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fix quantifier elimination bugs reported by Berdine and Bornat

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2014-07-14 15:38:22 +02:00
parent 4f7d872d59
commit e4dedbbefc
5 changed files with 137 additions and 60 deletions
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2
src/ast/rewriter/arith_rewriter.cpp
View file

@ -704,7 +704,7 @@ br_status arith_rewriter::mk_mod_core(expr * arg1, expr * arg2, expr_ref & resul
}
// propagate mod inside only if not all arguments are not already mod.
if (m_util.is_numeral(arg2, v2, is_int) && is_int && v2.is_pos() && (is_add(arg1) || is_mul(arg1))) {
if (false && m_util.is_numeral(arg2, v2, is_int) && is_int && v2.is_pos() && (is_add(arg1) || is_mul(arg1))) {
TRACE("mod_bug", tout << "mk_mod:\n" << mk_ismt2_pp(arg1, m()) << "\n" << mk_ismt2_pp(arg2, m()) << "\n";);
unsigned num_args = to_app(arg1)->get_num_args();
unsigned i;

115
src/qe/qe.cpp
View file

@ -1120,6 +1120,7 @@ namespace qe {
st->init(fml);
st->m_vars.append(m_vars.size(), m_vars.c_ptr());
SASSERT(invariant());
TRACE("qe", tout << mk_pp(m_fml, m) << " child: " << mk_pp(fml, m) << "\n";);
return st;
}
@ -1133,6 +1134,7 @@ namespace qe {
m_branch_index.insert(branch_id, index);
st->m_vars.append(m_vars.size(), m_vars.c_ptr());
SASSERT(invariant());
//TRACE("qe", tout << mk_pp(m_fml, m) << " child: " << mk_pp(st->fml(), m) << "\n";);
return st;
}
@ -1164,6 +1166,16 @@ namespace qe {
}
}
expr_ref abstract_variable(app* x, expr* fml) const {
expr_ref result(m);
expr* y = x;
expr_abstract(m, 0, 1, &y, fml, result);
symbol X(x->get_decl()->get_name());
sort* s = m.get_sort(x);
result = m.mk_exists(1, &s, &X, result);
return result;
}
void display_validate(std::ostream& out) const {
if (m_children.empty()) {
return;
@ -1171,25 +1183,53 @@ namespace qe {
expr_ref q(m);
expr* x = m_var;
if (x) {
expr_abstract(m, 0, 1, &x, m_fml, q);
ptr_vector<expr> fmls;
q = abstract_variable(m_var, m_fml);
expr_ref_vector fmls(m);
expr_ref fml(m);
for (unsigned i = 0; i < m_children.size(); ++i) {
expr* fml = m_children[i]->fml();
search_tree const& child = *m_children[i];
fml = child.fml();
if (fml) {
// abstract free variables in children.
ptr_vector<app> child_vars, new_vars;
child_vars.append(child.m_vars.size(), child.m_vars.c_ptr());
if (child.m_var) {
child_vars.push_back(child.m_var);
}
for (unsigned j = 0; j < child_vars.size(); ++j) {
if (!m_vars.contains(child_vars[j]) &&
!new_vars.contains(child_vars[j])) {
fml = abstract_variable(child_vars[j], fml);
new_vars.push_back(child_vars[j]);
}
}
fmls.push_back(fml);
}
}
symbol X(m_var->get_decl()->get_name());
sort* s = m.get_sort(x);
q = m.mk_exists(1, &s, &X, q);
expr_ref tmp(m);
bool_rewriter(m).mk_or(fmls.size(), fmls.c_ptr(), tmp);
expr_ref f(m.mk_not(m.mk_iff(q, tmp)), m);
bool_rewriter(m).mk_or(fmls.size(), fmls.c_ptr(), fml);
fml = m.mk_not(m.mk_iff(q, fml));
ast_smt_pp pp(m);
out << "(echo " << m_var->get_decl()->get_name() << ")\n";
out << "; eliminate " << mk_pp(m_var, m) << "\n";
out << "(push)\n";
pp.display_smt2(out, f);
pp.display_smt2(out, fml);
out << "(pop)\n\n";
DEBUG_CODE(
smt_params params;
params.m_simplify_bit2int = true;
