#include "ast/ast_util.h"
#include "ast/recfun_decl_plugin.h"
#include "ast/well_sorted.h"
#include "ast/rewriter/var_subst.h"
#include "ast/normal_forms/pull_quant.h"
#include "ast/rewriter/inj_axiom.h"
#include "sat/smt/q_solver.h"
#include "sat/smt/euf_solver.h"
#include "sat/smt/sat_th.h"
#include "qe/lite/qe_lite_tactic.h"
#include <iostream>
namespace q {
solver::solver(euf::solver& ctx, family_id fid) :
th_euf_solver(ctx, ctx.get_manager().get_family_name(fid), fid),
m_mbqi(ctx, *this),
m_ematch(ctx, *this),
m_expanded(ctx.get_manager()),
m_der(ctx.get_manager())
{
}
void solver::asserted(sat::literal l) {
expr* e = bool_var2expr(l.var());
if (!is_forall(e) && !is_exists(e))
return;
quantifier* q = to_quantifier(e);
if (l.sign() == is_forall(e)) {
sat::literal lit = skolemize(q);
add_clause(~l, lit);
return;
}
quantifier* q_flat = nullptr;
if (!m_flat.find(q, q_flat)) {
if (expand(q)) {
for (expr* e : m_expanded) {
sat::literal lit = ctx.internalize(e, l.sign(), false);
add_clause(~l, lit);
}
return;
}
q_flat = flatten(q);
}
if (is_ground(q_flat->get_expr())) {
auto lit = ctx.internalize(q_flat->get_expr(), l.sign(), false);
add_clause(~l, lit);
}
else {
ctx.push_vec(m_universal, l);
if (ctx.get_config().m_ematching)
m_ematch.add(q);
}
m_stats.m_num_quantifier_asserts++;
}
sat::check_result solver::check() {
if (ctx.get_config().m_ematching && m_ematch())
return sat::check_result::CR_CONTINUE;
if (ctx.get_config().m_mbqi) {
switch (m_mbqi()) {
case l_true:
return sat::check_result::CR_DONE;
case l_false:
return sat::check_result::CR_CONTINUE;
case l_undef:
break;
}
}
return sat::check_result::CR_GIVEUP;
}
std::ostream& solver::display(std::ostream& out) const {
return m_ematch.display(out);
}
std::ostream& solver::display_constraint(std::ostream& out, sat::ext_constraint_idx idx) const {
return m_ematch.display_constraint(out, idx);
}
void solver::collect_statistics(statistics& st) const {
st.update("q asserts", m_stats.m_num_quantifier_asserts);
m_mbqi.collect_statistics(st);
m_ematch.collect_statistics(st);
}
euf::th_solver* solver::clone(euf::solver& ctx) {
family_id fid = ctx.get_manager().mk_family_id(symbol("quant"));
return alloc(solver, ctx, fid);
}
bool solver::unit_propagate() {
return m_ematch.unit_propagate();
}
euf::theory_var solver::mk_var(euf::enode* n) {
auto v = euf::th_euf_solver::mk_var(n);
ctx.attach_th_var(n, this, v);
return v;
}
sat::literal solver::instantiate(quantifier* _q, bool negate, std::function<expr* (quantifier*, unsigned)>& mk_var) {
expr_ref tmp(m);
quantifier_ref q(_q, m);
expr_ref_vector vars(m);
if (negate) {
q = m.mk_quantifier(
is_forall(q) ? quantifier_kind::exists_k : quantifier_kind::forall_k,
q->get_num_decls(), q->get_decl_sorts(), q->get_decl_names(), m.mk_not(q->get_expr()),
q->get_weight(), q->get_qid(), q->get_skid());
}
quantifier* q_flat = flatten(q);
unsigned sz = q_flat->get_num_decls();
vars.resize(sz, nullptr);
for (unsigned i = 0; i < sz; ++i)
vars[i] = mk_var(q_flat, i);
var_subst subst(m);
expr_ref body = subst(q_flat->get_expr(), vars);
rewrite(body);
return mk_literal(body);
}
sat::literal solver::skolemize(quantifier* q) {
std::function<expr* (quantifier*, unsigned)> mk_var = [&](quantifier* q, unsigned i) {
