double nlopt_eval_enode(const double* x, void * extra) {
auto extra_info = static_cast<tuple<Enode *, box const &, bool> *>(extra);
Enode * e = get<0>(*extra_info);
box const & b = get<1>(*extra_info);
bool const polarity = get<2>(*extra_info);
unordered_map<Enode *, double> var_map;
unsigned i = 0;
for (Enode * e : b.get_vars()) {
if (e->isForallVar()) {
var_map.emplace(e, x[i]);
i++;
} else {
var_map.emplace(e, b[e].mid());
}
}
try {
double const ret1 = eval_enode(e->get1st(), var_map);
double const ret2 = eval_enode(e->get2nd(), var_map);
double ret = 0;
if (e->isLt() || e->isLeq() || e->isEq()) {
ret = ret1 - ret2;
} else if (e->isGt() || e->isGeq()) {
ret = ret2 - ret1;
} else if (e->isEq()) {
throw runtime_error("nlopt_obj: something is wrong.");
}
if (!polarity) {
ret = - ret;
}
return ret;
} catch (exception & e) {
DREAL_LOG_FATAL << "Exception in nlopt_eval_enode: " << e.what() << endl;
throw e;
}
}
box refine_CE_with_nlopt_core(box counterexample, vector<Enode*> const & opt_ctrs, vector<Enode*> const & side_ctrs) {
// Plug-in `a` into the constraint and optimize `b` in the counterexample `M` by solving:
//
// ∃ y_opt ∈ I_y. ∀ y ∈ I_y. f(a, y_opt) >= f(a, y) — (2)
//
// using local optimizer (i.e. nlopt).
// Let `M’ = (a, b_opt)` be a model for (2).
DREAL_LOG_DEBUG << "================================" << endl;
DREAL_LOG_DEBUG << " Before Refinement " << endl;
DREAL_LOG_DEBUG << "================================" << endl;
DREAL_LOG_DEBUG << counterexample << endl;
DREAL_LOG_DEBUG << "================================" << endl;
static bool initialized = false;
static vector<double> lb, ub, init;
init.clear();
for (Enode * e : counterexample.get_vars()) {
if (e->isForallVar()) {
if (!initialized) {
lb.push_back(e->getDomainLowerBound());
ub.push_back(e->getDomainUpperBound());
}
init.push_back(counterexample[e].mid());
DREAL_LOG_DEBUG << lb.back() << " <= " << init.back() << " <= " << ub.back() << endl;
}
}
auto const n = init.size();
static nlopt::opt opt(nlopt::LD_SLSQP, n);
if (!initialized) {
opt.set_lower_bounds(lb);
opt.set_upper_bounds(ub);
// set tollerance
// TODO(soonhok): set precision
// opt.set_xtol_rel(0.0001);
opt.set_xtol_abs(0.001);
opt.set_maxtime(0.01);
initialized = true;
}
opt.remove_equality_constraints();
opt.remove_inequality_constraints();
// set objective function
vector<tuple<Enode *, box const &, bool> *> extra_vec;
Enode * e = opt_ctrs[0];
bool polarity = false;
while (e->isNot()) {
e = e->get1st();
polarity = !polarity;
}
auto extra = new tuple<Enode *, box const &, bool>(e, counterexample, polarity);
extra_vec.push_back(extra);
opt.set_min_objective(nlopt_obj, extra);
opt.add_inequality_constraint(nlopt_side_condition, extra);
DREAL_LOG_DEBUG << "objective function is added: " << e << endl;
// set side conditions
for (Enode * e : side_ctrs) {
bool polarity = false;
while (e->isNot()) {
e = e->get1st();
polarity = !polarity;
}
auto extra = new tuple<Enode *, box const &, bool>(e, counterexample, polarity);
extra_vec.push_back(extra);
DREAL_LOG_DEBUG << "refine_counterexample_with_nlopt: Side condition is added: " << e << endl;
if (e->isEq()) {
opt.add_equality_constraint(nlopt_side_condition, extra);
} else if (e->isLt() || e->isLeq() || e->isGt() || e->isGeq()) {
opt.add_inequality_constraint(nlopt_side_condition, extra);
}
}
try {
vector<double> output = opt.optimize(init);
unsigned i = 0;
for (Enode * e : counterexample.get_vars()) {
if (e->isForallVar()) {
counterexample[e] = output[i];
i++;
}
}
} catch (nlopt::roundoff_limited & e) {
} catch (std::runtime_error & e) {
DREAL_LOG_DEBUG << e.what() << endl;
}
for (auto extra : extra_vec) {
delete extra;
}
DREAL_LOG_DEBUG << "================================" << endl;
DREAL_LOG_DEBUG << " After Refinement " << endl;