params.m_arith_enum_const_mod = true;
params.m_bv_enable_int2bv2int = true;
params.m_relevancy_lvl = 0;
smt::kernel ctx(m, params);
ctx.assert_expr(fml);
lbool is_sat = ctx.check();
if (is_sat == l_true) {
std::cout << "; Validation failed:\n";
std::cout << mk_pp(fml, m) << "\n";
}
);
}
for (unsigned i = 0; i < m_children.size(); ++i) {
if (m_children[i]->fml()) {
@ -1410,13 +1450,9 @@ namespace qe {
m_solver.assert_expr(m_fml);
if (assumption) m_solver.assert_expr(assumption);
bool is_sat = false;
while (l_false != m_solver.check()) {
while (l_true == m_solver.check()) {
is_sat = true;
model_ref model;
m_solver.get_model(model);
TRACE("qe", model_v2_pp(tout, *model););
model_evaluator model_eval(*model);
final_check(model_eval);
final_check();
}
if (!is_sat) {
@ -1466,14 +1502,30 @@ namespace qe {
private:
void final_check(model_evaluator& model_eval) {
TRACE("qe", tout << "\n";);
while (can_propagate_assignment(model_eval)) {
propagate_assignment(model_eval);
}
VERIFY(CHOOSE_VAR == update_current(model_eval, true));
SASSERT(m_current->fml());
pop(model_eval);
void final_check() {
model_ref model;
m_solver.get_model(model);
scoped_ptr<model_evaluator> model_eval = alloc(model_evaluator, *model);
while (true) {
TRACE("qe", model_v2_pp(tout, *model););
while (can_propagate_assignment(*model_eval)) {
propagate_assignment(*model_eval);
}
VERIFY(CHOOSE_VAR == update_current(*model_eval, true));
SASSERT(m_current->fml());
if (l_true != m_solver.check()) {
return;
}
m_solver.get_model(model);
model_eval = alloc(model_evaluator, *model);
search_tree* st = m_current;
update_current(*model_eval, false);
if (st == m_current) {
break;
}
}
pop(*model_eval);
}
ast_manager& get_manager() { return m; }
@ -1633,6 +1685,7 @@ namespace qe {
nb = m_current->get_num_branches();
expr_ref fml(m_current->fml(), m);
if (!eval(model_eval, b, branch) || branch >= nb) {
TRACE("qe", tout << "evaluation failed: setting branch to 0\n";);
branch = rational::zero();
}
SASSERT(!branch.is_neg());
@ -1694,11 +1747,12 @@ namespace qe {
}
//
// The current state is satisfiable
// and the closed portion of the formula
// can be used as the quantifier-free portion.
// The closed portion of the formula
// can be used as the quantifier-free portion,
// unless the current state is unsatisfiable.
//
if (m.is_true(fml_mixed)) {
SASSERT(l_true == m_solver.check());
m_current = m_current->add_child(fml_closed);
for (unsigned i = 0; m_defs && i < m_current->num_free_vars(); ++i) {
expr_ref val(m);
@ -1708,6 +1762,7 @@ namespace qe {
if (val == x) {
model_ref model;
lbool is_sat = m_solver.check();
if (is_sat == l_undef) return;
m_solver.get_model(model);
SASSERT(is_sat == l_true);
model_evaluator model_eval2(*model);
@ -1890,7 +1945,7 @@ namespace qe {
vars.reset();
closed = closed && (r != l_undef);
}
TRACE("qe", tout << mk_ismt2_pp(fml, m) << "\n";);
TRACE("qe", tout << mk_pp(fml, m) << "\n";);
m_current->add_child(fml)->reset_free_vars();
block_assignment();
}
@ -1959,7 +2014,7 @@ namespace qe {
class quant_elim_new : public quant_elim {
ast_manager& m;
smt_params& m_fparams;
smt_params& m_fparams;
expr_ref m_assumption;
bool m_produce_models;
ptr_vector<quant_elim_plugin> m_plugins;