return m.mk_fresh_const(q->get_decl_name(i), q->get_decl_sort(i));
};
return instantiate(q, is_forall(q), mk_var);
}
sat::literal solver::specialize(quantifier* q) {
std::function<expr* (quantifier*, unsigned)> mk_var = [&](quantifier* q, unsigned i) {
return get_unit(q->get_decl_sort(i));
};
return instantiate(q, is_exists(q), mk_var);
}
void solver::init_search() {
m_mbqi.init_search();
}
sat::literal solver::internalize(expr* e, bool sign, bool root) {
SASSERT(is_forall(e) || is_exists(e));
sat::bool_var v = ctx.get_si().add_bool_var(e);
sat::literal lit = ctx.attach_lit(sat::literal(v, false), e);
mk_var(ctx.get_egraph().find(e));
if (sign)
lit.neg();
return lit;
}
void solver::finalize_model(model& mdl) {
m_mbqi.finalize_model(mdl);
}
quantifier* solver::flatten(quantifier* q) {
quantifier* q_flat = nullptr;
if (m_flat.find(q, q_flat))
return q_flat;
expr_ref new_q(q, m), r(m);
proof_ref pr(m);
if (!has_quantifiers(q->get_expr())) {
if (!ctx.get_config().m_refine_inj_axiom)
return q;
if (!simplify_inj_axiom(m, q, new_q))
return q;
}
else if (is_forall(q)) {
pull_quant pull(m);
pull(q, new_q, pr);
SASSERT(is_well_sorted(m, new_q));
}
else {
new_q = q;
}
q_flat = to_quantifier(new_q);
m.inc_ref(q_flat);
m.inc_ref(q);
m_flat.insert(q, q_flat);
ctx.push(insert_ref2_map<ast_manager, quantifier, quantifier>(m, m_flat, q, q_flat));
return q_flat;
}
void solver::init_units() {
if (!m_unit_table.empty())
return;
for (euf::enode* n : ctx.get_egraph().nodes()) {
if (!n->interpreted() && !m.is_uninterp(n->get_expr()->get_sort()))
continue;
expr* e = n->get_expr();
sort* s = e->get_sort();
if (m_unit_table.contains(s))
continue;
m_unit_table.insert(s, e);
ctx.push(insert_map<obj_map<sort, expr*>, sort*>(m_unit_table, s));
}
}
expr* solver::get_unit(sort* s) {
expr* u = nullptr;
if (m_unit_table.find(s, u))
return u;
init_units();
if (m_unit_table.find(s, u))
return u;
model mdl(m);
expr* val = mdl.get_some_value(s);
m.inc_ref(val);
m.inc_ref(s);
ctx.push(insert_ref2_map<ast_manager, sort, expr>(m, m_unit_table, s, val));
return val;
}
bool solver::expand(quantifier* q) {
expr_ref r(q, m);
proof_ref pr(m);
ctx.rewrite(r);
m_der(r, r, pr);
if (ctx.get_config().m_qe_lite) {
qe_lite qe(m, ctx.s().params());
qe(r);
}
m_expanded.reset();
bool updated = q != r;
if (updated) {
ctx.rewrite(r);
if (!is_quantifier(r)) {
m_expanded.push_back(r);
return true;
}
if (is_forall(q) != is_forall(r)) {
m_expanded.push_back(r);
return true;
}
if (r == q)
return false;
q = to_quantifier(r);
}
if (is_forall(q))
flatten_and(q->get_expr(), m_expanded);
else if (is_exists(q))
flatten_or(q->get_expr(), m_expanded);
else
UNREACHABLE();
if (m_expanded.size() == 1 && is_forall(q) && !recfun::util(m).contains_def(q->get_expr())) {
m_expanded.reset();
flatten_or(q->get_expr(), m_expanded);
expr_ref split1(m), split2(m), e1(m), e2(m);
unsigned idx = 0;
for (unsigned i = m_expanded.size(); i-- > 0; ) {
expr* arg = m_expanded.get(i);
if (split(arg, split1, split2)) {
if (e1)
return false;
e1 = split1;
e2 = split2;
idx = i;
}
}
if (!e1 && updated) {
m_expanded.reset();
m_expanded.push_back(r);
return true;
}
if (!e1)
return false;
m_expanded[idx] = e1;
e1 = mk_or(m_expanded);
m_expanded[idx] = e2;
e2 = mk_or(m_expanded);
m_expanded.reset();
m_expanded.push_back(e1);
