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z3-z3-4.12.6.src.ast.rewriter.quant_hoist.cpp Maven / Gradle / Ivy
/*++
Copyright (c) 2010 Microsoft Corporation
Module Name:
quant_hoist.cpp
Abstract:
Quantifier hoisting utility.
Author:
Nikolaj Bjorner (nbjorner) 2010-02-19
Revision History:
Hoisted from quant_elim.
--*/
#include "ast/rewriter/quant_hoist.h"
#include "ast/expr_functors.h"
#include "ast/ast_smt_pp.h"
#include "ast/rewriter/bool_rewriter.h"
#include "ast/rewriter/var_subst.h"
#include "ast/ast_pp.h"
#include "ast/rewriter/ast_counter.h"
#include "ast/rewriter/expr_safe_replace.h"
//
// Bring quantifiers of common type into prenex form.
//
class quantifier_hoister::impl {
ast_manager& m;
bool_rewriter m_rewriter;
public:
impl(ast_manager& m) :
m(m),
m_rewriter(m)
{}
void operator()(expr* fml, app_ref_vector& vars, bool& is_fa, expr_ref& result, bool use_fresh, bool rewrite_ok) {
quantifier_type qt = Q_none_pos;
pull_quantifier(fml, qt, vars, result, use_fresh, rewrite_ok);
TRACE("qe_verbose",
tout << mk_pp(fml, m) << "\n";
tout << mk_pp(result, m) << "\n";);
SASSERT(is_positive(qt));
is_fa = (Q_forall_pos == qt);
}
void pull_exists(expr* fml, app_ref_vector& vars, expr_ref& result, bool use_fresh, bool rewrite_ok) {
quantifier_type qt = Q_exists_pos;
pull_quantifier(fml, qt, vars, result, use_fresh, rewrite_ok);
TRACE("qe_verbose",
tout << mk_pp(fml, m) << "\n";
tout << mk_pp(result, m) << "\n";);
}
void pull_quantifier(bool is_forall, expr_ref& fml, app_ref_vector& vars, bool use_fresh, bool rewrite_ok) {
quantifier_type qt = is_forall?Q_forall_pos:Q_exists_pos;
expr_ref result(m);
pull_quantifier(fml, qt, vars, result, use_fresh, rewrite_ok);
TRACE("qe_verbose",
tout << mk_pp(fml, m) << "\n";
tout << mk_pp(result, m) << "\n";);
fml = std::move(result);
}
void extract_quantifier(quantifier* q, app_ref_vector& vars, expr_ref& result, bool use_fresh) {
unsigned nd = q->get_num_decls();
for (unsigned i = 0; i < nd; ++i) {
sort* s = q->get_decl_sort(i);
symbol const& sym = q->get_decl_name (i);
app* a = use_fresh ? m.mk_fresh_const(sym.str ().c_str (), s)
: m.mk_const (sym, s);
vars.push_back(a);
}
expr * const * exprs = (expr* const*) (vars.data() + vars.size()- nd);
result = instantiate(m, q, exprs);
}
unsigned pull_quantifier(bool _is_forall, expr_ref& fml, ptr_vector* sorts, svector* names, bool use_fresh, bool rewrite_ok) {
unsigned index = var_counter().get_next_var(fml);
while (is_quantifier(fml) && _is_forall == is_forall(fml)) {
quantifier* q = to_quantifier(fml);
index += q->get_num_decls();
if (names) {
names->append(q->get_num_decls(), q->get_decl_names());
}
if (sorts) {
sorts->append(q->get_num_decls(), q->get_decl_sorts());
}
fml = q->get_expr();
}
if (!has_quantifiers(fml)) {
return index;
}
app_ref_vector vars(m);
pull_quantifier(_is_forall, fml, vars, use_fresh, rewrite_ok);
if (vars.empty()) {
return index;
}