73
src/qe/qe_arith_plugin.cpp
View file

@ -31,6 +31,7 @@ Revision History:
#include "obj_pair_hashtable.h"
#include "nlarith_util.h"
#include "model_evaluator.h"
#include "smt_kernel.h"
namespace qe {
@ -80,9 +81,9 @@ namespace qe {
ast_manager& m;
i_solver_context& m_ctx;
public:
arith_util m_arith; // initialize before m_zero_i, etc.
arith_util m_arith; // initialize before m_zero_i, etc.
th_rewriter simplify;
private:
th_rewriter m_rewriter;
arith_eq_solver m_arith_solver;
bv_util m_bv;
@ -102,7 +103,7 @@ namespace qe {
m(m),
m_ctx(ctx),
m_arith(m),
m_rewriter(m),
simplify(m),
m_arith_solver(m),
m_bv(m),
m_zero_i(m_arith.mk_numeral(numeral(0), true), m),
@ -434,7 +435,6 @@ namespace qe {
expr_ref tmp(e, m);
simplify(tmp);
m_arith_rewriter.mk_le(tmp, mk_zero(e), result);
TRACE("qe_verbose", tout << "mk_le " << mk_pp(result, m) << "\n";);
}
void mk_lt(expr* e, expr_ref& result) {
@ -521,7 +521,8 @@ namespace qe {
expr_ref result1(m), result2(m);
// a*s + b*t <= 0
expr_ref as_bt_le_0(result, m), tmp2(m), tmp3(m), tmp4(m);
expr_ref as_bt_le_0(result, m), tmp2(m), asz_bt_le_0(m), tmp3(m), tmp4(m);
expr_ref b_divides_sz(m);
// a*s + b*t + (a-1)(b-1) <= 0
tmp2 = m_arith.mk_add(as_bt, slack);
@ -560,30 +561,36 @@ namespace qe {
sz = m_arith.mk_uminus(sz);
}
tmp4 = mk_add(mk_mul(a1, sz), bt);
mk_le(tmp4, tmp3);
mk_le(tmp4, asz_bt_le_0);
if (to_app(tmp3)->get_arg(0) == x &&
m_arith.is_zero(to_app(tmp3)->get_arg(1))) {
if (to_app(asz_bt_le_0)->get_arg(0) == x &&
m_arith.is_zero(to_app(asz_bt_le_0)->get_arg(1))) {
// exists z in [0 .. |b|-2] . |b| | (z + s) && z <= 0
// <=>
// |b| | s
mk_divides(abs_b, s, tmp2);
}
else {
mk_divides(abs_b, sz, tmp2);
mk_and(tmp2, tmp3, tmp4);
mk_big_or(abs_b - numeral(2), x, tmp4, tmp2);
mk_divides(abs_b, sz, b_divides_sz);
mk_and(b_divides_sz, asz_bt_le_0, tmp4);
mk_big_or(abs_b - numeral(2), x, tmp4, tmp2);
TRACE("qe",
tout << "b | s + z: " << mk_pp(b_divides_sz, m) << "\n";
tout << "a(s+z) + bt <= 0: " << mk_pp(asz_bt_le_0, m) << "\n";
);
}
mk_flat_and(as_bt_le_0, tmp2, result2);
mk_or(result1, result2, result);
simplify(result);
// a*s + b*t + (a-1)(b-1) <= 0
// or exists z in [0 .. |b|-2] . |b| | (z + s) && a*n_sign(b)(s + z) + |b|t <= 0
}
TRACE("qe",
{
expr_ref_vector trail(m);
tout << "is_strict: " << (is_strict?"true":"false") << "\n";
tout << (is_strict?"strict":"non-strict") << "\n";
bound(m, a, t, false).pp(tout, x);
tout << "\n";
bound(m, b, s, false).pp(tout, x);
@ -592,10 +599,6 @@ namespace qe {
});
}
void simplify(expr_ref& p) {
m_rewriter(p);
}
struct mul_lt {
arith_util& u;
mul_lt(arith_qe_util& u): u(u.m_arith) {}
@ -1052,7 +1055,6 @@ namespace qe {
}
bool reduce_equation(expr* p, expr* fml) {
TRACE("qe", tout << mk_pp(p, m) << "\n";);
numeral k;
if (m_arith.is_numeral(p, k) && k.is_zero()) {
@ -1555,9 +1557,10 @@ public:
mk_non_resolve(bounds, true, is_lower, result);
mk_non_resolve(bounds, false, is_lower, result);
m_util.simplify(result);
add_cache(x, fml, v, result, x_t.get_coeff(), x_t.get_term());
TRACE("qe",
tout << vl << " " << mk_pp(x, m) << "\n";
tout << vl << " " << mk_pp(x, m) << " infinite case\n";
