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z3/src/qe/qe_mbi.cpp
Nikolaj Bjorner 076cfa5813 working on revising project0 to project
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
2018-12-26 21:04:35 +08:00

688 lines
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C++

/*++
Copyright (c) 2018 Microsoft Corporation
Module Name:
qe_mbi.cpp
Abstract:
Model-based interpolation utilities
Author:
Nikolaj Bjorner (nbjorner), Arie Gurfinkel 2018-6-8
Revision History:
Notes:
Reduction into:
T_EUF
T_LIRA
Other theories: DT, ARR reduced to EUF
BV is EUF/Boolean.
--*/
#include "ast/ast_util.h"
#include "ast/for_each_expr.h"
#include "ast/rewriter/expr_safe_replace.h"
#include "ast/rewriter/bool_rewriter.h"
#include "ast/arith_decl_plugin.h"
#include "model/model_evaluator.h"
#include "solver/solver.h"
#include "qe/qe_mbi.h"
#include "qe/qe_term_graph.h"
#include "qe/qe_arith.h"
namespace qe {
lbool mbi_plugin::check(expr_ref_vector& lits, model_ref& mdl) {
while (true) {
switch ((*this)(lits, mdl)) {
case mbi_sat:
return l_true;
case mbi_unsat:
return l_false;
case mbi_undef:
return l_undef;
case mbi_augment:
break;
}
}
}
// -------------------------------
// prop_mbi
prop_mbi_plugin::prop_mbi_plugin(solver* s): mbi_plugin(s->get_manager()), m_solver(s) {}
// sketch of propositional
mbi_result prop_mbi_plugin::operator()(expr_ref_vector& lits, model_ref& mdl) {
lbool r = m_solver->check_sat(lits);
switch (r) {
case l_false:
lits.reset();
m_solver->get_unsat_core(lits);
return mbi_unsat;
case l_true:
m_solver->get_model(mdl);
lits.reset();
for (unsigned i = 0, sz = mdl->get_num_constants(); i < sz; ++i) {
func_decl* c = mdl->get_constant(i);
if (m_shared.contains(c)) {
if (m.is_true(mdl->get_const_interp(c))) {
lits.push_back(m.mk_const(c));
}
else if (m.is_false(mdl->get_const_interp(c))) {
lits.push_back(m.mk_not(m.mk_const(c)));
}
}
}
return mbi_sat;
default:
return mbi_undef;
}
}
void prop_mbi_plugin::block(expr_ref_vector const& lits) {
m_solver->assert_expr(mk_not(mk_and(lits)));
}
// -------------------------------
// euf_mbi
struct euf_mbi_plugin::is_atom_proc {
ast_manager& m;
expr_ref_vector& m_atoms;
is_atom_proc(expr_ref_vector& atoms): m(atoms.m()), m_atoms(atoms) {}
void operator()(app* a) {
if (m.is_eq(a)) {
m_atoms.push_back(a);
}
else if (m.is_bool(a) && a->get_family_id() != m.get_basic_family_id()) {
m_atoms.push_back(a);
}
}
void operator()(expr*) {}
};
euf_mbi_plugin::euf_mbi_plugin(solver* s, solver* sNot):
mbi_plugin(s->get_manager()),
m_atoms(m),
m_solver(s),
m_dual_solver(sNot) {
params_ref p;
p.set_bool("core.minimize", true);
m_solver->updt_params(p);
m_dual_solver->updt_params(p);
expr_ref_vector fmls(m);
m_solver->get_assertions(fmls);
expr_fast_mark1 marks;
is_atom_proc proc(m_atoms);
for (expr* e : fmls) {
quick_for_each_expr(proc, marks, e);
}
}
mbi_result euf_mbi_plugin::operator()(expr_ref_vector& lits, model_ref& mdl) {
lbool r = m_solver->check_sat(lits);
switch (r) {
case l_false:
lits.reset();
m_solver->get_unsat_core(lits);
// optionally minimize core using superposition.
