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experiment with arithmetic core generalizers

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2013-02-07 19:21:52 -08:00
parent 23c5c94311
commit 2e2fa84d40
5 changed files with 195 additions and 2 deletions
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159
src/muz_qe/pdr_generalizers.cpp
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@ -28,7 +28,9 @@ Revision History:
namespace pdr {
//
// ------------------------
// core_bool_inductive_generalizer
// main propositional induction generalizer.
// drop literals one by one from the core and check if the core is still inductive.
//
@ -97,6 +99,9 @@ namespace pdr {
}
}
// ------------------------
// core_farkas_generalizer
//
// for each disjunct of core:
// weaken predecessor.
@ -142,6 +147,158 @@ namespace pdr {
}
// -----------------------------
// core_arith_inductive_generalizer
core_arith_inductive_generalizer::core_arith_inductive_generalizer(context& ctx):
core_generalizer(ctx),
m(ctx.get_manager()),
a(m),
m_refs(m) {}
void core_arith_inductive_generalizer::operator()(model_node& n, expr_ref_vector& core, bool& uses_level) {
if (core.size() <= 1) {
return;
}
reset();
expr_ref e(m), t1(m), t2(m), t3(m);
rational r;
TRACE("pdr", for (unsigned i = 0; i < core.size(); ++i) { tout << mk_pp(core[i].get(), m) << "\n"; });
svector<eq> eqs;
get_eqs(core, eqs);
for (unsigned eq = 0; eq < eqs.size(); ++eq) {
rational r = eqs[eq].m_value;
expr* x = eqs[eq].m_term;
unsigned k = eqs[eq].m_i;
unsigned l = eqs[eq].m_j;
expr_ref_vector new_core(m);
for (unsigned i = 0; i < core.size(); ++i) {
if (i == k || k == l) {
new_core.push_back(m.mk_true());
}
else {
if (!substitute_alias(r, x, core[i].get(), e)) {
e = core[i].get();
}
new_core.push_back(e);
}
}
if (abs(r) >= rational(2) && a.is_int(x)) {
new_core[k] = m.mk_eq(a.mk_mod(x, a.mk_numeral(abs(r), true)), a.mk_numeral(rational(0), true));
new_core[l] = a.mk_ge(x, a.mk_numeral(r, true));
}
bool inductive = n.pt().check_inductive(n.level(), new_core, uses_level);
IF_VERBOSE(1,
verbose_stream() << (inductive?"":"non") << "inductive\n";
for (unsigned j = 0; j < new_core.size(); ++j) {
verbose_stream() << mk_pp(new_core[j].get(), m) << "\n";
});
if (inductive) {
core.reset();
core.append(new_core);
}
}
}
void core_arith_inductive_generalizer::insert_bound(bool is_lower, expr* x, rational const& r, unsigned i) {
if (r.is_neg()) {
expr_ref e(m);
e = a.mk_uminus(x);
m_refs.push_back(e);
x = e;
is_lower = !is_lower;
}
if (is_lower) {
m_lb.insert(abs(r), std::make_pair(x, i));
}
else {
m_ub.insert(abs(r), std::make_pair(x, i));
}
}
void core_arith_inductive_generalizer::reset() {
m_refs.reset();
m_lb.reset();
m_ub.reset();
}
void core_arith_inductive_generalizer::get_eqs(expr_ref_vector const& core, svector<eq>& eqs) {
expr* e1, *x, *y;
expr_ref e(m);
rational r;
for (unsigned i = 0; i < core.size(); ++i) {
e = core[i];
if (m.is_not(e, e1) && a.is_le(e1, x, y) && a.is_numeral(y, r) && a.is_int(x)) {
// not (<= x r) <=> x >= r + 1
insert_bound(true, x, r + rational(1), i);
}
else if (m.is_not(e, e1) && a.is_ge(e1, x, y) && a.is_numeral(y, r) && a.is_int(x)) {
// not (>= x r) <=> x <= r - 1
insert_bound(false, x, r - rational(1), i);
}
else if (a.is_le(e, x, y) && a.is_numeral(y, r)) {
insert_bound(false, x, r, i);
}
else if (a.is_ge(e, x, y) && a.is_numeral(y, r)) {
insert_bound(true, x, r, i);
}
}
bounds_t::iterator it = m_lb.begin(), end = m_lb.end();
for (; it != end; ++it) {
rational r = it->m_key;
vector<term_loc_t> & terms1 = it->m_value;
vector<term_loc_t> terms2;
if (r >= rational(2) && m_ub.find(r, terms2)) {
bool done = false;
for (unsigned i = 0; !done && i < terms1.size(); ++i) {
for (unsigned j = 0; !done && j < terms2.size(); ++j) {
expr* t1 = terms1[i].first;
expr* t2 = terms2[j].first;
if (t1 == t2) {
eqs.push_back(eq(t1, r, terms1[i].second, terms2[j].second));
done = true;
}
else {
e = m.mk_eq(t1, t2);
th_rewriter rw(m);
rw(e);
if (m.is_true(e)) {
eqs.push_back(eq(t1, r, terms1[i].second, terms2[j].second));
done = true;
}
}
}
}
}
}
}
bool core_arith_inductive_generalizer::substitute_alias(rational const& r, expr* x, expr* e, expr_ref& result) {
rational r2;
expr* y, *z, *e1;
if (m.is_not(e, e1) && substitute_alias(r, x, e1, result)) {
result = m.mk_not(result);
return true;
}
if (a.is_le(e, y, z) && a.is_numeral(z, r2) && r == r2) {
result = a.mk_le(y, x);
return true;
}
if (a.is_ge(e, y, z) && a.is_numeral(z, r2) && r == r2) {
result = a.mk_ge(y, x);
return true;
}
return false;
}
//