tout << mk_pp(fml, m) << "\n";
tout << mk_pp(result, m) << "\n";);
return;
@ -1591,19 +1594,22 @@ public:
SASSERT(index < bounds.size(is_strict, is_lower));
expr_ref t(bounds.exprs(is_strict, is_lower)[index], m);
rational a = bounds.coeffs(is_strict, is_lower)[index];
t = x_t.mk_term(a, t);
a = x_t.mk_coeff(a);
mk_bounds(bounds, x, true, is_eq, is_strict, is_lower, index, a, t, result);
mk_bounds(bounds, x, false, is_eq, is_strict, is_lower, index, a, t, result);
t = x_t.mk_term(a, t);
a = x_t.mk_coeff(a);
mk_resolve(bounds, x, x_t, true, is_eq, is_strict, is_lower, index, a, t, result);
mk_resolve(bounds, x, x_t, false, is_eq, is_strict, is_lower, index, a, t, result);
m_util.simplify(result);
add_cache(x, fml, v, result, x_t.get_coeff(), x_t.get_term());
TRACE("qe",
{
tout << vl << " " << mk_pp(x, m) << "\n";
tout << vl << " " << mk_pp(bounds.atoms(is_strict, is_lower)[index],m) << "\n";
tout << mk_pp(fml, m) << "\n";
tout << mk_pp(result, m) << "\n";
}
@ -2225,6 +2231,12 @@ public:
}
}
m_util.simplify(result);
TRACE("qe",
tout << (is_strict?"strict":"non-strict") << "\n";
tout << (is_lower?"is-lower":"is-upper") << "\n";
tout << "a: " << a << " " << mk_pp(t, m) << "\n";
tout << "b: " << b << " " << mk_pp(s, m) << "\n";
tout << mk_pp(result, m) << "\n";);
}
//
@ -2245,10 +2257,12 @@ public:
void mk_bounds(bounds_proc& bounds,
app* x, bool is_strict, bool is_eq_ctx, bool is_strict_ctx, bool is_lower, unsigned index,
app* x, bool is_strict, bool is_eq_ctx,
bool is_strict_ctx, bool is_lower, unsigned index,
rational const& a, expr* t,
expr_ref& result)
{
TRACE("qe", tout << mk_pp(t, m) << "\n";);
SASSERT(!is_eq_ctx || !is_strict_ctx);
unsigned sz = bounds.size(is_strict, is_lower);
expr_ref tmp(m), eq(m);
@ -2258,13 +2272,14 @@ public:
for (unsigned i = 0; i < sz; ++i) {
app* e = bounds.atoms(is_strict, is_lower)[i];
expr* s = bounds.exprs(is_strict, is_lower)[i];
expr_ref s(bounds.exprs(is_strict, is_lower)[i], m);
rational b = bounds.coeffs(is_strict, is_lower)[i];
if (same_strict && i == index) {
if (non_strict_real) {
m_util.mk_eq(a, x, t, eq);
TRACE("qe", tout << "a:" << a << " x: " << mk_pp(x, m) << " t: " << mk_pp(t, m) << " eq: " << mk_pp(eq, m) << "\n";);
TRACE("qe", tout << "a:" << a << " x: " << mk_pp(x, m) << "t: " <<
mk_pp(t, m) << " eq: " << mk_pp(eq, m) << "\n";);
if (is_eq_ctx) {
m_ctx.add_constraint(true, eq);
}
@ -2292,6 +2307,7 @@ public:
(non_strict_real && is_eq_ctx && is_strict) ||
(same_strict && i < index);
mk_bound(result_is_strict, is_lower, a, t, b, s, tmp);
m_util.m_replace.apply_substitution(e, tmp.get(), result);
@ -2330,14 +2346,17 @@ public:
s = x_t.mk_term(b, s);
b = x_t.mk_coeff(b);
m_util.mk_resolve(x, strict_resolve, a, t, b, s, tmp);
expr_ref save_result(result);
m_util.m_replace.apply_substitution(e, tmp.get(), result);
m_ctx.add_constraint(true, mk_not(e), tmp);
TRACE("qe_verbose",
tout << mk_pp(atm, m) << " ";
tout << mk_pp(e, m) << " ==> ";
tout << mk_pp(e, m) << " ==>\n";
tout << mk_pp(tmp, m) << "\n";
tout << "old fml: " << mk_pp(save_result, m) << "\n";
tout << "new fml: " << mk_pp(result, m) << "\n";
);
}
}