// replace vars by de-bruijn indices
expr_safe_replace rep(m);
svector bound_names;
ptr_vector bound_sorts;
for (unsigned i = 0; i < vars.size(); ++i) {
app* v = vars[i].get();
if (names) {
bound_names.push_back(v->get_decl()->get_name());
}
if (sorts) {
bound_sorts.push_back(v->get_sort());
}
rep.insert(v, m.mk_var(index++, v->get_sort()));
}
if (names && !bound_names.empty()) {
bound_names.reverse();
bound_names.append(*names);
names->reset();
names->append(bound_names);
}
if (sorts && !bound_sorts.empty()) {
bound_sorts.reverse();
bound_sorts.append(*sorts);
sorts->reset();
sorts->append(bound_sorts);
}
rep(fml);
return index;
}
private:
enum quantifier_type {
Q_forall_pos = 0x10,
Q_exists_pos = 0x20,
Q_none_pos = 0x40,
Q_forall_neg = 0x11,
Q_exists_neg = 0x21,
Q_none_neg = 0x41
};
void display(quantifier_type qt, std::ostream& out) {
switch(qt) {
case Q_forall_pos: out << "Forall+"; break;
case Q_exists_pos: out << "Exists+"; break;
case Q_none_pos: out << "None+"; break;
case Q_forall_neg: out << "Forall-"; break;
case Q_exists_neg: out << "Exists-"; break;
case Q_none_neg: out << "None-"; break;
}
}
quantifier_type& negate(quantifier_type& qt) {
qt = static_cast(qt ^0x1);
return qt;
}
static bool is_negative(quantifier_type qt) {
return 0 != (qt & 0x1);
}
static bool is_positive(quantifier_type qt) {
return 0 == (qt & 0x1);
}
static void set_quantifier_type(quantifier_type& qt, bool is_forall) {
switch(qt) {
case Q_forall_pos: SASSERT(is_forall); break;
case Q_forall_neg: SASSERT(!is_forall); break;
case Q_exists_pos: SASSERT(!is_forall); break;
case Q_exists_neg: SASSERT(is_forall); break;
case Q_none_pos: qt = is_forall?Q_forall_pos:Q_exists_pos; break;
case Q_none_neg: qt = is_forall?Q_exists_neg:Q_forall_neg; break;
}
}
bool is_compatible(quantifier_type qt, bool is_forall) {
switch(qt) {
case Q_forall_pos: return is_forall;
case Q_forall_neg: return !is_forall;
case Q_exists_pos: return !is_forall;
case Q_exists_neg: return is_forall;
case Q_none_pos: return true;
case Q_none_neg: return true;
default:
UNREACHABLE();
}
return false;
}
void pull_quantifier(expr* fml, quantifier_type& qt, app_ref_vector& vars, expr_ref& result, bool use_fresh, bool rewrite_ok) {
if (!has_quantifiers(fml)) {
result = fml;
return;
}
switch(fml->get_kind()) {
case AST_APP: {
expr_ref_vector args(m);
expr_ref tmp(m);
expr* t1, *t2, *t3;
unsigned num_args = 0;
app* a = to_app(fml);
if (m.is_and(fml)) {
num_args = a->get_num_args();
for (unsigned i = 0; i < num_args; ++i) {
pull_quantifier(a->get_arg(i), qt, vars, tmp, use_fresh, rewrite_ok);
args.push_back(tmp);
}
if (rewrite_ok)
m_rewriter.mk_and(args.size(), args.data(), result);
else
result = m.mk_and (args.size (), args.data ());
}
else if (m.is_or(fml)) {
num_args = to_app(fml)->get_num_args();
for (unsigned i = 0; i < num_args; ++i) {
pull_quantifier(to_app(fml)->get_arg(i), qt, vars, tmp, use_fresh, rewrite_ok);
args.push_back(tmp);