return mbi_unsat;
case l_true: {
m_solver->get_model(mdl);
model_evaluator mev(*mdl.get());
lits.reset();
for (expr* e : m_atoms) {
if (mev.is_true(e)) {
lits.push_back(e);
}
else if (mev.is_false(e)) {
lits.push_back(m.mk_not(e));
}
}
TRACE("qe", tout << "atoms from model: " << lits << "\n";);
r = m_dual_solver->check_sat(lits);
expr_ref_vector core(m);
term_graph tg(m);
switch (r) {
case l_false:
// use the dual solver to find a 'small' implicant
m_dual_solver->get_unsat_core(core);
TRACE("qe", tout << "core: " << core << "\n";);
// project the implicant onto vars
tg.set_vars(m_shared, false);
tg.add_lits(core);
lits.reset();
lits.append(tg.project(*mdl));
TRACE("qe", tout << "project: " << lits << "\n";);
return mbi_sat;
case l_undef:
return mbi_undef;
case l_true:
UNREACHABLE();
return mbi_undef;
}
return mbi_sat;
}
default:
// TBD: if not running solver to completion, then:
// 1. extract unit literals from m_solver.
// 2. run a cc over the units
// 3. extract equalities or other assignments over the congruence classes
// 4. ensure that at least some progress is made over original lits.
return mbi_undef;
}
}
void euf_mbi_plugin::block(expr_ref_vector const& lits) {
m_solver->assert_expr(mk_not(mk_and(lits)));
}
// -------------------------------
// euf_arith_mbi
struct euf_arith_mbi_plugin::is_atom_proc {
ast_manager& m;
expr_ref_vector& m_atoms;
obj_hashtable<expr>& m_atom_set;
is_atom_proc(expr_ref_vector& atoms, obj_hashtable<expr>& atom_set):
m(atoms.m()), m_atoms(atoms), m_atom_set(atom_set) {}
void operator()(app* a) {
if (m_atom_set.contains(a)) {
// continue
}
else if (m.is_eq(a)) {
m_atoms.push_back(a);
m_atom_set.insert(a);
}
else if (m.is_bool(a) && a->get_family_id() != m.get_basic_family_id()) {
m_atoms.push_back(a);
m_atom_set.insert(a);
}
}
void operator()(expr*) {}
};
struct euf_arith_mbi_plugin::is_arith_var_proc {
ast_manager& m;
app_ref_vector& m_pvars;
app_ref_vector& m_svars;
arith_util arith;
obj_hashtable<func_decl> m_shared;
is_arith_var_proc(func_decl_ref_vector const& shared, app_ref_vector& pvars, app_ref_vector& svars):
m(pvars.m()), m_pvars(pvars), m_svars(svars), arith(m) {
for (func_decl* f : shared) m_shared.insert(f);
}
void operator()(app* a) {
if (!arith.is_int_real(a) || a->get_family_id() == arith.get_family_id()) {
// no-op
}
else if (m_shared.contains(a->get_decl())) {
m_svars.push_back(a);
}
else {
m_pvars.push_back(a);
}
}
void operator()(expr*) {}
};
euf_arith_mbi_plugin::euf_arith_mbi_plugin(solver* s, solver* sNot):
mbi_plugin(s->get_manager()),
m_atoms(m),
m_fmls(m),
m_solver(s),
m_dual_solver(sNot) {
params_ref p;
p.set_bool("core.minimize", true);
m_solver->updt_params(p);
m_dual_solver->updt_params(p);
m_solver->get_assertions(m_fmls);
collect_atoms(m_fmls);
}
void euf_arith_mbi_plugin::collect_atoms(expr_ref_vector const& fmls) {
expr_fast_mark1 marks;
is_atom_proc proc(m_atoms, m_atom_set);
for (expr* e : fmls) {
quick_for_each_expr(proc, marks, e);
}
}
bool euf_arith_mbi_plugin::get_literals(model_ref& mdl, expr_ref_vector& lits) {
lits.reset();
for (expr* e : m_atoms) {
if (mdl->is_true(e)) {
lits.push_back(e);
}
else if (mdl->is_false(e)) {
lits.push_back(m.mk_not(e));
}
}
TRACE("qe", tout << "atoms from model: " << lits << "\n";);
solver_ref dual = m_dual_solver->translate(m, m_dual_solver->get_params());
dual->assert_expr(mk_not(mk_and(m_fmls)));
lbool r = dual->check_sat(lits);
TRACE("qe", dual->display(tout << "dual result " << r << "\n"););
if (l_false == r) {
// use the dual solver to find a 'small' implicant
lits.reset();
dual->get_unsat_core(lits);
return true;
}
else {
return false;
}
}
app_ref_vector euf_arith_mbi_plugin::get_arith_vars(model_ref& mdl, expr_ref_vector& lits) {
arith_util a(m);
app_ref_vector pvars(m), svars(m); // private and shared arithmetic variables.
is_arith_var_proc _proc(m_shared, pvars, svars);
for_each_expr(_proc, lits);
rational v1, v2;
for (expr* p : pvars) {
VERIFY(a.is_numeral((*mdl)(p), v1));
for (expr* s : svars) {
VERIFY(a.is_numeral((*mdl)(s), v2));
if (v1 < v2) {
lits.push_back(a.mk_lt(p, s));
}
else if (v2 < v1) {
lits.push_back(a.mk_lt(s, p));
}
else {
lits.push_back(m.mk_eq(s, p));
}
}
}
return pvars;
}
mbi_result euf_arith_mbi_plugin::operator()(expr_ref_vector& lits, model_ref& mdl) {
lbool r = m_solver->check_sat(lits);
switch (r) {
case l_false:
lits.reset();
m_solver->get_unsat_core(lits);
TRACE("qe", tout << "unsat core: " << lits << "\n";);
// optionally minimize core using superposition.
return mbi_unsat;
case l_true: {
m_solver->get_model(mdl);
if (!get_literals(mdl, lits)) {
return mbi_undef;
}
project0(mdl, lits);
return mbi_sat;
}
default:
// TBD: if not running solver to completion, then:
// 1. extract unit literals from m_solver.
// 2. run a cc over the units
// 3. extract equalities or other assignments over the congruence classes
// 4. ensure that at least some progress is made over original lits.
return mbi_undef;
}
}
/**
1. extract arithmetical variables, purify.
2. project private variables from lits
3. Order arithmetical variables.
4. Perform arithmetical projection.
5. Substitute solution into lits
*/
void euf_arith_mbi_plugin::project(model_ref& mdl, expr_ref_vector& lits) {
TRACE("qe", tout << lits << "\n" << *mdl << "\n";);
// 1. arithmetical variables
app_ref_vector avars = get_arith_vars(mdl, lits);
TRACE("qe", tout << "vars: " << avars << " lits: " << lits << "\n";);
// 2. project private variables from lits
{
term_graph tg(m);
func_decl_ref_vector shared(m_shared);
for (app* a : avars) shared.push_back(a->get_decl());
tg.set_vars(shared, false);
tg.add_lits(lits);
lits.reset();
lits.append(tg.project(*mdl.get()));
TRACE("qe", tout << "project: " << lits << "\n";);
}
// 3. Order arithmetical variables
order_avars(mdl, lits, avars);
// 4. Arithmetical projection
arith_project_plugin ap(m);
ap.set_check_purified(false);
auto defs = ap.project(*mdl.get(), avars, lits);
// 5. Substitute solution
for (auto const& def : defs) {
expr_safe_replace rep(m);
rep.insert(def.var, def.term);
for (unsigned i = 0; i < lits.size(); ++i) {
expr_ref tmp(m);
rep(lits.get(i), tmp);
lits[i] = tmp;
}
}
}
void euf_arith_mbi_plugin::order_avars(model_ref& mdl, expr_ref_vector& lits, app_ref_vector& avars) {
arith_util a(m);
model_evaluator mev(*mdl.get());
vector<std::pair<rational, app*>> vals;
for (app* v : avars) {
rational val;
expr_ref tmp = mev(v);
VERIFY(a.is_numeral(tmp, val));
vals.push_back(std::make_pair(val, v));
}
struct compare_first {
bool operator()(std::pair<rational, app*> const& x,
std::pair<rational, app*> const& y) const {
return x.first < y.first;
}
};
// add linear order between avars
compare_first cmp;
std::sort(vals.begin(), vals.end(), cmp);
for (unsigned i = 1; i < vals.size(); ++i) {
if (vals[i-1].first == vals[i].first) {
lits.push_back(m.mk_eq(vals[i-1].second, vals[i].second));
}
else {
lits.push_back(a.mk_lt(vals[i-1].second, vals[i].second));
}
}
// sort avars based on depth
struct compare_depth {
bool operator()(app* x, app* y) const {
return x->get_depth() > y->get_depth();
}
};
compare_depth cmpd;
std::sort(avars.c_ptr(), avars.c_ptr() + avars.size(), cmpd);
TRACE("qe", tout << lits << "\navars:" << avars << "\n" << *mdl << "\n";);
}
void euf_arith_mbi_plugin::project0(model_ref& mdl, expr_ref_vector& lits) {
TRACE("qe", tout << lits << "\n" << *mdl << "\n";);
// 1. Extract projected variables, add inequalities between
// projected variables and non-projected terms according to model.
// 2. Extract disequalities implied by congruence closure.
// 3. project arithmetic variables from pure literals.
// 4. Add projected definitions as equalities to EUF.
// 5. project remaining literals with respect to EUF.
app_ref_vector avars = get_arith_vars(mdl, lits);
TRACE("qe", tout << "vars: " << avars << " lits: " << lits << "\n";);
// 2.
term_graph tg1(m);
func_decl_ref_vector no_shared(m);
tg1.set_vars(no_shared, false);
tg1.add_lits(lits);
arith_util a(m);
expr_ref_vector foreign = tg1.shared_occurrences(a.get_family_id());
obj_hashtable<expr> _foreign;
for (expr* e : foreign) _foreign.insert(e);
vector<expr_ref_vector> partition = tg1.get_partition(*mdl);
expr_ref_vector diseq = tg1.get_ackerman_disequalities();
lits.append(diseq);
TRACE("qe", tout << "diseq: " << diseq << "\n";
tout << "foreign: " << foreign << "\n";
for (auto const& v : partition) {
tout << "partition: {";
bool first = true;
for (expr* e : v) {
if (first) first = false; else tout << ", ";
tout << expr_ref(e, m);
}
tout << "}\n";
}
);
vector<expr_ref_vector> refined_partition;
for (auto & p : partition) {
unsigned j = 0;
for (expr* e : p) {
if (_foreign.contains(e) ||
(is_app(e) && m_shared.contains(to_app(e)->get_decl()))) {
p[j++] = e;
}
}
p.shrink(j);
if (!p.empty()) refined_partition.push_back(p);
}
TRACE("qe",
for (auto const& v : refined_partition) {
tout << "partition: {";
bool first = true;
for (expr* e : v) {
if (first) first = false; else tout << ", ";
tout << expr_ref(e, m);
}
tout << "}\n";
});
arith_project_plugin ap(m);
ap.set_check_purified(false);
// 3.
auto defs = ap.project(*mdl.get(), avars, lits);
// 4.
for (auto const& def : defs) {
lits.push_back(m.mk_eq(def.var, def.term));
}
TRACE("qe", tout << "# arith defs " << defs.size() << " avars: " << avars << " " << lits << "\n";);
// 5.
term_graph tg2(m);
tg2.set_vars(m_shared, false);
tg2.add_lits(lits);
lits.reset();
lits.append(tg2.project());
TRACE("qe", tout << "project: " << lits << "\n";);
}
void euf_arith_mbi_plugin::block(expr_ref_vector const& lits) {
collect_atoms(lits);
m_fmls.push_back(mk_not(mk_and(lits)));
m_solver->assert_expr(m_fmls.back());
}
/** --------------------------------------------------------------
* ping-pong interpolation of Gurfinkel & Vizel
* compute a binary interpolant.
*/
lbool interpolator::pingpong(mbi_plugin& a, mbi_plugin& b, expr_ref& itp) {
model_ref mdl;
expr_ref_vector lits(m);
bool turn = true;
vector<expr_ref_vector> itps, blocks;
itps.push_back(expr_ref_vector(m));
itps.push_back(expr_ref_vector(m));
blocks.push_back(expr_ref_vector(m));
blocks.push_back(expr_ref_vector(m));
mbi_result last_res = mbi_undef;
bool_rewriter rw(m);
while (true) {
auto* t1 = turn ? &a : &b;
auto* t2 = turn ? &b : &a;
mbi_result next_res = (*t1)(lits, mdl);
switch (next_res) {
case mbi_sat:
if (last_res == mbi_sat) {
itp = nullptr;
return l_true;
}
TRACE("mbi", tout << "new lits " << lits << "\n";);
break; // continue
case mbi_unsat: {
if (lits.empty()) {
// TBD, either a => itp and itp => !b
// or b => itp and itp => !a
itp = mk_and(itps[!turn]);
return l_false;
}
t2->block(lits);
expr_ref lemma(mk_not(mk_and(lits)));
TRACE("mbi", tout << lemma << "\n";);
blocks[turn].push_back(lemma);
itp = m.mk_implies(mk_and(blocks[!turn]), lemma);
// TBD: compute closure over variables not in vars
itps[turn].push_back(itp);
lits.reset(); // or find a prefix of lits?
break;
}
case mbi_augment:
break;
case mbi_undef:
return l_undef;
}
turn = !turn;
last_res = next_res;
}
}
/**
* One-sided pogo creates clausal interpolants.
* It creates a set of consequences of b that are inconsistent with a.
*/
lbool interpolator::pogo(mbi_plugin& a, mbi_plugin& b, expr_ref& itp) {
expr_ref_vector lits(m), itps(m);
while (true) {
model_ref mdl;
lits.reset();
switch (a.check(lits, mdl)) {
case l_true:
switch (b.check(lits, mdl)) {
case l_true:
return l_true;
case l_false:
a.block(lits);
itps.push_back(mk_not(mk_and(lits)));
break;
case l_undef:
return l_undef;
}
break;
case l_false:
itp = mk_and(itps);
return l_false;
case l_undef:
return l_undef;
}
}
}
lbool interpolator::vurtego(mbi_plugin& a, mbi_plugin& b, expr_ref& itp, model_ref &mdl) {
/**
Assumptions on mbi_plugin()
Let local be assertions local to the plugin
Let blocked be clauses added by blocked, kept separately from local
mbi_plugin::check(lits, mdl, bool force_model):
if lits.empty() and mdl == nullptr then
if is_sat(local & blocked) then
return l_true, mbp of local, mdl of local & blocked
else
return l_false
else if !lits.empty() then
if is_sat(local & mdl & blocked)
return l_true, lits, extension of mdl to local
else if is_sat(local & lits & blocked)
if (force_model) then
return l_false, core of model, nullptr
else
return l_true, mbp of local, mdl of local & blocked
else if !is_sat(local & lits) then
return l_false, mbp of local, nullptr
else if is_sat(local & lits) && !is_sat(local & lits & blocked)
MISSING CASE
MUST PRODUCE AN IMPLICANT OF LOCAL that is inconsistent with lits & blocked
in this case !is_sat(local & lits & mdl) and is_sat(mdl, blocked)
let mdl_blocked be lits of blocked that are true in mdl
return l_false, core of lits & mdl_blocked, nullptr
mbi_plugin::block(phi): add phi to blocked
probably should use the operator() instead of check.
mbi_augment -- means consistent with lits but not with the mdl
mbi_sat -- means consistent with lits and mdl
*/
expr_ref_vector lits(m), itps(m);
while (true) {
// when lits.empty(), this picks an A-implicant consistent with B
// when !lits.empty(), checks whether mdl of shared vocab extends to A
bool force_model = !lits.empty();
switch (a.check_ag(lits, mdl, force_model)) {
case l_true:
if (force_model)
// mdl is a model for a && b
return l_true;
switch (b.check_ag(lits, mdl, false)) {
case l_true:
/* can return true if know that b did not change
the model. For now, cycle back to A. */
SASSERT(!lits.empty());
SASSERT(mdl);
break;
case l_false:
// Force a different A-implicant
a.block(lits);
lits.reset();
mdl.reset();
break;
case l_undef:
return l_undef;
}
case l_false:
if (lits.empty()) {
// no more A-implicants, terminate
itp = mk_and(itps);
return l_false;
}
// force B to pick a different model or a different implicant
b.block(lits);
itps.push_back(mk_not(mk_and(lits)));
lits.reset();
mdl.reset();
break;
case l_undef:
return l_undef;
}
}
}
};