5
src/smt/theory_bv.cpp
View file

@ -1198,6 +1198,7 @@ namespace smt {
void theory_bv::relevant_eh(app * n) {
ast_manager & m = get_manager();
context & ctx = get_context();
TRACE("bv", tout << "relevant: " << mk_pp(n, m) << "\n";);
if (m.is_bool(n)) {
bool_var v = ctx.get_bool_var(n);
atom * a = get_bv2a(v);
@ -1210,11 +1211,11 @@ namespace smt {
}
}
}
else if (m_params.m_bv_enable_int2bv2int && m_util.is_bv2int(n)) {
else if (/*m_params.m_bv_enable_int2bv2int &&*/ m_util.is_bv2int(n)) {
ctx.mark_as_relevant(n->get_arg(0));
assert_bv2int_axiom(n);
}
else if (m_params.m_bv_enable_int2bv2int && m_util.is_int2bv(n)) {
else if (/*m_params.m_bv_enable_int2bv2int &&*/ m_util.is_int2bv(n)) {
ctx.mark_as_relevant(n->get_arg(0));
assert_int2bv_axiom(n);
}

2
src/tactic/arith/bv2int_rewriter.cpp
View file

@ -218,6 +218,7 @@ br_status bv2int_rewriter::mk_mod(expr * s, expr * t, expr_ref & result) {
if (is_bv2int(s, s1) && is_bv2int(t, t1)) {
align_sizes(s1, t1, false);
result = m_bv.mk_bv2int(m_bv.mk_bv_urem(s1, t1));
TRACE("bv2int_rewriter", tout << mk_pp(result,m()) << "\n";);
return BR_DONE;
}
@ -232,6 +233,7 @@ br_status bv2int_rewriter::mk_mod(expr * s, expr * t, expr_ref & result) {
u1 = mk_bv_add(s1, u1, false);
align_sizes(u1, t1, false);
result = m_bv.mk_bv2int(m_bv.mk_bv_urem(u1, t1));
TRACE("bv2int_rewriter", tout << mk_pp(result,m()) << "\n";);
return BR_DONE;
}