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z3/src/nlsat/nlsat_solver.cpp
Nikolaj Bjorner 680c28d083 remove nnf conversion which breaks NRA property 
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2016-03-20 16:34:04 -07:00

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/*++
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"nlsat_solver.h"
#include"nlsat_clause.h"
#include"nlsat_assignment.h"
#include"nlsat_justification.h"
#include"nlsat_evaluator.h"
#include"nlsat_explain.h"
#include"algebraic_numbers.h"
#include"z3_exception.h"
#include"chashtable.h"
#include"id_gen.h"
#include"dependency.h"
#include"polynomial_cache.h"
#include"permutation.h"
#include"nlsat_params.hpp"
#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) {
std::swap(c1, c2);
}
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;
reslimit& m_rlimit;
small_object_allocator m_allocator;
unsynch_mpq_manager m_qm;
pmanager m_pm;
cache m_cache;
anum_manager m_am;
assumption_manager m_asm;
assignment m_assignment; // partial interpretation
evaluator m_evaluator;
interval_set_manager & m_ism;
ineq_atom_table m_ineq_atoms;
root_atom_table m_root_atoms;
id_gen m_cid_gen;
clause_vector m_clauses; // set of clauses
clause_vector m_learned; // set of learned clauses
unsigned m_num_bool_vars;
atom_vector m_atoms; // bool_var -> atom
svector<lbool> m_bvalues; // boolean assigment
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
svector<bool> m_dead; // mark dead boolean variables
id_gen m_bid_gen;
svector<bool> 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(0) {
}
virtual void operator()(std::ostream & out, var x) const {
if (m_proc == 0)
m_default_display_var(out, x);
else
(*m_proc)(out, m_perm[x]);
}
};
perm_display_var_proc m_display_var;
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 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):m_kind(BVAR_ASSIGNMENT), m_b(b) {}
trail(interval_set * old_set):m_kind(INFEASIBLE_UPDT), m_old_set(old_set) {}
trail(bool stage):m_kind(stage ? 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;
unsigned m_max_conflicts;
// statistics
unsigned m_conflicts;
unsigned m_propagations;
unsigned m_decisions;
unsigned m_stages;
unsigned m_irrational_assignments; // number of irrational witnesses
imp(solver& s, reslimit& rlim, params_ref const & p):
m_rlimit(rlim),
m_allocator("nlsat"),
m_pm(rlim, m_qm, &m_allocator),
m_cache(m_pm),
m_am(rlim, m_qm, p, &m_allocator),
m_asm(*this, m_allocator),
m_assignment(m_am),
m_evaluator(s, m_assignment, m_pm, m_allocator),
m_ism(m_evaluator.ism()),
m_num_bool_vars(0),
m_display_var(m_perm),
m_explain(s, m_assignment, m_cache, m_atoms, m_var2eq, m_evaluator),
m_scope_lvl(0),
m_lemma(s),
m_lazy_clause(s),
m_lemma_assumptions(m_asm) {
updt_params(p);
reset_statistics();
mk_true_bvar();
}
~imp() {
reset();
}
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, 0);
}
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_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();
}
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 != 0) m_asm.inc_ref(a);
}
void dec_ref(_assumption_set a) {
if (a != 0) m_asm.dec_ref(a);
}
void inc_ref(bool_var b) {
TRACE("ref", tout << "inc: " << b << "\n";);
if (b == null_bool_var)
return;
if (m_atoms[b] == 0)
return;
m_atoms[b]->inc_ref();
}
void inc_ref(literal l) {
inc_ref(l.var());
}
void dec_ref(bool_var b) {
TRACE("ref", tout << "dec: " << b << "\n";);
if (b == null_bool_var)
return;
atom * a = m_atoms[b];
if (a == 0)
return;
SASSERT(a->ref_count() > 0);
a->dec_ref();
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] != 0; }
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.c_ptr());
}
/**
\brief Return the maximum Boolean variable occurring in cls.
