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fix regression for simplifying tails with quantifiers, add some more handling for quantified tails

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2012-11-30 15:58:06 -08:00
parent 692593baaa
commit 2d1a6bf270
10 changed files with 888 additions and 627 deletions
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5
src/ast/ast.cpp
View file

@ -2637,12 +2637,13 @@ proof * ast_manager::mk_unit_resolution(unsigned num_proofs, proof * const * pro
ptr_buffer<expr> args; ptr_buffer<expr> args;
args.append(num_proofs, (expr**) proofs); args.append(num_proofs, (expr**) proofs);
expr * fact; expr * fact;
expr const * f1 = get_fact(proofs[0]); expr * f1 = get_fact(proofs[0]);
expr const * f2 = get_fact(proofs[1]); expr * f2 = get_fact(proofs[1]);
if (num_proofs == 2 && is_complement(f1, f2)) { if (num_proofs == 2 && is_complement(f1, f2)) {
fact = mk_false(); fact = mk_false();
} }
else { else {
CTRACE("mk_unit_resolution_bug", !is_or(f1), tout << mk_pp(f1, *this) << " " << mk_pp(f2, *this) << "\n";);
SASSERT(is_or(f1)); SASSERT(is_or(f1));
ptr_buffer<expr> new_lits; ptr_buffer<expr> new_lits;
app const * cls = to_app(f1); app const * cls = to_app(f1);

2
src/muz_qe/dl_context.cpp
View file

@ -1769,7 +1769,7 @@ namespace datalog {
if (use_fixedpoint_extensions) { if (use_fixedpoint_extensions) {
for (unsigned i = 0; i < num_queries; ++i) { for (unsigned i = 0; i < num_queries; ++i) {
out << "(query "; out << "(query ";
PP(queries[i]); PP(queries[i]);
out << ")\n"; out << ")\n";
} }
} }

2
src/muz_qe/dl_mk_interp_tail_simplifier.cpp
View file

@ -463,7 +463,7 @@ namespace datalog {
if (r->has_quantifiers()) { if (r->has_quantifiers()) {
res = r; res = r;
return false; return true;
} }
start: start:

5
src/muz_qe/dl_util.h
View file

@ -191,6 +191,11 @@ namespace datalog {
scoped_coarse_proof(ast_manager& m): scoped_proof_mode(m, PGM_COARSE) {} scoped_coarse_proof(ast_manager& m): scoped_proof_mode(m, PGM_COARSE) {}
}; };
class scoped_fine_proof : public scoped_proof_mode {
public:
scoped_fine_proof(ast_manager& m): scoped_proof_mode(m, PGM_FINE) {}
};
class scoped_no_proof : public scoped_proof_mode { class scoped_no_proof : public scoped_proof_mode {
public: public:
scoped_no_proof(ast_manager& m): scoped_proof_mode(m, PGM_DISABLED) {} scoped_no_proof(ast_manager& m): scoped_proof_mode(m, PGM_DISABLED) {}

102
src/muz_qe/expr_safe_replace.cpp Normal file
View file

@ -0,0 +1,102 @@
/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
expr_safe_replace.cpp
Abstract:
Version of expr_replace/expr_substitution that is safe for quantifiers.
Author:
Nikolaj Bjorner (nbjorner) 2012-11-30
Revision History:
--*/
#include "expr_safe_replace.h"
#include "rewriter.h"
void expr_safe_replace::insert(expr* src, expr* dst) {
m_src.push_back(src);
m_dst.push_back(dst);
m_subst.insert(src, dst);
}
void expr_safe_replace::operator()(expr* e, expr_ref& res) {
obj_map<expr,expr*> cache;
ptr_vector<expr> todo, args;
expr_ref_vector refs(m);
todo.push_back(e);
expr* a, *b, *d;
todo.push_back(e);
while (!todo.empty()) {
a = todo.back();
if (cache.contains(a)) {
todo.pop_back();
}
else if (m_subst.find(a, b)) {
cache.insert(a, b);
todo.pop_back();
}
else if (is_var(a)) {
cache.insert(a, a);
todo.pop_back();
}
else if (is_app(a)) {
app* c = to_app(a);
unsigned n = c->get_num_args();
args.reset();
for (unsigned i = 0; i < n; ++i) {
if (cache.find(c->get_arg(i), d)) {
args.push_back(d);
}
else {
todo.push_back(c->get_arg(i));
}
}
if (args.size() == n) {
b = m.mk_app(c->get_decl(), args.size(), args.c_ptr());
refs.push_back(b);
cache.insert(a, b);
todo.pop_back();
}
}
else {
SASSERT(is_quantifier(a));
quantifier* q = to_quantifier(a);
expr_safe_replace replace(m);
var_shifter shift(m);
expr_ref new_body(m), src(m), dst(m), tmp(m);
expr_ref_vector pats(m), nopats(m);
unsigned num_decls = q->get_num_decls();
for (unsigned i = 0; i < m_src.size(); ++i) {
shift(m_src[i].get(), num_decls, src);
shift(m_dst[i].get(), num_decls, dst);
replace.insert(src, dst);
}
unsigned np = q->get_num_patterns();
for (unsigned i = 0; i < np; ++i) {
replace(q->get_pattern(i), tmp);
pats.push_back(tmp);
}
np = q->get_num_no_patterns();
for (unsigned i = 0; i < np; ++i) {
replace(q->get_no_pattern(i), tmp);
nopats.push_back(tmp);
}
replace(q->get_expr(), new_body);
b = m.update_quantifier(q, pats.size(), pats.c_ptr(), nopats.size(), nopats.c_ptr(), new_body);
refs.push_back(b);
cache.insert(a, b);
todo.pop_back();
}
}
res = cache.find(e);
}

43
src/muz_qe/expr_safe_replace.h Normal file
View file

@ -0,0 +1,43 @@
/*++
Copyright (c) 2012 Microsoft Corporation
Module Name:
expr_safe_replace.h
Abstract:
Version of expr_replace/expr_substitution that is safe for quantifiers.
Author:
Nikolaj Bjorner (nbjorner) 2012-11-30
Revision History:
--*/
#ifndef __EXPR_SAFE_REPLACE_H__
#define __EXPR_SAFE_REPLACE_H__
#include "ast.h"
class expr_safe_replace {
ast_manager& m;
expr_ref_vector m_src;
expr_ref_vector m_dst;
obj_map<expr, expr*> m_subst;
public:
expr_safe_replace(ast_manager& m): m(m), m_src(m), m_dst(m) {}
void insert(expr* src, expr* dst);
void operator()(expr_ref& e) { (*this)(e.get(), e); }
void operator()(expr* src, expr_ref& e);
};
#endif /* __EXPR_SAFE_REPLACE_H__ */