m_expanded.push_back(e2);
}
if (m_expanded.size() > 1) {
for (unsigned i = m_expanded.size(); i-- > 0; ) {
expr_ref tmp(m.update_quantifier(q, m_expanded.get(i)), m);
ctx.rewrite(tmp);
m_expanded[i] = tmp;
}
return true;
}
else if (m_expanded.size() == 1 && updated) {
m_expanded[0] = r;
flatten(to_quantifier(r));
return true;
}
else {
return false;
}
}
bool solver::split(expr* arg, expr_ref& e1, expr_ref& e2) {
expr* x, * y, * z;
if (m.is_not(arg, x) && m.is_or(x, y, z) && is_literal(y) && is_literal(z)) {
e1 = mk_not(m, y);
e2 = mk_not(m, z);
return true;
}
if (m.is_iff(arg, x, y) && is_literal(x) && is_literal(y)) {
e1 = m.mk_implies(x, y);
e2 = m.mk_implies(y, x);
return true;
}
if (m.is_and(arg, x, y) && is_literal(x) && is_literal(y)) {
e1 = x;
e2 = y;
return true;
}
if (m.is_not(arg, z) && m.is_iff(z, x, y) && is_literal(x) && is_literal(y)) {
e1 = m.mk_or(x, y);
expr_ref not_x(mk_not(m, x), m);
e2 = m.mk_or(not_x, mk_not(m, y));
return true;
}
return false;
}
bool solver::is_literal(expr* arg) {
m.is_not(arg, arg);
return !m.is_and(arg) && !m.is_or(arg) && !m.is_iff(arg) && !m.is_implies(arg);
}
void solver::get_antecedents(sat::literal l, sat::ext_justification_idx idx, sat::literal_vector& r, bool probing) {
m_ematch.get_antecedents(l, idx, r, probing);
}
void solver::log_instantiation(unsigned n, sat::literal const* lits, justification* j) {
TRACE(q, for (unsigned i = 0; i < n; ++i) tout << literal2expr(lits[i]) << "\n";);
if (get_config().m_instantiations2console) {
ctx.on_instantiation(n, lits, j ? j->m_clause.num_decls() : 0, j ? j->m_binding : nullptr);
}
}
q_proof_hint* q_proof_hint::mk(euf::solver& s, symbol const& method, unsigned generation, sat::literal_vector const& lits, unsigned n, euf::enode* const* bindings) {
SASSERT(n > 0);
auto* mem = s.get_region().allocate(q_proof_hint::get_obj_size(n, lits.size()));
q_proof_hint* ph = new (mem) q_proof_hint(method, generation, n, lits.size());
for (unsigned i = 0; i < n; ++i)
ph->m_bindings[i] = bindings[i]->get_expr();
for (unsigned i = 0; i < lits.size(); ++i)
ph->m_literals[i] = lits[i];
return ph;
}
q_proof_hint* q_proof_hint::mk(euf::solver& s, symbol const& method, unsigned generation, sat::literal l1, sat::literal l2, unsigned n, expr* const* bindings) {
SASSERT(n > 0);
auto* mem = s.get_region().allocate(q_proof_hint::get_obj_size(n, 2));
q_proof_hint* ph = new (mem) q_proof_hint(method, generation, n, 2);
for (unsigned i = 0; i < n; ++i)
ph->m_bindings[i] = bindings[i];
ph->m_literals[0] = l1;
ph->m_literals[1] = l2;
return ph;
}
expr* q_proof_hint::get_hint(euf::solver& s) const {
ast_manager& m = s.get_manager();
expr_ref_vector args(m);
expr_ref binding(m);
arith_util a(m);
expr_ref gen(a.mk_int(m_generation), m);
expr* gens[1] = { gen.get() };
sort* range = m.mk_proof_sort();
for (unsigned i = 0; i < m_num_bindings; ++i)
args.push_back(m_bindings[i]);
binding = m.mk_app(symbol("bind"), args.size(), args.data(), range);
args.reset();
for (unsigned i = 0; i < m_num_literals; ++i)
args.push_back(s.literal2expr(~m_literals[i]));
args.push_back(binding);
args.push_back(m.mk_app(symbol("gen"), 1, gens, range));
args.push_back(m.mk_const(m_method, range));
return m.mk_app(symbol("inst"), args.size(), args.data(), range);
}
}