*/
bool_var max_bvar(clause const & cls) const {
bool_var b = null_bool_var;
unsigned sz = cls.size();
for (unsigned i = 0; i < sz; i++) {
literal l = cls[i];
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;
unsigned sz = c.size();
for (unsigned i = 0; i < sz; i++) {
literal l = c[i];
atom const * a = m_atoms[l.var()];
if (a == 0)
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, 0, 0);
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();
SASSERT(x == num_vars());
m_is_int. push_back(is_int);
m_watches. push_back(clause_vector());
m_infeasible.push_back(0);
m_var2eq. push_back(0);
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());
return x;
}
svector<bool> m_found_vars;
void vars(literal l, var_vector& vs) {
vs.reset();
atom * a = m_atoms[l.var()];
if (a == 0) {
}
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] = 0;
m_bid_gen.recycle(b);
}
void del(ineq_atom * a) {
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 == 0)
return ;
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() {
unsigned sz = m_atoms.size();
for (unsigned i = 0; i < sz; i++) {
del(m_atoms[i]);
}
}
bool_var mk_ineq_atom(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even) {
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])
sign = -sign;
var curr_max = max_var(p.get());
if (curr_max > max || max == null_var)
max = curr_max;
uniq_ps.push_back(m_cache.mk_unique(p));
TRACE("nlsat_table_bug", tout << "p: " << p << ", 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 * new_atom = new (mem) ineq_atom(k, sz, uniq_ps.c_ptr(), is_even, max);
TRACE("nlsat_table_bug", ineq_atom::hash_proc h;
tout << "mk_ineq_atom hash: " << h(new_atom) << "\n"; display(tout, *new_atom, m_display_var); tout << "\n";);
ineq_atom * old_atom = m_ineq_atoms.insert_if_not_there(new_atom);
CTRACE("nlsat_table_bug", old_atom->max_var() != max, display(tout, *old_atom, m_display_var); tout << "\n";);
SASSERT(old_atom->max_var() == max);
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;
for (unsigned i = 0; i < sz; i++) {
m_pm.inc_ref(new_atom->p(i));
}
return b;
}
literal mk_ineq_literal(atom::kind k, unsigned sz, poly * const * ps, bool const * is_even) {
SASSERT(k == atom::LT || k == atom::GT || k == atom::EQ);
if (sz == 0) {
switch (k) {
case atom::LT: return false_literal; // 1 < 0
case atom::EQ: return false_literal; // 1 == 0
case atom::GT: return true_literal; // 1 > 0
default:
UNREACHABLE();
return null_literal;
}
}
else {
return literal(mk_ineq_atom(k, sz, ps, is_even), false);
}
}
bool_var mk_root_atom(atom::kind k, var x, unsigned i, poly * p) {
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);
polynomial_ref p1(m_pm);
p1 = m_pm.flip_sign_if_lm_neg(p); // flipping the sign of the polynomial will not change its roots.
poly * uniq_p = m_cache.mk_unique(p1);
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_clauses(ptr_vector<clause> & cs) {
unsigned sz = cs.size();
for (unsigned i = 0; i < sz; i++)
del_clause(cs[i]);
}
void del_clauses() {
del_clauses(m_clauses);
del_clauses(m_learned);
}
// 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 == 0 && a2 == 0)
return l1.index() < l2.index();
if (a1 == 0)
return true;
if (a2 == 0)
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();
}
};
clause * mk_clause(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);
TRACE("nlsat_sort", tout << "mk_clause:\n"; display(tout, *cls); tout << "\n";);
std::sort(cls->begin(), cls->end(), lit_lt(*this));
TRACE("nlsat_sort", tout << "after sort:\n"; display(tout, *cls); tout << "\n";);
if (learned)
m_learned.push_back(cls);
else
m_clauses.push_back(cls);
attach_clause(*cls);
return cls;
}
void mk_clause(unsigned num_lits, literal const * lits, assumption a) {
SASSERT(num_lits > 0);
_assumption_set as = 0;
if (a != 0)
as = m_asm.mk_leaf(a);
mk_clause(num_lits, lits, false, as);
}
// -----------------------
//
// Search
//
// -----------------------
void save_assign_trail(bool_var b) {
m_trail.push_back(trail(b));
}
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));
}
void save_new_level_trail() {
m_trail.push_back(trail(false));
}
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] == 0 && b < m_bk)
m_bk = b;
}
void undo_set_updt(interval_set * old_set) {
SASSERT(m_xk != null_var);
var x = m_xk;
m_ism.dec_ref(m_infeasible[x]);
