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#2379 and #2380

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2019-07-04 06:20:24 +07:00
parent 1517ca907e
commit 8e2ad4e461
7 changed files with 68 additions and 25 deletions
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42
src/qe/nlqsat.cpp
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@ -86,6 +86,7 @@ namespace qe {
nlsat::literal_vector m_assumptions;
u_map<expr*> m_asm2fml;
expr_ref_vector m_trail;
app_ref m_delta0, m_delta1;
lbool check_sat() {
while (true) {
@ -511,6 +512,20 @@ namespace qe {
bool has_divs() const { return m_has_divs; }
};
/*
Ackermanize division
For each p/q:
p = 0 & q = 0 => div = delta0
p != 0 & q = 0 => div = p*delta1
q != 0 => div*q = p
delta0 stands for 0/0
delta1 stands for 1/0
assumption: p * 1/0 = p/0 for p != 0,
so 2/0 != a * 1/0 & a = 2 is unsat by fiat.
*/
void purify(expr_ref& fml, div_rewriter_star& rw, expr_ref_vector& paxioms) {
is_pure_proc is_pure(*this);
{
@ -520,14 +535,16 @@ namespace qe {
if (is_pure.has_divs()) {
arith_util arith(m);
proof_ref pr(m);
TRACE("qe", tout << fml << "\n";);
rw(fml, fml, pr);
TRACE("qe", tout << fml << "\n";);
m_delta0 = m.mk_fresh_const("delta0", arith.mk_real());
m_delta1 = m.mk_fresh_const("delta1", arith.mk_real());
vector<div> const& divs = rw.divs();
for (unsigned i = 0; i < divs.size(); ++i) {
paxioms.push_back(
m.mk_or(m.mk_eq(divs[i].den, arith.mk_numeral(rational(0), false)),
m.mk_eq(divs[i].num, arith.mk_mul(divs[i].den, divs[i].name))));
expr_ref den_is0(m.mk_eq(divs[i].den, arith.mk_real(0)), m);
expr_ref num_is0(m.mk_eq(divs[i].num, arith.mk_real(0)), m);
paxioms.push_back(m.mk_or(den_is0, m.mk_eq(divs[i].num, arith.mk_mul(divs[i].den, divs[i].name))));
paxioms.push_back(m.mk_or(m.mk_not(den_is0), m.mk_not(num_is0), m.mk_eq(divs[i].name, m_delta0)));
paxioms.push_back(m.mk_or(m.mk_not(den_is0), num_is0, m.mk_eq(divs[i].name, arith.mk_mul(divs[i].num, m_delta1))));
for (unsigned j = i + 1; j < divs.size(); ++j) {
paxioms.push_back(m.mk_or(m.mk_not(m.mk_eq(divs[i].den, divs[j].den)),
m.mk_not(m.mk_eq(divs[i].num, divs[j].num)),
@ -546,6 +563,8 @@ namespace qe {
return;
}
expr_ref ante = mk_and(paxioms);
qvars[0].push_back(m_delta0);
qvars[0].push_back(m_delta1);
for (div const& d : rw.divs()) {
qvars[qvars.size()-2].push_back(d.name);
}
@ -555,6 +574,7 @@ namespace qe {
else {
fml = m.mk_and(fml, ante);
}
TRACE("qe", tout << fml << "\n";);
}
@ -675,6 +695,7 @@ namespace qe {
if (m_a2b.is_var(v)) {
SASSERT(m.is_bool(v));
nlsat::bool_var b = m_a2b.to_var(v);
TRACE("qe", tout << mk_pp(v, m) << " |-> b" << b << "\n";);
m_bound_bvars.back().push_back(b);
set_level(b, lvl);
}
@ -703,14 +724,13 @@ namespace qe {
}
void init_expr2var(vector<app_ref_vector> const& qvars) {
for (unsigned i = 0; i < qvars.size(); ++i) {
init_expr2var(qvars[i]);
for (app_ref_vector const& qvs : qvars) {
init_expr2var(qvs);
}
}
void init_expr2var(app_ref_vector const& qvars) {
for (unsigned i = 0; i < qvars.size(); ++i) {
app* v = qvars[i];
for (app* v : qvars) {
if (m.is_bool(v)) {
m_a2b.insert(v, m_solver.mk_bool_var());
}
@ -784,7 +804,9 @@ namespace qe {
m_cancel(false),
m_answer(m),
m_answer_simplify(m),
m_trail(m)
m_trail(m),
m_delta0(m),
m_delta1(m)
{
m_solver.get_explain().set_signed_project(true);
m_nftactic = mk_tseitin_cnf_tactic(m);