433
src/muz_qe/pdr_quantifiers.cpp
View file

@ -27,6 +27,9 @@ Revision History:
#include "ast_smt_pp.h" #include "ast_smt_pp.h"
#include "expr_abstract.h" #include "expr_abstract.h"
#include "dl_mk_extract_quantifiers.h" #include "dl_mk_extract_quantifiers.h"
#include "qe_lite.h"
#include "well_sorted.h"
#include "expr_safe_replace.h"
namespace pdr { namespace pdr {
@ -49,6 +52,12 @@ namespace pdr {
} }
} }
quantifier_model_checker::~quantifier_model_checker() {
obj_map<func_decl,expr*>::iterator it = m_reachable.begin(), end = m_reachable.end();
for (; it != end; ++it) {
m.dec_ref(it->m_value);
}
}
void quantifier_model_checker::generalize_binding(expr_ref_vector const& binding, vector<expr_ref_vector>& bindings) { void quantifier_model_checker::generalize_binding(expr_ref_vector const& binding, vector<expr_ref_vector>& bindings) {
expr_ref_vector new_binding(m); expr_ref_vector new_binding(m);
@ -193,13 +202,12 @@ namespace pdr {
bool quantifier_model_checker::find_instantiations_proof_based(quantifier_ref_vector const& qs, unsigned level) { bool quantifier_model_checker::find_instantiations_proof_based(quantifier_ref_vector const& qs, unsigned level) {
bool found_instance = false; bool found_instance = false;
TRACE("pdr", tout << mk_pp(m_A,m) << "\n";);
datalog::scoped_coarse_proof _scp(m); datalog::scoped_fine_proof _scp(m);
expr_ref_vector fmls(m); expr_ref_vector fmls(m);
front_end_params fparams; front_end_params fparams;
fparams.m_proof_mode = PGM_COARSE; fparams.m_proof_mode = PGM_FINE;
fparams.m_mbqi = true; fparams.m_mbqi = true;
fmls.push_back(m_A.get()); fmls.push_back(m_A.get());
@ -209,15 +217,20 @@ namespace pdr {
for (unsigned i = 0; i < fmls.size(); ++i) { for (unsigned i = 0; i < fmls.size(); ++i) {
tout << mk_pp(fmls[i].get(), m) << "\n"; tout << mk_pp(fmls[i].get(), m) << "\n";
}); });
smt::kernel solver(m, fparams); smt::kernel solver(m, fparams);
for (unsigned i = 0; i < fmls.size(); ++i) { for (unsigned i = 0; i < fmls.size(); ++i) {
solver.assert_expr(fmls[i].get()); solver.assert_expr(fmls[i].get());
} }
lbool result = solver.check(); lbool result = solver.check();
TRACE("pdr", tout << result << "\n";);
if (result != l_false) { if (result != l_false) {
TRACE("pdr", tout << result << "\n";); return false;
return found_instance;
} }
m_rules_model_check = false;
map<symbol, quantifier*, symbol_hash_proc, symbol_eq_proc> qid_map; map<symbol, quantifier*, symbol_hash_proc, symbol_eq_proc> qid_map;
quantifier* q; quantifier* q;
for (unsigned i = 0; i < qs.size(); ++i) { for (unsigned i = 0; i < qs.size(); ++i) {
@ -234,8 +247,7 @@ namespace pdr {
for (unsigned i = 0; i < collector.size(); ++i) { for (unsigned i = 0; i < collector.size(); ++i) {
symbol qid = quants[i]->get_qid(); symbol qid = quants[i]->get_qid();
if (!qid_map.find(qid, q)) { if (!qid_map.find(qid, q)) {
TRACE("pdr", tout << "Could not find quantifier " TRACE("pdr", tout << "Could not find quantifier " << mk_pp(quants[i], m) << "\n";);
<< mk_pp(quants[i], m) << "\n";);
continue; continue;
} }
expr_ref_vector const& binding = collector.bindings()[i]; expr_ref_vector const& binding = collector.bindings()[i];
@ -256,8 +268,43 @@ namespace pdr {
return found_instance; return found_instance;
} }
/** /**
Given node: For under-approximations:
m_reachable: set of reachable states, per predicate
rules: P(x) :- B[x,y] & Fa z . Q(y,z)
Q(y,z) :- C[y,z,u] & Fa w . R(u,w)
qis: Fa z . Q(y,z)
M: model satisfying P(x) & B[x,y]
B'[x,y]: body with reachable states substituted for predicates.
Q'[y,z]: reachable states substituted for Q.
S'[x]: Ex y . B'[x,y] & Fa z . Q'[y, z]
Method:
1. M |= Fa z . Q'[y, z] => done
Weaker variant:
Check B[x,y] & Fa z . Q'[y, z] for consistency.
2. Otherwise, extract instantiations.
3. Update reachable (for next round):
Q'[y,z] := Q'[y,z] \/ C'[y,z,u] & Fa w . R'(u,w)
*/
/**
For over-approximations:
- pt - predicate transformer for rule: - pt - predicate transformer for rule:
P(x) :- Body1(x,y) || Body2(x,z) & (Fa u . Q(u,x,z)). P(x) :- Body1(x,y) || Body2(x,z) & (Fa u . Q(u,x,z)).
@ -267,22 +314,201 @@ namespace pdr {
- A := node.state(x) && Body2(x,y) - A := node.state(x) && Body2(x,y)
- Bs := array of Bs of the form: - Bs := array of Bs of the form:
. Fa u . Q(u, P_x, P_y) - instantiate quantifier to P variables. . Fa u . Q(u, P_x, P_y) - instantiate quantifier to P variables.
. B := inv(Q_0,Q_1,Q_2) . B := inv(Q_0,Q_1,Q_2)
. B := inv(u, P_x, P_y) := B[u/Q_0, P_x/Q_1, P_y/Q_2] . B := inv(u, P_x, P_y) := B[u/Q_0, P_x/Q_1, P_y/Q_2]
. B := Fa u . inv(u, P_x, P_y) . B := Fa u . inv(u, P_x, P_y)
*/ */
void quantifier_model_checker::update_reachable(func_decl* f, expr* e) {
expr* e_old;
m.inc_ref(e);
if (m_reachable.find(f, e_old)) {
m.dec_ref(e_old);
}
m_reachable.insert(f, e);
}
expr_ref quantifier_model_checker::get_reachable(func_decl* p) {
expr* e = 0;
if (!m_reachable.find(p, e)) {
e = m_ctx.get_pred_transformer(p).initial_state();
update_reachable(p, e);
}
return expr_ref(e, m);
}
void quantifier_model_checker::add_over_approximations(quantifier_ref_vector& qis, model_node& n) {
add_approximations(qis, n, true);
}
void quantifier_model_checker::add_under_approximations(quantifier_ref_vector& qis, model_node& n) {
add_approximations(qis, n, false);
}
void quantifier_model_checker::add_approximations(quantifier_ref_vector& qis, model_node& n, bool is_over) {
pred_transformer& pt = n.pt();
manager& pm = pt.get_pdr_manager();
unsigned level = n.level();
expr_ref_vector Bs(m);
expr_ref B(m), v(m);
quantifier_ref q(m);
datalog::scoped_no_proof _no_proof(m);
scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
for (unsigned j = 0; j < qis.size(); ++j) {
q = qis[j].get();
app_ref_vector& inst = pt.get_inst(m_current_rule);
TRACE("pdr",
tout << "q:\n" << mk_pp(q, m) << "\n";
tout << "level: " << level << "\n";
model_smt2_pp(tout, m, n.get_model(), 0);
m_current_rule->display(m_ctx.get_context(), tout << "rule:\n");
);
var_subst vs(m, false);
vs(q, inst.size(), (expr*const*)inst.c_ptr(), B);
q = to_quantifier(B);
TRACE("pdr", tout << "q instantiated:\n" << mk_pp(q, m) << "\n";);
app* a = to_app(q->get_expr());
func_decl* f = a->get_decl();
pred_transformer& pt2 = m_ctx.get_pred_transformer(f);
if (is_over) {
B = pt2.get_formulas(level - 1, false);
}
else {
B = get_reachable(f);
SASSERT(is_well_sorted(m, B));
}
TRACE("pdr", tout << "B:\n" << mk_pp(B, m) << "\n";);
expr_safe_replace sub(m);
for (unsigned i = 0; i < a->get_num_args(); ++i) {
v = m.mk_const(pm.o2n(pt2.sig(i),0));
sub.insert(v, a->get_arg(i));
}
sub(B);
TRACE("pdr", tout << "B substituted:\n" << mk_pp(B, m) << "\n";);
datalog::flatten_and(B, Bs);
for (unsigned i = 0; i < Bs.size(); ++i) {
m_Bs.push_back(m.update_quantifier(q, Bs[i].get()));
}
}
}
/**
\brief compute strongest post-conditions for each predicate transformer.
(or at least something sufficient to change the set of current counter-examples)
*/
void quantifier_model_checker::weaken_under_approximation() {
datalog::rule_set::decl2rules::iterator it = m_rules.begin_grouped_rules(), end = m_rules.end_grouped_rules();
for (; it != end; ++it) {
func_decl* p = it->m_key;
datalog::rule_vector& rules = *it->m_value;
expr_ref_vector bodies(m);
for (unsigned i = 0; i < rules.size(); ++i) {
bodies.push_back(strongest_post_condition(*rules[i]));
}
update_reachable(p, m.mk_or(bodies.size(), bodies.c_ptr()));
}
}
expr_ref quantifier_model_checker::strongest_post_condition(datalog::rule& r) {
pred_transformer& pt = m_ctx.get_pred_transformer(r.get_decl());
manager& pm = pt.get_pdr_manager();
quantifier_ref_vector* qis = 0;
m_quantifiers.find(&r, qis);
expr_ref_vector body(m), inst(m);
expr_ref fml(m), v(m);
app* a;
func_decl* p;
svector<symbol> names;
unsigned ut_size = r.get_uninterpreted_tail_size();
unsigned t_size = r.get_tail_size();
var_subst vs(m, false);
sort_ref_vector vars(m);
r.get_vars(vars);
if (qis) {
quantifier_ref_vector const& qi = *qis;
for (unsigned i = 0; i < qi.size(); ++i) {
fml = qi[i]->get_expr();
a = to_app(fml);
p = a->get_decl();
expr* p_reach = get_reachable(p);
pred_transformer& pt2 = m_ctx.get_pred_transformer(p);
expr_safe_replace sub(m);
for (unsigned j = 0; j < a->get_num_args(); ++j) {
v = m.mk_const(pm.o2n(pt2.sig(j),0));
sub.insert(v, a->get_arg(j));
}
sub(p_reach, fml);
body.push_back(m.update_quantifier(qi[i], fml));
}
}
a = r.get_head();
for (unsigned i = 0; i < a->get_num_args(); ++i) {