m_infeasible[x] = old_set;
}
void undo_new_stage() {
SASSERT(m_xk != null_var);
if (m_xk == 0) {
m_xk = null_var;
}
else {
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) {
SASSERT(m_xk != null_var);
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", tout << "assigning literal:\n"; display(tout, l);
tout << "\njustification kind: " << j.get_kind() << "\n";);
SASSERT(assigned_value(l) == l_undef);
SASSERT(j != null_justification);
SASSERT(!j.is_null());
if (j.is_decision())
m_decisions++;
else
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);
TRACE("nlsat_assign", tout << "b" << b << " -> " << m_bvalues[b] << " " << m_atoms[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)
return val;
bool_var b = l.var();
atom * a = m_atoms[b];
if (a == 0)
return l_undef;
var max = a->max_var();
if (!m_assignment.is_assigned(max))
return l_undef;
val = to_lbool(m_evaluator.eval(a, l.sign()));
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 {
unsigned sz = cls.size();
for (unsigned i = 0; i < sz; i++) {
if (const_cast<imp*>(this)->value(cls[i]) == l_true) {
TRACE("value_bug:", tout << cls[i] << " := 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()] == 0);
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;
void R_propagate(literal l, interval_set const * s, bool include_l = true) {
m_ism.get_justifications(s, core);
if (include_l)
core.push_back(~l);
assign(l, mk_lazy_jst(m_allocator, core.size(), core.c_ptr()));
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); tout << "\n"; m_ism.display(tout, s); tout << "\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); tout << "\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) {
if (!m_simplify_cores)
return;
if (m_bvalues[b] != l_true)
return;
atom * a = m_atoms[b];
if (a == 0 || a->get_kind() != atom::EQ || to_ineq_atom(a)->size() > 1 || to_ineq_atom(a)->is_even(0))
return;
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("simplify_core", tout << "Saving equality for "; m_display_var(tout, x); tout << " (x" << x << ") ";
tout << "scope-lvl: " << scope_lvl() << "\n"; display(tout, literal(b, false)); tout << "\n";);
save_updt_eq_trail(m_var2eq[x]);
m_var2eq[x] = a;
}
/**
\brief Process a clause that contains nonlinar 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));
unsigned sz = cls.size();
for (unsigned i = 0; i < sz; i++) {
checkpoint();
literal l = cls[i];
if (value(l) == l_false)
continue;
SASSERT(value(l) == l_undef);
SASSERT(max_var(l) == m_xk);
bool_var b = l.var();
atom * a = m_atoms[b];
SASSERT(a != 0);
interval_set_ref curr_set(m_ism);
TRACE("nlsat_inf_set", tout << "xk: " << m_xk << ", max_var(l): " << max_var(l) << ", l: "; display(tout, l); tout << "\n";);
curr_set = m_evaluator.infeasible_intervals(a, l.sign());
TRACE("nlsat_inf_set", tout << "infeasible set for literal: "; display(tout, l); tout << "\n"; m_ism.display(tout, curr_set); tout << "\n";);
if (m_ism.is_empty(curr_set)) {
TRACE("nlsat_inf_set", tout << "infeasible set is empty, found literal\n";);
R_propagate(l, 0);
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, 0);
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";);
R_propagate(~l, tmp, false);
continue;
}
num_undef++;
if (first_undef == UINT_MAX) {
first_undef = i;
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) {
TRACE("nlsat", tout << "processing clause: "; display(tout, cls); tout << "\n";);
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) {
unsigned sz = cs.size();
for (unsigned i = 0; i < sz; i++) {
clause * c = cs[i];
if (!process_clause(*c, false))
return c;
}
return 0; // 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] == 0 && 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_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.peek_in_complement(m_infeasible[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); tout << "(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_irrational_assignments++;
m_assignment.set_core(m_xk, w);
}
/**
\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););
m_bk = 0;
m_xk = null_var;
while (true) {
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 (m_bk == null_bool_var && m_xk >= num_vars()) {
TRACE("nlsat", tout << "found model\n"; display_assignment(tout););
return l_true; // all variables were assigned, and all clauses were satisfied.