}
if (rewrite_ok)
m_rewriter.mk_or(args.size(), args.data(), result);
else
result = m.mk_or (args.size (), args.data ());
}
else if (m.is_not(fml)) {
pull_quantifier(to_app(fml)->get_arg(0), negate(qt), vars, tmp, use_fresh, rewrite_ok);
negate(qt);
result = m.mk_not(tmp);
}
else if (m.is_implies(fml, t1, t2)) {
pull_quantifier(t1, negate(qt), vars, tmp, use_fresh, rewrite_ok);
negate(qt);
pull_quantifier(t2, qt, vars, result, use_fresh, rewrite_ok);
result = m.mk_implies(tmp, result);
}
else if (m.is_ite(fml, t1, t2, t3)) {
expr_ref tt1(m), tt2(m), tt3(m), ntt1(m), nt1(m);
pull_quantifier(t2, qt, vars, tt2, use_fresh, rewrite_ok);
pull_quantifier(t3, qt, vars, tt3, use_fresh, rewrite_ok);
if (has_quantifiers(t1)) {
pull_quantifier(t1, qt, vars, tt1, use_fresh, rewrite_ok);
nt1 = m.mk_not(t1);
pull_quantifier(nt1, qt, vars, ntt1, use_fresh, rewrite_ok);
result = m.mk_and(m.mk_or(ntt1, tt2), m.mk_or(tt1, tt3));
}
else {
result = m.mk_ite(t1, tt2, tt3);
}
}
else if (m.is_eq(fml, t1, t2) && m.is_bool(t1)) {
expr_ref tt1(m), tt2(m), ntt1(m), ntt2(m), nt1(m), nt2(m);
pull_quantifier(t1, qt, vars, tt1, use_fresh, rewrite_ok);
pull_quantifier(t2, qt, vars, tt2, use_fresh, rewrite_ok);
nt1 = m.mk_not(t1);
nt2 = m.mk_not(t2);
pull_quantifier(nt1, qt, vars, ntt1, use_fresh, rewrite_ok);
pull_quantifier(nt2, qt, vars, ntt2, use_fresh, rewrite_ok);
result = m.mk_and(m.mk_or(ntt1, tt2), m.mk_or(ntt2, tt1));
}
else {
// the formula contains a quantifier, but it is "inaccessible"
result = fml;
}
break;
}
case AST_QUANTIFIER: {
quantifier* q = to_quantifier(fml);
if (is_lambda(q)) {
result = fml;
break;
}
expr_ref tmp(m);
if (!is_compatible(qt, is_forall(q))) {
result = fml;
break;
}
set_quantifier_type(qt, is_forall(q));
extract_quantifier(q, vars, tmp, use_fresh);
pull_quantifier(tmp, qt, vars, result, use_fresh, rewrite_ok);
break;
}
case AST_VAR:
result = fml;
break;
default:
UNREACHABLE();
result = fml;
break;
}
}
};
quantifier_hoister::quantifier_hoister(ast_manager& m) {
m_impl = alloc(impl, m);
}
quantifier_hoister::~quantifier_hoister() {
dealloc(m_impl);
}
void quantifier_hoister::operator()(expr* fml, app_ref_vector& vars, bool& is_fa, expr_ref& result, bool use_fresh, bool rewrite_ok) {
(*m_impl)(fml, vars, is_fa, result, use_fresh, rewrite_ok);
}
void quantifier_hoister::pull_exists(expr* fml, app_ref_vector& vars, expr_ref& result, bool use_fresh, bool rewrite_ok) {
m_impl->pull_exists(fml, vars, result, use_fresh, rewrite_ok);
}
void quantifier_hoister::pull_quantifier(bool is_forall, expr_ref& fml, app_ref_vector& vars, bool use_fresh, bool rewrite_ok) {
m_impl->pull_quantifier(is_forall, fml, vars, use_fresh, rewrite_ok);
}
unsigned quantifier_hoister::pull_quantifier(bool is_forall, expr_ref& fml, ptr_vector* sorts, svector* names, bool use_fresh, bool rewrite_ok) {
return m_impl->pull_quantifier(is_forall, fml, sorts, names, use_fresh, rewrite_ok);
}