v = m.mk_var(vars.size()+i, m.get_sort(a->get_arg(i)));
body.push_back(m.mk_eq(v, a->get_arg(i)));
}
for (unsigned i = 0; i < ut_size; ++i) {
a = r.get_tail(i);
p = a->get_decl();
pred_transformer& pt2 = m_ctx.get_pred_transformer(p);
expr* p_reach = get_reachable(p);
expr_safe_replace sub(m);
for (unsigned i = 0; i < a->get_num_args(); ++i) {
v = m.mk_const(pm.o2n(pt2.sig(i),0));
sub.insert(v, a->get_arg(i));
}
sub(p_reach, fml);
body.push_back(fml);
}
for (unsigned i = ut_size; i < t_size; ++i) {
body.push_back(r.get_tail(i));
}
fml = m.mk_and(body.size(), body.c_ptr());
vars.reverse();
for (unsigned i = 0; i < vars.size(); ++i) {
names.push_back(symbol(i));
}
if (!vars.empty()) {
fml = m.mk_exists(vars.size(), vars.c_ptr(), names.c_ptr(), fml);
SASSERT(is_well_sorted(m, fml));
}
for (unsigned i = 0; i < r.get_head()->get_num_args(); ++i) {
inst.push_back(m.mk_const(pm.o2n(pt.sig(i),0)));
}
vs(fml, inst.size(), inst.c_ptr(), fml);
SASSERT(is_well_sorted(m, fml));
if (!vars.empty()) {
fml = to_quantifier(fml)->get_expr();
uint_set empty_index_set;
qe_lite qe(m);
qe(empty_index_set, false, fml);
fml = m.mk_exists(vars.size(), vars.c_ptr(), names.c_ptr(), fml);
SASSERT(is_well_sorted(m, fml));
m_ctx.get_context().get_rewriter()(fml);
}
SASSERT(is_well_sorted(m, fml));
IF_VERBOSE(0, verbose_stream() << "instantiate to\n:" << mk_pp(fml, m) << "\n";);
return fml;
}
void quantifier_model_checker::model_check_node(model_node& node) { void quantifier_model_checker::model_check_node(model_node& node) {
TRACE("pdr", node.display(tout, 0);); TRACE("pdr", node.display(tout, 0););
pred_transformer& pt = node.pt(); pred_transformer& pt = node.pt();
manager& pm = pt.get_pdr_manager(); manager& pm = pt.get_pdr_manager();
expr_ref A(m), B(m), C(m), v(m); expr_ref A(m), C(m);
expr_ref_vector As(m), Bs(m); expr_ref_vector As(m);
m_Bs.reset(); m_Bs.reset();
// //
// nodes from leaves that are repeated // nodes from leaves that are repeated
@ -307,8 +533,6 @@ namespace pdr {
if (level == 0) { if (level == 0) {
return; return;
} }
unsigned previous_level = level - 1;
As.push_back(pt.get_propagation_formula(m_ctx.get_pred_transformers(), level)); As.push_back(pt.get_propagation_formula(m_ctx.get_pred_transformers(), level));
As.push_back(node.state()); As.push_back(node.state());
@ -316,48 +540,8 @@ namespace pdr {
m_A = pm.mk_and(As); m_A = pm.mk_and(As);
// Add quantifiers: // Add quantifiers:
// add_over_approximations(*qis, node);
{ add_under_approximations(*qis, node);
datalog::scoped_no_proof _no_proof(m);
quantifier_ref q(m);
scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
for (unsigned j = 0; j < qis->size(); ++j) {
q = (*qis)[j].get();
app_ref_vector& inst = pt.get_inst(m_current_rule);
TRACE("pdr",
tout << "q:\n" << mk_pp(q, m) << "\n";
tout << "level: " << level << "\n";
model_smt2_pp(tout, m, node.get_model(), 0);
m_current_rule->display(m_ctx.get_context(), tout << "rule:\n");
);
var_subst vs(m, false);
vs(q, inst.size(), (expr*const*)inst.c_ptr(), B);
q = to_quantifier(B);
TRACE("pdr", tout << "q instantiated:\n" << mk_pp(q, m) << "\n";);
app* a = to_app(q->get_expr());
func_decl* f = a->get_decl();
pred_transformer& pt2 = m_ctx.get_pred_transformer(f);
B = pt2.get_formulas(previous_level, false);
TRACE("pdr", tout << "B:\n" << mk_pp(B, m) << "\n";);
expr_substitution sub(m);
for (unsigned i = 0; i < a->get_num_args(); ++i) {
v = m.mk_const(pm.o2n(pt2.sig(i),0));
sub.insert(v, a->get_arg(i));
}
rep->set_substitution(&sub);
(*rep)(B);
TRACE("pdr", tout << "B substituted:\n" << mk_pp(B, m) << "\n";);
datalog::flatten_and(B, Bs);
for (unsigned i = 0; i < Bs.size(); ++i) {
m_Bs.push_back(m.update_quantifier(q, Bs[i].get()));
}
}
}
TRACE("pdr", TRACE("pdr",
tout << "A:\n" << mk_pp(m_A, m) << "\n"; tout << "A:\n" << mk_pp(m_A, m) << "\n";
@ -384,13 +568,17 @@ namespace pdr {
bool quantifier_model_checker::model_check(model_node& root) { bool quantifier_model_checker::model_check(model_node& root) {
m_instantiations.reset(); m_instantiations.reset();
m_instantiated_rules.reset(); m_instantiated_rules.reset();
m_rules_model_check = true;
ptr_vector<model_node> nodes; ptr_vector<model_node> nodes;
get_nodes(root, nodes); get_nodes(root, nodes);
for (unsigned i = nodes.size(); i > 0; ) { for (unsigned i = nodes.size(); i > 0; ) {
--i; --i;
model_check_node(*nodes[i]); model_check_node(*nodes[i]);
} }
return m_instantiations.empty(); if (!m_rules_model_check) {
weaken_under_approximation();
}
return m_rules_model_check;
} }
void quantifier_model_checker::refine() { void quantifier_model_checker::refine() {
@ -446,136 +634,3 @@ namespace pdr {
} }
}; };
#if 0
//
// Build:
//
// A & forall x . B1 & forall y . B2 & ...
// =
// not exists x y . (!A or !B1 or !B2 or ...)
//
// Find an instance that satisfies formula.
// (or find all instances?)
//
bool quantifier_model_checker::find_instantiations_qe_based(quantifier_ref_vector const& qs, unsigned level) {
expr_ref_vector fmls(m), conjs(m), fresh_vars(m);
app_ref_vector all_vars(m);
expr_ref C(m);
qe::def_vector defs(m);
front_end_params fparams;
qe::expr_quant_elim qe(m, fparams);
for (unsigned i = 0; i < m_Bs.size(); ++i) {
quantifier* q = qs[i];
unsigned num_decls = q->get_num_decls();
unsigned offset = all_vars.size();
for (unsigned j = 0; j < num_decls; ++j) {
all_vars.push_back(m.mk_fresh_const("V",q->get_decl_sort(j)));
}
var_subst varsubst(m, false);
varsubst(m_Bs[i].get(), num_decls, (expr**)(all_vars.c_ptr() + offset), C);
fmls.push_back(C);
}
conjs.push_back(m_A);
conjs.push_back(m.mk_not(m.mk_and(fmls.size(), fmls.c_ptr())));
// add previous instances.
expr* r = m.mk_and(m_Bs.size(), m_Bs.c_ptr());
m_trail.push_back(r);
expr* inst;
if (!m_bound.find(m_current_rule, r, inst)) {
TRACE("pdr", tout << "did not find: " << mk_pp(r, m) << "\n";);
m_trail.push_back(r);Newton Sanches
inst = m.mk_true();
m_bound.insert(m_current_rule, r, inst);
}
else {
TRACE("pdr", tout << "blocking: " << mk_pp(inst, m) << "\n";);
conjs.push_back(inst);
}
C = m.mk_and(conjs.size(), conjs.c_ptr());
lbool result = qe.first_elim(all_vars.size(), all_vars.c_ptr(), C, defs);
TRACE("pdr", tout << mk_pp(C.get(), m) << "\n" << result << "\n";);
if (result != l_true) {
return false;
}
inst = m.mk_and(inst, m.mk_not(C));
m_trail.push_back(inst);
m_bound.insert(m_current_rule, r, inst);
TRACE("pdr",
tout << "Instantiating\n";
for (unsigned i = 0; i < defs.size(); ++i) {
tout << defs.var(i)->get_name() << " " << mk_pp(defs.def(i), m) << "\n";
}
);
expr_substitution sub(m);
for (unsigned i = 0; i < defs.size(); ++i) {
sub.insert(m.mk_const(defs.var(i)), defs.def(i));
}
scoped_ptr<expr_replacer> rep = mk_default_expr_replacer(m);
rep->set_substitution(&sub);
for (unsigned i = 0; i < all_vars.size(); ++i) {
expr_ref tmp(all_vars[i].get(), m);
(*rep)(tmp);
all_vars[i] = to_app(tmp);
}
unsigned offset = 0;
for (unsigned i = 0; i < m_Bs.size(); ++i) {
quantifier* q = qs[i];
unsigned num_decls = q->get_num_decls();
expr_ref_vector new_binding(m);
for (unsigned j = 0; j < num_decls; ++j) {
new_binding.push_back(all_vars[offset+j].get());
}
offset += num_decls;
add_binding(q, new_binding);
}
return true;
}
bool quantifier_model_checker::find_instantiations_model_based(quantifier_ref_vector const& qs, unsigned level) {
bool found_instance = false;
expr_ref C(m);
front_end_params fparams;
smt::kernel solver(m, fparams);
solver.assert_expr(m_A);
for (unsigned i = 0; i < m_Bs.size(); ++i) {
expr_ref_vector fresh_vars(m);
quantifier* q = qs[i];
for (unsigned j = 0; j < q->get_num_decls(); ++j) {
fresh_vars.push_back(m.mk_fresh_const("V",q->get_decl_sort(j)));
}
var_subst varsubst(m, false);
varsubst(m_Bs[i].get(), fresh_vars.size(), fresh_vars.c_ptr(), C);
TRACE("pdr", tout << "updated propagation formula: " << mk_pp(C,m) << "\n";);
solver.push();
// TBD: what to do with the different tags when unfolding the same predicate twice?
solver.assert_expr(m.mk_not(C));
lbool result = solver.check();
if (result == l_true) {
found_instance = true;
model_ref mr;
solver.get_model(mr);
TRACE("pdr", model_smt2_pp(tout, m, *mr, 0););
expr_ref_vector insts(m);
for (unsigned j = 0; j < fresh_vars.size(); ++j) {
expr* interp = mr->get_const_interp(to_app(fresh_vars[j].get())->get_decl());
if (interp) {
insts.push_back(interp);
}
else {
insts.push_back(fresh_vars[j].get());
}
TRACE("pdr", tout << mk_pp(insts.back(), m) << "\n";);
}
add_binding(q, insts);
}
solver.pop(1);
}
return found_instance;
}
#endif