}
TRACE("nlsat", tout << "processing variable ";
if (m_xk != null_var) m_display_var(tout, m_xk); else tout << "boolean b" << m_bk; tout << "\n";);
while (true) {
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 == 0)
break;
if (!resolve(*conflict_clause))
return l_false;
if (m_conflicts >= m_max_conflicts)
return l_undef;
}
if (m_xk == null_var) {
if (m_bvalues[m_bk] == l_undef) {
decide(literal(m_bk, true));
m_bk++;
}
}
else {
select_witness();
}
}
}
lbool check() {
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_random_order) {
shuffle_vars();
reordered = true;
}
else if (m_reorder) {
heuristic_reorder();
reordered = true;
}
sort_watched_clauses();
lbool r = search();
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););
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.c_ptr();
for (unsigned i = 0; i < sz; ++i) {
mk_clause(1, ptr+i, (assumption)(ptr+i));
}
lbool r = check();
if (r == l_false) {
// collect used literals from m_lemma_assumptions
vector<assumption, false> deps;
m_asm.linearize(m_lemma_assumptions.get(), 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);
assumptions.reset();
assumptions.append(result);
return r;
}
void collect(literal_vector const& assumptions, clause_vector& clauses) {
unsigned n = clauses.size();
unsigned j = 0;
for (unsigned i = 0; i < n; i++) {
clause * c = clauses[i];
if (collect(assumptions, *c)) {
del_clause(c);
}
else {
clauses[j] = c;
j++;
}
}
clauses.shrink(j);
}
bool collect(literal_vector const& assumptions, clause const& c) {
unsigned sz = assumptions.size();
literal const* ptr = assumptions.c_ptr();
_assumption_set asms = static_cast<_assumption_set>(c.assumptions());
if (asms == 0) {
return false;
}
vector<assumption, false> deps;
m_asm.linearize(asms, deps);
bool found = false;
for (unsigned i = 0; !found && i < deps.size(); ++i) {
found = ptr <= deps[i] && deps[i] < ptr + sz;
}
return found;
}
// -----------------------
//
// 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 i = 0; i < m_marks.size(); i++) {
SASSERT(m_marks[i] == 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() {
unsigned sz = m_lemma.size();
for (unsigned i = 0; i < sz; i++) {
reset_mark(m_lemma[i].var());
}
}
void process_antecedent(literal antecedent) {
bool_var b = antecedent.var();
TRACE("nlsat_resolve", tout << "resolving antecedent, l:\n"; display(tout, antecedent); tout << "\n";);
if (assigned_value(antecedent) == l_undef) {
// antecedent must be false in the current arith interpretation
SASSERT(value(antecedent) == l_false);
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); tout << "\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 const & c) {
TRACE("nlsat_resolve", tout << "resolving clause for b: " << b << "\n";);
resolve_clause(b, c.size(), c.c_ptr());
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.size();
// 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[i]);
}
display_mathematica_lemma(tout, core.size(), core.c_ptr(), true););
m_lazy_clause.reset();
m_explain(jst.size(), jst.lits(), m_lazy_clause);
for (unsigned i = 0; i < sz; i++)
m_lazy_clause.push_back(~jst[i]);
// lazy clause is a valid clause
TRACE("nlsat_mathematica", display_mathematica_lemma(tout, m_lazy_clause.size(), m_lazy_clause.c_ptr()););
TRACE("nlsat_proof_sk", tout << "theory lemma\n"; display_abst(tout, m_lazy_clause.size(), m_lazy_clause.c_ptr()); tout << "\n";);
TRACE("nlsat_resolve",
tout << "m_xk: " << m_xk << ", "; m_display_var(tout, m_xk); tout << "\n";
tout << "new valid clause:\n";
display(tout, m_lazy_clause.size(), m_lazy_clause.c_ptr()); tout << "\n";);
DEBUG_CODE({
unsigned sz = m_lazy_clause.size();
for (unsigned i = 0; i < sz; i++) {
literal l = m_lazy_clause[i];
if (l.var() != b) {
SASSERT(value(l) == l_false);
}
else {
SASSERT(value(l) == l_true);
SASSERT(!l.sign() || m_bvalues[b] == l_false);
SASSERT(l.sign() || m_bvalues[b] == l_true);
}
}
});
resolve_clause(b, m_lazy_clause.size(), m_lazy_clause.c_ptr());
}
/**
\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 intepretation
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()] != 0)
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;
}
/**
\brief Return true if the conflict was solved.
