|
}
|
|
|
|
anum const & solver::value(var x) const {
|
|
if (m_imp->m_assignment.is_assigned(x))
|
|
return m_imp->m_assignment.value(x);
|
|
return m_imp->m_zero;
|
|
}
|
|
|
|
lbool solver::bvalue(bool_var b) const {
|
|
return m_imp->m_bvalues[b];
|
|
}
|
|
|
|
lbool solver::value(literal l) const {
|
|
return m_imp->value(l);
|
|
}
|
|
|
|
bool solver::is_interpreted(bool_var b) const {
|
|
return m_imp->m_atoms[b] != 0;
|
|
}
|
|
|
|
void solver::reset_statistics() {
|
|
return m_imp->reset_statistics();
|
|
}
|
|
|
|
void solver::collect_statistics(statistics & st) {
|
|
return m_imp->collect_statistics(st);
|
|
}
|
|
|
|
clause* solver::mk_clause(unsigned n, literal const* lits, bool learned, internal_assumption a) {
|
|
return m_imp->mk_clause(n, lits, learned, static_cast<imp::_assumption_set>(a));
|
|
}
|
|
|
|
void solver::inc_simplify() {
|
|
m_imp->m_stats.m_simplifications++;
|
|
}
|
|
|
|
bool solver::has_root_atom(clause const& c) const {
|
|
return m_imp->has_root_atom(c);
|
|
}
|
|
|
|
void solver::add_bound(bound_constraint const& c) {
|
|
m_imp->m_bounds.push_back(c);
|
|
}
|
|
|
|
assumption solver::join(assumption a, assumption b) {
|
|
return (m_imp->m_asm.mk_join(static_cast<imp::_assumption_set>(a), static_cast<imp::_assumption_set>(b)));
|
|
}
|
|
|
|
};
|