32
src/muz_qe/pdr_quantifiers.h
View file

@ -33,24 +33,27 @@ namespace pdr {
class model_node; class model_node;
class pred_transformer; class pred_transformer;
class context; class context;
class quantifier_model_checker { class quantifier_model_checker {
context& m_ctx; context& m_ctx;
ast_manager& m; ast_manager& m;
obj_map<datalog::rule const, quantifier_ref_vector*>& m_quantifiers; obj_map<datalog::rule const, quantifier_ref_vector*>& m_quantifiers;
datalog::rule_set& m_rules; datalog::rule_set& m_rules;
expr_ref_vector m_trail;
obj_map<func_decl, expr*> m_reachable; // set of reachable states
expr_ref m_A; expr_ref m_A;
expr_ref_vector m_Bs; expr_ref_vector m_Bs;
pred_transformer* m_current_pt; pred_transformer* m_current_pt;
datalog::rule const* m_current_rule; datalog::rule const* m_current_rule;
model_node* m_current_node; model_node* m_current_node;
bool m_rules_model_check;
app_ref_vector m_instantiations; app_ref_vector m_instantiations;
ptr_vector<datalog::rule const> m_instantiated_rules; ptr_vector<datalog::rule const> m_instantiated_rules;
void model_check_node(model_node& node); void model_check_node(model_node& node);
void weaken_under_approximation();
bool find_instantiations(quantifier_ref_vector const& qs, unsigned level); bool find_instantiations(quantifier_ref_vector const& qs, unsigned level);
bool find_instantiations_model_based(quantifier_ref_vector const& qs, unsigned level); bool find_instantiations_model_based(quantifier_ref_vector const& qs, unsigned level);
@ -79,6 +82,18 @@ namespace pdr {
bool model_check(model_node& root); bool model_check(model_node& root);
void add_over_approximations(quantifier_ref_vector& qis, model_node& n);
void add_under_approximations(quantifier_ref_vector& qis, model_node& n);
void add_approximations(quantifier_ref_vector& qis, model_node& n, bool is_over);
expr_ref get_reachable(func_decl* f);
void update_reachable(func_decl* f, expr* e);
expr_ref strongest_post_condition(datalog::rule& r);
public: public:
quantifier_model_checker( quantifier_model_checker(
context& ctx, context& ctx,
@ -89,9 +104,14 @@ namespace pdr {
m(m), m(m),
m_quantifiers(quantifiers), m_quantifiers(quantifiers),
m_rules(rules), m_rules(rules),
m_trail(m), m_A(m), m_Bs(m), m_A(m),
m_current_pt(0), m_current_rule(0), m_Bs(m),
m_current_node(0), m_instantiations(m) {} m_current_pt(0),
m_current_rule(0),
m_current_node(0),
m_instantiations(m) {}
~quantifier_model_checker();
bool check(); bool check();
}; };