*/
bool resolve(clause const & conflict) {
clause const * conflict_clause = &conflict;
start:
SASSERT(check_marks());
TRACE("nlsat_proof", tout << "STARTING RESOLUTION\n";);
TRACE("nlsat_proof_sk", tout << "STARTING RESOLUTION\n";);
m_conflicts++;
TRACE("nlsat", tout << "resolve, conflicting clause:\n"; display(tout, *conflict_clause); tout << "\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););
// static unsigned counter = 0;
// counter++;
// if (counter > 6)
// exit(0);
m_num_marks = 0;
m_lemma.reset();
m_lemma_assumptions = 0;
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) {
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 bool_var: " << b << "\n"; display_atom(tout, b); tout << "\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.c_ptr()))
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.c_ptr());
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.c_ptr()); tout << "\n";
tout << "found_decision: " << found_decision << "\n";);
// 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 = 0;
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.c_ptr());
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.c_ptr(), true, m_lemma_assumptions.get());
TRACE("nlsat", tout << "new_level: " << scope_lvl() << "\nnew_stage: " << new_max_var << " ";
if (new_max_var != null_var) m_display_var(tout, new_max_var); tout << "\n";);
}
else {
SASSERT(scope_lvl() >= 1);
// Case 2)
if (is_bool_lemma(m_lemma.size(), m_lemma.c_ptr())) {
// 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.c_ptr());
TRACE("nlsat", tout << "backtracking to new level: " << new_lvl << ", curr: " << m_scope_lvl << "\n";);
undo_until_level(new_lvl);
}
new_cls = mk_clause(sz, m_lemma.c_ptr(), true, m_lemma_assumptions.get());
}
NLSAT_VERBOSE(display(verbose_stream(), *new_cls); verbose_stream() << "\n";);
if (!process_clause(*new_cls, true)) {
TRACE("nlsat", tout << "new clause triggered another conflict, restarting conflict resolution...\n";);
// we are still in conflict
conflict_clause = new_cls;
goto start;
}
TRACE("nlsat_resolve_done", display_assignment(tout););
return true;
}
// -----------------------
//
// Debugging
//
// -----------------------
bool check_watches() const {
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++) {
clause const & c = *(cs[i]);
SASSERT(max_var(c) == x);
}
}
return true;
}
bool check_bwatches() const {
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);
}
}
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";);
UNREACHABLE();
}
}
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++) {
SASSERT(check_satisfied(m_bwatches[b]));
}
if (m_xk != null_var) {
for (var x = 0; x < m_xk; x++) {
SASSERT(check_satisfied(m_watches[x]));
}
}
return true;
}
// -----------------------
//
// Statistics
//
// -----------------------
void collect_statistics(statistics & st) {
st.update("nlsat conflicts", m_conflicts);
st.update("nlsat propagations", m_propagations);
st.update("nlsat decisions", m_decisions);
st.update("nlsat stages", m_stages);
st.update("nlsat irrational assignments", m_irrational_assignments);
}
void reset_statistics() {
m_conflicts = 0;
m_propagations = 0;
m_decisions = 0;
m_stages = 0;
m_irrational_assignments = 0;
}
// -----------------------
//
// Variable reodering
//
// -----------------------
struct var_info_collector {
pmanager & pm;
atom_vector const & m_atoms;
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 == 0)
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]));
}
void 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";
}
}
};
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 x < 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);
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.c_ptr());
SASSERT(check_invariant());
}
void shuffle_vars() {
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.c_ptr(), r);
reorder(p.size(), p.c_ptr());
}
bool can_reorder() const {
for (unsigned i = 0; i < m_atoms.size(); ++i) {
if (m_atoms[i]) {
if (m_atoms[i]->is_root_atom()) return false;
}
}
return true;
}
/**
\brief Reorder variables using the giving permutation.