DREAL_LOG_DEBUG << "================================" << endl;
DREAL_LOG_DEBUG << counterexample << endl;
DREAL_LOG_DEBUG << "================================" << endl;
return counterexample;
}
Enode * Egraph::canonizeDTC( Enode * formula, bool split_eqs )
{
assert( config.sat_lazy_dtc != 0 );
assert( config.logic == QF_UFLRA
|| config.logic == QF_UFIDL );
list< Enode * > dtc_axioms;
vector< Enode * > unprocessed_enodes;
initDupMap1( );
unprocessed_enodes.push_back( formula );
//
// Visit the DAG of the formula from the leaves to the root
//
while( !unprocessed_enodes.empty( ) )
{
Enode * enode = unprocessed_enodes.back( );
//
// Skip if the node has already been processed before
//
if ( valDupMap1( enode ) != NULL )
{
unprocessed_enodes.pop_back( );
continue;
}
bool unprocessed_children = false;
Enode * arg_list;
for ( arg_list = enode->getCdr( )
; arg_list != enil
; arg_list = arg_list->getCdr( ) )
{
Enode * arg = arg_list->getCar( );
assert( arg->isTerm( ) );
//
// Push only if it is unprocessed
//
if ( valDupMap1( arg ) == NULL )
{
unprocessed_enodes.push_back( arg );
unprocessed_children = true;
}
}
//
// SKip if unprocessed_children
//
if ( unprocessed_children )
continue;
unprocessed_enodes.pop_back( );
Enode * result = NULL;
//
// Replace arithmetic atoms with canonized version
//
if ( enode->isTAtom( )
&& !enode->isUp( ) )
{
// No need to do anything if node is purely UF
if ( isRootUF( enode ) )
{
if ( config.verbosity > 2 )
cerr << "# Egraph::Skipping canonization of " << enode << " as it's root is purely UF" << endl;
result = enode;
}
else
{
LAExpression a( enode );
result = a.toEnode( *this );
#ifdef PRODUCE_PROOF
const uint64_t partitions = getIPartitions( enode );
assert( partitions != 0 );
setIPartitions( result, partitions );
#endif
if ( split_eqs && result->isEq( ) )
{
#ifdef PRODUCE_PROOF
if ( config.produce_inter > 0 )
opensmt_error2( "can't compute interpolant for equalities at the moment ", enode );
#endif
LAExpression aa( enode );
Enode * e = aa.toEnode( *this );
#ifdef PRODUCE_PROOF
assert( partitions != 0 );
setIPartitions( e, partitions );
#endif
Enode * lhs = e->get1st( );
Enode * rhs = e->get2nd( );
Enode * leq = mkLeq( cons( lhs, cons( rhs ) ) );
LAExpression b( leq );
leq = b.toEnode( *this );
#ifdef PRODUCE_PROOF
assert( partitions != 0 );
setIPartitions( leq, partitions );
#endif
Enode * geq = mkGeq( cons( lhs, cons( rhs ) ) );
LAExpression c( geq );
geq = c.toEnode( *this );
#ifdef PRODUCE_PROOF
assert( partitions != 0 );
setIPartitions( geq, partitions );
#endif
Enode * not_e = mkNot( cons( enode ) );
Enode * not_l = mkNot( cons( leq ) );
Enode * not_g = mkNot( cons( geq ) );
// Add clause ( !x=y v x<=y )
Enode * c1 = mkOr( cons( not_e
, cons( leq ) ) );
// Add clause ( !x=y v x>=y )
Enode * c2 = mkOr( cons( not_e
, cons( geq ) ) );
// Add clause ( x=y v !x>=y v !x<=y )
Enode * c3 = mkOr( cons( enode
, cons( not_l
, cons( not_g ) ) ) );
// Add conjunction of clauses
Enode * ax = mkAnd( cons( c1
, cons( c2
, cons( c3 ) ) ) );
dtc_axioms.push_back( ax );
result = enode;
}
}
}
//
// If nothing have been done copy and simplify
//
if ( result == NULL )
result = copyEnodeEtypeTermWithCache( enode );
assert( valDupMap1( enode ) == NULL );
storeDupMap1( enode, result );
#ifdef PRODUCE_PROOF
if ( config.produce_inter > 0 )
{
// Setting partitions for result
setIPartitions( result, getIPartitions( enode ) );
// Setting partitions for negation as well occ if atom
if ( result->hasSortBool( ) )
{
setIPartitions( mkNot( cons( result ) )
, getIPartitions( enode ) );
}
}
#endif
}
Enode * new_formula = valDupMap1( formula );
assert( new_formula );
doneDupMap1( );
if ( !dtc_axioms.empty( ) )
{
dtc_axioms.push_back( new_formula );
new_formula = mkAnd( cons( dtc_axioms ) );
}
return new_formula;
}