889
src/muz_qe/qe_lite.cpp
View file

@ -74,462 +74,489 @@ public:
}; };
class der2 { namespace eq {
ast_manager & m; class der {
is_variable_proc* m_is_variable; ast_manager & m;
var_subst m_subst; is_variable_proc* m_is_variable;
expr_ref_buffer m_new_exprs; var_subst m_subst;
expr_ref_buffer m_new_exprs;
ptr_vector<expr> m_map;
int_vector m_pos2var;
ptr_vector<var> m_inx2var;
unsigned_vector m_order;
expr_ref_vector m_subst_map;
expr_ref_buffer m_new_args;
th_rewriter m_rewriter;
void der_sort_vars(ptr_vector<var> & vars, ptr_vector<expr> & definitions, unsigned_vector & order) {
order.reset();
// eliminate self loops, and definitions containing quantifiers. ptr_vector<expr> m_map;
bool found = false; int_vector m_pos2var;
for (unsigned i = 0; i < definitions.size(); i++) { ptr_vector<var> m_inx2var;
var * v = vars[i]; unsigned_vector m_order;
expr * t = definitions[i]; expr_ref_vector m_subst_map;
if (t == 0 || has_quantifiers(t) || occurs(v, t)) expr_ref_buffer m_new_args;
definitions[i] = 0; th_rewriter m_rewriter;
else
found = true; // found at least one candidate
}
if (!found) void der_sort_vars(ptr_vector<var> & vars, ptr_vector<expr> & definitions, unsigned_vector & order) {
return; order.reset();
typedef std::pair<expr *, unsigned> frame; // eliminate self loops, and definitions containing quantifiers.
svector<frame> todo; bool found = false;
for (unsigned i = 0; i < definitions.size(); i++) {
expr_fast_mark1 visiting; var * v = vars[i];
expr_fast_mark2 done; expr * t = definitions[i];
if (t == 0 || has_quantifiers(t) || occurs(v, t))
unsigned vidx, num; definitions[i] = 0;
else
for (unsigned i = 0; i < definitions.size(); i++) { found = true; // found at least one candidate
if (definitions[i] == 0) }
continue;
var * v = vars[i]; if (!found)
SASSERT(v->get_idx() == i); return;
SASSERT(todo.empty());
todo.push_back(frame(v, 0)); typedef std::pair<expr *, unsigned> frame;
while (!todo.empty()) { svector<frame> todo;
start:
frame & fr = todo.back(); expr_fast_mark1 visiting;
expr * t = fr.first; expr_fast_mark2 done;
if (t->get_ref_count() > 1 && done.is_marked(t)) {
todo.pop_back(); unsigned vidx, num;
for (unsigned i = 0; i < definitions.size(); i++) {
if (definitions[i] == 0)
continue; continue;
} var * v = vars[i];
switch (t->get_kind()) { SASSERT(v->get_idx() == i);
case AST_VAR: SASSERT(todo.empty());
vidx = to_var(t)->get_idx(); todo.push_back(frame(v, 0));
if (fr.second == 0) { while (!todo.empty()) {
CTRACE("der_bug", vidx >= definitions.size(), tout << "vidx: " << vidx << "\n";); start:
// Remark: The size of definitions may be smaller than the number of variables occuring in the quantified formula. frame & fr = todo.back();
if (definitions.get(vidx, 0) != 0) { expr * t = fr.first;
if (visiting.is_marked(t)) { if (t->get_ref_count() > 1 && done.is_marked(t)) {
// cycle detected: remove t todo.pop_back();
visiting.reset_mark(t); continue;
definitions[vidx] = 0;
}
else {
visiting.mark(t);
fr.second = 1;
todo.push_back(frame(definitions[vidx], 0));
goto start;
}
}
} }
else { switch (t->get_kind()) {
SASSERT(fr.second == 1); case AST_VAR:
if (definitions.get(vidx, 0) != 0) { vidx = to_var(t)->get_idx();
visiting.reset_mark(t); if (fr.second == 0) {
order.push_back(vidx); CTRACE("der_bug", vidx >= definitions.size(), tout << "vidx: " << vidx << "\n";);
// Remark: The size of definitions may be smaller than the number of variables occuring in the quantified formula.
if (definitions.get(vidx, 0) != 0) {
if (visiting.is_marked(t)) {
// cycle detected: remove t
visiting.reset_mark(t);
definitions[vidx] = 0;
}
else {
visiting.mark(t);
fr.second = 1;
todo.push_back(frame(definitions[vidx], 0));
goto start;
}
}
} }
else { else {
// var was removed from the list of candidate vars to elim cycle SASSERT(fr.second == 1);
// do nothing if (definitions.get(vidx, 0) != 0) {
visiting.reset_mark(t);
order.push_back(vidx);
}
else {
// var was removed from the list of candidate vars to elim cycle
// do nothing
}
} }
if (t->get_ref_count() > 1)
done.mark(t);
todo.pop_back();
break;
case AST_QUANTIFIER:
UNREACHABLE();
todo.pop_back();
break;
case AST_APP:
num = to_app(t)->get_num_args();
while (fr.second < num) {
expr * arg = to_app(t)->get_arg(fr.second);
fr.second++;
if (arg->get_ref_count() > 1 && done.is_marked(arg))
continue;
todo.push_back(frame(arg, 0));
goto start;
}
if (t->get_ref_count() > 1)
done.mark(t);
todo.pop_back();
break;
default:
UNREACHABLE();
todo.pop_back();
break;
} }
if (t->get_ref_count() > 1)
done.mark(t);
todo.pop_back();
break;
case AST_QUANTIFIER:
UNREACHABLE();
todo.pop_back();
break;
case AST_APP:
num = to_app(t)->get_num_args();
while (fr.second < num) {
expr * arg = to_app(t)->get_arg(fr.second);
fr.second++;
if (arg->get_ref_count() > 1 && done.is_marked(arg))
continue;
todo.push_back(frame(arg, 0));
goto start;
}
if (t->get_ref_count() > 1)
done.mark(t);
todo.pop_back();
break;
default:
UNREACHABLE();
todo.pop_back();
break;
} }
} }
} }
}
bool is_variable(expr * e) const {
return (*m_is_variable)(e);
}
bool is_neg_var(ast_manager & m, expr * e) {
expr* e1;
return m.is_not(e, e1) && is_variable(e1);
}
/**
\brief Return true if e can be viewed as a variable disequality.
Store the variable id in v and the definition in t.
For example:
if e is (not (= (VAR 1) T)), then v assigned to 1, and t to T.
if e is (iff (VAR 2) T), then v is assigned to 2, and t to (not T).
(not T) is used because this formula is equivalent to (not (iff (VAR 2) (not T))),
and can be viewed as a disequality.
*/
bool is_var_diseq(expr * e, var * & v, expr_ref & t) {
expr* e1;
if (m.is_not(e, e1)) {
return is_var_eq(e, v, t);
}
else if (is_var_eq(e, v, t) && m.is_bool(v)) {
bool_rewriter(m).mk_not(t, t);
m_new_exprs.push_back(t);
return true;
}
else {
return false;
}
}
/**
\brief Return true if e can be viewed as a variable equality.
*/
bool is_var_eq(expr * e, var * & v, expr_ref & t) {
expr* lhs, *rhs;
// (= VAR t), (iff VAR t), (iff (not VAR) t), (iff t (not VAR)) cases bool is_variable(expr * e) const {