p maps internal variables to their new positions
*/
void reorder(unsigned sz, var const * p) {
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";
);
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();
DEBUG_CODE({
for (var x = 0; x < num_vars(); x++) {
SASSERT(m_watches[x].empty());
}
});
// 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);
}
svector<bool> 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);
DEBUG_CODE({
for (var x = 0; x < num_vars(); x++) {
SASSERT(x == m_inv_perm[m_perm[x]]);
SASSERT(m_watches[x].empty());
}
});
m_pm.rename(sz, p);
del_ill_formed_lemmas();
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.c_ptr());
DEBUG_CODE({
for (var x = 0; x < num_vars(); x++) {
SASSERT(m_perm[x] == x);
SASSERT(m_inv_perm[x] == x);
}
});
}
/**
\brief After variable reordering some lemmas containing root atoms may be ill-formed.
*/
void del_ill_formed_lemmas() {
unsigned sz = m_learned.size();
unsigned j = 0;
for (unsigned i = 0; i < sz; i++) {
clause * c = m_learned[i];
if (ill_formed(*c)) {
del_clause(c);
}
else {
m_learned[j] = c;
j++;
}
}
m_learned.shrink(j);
}
/**
\brief Return true if the clause contains an ill formed root atom
*/
bool ill_formed(clause const & c) {
unsigned sz = c.size();
for (unsigned i = 0; i < sz; i++) {
bool_var b = c[i].var();
atom * a = m_atoms[b];
if (a == 0)
continue;
if (a->is_ineq_atom())
continue;
if (to_root_atom(a)->x() < max_var(to_root_atom(a)->p()))
return true;
}
return false;
}
/**
\brief reinsert all polynomials in the unique cache
*/
void reinit_cache() {
reinit_cache(m_clauses);
reinit_cache(m_learned);
for (unsigned i = 0; i < m_atoms.size(); ++i) {
reinit_cache(m_atoms[i]);
}
}
void reinit_cache(clause_vector const & cs) {
unsigned sz = cs.size();
for (unsigned i = 0; i < sz; i++)
reinit_cache(*(cs[i]));
}
void reinit_cache(clause const & c) {
unsigned sz = c.size();
for (unsigned i = 0; i < sz; i++)
reinit_cache(c[i]);
}
void reinit_cache(literal l) {
bool_var b = l.var();
reinit_cache(m_atoms[b]);
}
void reinit_cache(atom* a) {
if (a == 0) {
}
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) {
unsigned sz = cs.size();
for (unsigned i = 0; i < sz; i++) {
clause & c = *cs[i];
var x = max_var(c);
if (x != null_var)
m_watches[x].push_back(&c);
}
}
// -----------------------
//
// 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.c_ptr());
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.c_ptr());
}
}
// -----------------------
//
// 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 == 0)
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 {
unsigned sz = c.size();
for (unsigned i = 0; i < sz; i++) {
if (!is_full_dimensional(c[i]))
return false;
}
return true;
}
bool is_full_dimensional(clause_vector const & cs) const {
unsigned sz = cs.size();
for (unsigned i = 0; i < sz; i++) {
if (!is_full_dimensional(*(cs[i])))
return false;
}
return true;
}
bool is_full_dimensional() const {
return is_full_dimensional(m_clauses);
}
// -----------------------
//
// Pretty printing
//
// -----------------------
void 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";
}
}
}
void display_bool_assignment(std::ostream & out) const {
unsigned sz = m_atoms.size();
for (bool_var b = 0; b < sz; b++) {
if (m_atoms[b] == 0 && m_bvalues[b] != l_undef) {
out << "b" << b << " -> " << (m_bvalues[b] == l_true ? "true" : "false") << "\n";
}
}
TRACE("nlsat_bool_assignment",
for (bool_var b = 0; b < sz; b++) {
out << "b" << b << " -> " << m_bvalues[b] << " " << m_atoms[b] << "\n";
});
}
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;
}
void display_num_assignment(std::ostream & out) const {
display_num_assignment(out, m_display_var);
}
void display_assignment(std::ostream& out) const {
display_bool_assignment(out);
display_num_assignment(out);
}
void display(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 << "(";
m_pm.display(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;
}
}
void 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;
}
}
void display_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 << "(* ";
m_pm.display_smt2(out, a.p(i), proc);
out << " ";
m_pm.display_smt2(out, a.p(i), proc);
out << ")";
}
else {
m_pm.display_smt2(out, a.p(i), proc);
}
}
if (sz > 1)
out << ")";
out << " 0)";
}
void display(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() << "](";
m_pm.display(out, a.p(), proc);
out << ")";
}
struct mathematica_var_proc : public display_var_proc {
var m_x;
public:
mathematica_var_proc(var x):m_x(x) {}
virtual void operator()(std::ostream & out, var x) const {
if (m_x == x)
out << "#1";
else
out << "x" << x;
}
};
void 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[";
m_pm.display(out, a.p(), mathematica_var_proc(a.x()), true);
out << " &, " << a.i() << "]";
}
void display_smt2(std::ostream & out, root_atom const & a) const {
NOT_IMPLEMENTED_YET();
}
void display(std::ostream & out, atom const & a, display_var_proc const & proc) const {
if (a.is_ineq_atom())
display(out, static_cast<ineq_atom const &>(a), proc);
else
display(out, static_cast<root_atom const &>(a), proc);
}
void display_mathematica(std::ostream & out, atom const & a) const {
if (a.is_ineq_atom())
display_mathematica(out, static_cast<ineq_atom const &>(a));
else
display_mathematica(out, static_cast<root_atom const &>(a));
}
void display_smt2(std::ostream & out, atom const & a, display_var_proc const & proc) const {
if (a.is_ineq_atom())
display_smt2(out, static_cast<ineq_atom const &>(a), proc);
else
display_smt2(out, static_cast<root_atom const &>(a), proc);
}
void 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);
}
void display_atom(std::ostream & out, bool_var b) const {
display_atom(out, b, m_display_var);
}
void 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]));
}
void 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);
}
void 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);
}
}
void display(std::ostream & out, literal l) const {
display(out, l, m_display_var);
}
void 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());
}
}
void 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);
}
}
void display_assumptions(std::ostream & out, _assumption_set s) const {
}
void 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);
}
}
void display(std::ostream & out, unsigned num, literal const * ls) {
display(out, num, ls, m_display_var);
}
void display(std::ostream & out, scoped_literal_vector const & cs) {
display(out, cs.size(), cs.c_ptr(), m_display_var);
}
void display(std::ostream & out, clause const & c, display_var_proc const & proc) const {
if (c.assumptions() != 0) {
display_assumptions(out, static_cast<_assumption_set>(c.assumptions()));
out << " |- ";
}
display(out, c.size(), c.c_ptr(), proc);
}
void display(std::ostream & out, clause const & c) const {
display(out, c, m_display_var);
}
void 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 << ")";
}
}
void display_smt2(std::ostream & out, clause const & c, display_var_proc const & proc = display_var_proc()) const {
display_smt2(out, c.size(), c.c_ptr(), proc);
}
void 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();
}
}
void 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]);
}
}
void display_abst(std::ostream & out, scoped_literal_vector const & cs) const {
display_abst(out, cs.size(), cs.c_ptr());
}
void display_abst(std::ostream & out, clause const & c) const {
display_abst(out, c.size(), c.c_ptr());
}
void 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 << ")";
}
// Debugging support:
// Display generated lemma in Mathematica format.
// Mathematica must reduce lemma to True (modulo resource constraints).
void 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
}
void display(std::ostream & out, clause_vector const & cs, display_var_proc const & proc) const {
unsigned sz = cs.size();
for (unsigned i = 0; i < sz; i++) {
display(out, *(cs[i]), proc);
out << "\n";
}
}
void display(std::ostream & out, clause_vector const & cs) const {
display(out, cs, m_display_var);
}
void 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";
out << " ";
display_mathematica(out, *(cs[i]));
}
}
void display_abst(std::ostream & out, clause_vector const & cs) const {
unsigned sz = cs.size();
for (unsigned i = 0; i < sz; i++) {
display_abst(out, *(cs[i]));
out << "\n";
}
}
void display(std::ostream & out, display_var_proc const & proc) const {
display(out, m_clauses, proc);
if (!m_learned.empty()) {
out << "Lemmas:\n";
display(out, m_learned, proc);
}
}
void display_mathematica(std::ostream & out) const {
out << "{\n";
display_mathematica(out, m_clauses);
out << "}\n";
}
void display_abst(std::ostream & out) const {
display_abst(out, m_clauses);
if (!m_learned.empty()) {
out << "Lemmas:\n";
display_abst(out, m_learned);
}
}
void display(std::ostream & out) const {
display(out, m_display_var);
display_assignment(out);
}
void display_vars(std::ostream & out) const {
for (unsigned i = 0; i < num_vars(); i++) {
out << i << " -> "; m_display_var(out, i); out << "\n";
}
}
void display_smt2_arith_decls(std::ostream & out) const {
unsigned sz = m_is_int.size();
for (unsigned i = 0; i < sz; i++) {
if (m_is_int[i])
out << "(declare-fun x" << i << " () Int)\n";
else
out << "(declare-fun x" << i << " () Real)\n";
}
}
void display_smt2_bool_decls(std::ostream & out) const {
unsigned sz = m_atoms.size();
for (unsigned i = 0; i < sz; i++) {
if (m_atoms[i] == 0)
out << "(declare-fun b" << i << " () Bool)\n";
}
}
void display_smt2(std::ostream & out) const {
display_smt2_bool_decls(out);
display_smt2_arith_decls(out);
out << "(assert (and true\n";
unsigned sz = m_clauses.size();
for (unsigned i = 0; i < sz; i++) {
display_smt2(out, *(m_clauses[i]));
out << "\n";
}
out << "))\n(check-sat)" << std::endl;
}
};
solver::solver(reslimit& rlim, params_ref const & p) {
m_imp = alloc(imp, *this, rlim, p);
}
solver::~solver() {
dealloc(m_imp);
}
lbool solver::check() {
return m_imp->check();
}
lbool solver::check(literal_vector& assumptions) {
return m_imp->check(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;
}
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<lbool>& vs) {
vs.reset();
vs.append(m_imp->m_bvalues);
}
void solver::set_bvalues(svector<lbool> const& vs) {
m_imp->m_bvalues.reset();
m_imp->m_bvalues.append(vs);
m_imp->m_bvalues.resize(m_imp->m_atoms.size(), l_undef);
}
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) {
return m_imp->mk_ineq_literal(k, sz, ps, is_even);
}
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::mk_clause(unsigned num_lits, literal * lits, assumption a) {
return m_imp->mk_clause(num_lits, lits, a);
}
void solver::display(std::ostream & out) const {
m_imp->display(out);
}
void solver::display(std::ostream & out, literal l) const {
m_imp->display(out, l);
}
void solver::display(std::ostream & out, unsigned n, literal const* ls) const {
for (unsigned i = 0; i < n; ++i) {
display(out, ls[i]);
out << "; ";
}
}
void solver::display(std::ostream & out, var x) const {
m_imp->m_display_var(out, x);
}
void solver::display(std::ostream & out, atom const& a) const {
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);
}
};
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