if (m.is_eq(e, lhs, rhs) || m.is_iff(e, lhs, rhs)) { return (*m_is_variable)(e);
// (iff (not VAR) t) (iff t (not VAR)) cases }
if (!is_variable(lhs) && !is_variable(rhs) && m.is_bool(lhs)) {
if (!is_neg_var(m, lhs)) { bool is_neg_var(ast_manager & m, expr * e) {
std::swap(lhs, rhs); expr* e1;
} return m.is_not(e, e1) && is_variable(e1);
if (!is_neg_var(m, lhs)) { }
return false;
}
v = to_var(lhs); /**
t = m.mk_not(rhs); \brief Return true if e can be viewed as a variable disequality.
Store the variable id in v and the definition in t.
For example:
if e is (not (= (VAR 1) T)), then v assigned to 1, and t to T.
if e is (iff (VAR 2) T), then v is assigned to 2, and t to (not T).
(not T) is used because this formula is equivalent to (not (iff (VAR 2) (not T))),
and can be viewed as a disequality.
*/
bool is_var_diseq(expr * e, var * & v, expr_ref & t) {
expr* e1;
if (m.is_not(e, e1)) {
return is_var_eq(e, v, t);
}
else if (is_var_eq(e, v, t) && m.is_bool(v)) {
bool_rewriter(m).mk_not(t, t);
m_new_exprs.push_back(t); m_new_exprs.push_back(t);
return true;
}
else {
return false;
}
}
/**
\brief Return true if e can be viewed as a variable equality.
*/
bool is_var_eq(expr * e, var * & v, expr_ref & t) {
expr* lhs, *rhs;
// (= VAR t), (iff VAR t), (iff (not VAR) t), (iff t (not VAR)) cases
if (m.is_eq(e, lhs, rhs) || m.is_iff(e, lhs, rhs)) {
// (iff (not VAR) t) (iff t (not VAR)) cases
if (!is_variable(lhs) && !is_variable(rhs) && m.is_bool(lhs)) {
if (!is_neg_var(m, lhs)) {
std::swap(lhs, rhs);
}
if (!is_neg_var(m, lhs)) {
return false;
}
v = to_var(lhs);
t = m.mk_not(rhs);
m_new_exprs.push_back(t);
TRACE("der", tout << mk_pp(e, m) << "\n";);
return true;
}
if (!is_variable(lhs))
std::swap(lhs, rhs);
if (!is_variable(lhs))
return false;
v = to_var(lhs);
t = rhs;
TRACE("der", tout << mk_pp(e, m) << "\n";); TRACE("der", tout << mk_pp(e, m) << "\n";);
return true; return true;
} }
if (!is_variable(lhs))
std::swap(lhs, rhs); // (ite cond (= VAR t) (= VAR t2)) case
if (!is_variable(lhs)) expr* cond, *e2, *e3;
if (m.is_ite(e, cond, e2, e3)) {
if (is_var_eq(e2, v, t)) {
expr_ref t2(m);
var* v2;
if (is_var_eq(e3, v2, t2) && v2 == v) {
t = m.mk_ite(cond, t, t2);
m_new_exprs.push_back(t);
return true;
}
}
return false; return false;
v = to_var(lhs); }
t = rhs;
TRACE("der", tout << mk_pp(e, m) << "\n";); // VAR = true case
return true; if (is_variable(e)) {
t = m.mk_true();
v = to_var(e);
TRACE("der", tout << mk_pp(e, m) << "\n";);
return true;
}
// VAR = false case
if (is_neg_var(m, e)) {
t = m.mk_false();
v = to_var(to_app(e)->get_arg(0));
TRACE("der", tout << mk_pp(e, m) << "\n";);
return true;
}
return false;
} }
// (ite cond (= VAR t) (= VAR t2)) case
expr* cond, *e2, *e3; bool is_var_def(bool check_eq, expr* e, var*& v, expr_ref& t) {
if (m.is_ite(e, cond, e2, e3)) { if (check_eq) {
if (is_var_eq(e2, v, t)) { return is_var_eq(e, v, t);
expr_ref t2(m); }
var* v2; else {
if (is_var_eq(e3, v2, t2) && v2 == v) { return is_var_diseq(e, v, t);
t = m.mk_ite(cond, t, t2); }
m_new_exprs.push_back(t); }
void get_elimination_order() {
m_order.reset();
TRACE("top_sort",
tout << "DEFINITIONS: " << std::endl;
for(unsigned i = 0; i < m_map.size(); i++)
if(m_map[i]) tout << "VAR " << i << " = " << mk_pp(m_map[i], m) << std::endl;
);
der_sort_vars(m_inx2var, m_map, m_order);
TRACE("der",
tout << "Elimination m_order:" << std::endl;
for(unsigned i=0; i<m_order.size(); i++)
{
if (i != 0) tout << ",";
tout << m_order[i];
}
tout << std::endl;
);
}
void create_substitution(unsigned sz) {
m_subst_map.reset();
m_subst_map.resize(sz, 0);
for (unsigned i = 0; i < m_order.size(); i++) {
expr_ref cur(m_map[m_order[i]], m);
// do all the previous substitutions before inserting
expr_ref r(m);
m_subst(cur, m_subst_map.size(), m_subst_map.c_ptr(), r);
unsigned inx = sz - m_order[i]- 1;
SASSERT(m_subst_map[inx]==0);
m_subst_map[inx] = r;
}
}
void flatten_args(quantifier* q, unsigned& num_args, expr*const*& args) {
expr * e = q->get_expr();
if ((q->is_forall() && m.is_or(e)) ||
(q->is_exists() && m.is_and(e))) {
num_args = to_app(e)->get_num_args();
args = to_app(e)->get_args();
}
}
void apply_substitution(quantifier * q, expr_ref & r) {
expr * e = q->get_expr();
unsigned num_args = 1;
expr* const* args = &e;
flatten_args(q, num_args, args);
bool_rewriter rw(m);
// get a new expression
m_new_args.reset();
for(unsigned i = 0; i < num_args; i++) {
int x = m_pos2var[i];
if (x == -1 || m_map[x] == 0) {
m_new_args.push_back(args[i]);
}
}
expr_ref t(m);
if (q->is_forall()) {
rw.mk_or(m_new_args.size(), m_new_args.c_ptr(), t);
}
else {
rw.mk_and(m_new_args.size(), m_new_args.c_ptr(), t);
}
expr_ref new_e(m);
m_subst(t, m_subst_map.size(), m_subst_map.c_ptr(), new_e);
// don't forget to update the quantifier patterns
expr_ref_buffer new_patterns(m);
expr_ref_buffer new_no_patterns(m);
for (unsigned j = 0; j < q->get_num_patterns(); j++) {
expr_ref new_pat(m);
m_subst(q->get_pattern(j), m_subst_map.size(), m_subst_map.c_ptr(), new_pat);
new_patterns.push_back(new_pat);
}
for (unsigned j = 0; j < q->get_num_no_patterns(); j++) {
expr_ref new_nopat(m);
m_subst(q->get_no_pattern(j), m_subst_map.size(), m_subst_map.c_ptr(), new_nopat);
new_no_patterns.push_back(new_nopat);
}
r = m.update_quantifier(q, new_patterns.size(), new_patterns.c_ptr(),
new_no_patterns.size(), new_no_patterns.c_ptr(), new_e);
}
void reduce_quantifier1(quantifier * q, expr_ref & r, proof_ref & pr) {
expr * e = q->get_expr();
is_variable_test is_v(q->get_num_decls());
set_is_variable_proc(is_v);
unsigned num_args = 1;
expr* const* args = &e;
flatten_args(q, num_args, args);
unsigned def_count = 0;
unsigned largest_vinx = 0;
find_definitions(num_args, args, q->is_exists(), def_count, largest_vinx);
if (def_count > 0) {
get_elimination_order();
SASSERT(m_order.size() <= def_count); // some might be missing because of cycles
if (!m_order.empty()) {
create_substitution(largest_vinx + 1);
apply_substitution(q, r);
}
else {
r = q;
}
}
else {
TRACE("der_bug", tout << "Did not find any diseq\n" << mk_pp(q, m) << "\n";);
r = q;
}
if (m.proofs_enabled()) {
pr = r == q ? 0 : m.mk_der(q, r);
}
}
void elim_unused_vars(expr_ref& r, proof_ref &pr) {
if (is_quantifier(r)) {
quantifier * q = to_quantifier(r);
::elim_unused_vars(m, q, r);
if (m.proofs_enabled()) {
proof * p1 = m.mk_elim_unused_vars(q, r);
pr = m.mk_transitivity(pr, p1);
}
}
}
void find_definitions(unsigned num_args, expr* const* args, bool is_exists, unsigned& def_count, unsigned& largest_vinx) {
var * v = 0;
expr_ref t(m);
def_count = 0;
largest_vinx = 0;
m_map.reset();
m_pos2var.reset();
m_inx2var.reset();
m_pos2var.reserve(num_args, -1);
// Find all definitions
for (unsigned i = 0; i < num_args; i++) {
if (is_var_def(is_exists, args[i], v, t)) {
unsigned idx = v->get_idx();
if(m_map.get(idx, 0) == 0) {
m_map.reserve(idx + 1, 0);
m_inx2var.reserve(idx + 1, 0);
m_map[idx] = t;
m_inx2var[idx] = v;
m_pos2var[i] = idx;
def_count++;
largest_vinx = std::max(idx, largest_vinx);
}
}
}
}
bool reduce_var_set(expr_ref_vector& conjs) {
unsigned def_count = 0;
unsigned largest_vinx = 0;
find_definitions(conjs.size(), conjs.c_ptr(), true, def_count, largest_vinx);
if (def_count > 0) {
get_elimination_order();
SASSERT(m_order.size() <= def_count); // some might be missing because of cycles
if (!m_order.empty()) {
expr_ref r(m), new_r(m);
r = m.mk_and(conjs.size(), conjs.c_ptr());
create_substitution(largest_vinx + 1);
m_subst(r, m_subst_map.size(), m_subst_map.c_ptr(), new_r);
m_rewriter(new_r);
conjs.reset();
datalog::flatten_and(new_r, conjs);
return true; return true;
} }
} }
return false; return false;
} }
// VAR = true case
if (is_variable(e)) {
t = m.mk_true();
v = to_var(e);
TRACE("der", tout << mk_pp(e, m) << "\n";);
return true;
}
// VAR = false case
if (is_neg_var(m, e)) {
t = m.mk_false();
v = to_var(to_app(e)->get_arg(0));
TRACE("der", tout << mk_pp(e, m) << "\n";);
return true;
}
return false;
}
public:
bool is_var_def(bool check_eq, expr* e, var*& v, expr_ref& t) { der(ast_manager & m): m(m), m_is_variable(0), m_subst(m), m_new_exprs(m), m_subst_map(m), m_new_args(m), m_rewriter(m) {}
if (check_eq) {
return is_var_eq(e, v, t);
}
else {
return is_var_diseq(e, v, t);
}
}
void get_elimination_order() {
m_order.reset();
TRACE("top_sort",
tout << "DEFINITIONS: " << std::endl;
for(unsigned i = 0; i < m_map.size(); i++)
if(m_map[i]) tout << "VAR " << i << " = " << mk_pp(m_map[i], m) << std::endl;
);
der_sort_vars(m_inx2var, m_map, m_order); void set_is_variable_proc(is_variable_proc& proc) { m_is_variable = &proc;}
TRACE("der", void operator()(quantifier * q, expr_ref & r, proof_ref & pr) {
tout << "Elimination m_order:" << std::endl; TRACE("der", tout << mk_pp(q, m) << "\n";);
for(unsigned i=0; i<m_order.size(); i++) pr = 0;
{ r = q;
if (i != 0) tout << ","; reduce_quantifier(q, r, pr);
tout << m_order[i]; if (r != q) {
} elim_unused_vars(r, pr);
tout << std::endl;
);
}
void create_substitution(unsigned sz) {
m_subst_map.reset();
m_subst_map.resize(sz, 0);
for (unsigned i = 0; i < m_order.size(); i++) {
expr_ref cur(m_map[m_order[i]], m);
// do all the previous substitutions before inserting
expr_ref r(m);
m_subst(cur, m_subst_map.size(), m_subst_map.c_ptr(), r);
unsigned inx = sz - m_order[i]- 1;
SASSERT(m_subst_map[inx]==0);
m_subst_map[inx] = r;
}
}
void flatten_args(quantifier* q, unsigned& num_args, expr*const*& args) {
expr * e = q->get_expr();
if ((q->is_forall() && m.is_or(e)) ||
(q->is_exists() && m.is_and(e))) {
num_args = to_app(e)->get_num_args();
args = to_app(e)->get_args();
}
}
void apply_substitution(quantifier * q, expr_ref & r) {
expr * e = q->get_expr();
unsigned num_args = 1;
expr* const* args = &e;
flatten_args(q, num_args, args);
bool_rewriter rw(m);
// get a new expression
m_new_args.reset();
for(unsigned i = 0; i < num_args; i++) {
int x = m_pos2var[i];
if (x == -1 || m_map[x] == 0) {
m_new_args.push_back(args[i]);
} }
} }
expr_ref t(m); void reduce_quantifier(quantifier * q, expr_ref & r, proof_ref & pr) {
if (q->is_forall()) {
rw.mk_or(m_new_args.size(), m_new_args.c_ptr(), t);
}
else {
rw.mk_and(m_new_args.size(), m_new_args.c_ptr(), t);
}
expr_ref new_e(m);
m_subst(t, m_subst_map.size(), m_subst_map.c_ptr(), new_e);
// don't forget to update the quantifier patterns
expr_ref_buffer new_patterns(m);
expr_ref_buffer new_no_patterns(m);
for (unsigned j = 0; j < q->get_num_patterns(); j++) {
expr_ref new_pat(m);
m_subst(q->get_pattern(j), m_subst_map.size(), m_subst_map.c_ptr(), new_pat);
new_patterns.push_back(new_pat);
}
for (unsigned j = 0; j < q->get_num_no_patterns(); j++) {
expr_ref new_nopat(m);
m_subst(q->get_no_pattern(j), m_subst_map.size(), m_subst_map.c_ptr(), new_nopat);
new_no_patterns.push_back(new_nopat);
}
r = m.update_quantifier(q, new_patterns.size(), new_patterns.c_ptr(),
new_no_patterns.size(), new_no_patterns.c_ptr(), new_e);
}
void reduce_quantifier1(quantifier * q, expr_ref & r, proof_ref & pr) {
expr * e = q->get_expr();
is_variable_test is_v(q->get_num_decls());
set_is_variable_proc(is_v);
unsigned num_args = 1;
expr* const* args = &e;
flatten_args(q, num_args, args);
unsigned def_count = 0;
unsigned largest_vinx = 0;
find_definitions(num_args, args, q->is_exists(), def_count, largest_vinx);
if (def_count > 0) {
get_elimination_order();
SASSERT(m_order.size() <= def_count); // some might be missing because of cycles
if (!m_order.empty()) {
create_substitution(largest_vinx + 1);
apply_substitution(q, r);
}
else {
r = q;
}
}
else {
TRACE("der_bug", tout << "Did not find any diseq\n" << mk_pp(q, m) << "\n";);
r = q; r = q;
} // Keep applying reduce_quantifier1 until r doesn't change anymore
do {
if (m.proofs_enabled()) { proof_ref curr_pr(m);
pr = r == q ? 0 : m.mk_der(q, r); q = to_quantifier(r);
} reduce_quantifier1(q, r, curr_pr);
} if (m.proofs_enabled()) {
pr = m.mk_transitivity(pr, curr_pr);
void elim_unused_vars(expr_ref& r, proof_ref &pr) {
if (is_quantifier(r)) {
quantifier * q = to_quantifier(r);
::elim_unused_vars(m, q, r);
if (m.proofs_enabled()) {
proof * p1 = m.mk_elim_unused_vars(q, r);
pr = m.mk_transitivity(pr, p1);
}
}
}
void find_definitions(unsigned num_args, expr* const* args, bool is_exists, unsigned& def_count, unsigned& largest_vinx) {
var * v = 0;
expr_ref t(m);
def_count = 0;
largest_vinx = 0;
m_map.reset();
m_pos2var.reset();
m_inx2var.reset();
m_pos2var.reserve(num_args, -1);
// Find all definitions
for (unsigned i = 0; i < num_args; i++) {
if (is_var_def(is_exists, args[i], v, t)) {
unsigned idx = v->get_idx();
if(m_map.get(idx, 0) == 0) {
m_map.reserve(idx + 1, 0);
m_inx2var.reserve(idx + 1, 0);
m_map[idx] = t;
m_inx2var[idx] = v;
m_pos2var[i] = idx;
def_count++;
largest_vinx = std::max(idx, largest_vinx);
} }
} } while (q != r && is_quantifier(r));
}
}
bool reduce_var_set(expr_ref_vector& conjs) {
unsigned def_count = 0;
unsigned largest_vinx = 0;
find_definitions(conjs.size(), conjs.c_ptr(), true, def_count, largest_vinx);
if (def_count > 0) {
get_elimination_order();
SASSERT(m_order.size() <= def_count); // some might be missing because of cycles
if (!m_order.empty()) { m_new_exprs.reset();
expr_ref r(m), new_r(m);
r = m.mk_and(conjs.size(), conjs.c_ptr());
create_substitution(largest_vinx + 1);
m_subst(r, m_subst_map.size(), m_subst_map.c_ptr(), new_r);
m_rewriter(new_r);
conjs.reset();
datalog::flatten_and(new_r, conjs);
return true;
}
} }
return false;
}
public:
der2(ast_manager & m): m(m), m_is_variable(0), m_subst(m), m_new_exprs(m), m_subst_map(m), m_new_args(m), m_rewriter(m) {}
void set_is_variable_proc(is_variable_proc& proc) { m_is_variable = &proc;}
void operator()(quantifier * q, expr_ref & r, proof_ref & pr) {
TRACE("der", tout << mk_pp(q, m) << "\n";);
pr = 0;
r = q;
reduce_quantifier(q, r, pr);
if (r != q) {
elim_unused_vars(r, pr);
}
}
void reduce_quantifier(quantifier * q, expr_ref & r, proof_ref & pr) {
r = q;
// Keep applying reduce_quantifier1 until r doesn't change anymore
do {
proof_ref curr_pr(m);
q = to_quantifier(r);
reduce_quantifier1(q, r, curr_pr);
if (m.proofs_enabled()) {
pr = m.mk_transitivity(pr, curr_pr);
}
} while (q != r && is_quantifier(r));
m_new_exprs.reset(); void operator()(expr_ref_vector& r) {
} while (reduce_var_set(r)) ;
m_new_exprs.reset();
}
ast_manager& get_manager() const { return m; }
};
}; // namespace eq
void operator()(expr_ref_vector& r) { // ------------------------------------------------------------
while (reduce_var_set(r)) ; // basic destructive equality (and disequality) resolution for arrays.
m_new_exprs.reset();
} namespace ar {
class der {
ast_manager& m;
is_variable_proc* m_is_variable;
bool is_variable(expr * e) const {
return (*m_is_variable)(e);
}
public:
der(ast_manager& m): m(m), m_is_variable(0) {}
void operator()(expr_ref_vector& fmls) {
IF_VERBOSE(1, verbose_stream() << "Todo: eliminate arrays\n";);
}
void set_is_variable_proc(is_variable_proc& proc) { m_is_variable = &proc;}
};
}; // namespace ar
ast_manager& get_manager() const { return m; }
};
// ------------------------------------------------------------ // ------------------------------------------------------------
// fm_tactic adapted to eliminate designated de-Brujin indices. // fm_tactic adapted to eliminate designated de-Brujin indices.
@ -1808,7 +1835,6 @@ namespace fm {
void set_is_variable_proc(is_variable_proc& proc) { m_is_variable = &proc;} void set_is_variable_proc(is_variable_proc& proc) { m_is_variable = &proc;}
void operator()(expr_ref_vector& fmls) { void operator()(expr_ref_vector& fmls) {
init(fmls); init(fmls);
init_use_list(fmls); init_use_list(fmls);
@ -1873,12 +1899,13 @@ namespace fm {
class qe_lite::impl { class qe_lite::impl {
ast_manager& m; ast_manager& m;
der2 m_der;
params_ref m_params; params_ref m_params;
eq::der m_der;
fm::fm m_fm; fm::fm m_fm;
ar::der m_array_der;
public: public:
impl(ast_manager& m): m(m), m_der(m), m_fm(m, m_params) {} impl(ast_manager& m): m(m), m_der(m), m_fm(m, m_params), m_array_der(m) {}
void operator()(app_ref_vector& vars, expr_ref& fml) { void operator()(app_ref_vector& vars, expr_ref& fml) {
if (vars.empty()) { if (vars.empty()) {
@ -1928,10 +1955,16 @@ public:
} }
void operator()(uint_set const& index_set, bool index_of_bound, expr_ref& fml) { void operator()(uint_set const& index_set, bool index_of_bound, expr_ref& fml) {
expr_ref_vector conjs(m); expr_ref_vector disjs(m);
conjs.push_back(fml); datalog::flatten_or(fml, disjs);
(*this)(index_set, index_of_bound, conjs); for (unsigned i = 0; i < disjs.size(); ++i) {
bool_rewriter(m).mk_and(conjs.size(), conjs.c_ptr(), fml); expr_ref_vector conjs(m);
conjs.push_back(disjs[i].get());
(*this)(index_set, index_of_bound, conjs);
bool_rewriter(m).mk_and(conjs.size(), conjs.c_ptr(), fml);
disjs[i] = fml;
}
bool_rewriter(m).mk_or(disjs.size(), disjs.c_ptr(), fml);
} }
@ -1941,9 +1974,11 @@ public:
TRACE("qe_lite", for (unsigned i = 0; i < fmls.size(); ++i) tout << mk_pp(fmls[i].get(), m) << "\n";); TRACE("qe_lite", for (unsigned i = 0; i < fmls.size(); ++i) tout << mk_pp(fmls[i].get(), m) << "\n";);
IF_VERBOSE(3, for (unsigned i = 0; i < fmls.size(); ++i) verbose_stream() << mk_pp(fmls[i].get(), m) << "\n";); IF_VERBOSE(3, for (unsigned i = 0; i < fmls.size(); ++i) verbose_stream() << mk_pp(fmls[i].get(), m) << "\n";);
m_der.set_is_variable_proc(is_var); m_der.set_is_variable_proc(is_var);
m_der(fmls);
m_fm.set_is_variable_proc(is_var); m_fm.set_is_variable_proc(is_var);
m_array_der.set_is_variable_proc(is_var);
m_der(fmls);
m_fm(fmls); m_fm(fmls);
m_array_der(fmls);
TRACE("qe_lite", for (unsigned i = 0; i < fmls.size(); ++i) tout << mk_pp(fmls[i].get(), m) << "\n";); TRACE("qe_lite", for (unsigned i = 0; i < fmls.size(); ++i) tout << mk_pp(fmls[i].get(), m) << "\n";);
} }

2
src/muz_qe/qe_lite.h
View file

@ -1,5 +1,5 @@
/*++ /*++
Copyright (c) 2010 Microsoft Corporation Copyright (c) 2012 Microsoft Corporation
Module Name: Module Name: