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;
}
}
void nlopt_fill_gradient(const double * x, double * grad, 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;
vector<Enode*> forall_var_vec;
for (Enode * e : b.get_vars()) {
if (e->isForallVar()) {
var_map.emplace(e, x[i]);
i++;
forall_var_vec.push_back(e);
} else {
var_map.emplace(e, b[e].mid());
}
}
i = 0;
for (Enode * var : forall_var_vec) {
double deriv_i = deriv_enode(e->get1st(), var, var_map) - deriv_enode(e->get2nd(), var, var_map);
if (e->isGt() || e->isGeq()) {
deriv_i = - deriv_i;
}
if (!polarity) {
deriv_i = - deriv_i;
}
grad[i] = deriv_i;
i++;
}
}
// ∀a, i, b, j. ( a = b → i = j → W (a, i, R(b, j)) = a )
void Egraph::WoRAxiom( Enode * wor )
{
assert( false );
Enode * a = wor->get1st( );
Enode * i = wor->get2nd( );
Enode * worElement = wor->get3rd( );
Enode * b = worElement->get1st( );
Enode * j = worElement->get2nd( );
assert( worElement->isDTypeArrayElement( ) );
assert( a->isDTypeArray( ) );
assert( i->isDTypeArrayIndex( ) );
assert( b->isDTypeArray( ) );
assert( j->isDTypeArrayIndex( ) );
// create term W(a,i,R(b,j))
Enode * select = mkSelect( b, j );
Enode * store = mkStore(a,i,select);
// add clause IF a=b THEN IF i=j THEN W(a,i,R(b,j))=a
// that is (NOT(a=b) OR NOT(i=j) OR W(a,i,R(b,j))=a)
vector< Enode * > v;
Enode * lit1 = mkNot(cons(mkEq(cons(a,cons(b)))));
Enode * lit2 = mkNot(cons(mkEq(cons(i,cons(j)))));
Enode * lit3 = mkEq(cons(store,cons(a)));
v.push_back( lit1 );
v.push_back( lit2 );
v.push_back( lit3 );
#ifdef ARR_VERB
cout << "Axiom WoR -> " << "(or " << lit1 << " " << lit2 << " " << lit3 << " )" << endl;
#endif
splitOnDemand( v, id );
handleArrayAssertedAtomTerm( a );
}
void SimpSMTSolver::getDLVars( Enode * e, bool negate, Enode ** x, Enode ** y )
{
assert( config.sat_preprocess_theory != 0 );
assert( e->isLeq( ) );
Enode * lhs = e->get1st( );
Enode * rhs = e->get2nd( );
(void)rhs;
assert( lhs->isMinus( ) );
assert( rhs->isConstant( ) || ( rhs->isUminus( ) && rhs->get1st( )->isConstant( ) ) );
*x = lhs->get1st( );
*y = lhs->get2nd( );
if ( negate )
{
Enode *tmp = *x;
*x = *y;
*y = tmp;
}
}
//∀a, i, e, j, f i != j → W (W (a, i, e), j, f ) = W (W (a, j, f ), i, e)
void Egraph::WoWNeqAxiom( Enode * wow )
{
assert( false );
Enode * wowArray = wow->get1st( );
Enode * a = wowArray->get1st( );
Enode * i = wowArray->get2nd( );
Enode * e = wowArray->get3rd( );
Enode * j = wow->get2nd( );
Enode * f = wow->get3rd( );
assert( wowArray->isDTypeArray( ) );
assert( a->isDTypeArray( ) );
assert( i->isDTypeArrayIndex( ) );
assert( e->isDTypeArrayElement( ) );
assert( j->isDTypeArrayIndex( ) );
assert( f->isDTypeArrayElement( ) );
// Case i, j not coincident
if( i != j )
{
// create term W(W(a,j,f),i,e)
Enode * store1 = mkStore(a,j,f);
Enode * store2 = mkStore(store1,i,e);
// add clause IF i!=j THEN W(W(a,i,e),j,f)=W(W(a,j,f),i,e)
// that is (i=j OR W(W(a,i,e),j,f)=W(W(a,j,f),i,e))
vector< Enode * > v;
Enode * lit1 = mkEq(cons(i,cons(j)));
Enode * lit2 = mkEq(cons(wow,cons(store2)));
v.push_back( lit1 );
v.push_back( lit2 );
#ifdef ARR_VERB
cout << "Axiom WoW!= -> " << "(or " << lit1 << " " << lit2 << " )" << endl;
#endif
splitOnDemand( v, id );
handleArrayAssertedAtomTerm(store2);
}
}
map<Enode *, bool> CoreSMTSolver::getBoolModel() {
map<Enode *, bool> ret;
for (int i = 0; i < trail.size(); i++) {
Lit const & l = trail[i];
Var const v = var(l);
if (v >= 2) {
Enode * e = theory_handler->varToEnode(v);
bool p = value(l) == l_True;
if (e->isNot()) {
e = e->get1st();
p = !p;
}
if (e->isVar()) {
if (sign(l)) {
p = !p;
}
ret.emplace(e, p);
}
}
}
return ret;
}
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;
}
// ∀a, i, e, j, f. ( i = j → W ( W ( a, i, e ), j, f ) = W ( a, j, f ) )
void Egraph::WoWEqAxiom( Enode * wow )
{
assert( false );
Enode * wowArray = wow->get1st( );
Enode * a = wowArray->get1st( );
Enode * i = wowArray->get2nd( );
Enode * e = wowArray->get3rd( );
Enode * j = wow->get2nd( );
Enode * f = wow->get3rd( );
assert( wowArray->isDTypeArray( ) );
assert( a->isDTypeArray( ) );
assert( i->isDTypeArrayIndex( ) );
assert( e->isDTypeArrayElement( ) );
assert( j->isDTypeArrayIndex( ) );
assert( f->isDTypeArrayElement( ) );
//i,j not coincident
if( i != j )
{
// create term W(a,j,f)
Enode * store = mkStore( a, j, f );
#ifdef PRODUCE_PROOF
if ( config.gconfig.print_inter > 0 )
{
const uint64_t shared = getIPartitions( a )
& getIPartitions( j )
& getIPartitions( f );
// Mixed can't be one at this point
assert( shared != 1 );
// Set AB-mixed partition if no intersection
if ( shared == 0 )
setIPartitions( store, 1 );
// Otherwise they share something
else
setIPartitions( store, shared );
}
#endif
// add clause IF i=j THEN W(W(a,i,e),j,f)=W(a,j,f)
// that is (NOT(i=j) OR W(W(a,i,e),j,f)=W(a,j,f))
vector< Enode * > v;
Enode * lit1_pos = mkEq( cons( i, cons( j ) ) );
Enode * lit1 = mkNot( cons( lit1_pos ) );
#ifdef PRODUCE_PROOF
if ( config.gconfig.print_inter > 0 )
{
const uint64_t shared = getIPartitions( i )
& getIPartitions( j );
// Mixed can't be one at this point
assert( shared != 1 );
// Set AB-mixed partition if no intersection
if ( shared == 0 )
{
setIPartitions( lit1_pos, 1 );
setIPartitions( lit1, 1 );
}
// Otherwise they share something
else
{
setIPartitions( lit1_pos, shared );
setIPartitions( lit1, shared );
}
}
#endif
Enode * lit2 = mkEq( cons( wow, cons( store ) ) );
#ifdef PRODUCE_PROOF
if ( config.gconfig.print_inter > 0 )
{
const uint64_t shared = getIPartitions( wow )
& getIPartitions( store );
// Mixed can't be one at this point
assert( shared != 1 );
// Set AB-mixed partition if no intersection
if ( shared == 0 )
setIPartitions( lit2, 1 );
// Otherwise they share something
else
setIPartitions( lit2, shared );
}
#endif
v.push_back( lit1 );
v.push_back( lit2 );
#ifdef ARR_VERB
cout << "Axiom WoW= -> " << "(or " << lit1 << " " << lit2 << " )" << endl;
#endif
splitOnDemand( v, id );
handleArrayAssertedAtomTerm( store );
}
}
Enode *
ExpandITEs::doit( Enode * formula )
{
assert( formula );
list< Enode * > new_clauses;
vector< Enode * > unprocessed_enodes;
egraph.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 ( egraph.valDupMap1( enode ) != NULL )
{
unprocessed_enodes.pop_back( );
continue;
}
bool unprocessed_children = false;
Enode * arg_list;
for ( arg_list = enode->getCdr( ) ;
arg_list != egraph.enil ;
arg_list = arg_list->getCdr( ) )
{
Enode * arg = arg_list->getCar( );
assert( arg->isTerm( ) );
//
// Push only if it is unprocessed
//
if ( egraph.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;
//
// At this point, every child has been processed
//
char def_name[ 32 ];
if ( enode->isIte( ) )
{
//
// Retrieve arguments
//
Enode * i = egraph.valDupMap1( enode->get1st( ) );
Enode * t = egraph.valDupMap1( enode->get2nd( ) );
Enode * e = egraph.valDupMap1( enode->get3rd( ) );
Enode * not_i = egraph.mkNot( egraph.cons( i ) );
//
// Generate variable symbol
//
sprintf( def_name, ITE_STR, enode->getId( ) );
Snode * sort = enode->getLastSort( );
egraph.newSymbol( def_name, sort );
//
// Generate placeholder
//
result = egraph.mkVar( def_name );
//
// Generate additional clauses
//
Enode * eq_then = egraph.mkEq( egraph.cons( result
, egraph.cons( t ) ) );
Enode * eq_else = egraph.mkEq( egraph.cons( result
, egraph.cons( e ) ) );
new_clauses.push_back( egraph.mkOr( egraph.cons( not_i
, egraph.cons( eq_then ) ) ) );
new_clauses.push_back( egraph.mkOr( egraph.cons( i
, egraph.cons( eq_else ) ) ) );
}
else
{
result = egraph.copyEnodeEtypeTermWithCache( enode );
}
assert( result );
assert( egraph.valDupMap1( enode ) == NULL );
egraph.storeDupMap1( enode, result );
}
Enode * new_formula = egraph.valDupMap1( formula );
assert( new_formula );
egraph.doneDupMap1( );
new_clauses.push_back( new_formula );
return egraph.mkAnd( egraph.cons( new_clauses ) );
}
double eval_enode(Enode * const e, unordered_map<Enode*, double> const & var_map) {
if (e->isVar()) {
auto const it = var_map.find(e);
if (it == var_map.cend()) {
throw runtime_error("variable not found");
} else {
// Variable is found in var_map
return it->second;
}
} else if (e->isConstant()) {
double const v = e->getValue();
return v;
} else if (e->isSymb()) {
throw runtime_error("eval_enode: Symb");
} else if (e->isNumb()) {
throw runtime_error("eval_enode: Numb");
} else if (e->isTerm()) {
assert(e->getArity() >= 1);
enodeid_t id = e->getCar()->getId();
double ret = 0.0;
Enode * tmp = e;
switch (id) {
case ENODE_ID_PLUS:
ret = eval_enode(tmp->get1st(), var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret + eval_enode(tmp->getCar(), var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_MINUS:
ret = eval_enode(tmp->get1st(), var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret - eval_enode(tmp->getCar(), var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_UMINUS:
ret = eval_enode(tmp->get1st(), var_map);
assert(tmp->getArity() == 1);
return (- ret);
case ENODE_ID_TIMES:
ret = eval_enode(tmp->get1st(), var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret * eval_enode(tmp->getCar(), var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_DIV:
ret = eval_enode(tmp->get1st(), var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret / eval_enode(tmp->getCar(), var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_ACOS:
assert(e->getArity() == 1);
return acos(eval_enode(e->get1st(), var_map));
case ENODE_ID_ASIN:
assert(e->getArity() == 1);
return asin(eval_enode(e->get1st(), var_map));
case ENODE_ID_ATAN:
assert(e->getArity() == 1);
return atan(eval_enode(e->get1st(), var_map));
case ENODE_ID_ATAN2:
assert(e->getArity() == 2);
return atan2(eval_enode(e->get1st(), var_map),
eval_enode(e->get2nd(), var_map));
case ENODE_ID_MIN:
assert(e->getArity() == 2);
return fmin(eval_enode(e->get1st(), var_map),
eval_enode(e->get2nd(), var_map));
case ENODE_ID_MAX:
assert(e->getArity() == 2);
return fmax(eval_enode(e->get1st(), var_map),
eval_enode(e->get2nd(), var_map));
case ENODE_ID_MATAN:
assert(e->getArity() == 1);
throw runtime_error("eval_enode: MATAN");
case ENODE_ID_SAFESQRT:
assert(e->getArity() == 1);
throw runtime_error("eval_enode: SAFESQRT");
case ENODE_ID_SQRT:
assert(e->getArity() == 1);
return sqrt(eval_enode(e->get1st(), var_map));
case ENODE_ID_EXP:
assert(e->getArity() == 1);
return exp(eval_enode(e->get1st(), var_map));
case ENODE_ID_LOG:
assert(e->getArity() == 1);
return log(eval_enode(e->get1st(), var_map));
case ENODE_ID_POW:
assert(e->getArity() == 2);
return pow(eval_enode(e->get1st(), var_map),
eval_enode(e->get2nd(), var_map));
case ENODE_ID_ABS:
assert(e->getArity() == 1);
return fabs(eval_enode(e->get1st(), var_map));
case ENODE_ID_SIN:
assert(e->getArity() == 1);
return sin(eval_enode(e->get1st(), var_map));
case ENODE_ID_COS:
assert(e->getArity() == 1);
return cos(eval_enode(e->get1st(), var_map));
case ENODE_ID_TAN:
assert(e->getArity() == 1);
return tan(eval_enode(e->get1st(), var_map));
case ENODE_ID_SINH:
assert(e->getArity() == 1);
return sinh(eval_enode(e->get1st(), var_map));
case ENODE_ID_COSH:
assert(e->getArity() == 1);
return cosh(eval_enode(e->get1st(), var_map));
case ENODE_ID_TANH:
assert(e->getArity() == 1);
return tanh(eval_enode(e->get1st(), var_map));
default:
throw runtime_error("eval_enode: Unknown Term");
}
} else if (e->isList()) {
throw runtime_error("eval_enode: List");
} else if (e->isDef()) {
throw runtime_error("eval_enode: Def");
} else if (e->isEnil()) {
throw runtime_error("eval_enode: Nil");
} else {
throw runtime_error("eval_enode: unknown case");
}
throw runtime_error("Not implemented yet: eval_enode");
}
double deriv_enode(Enode * const e, Enode * const v, unordered_map<Enode*, double> const & var_map) {
if (e == v) {
return 1.0;
}
if (e->isVar()) {
auto const it = var_map.find(e);
if (it == var_map.cend()) {
throw runtime_error("variable not found");
} else {
// Variable is found in var_map
return 0.0;
}
} else if (e->isConstant()) {
return 0.0;
} else if (e->isSymb()) {
throw runtime_error("eval_enode: Symb");
} else if (e->isNumb()) {
throw runtime_error("eval_enode: Numb");
} else if (e->isTerm()) {
assert(e->getArity() >= 1);
enodeid_t id = e->getCar()->getId();
double ret = 0.0;
Enode * tmp = e;
switch (id) {
case ENODE_ID_PLUS:
ret = deriv_enode(tmp->get1st(), v, var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret + deriv_enode(tmp->getCar(), v, var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_MINUS:
ret = deriv_enode(tmp->get1st(), v, var_map);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = ret - deriv_enode(tmp->getCar(), v, var_map);
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_UMINUS:
ret = deriv_enode(tmp->get1st(), v, var_map);
assert(tmp->getArity() == 1);
return (- ret);
case ENODE_ID_TIMES: {
// (f * g)' = f' * g + f * g'
if (tmp->getArity() != 2) {
throw runtime_error("deriv_enode: only support arity = 2 case for multiplication");
}
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return f_ * g + f * g_;
}
case ENODE_ID_DIV: {
// (f / g)' = (f' * g - f * g') / g^2
if (tmp->getArity() != 2) {
throw runtime_error("deriv_enode: only support arity = 2 case for division");
}
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return (f_ * g - f * g_) / (g * g);
}
case ENODE_ID_ACOS: {
// (acos f)' = -(1 / sqrt(1 - f^2)) f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return - (1 / sqrt(1 - f * f)) * f_;
}
case ENODE_ID_ASIN: {
// (asin f)' = (1 / sqrt(1 - f^2)) f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return 1 / sqrt(1 - f * f) * f_;
}
case ENODE_ID_ATAN: {
// (atan f)' = (1 / (1 + f^2)) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return 1 / (1 + f * f) * f_;
}
case ENODE_ID_ATAN2: {
// atan2(x,y)' = -y / (x^2 + y^2) dx + x / (x^2 + y^2) dy
// = (-y dx + x dy) / (x^2 + y^2)
assert(e->getArity() == 2);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return (-g * f_ + f * g_) / (f * f + g * g);
}
case ENODE_ID_MIN:
assert(e->getArity() == 2);
throw runtime_error("deriv_enode: no support for min");
case ENODE_ID_MAX:
assert(e->getArity() == 2);
throw runtime_error("deriv_enode: no support for max");
case ENODE_ID_MATAN:
assert(e->getArity() == 1);
throw runtime_error("deriv_enode: no support for matan");
case ENODE_ID_SAFESQRT:
assert(e->getArity() == 1);
throw runtime_error("deriv_enode: no support for safesqrt");
case ENODE_ID_SQRT: {
// (sqrt(f))' = 1/2 * 1/(sqrt(f)) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return 0.5 * 1 / sqrt(f) * f_;
}
case ENODE_ID_EXP: {
// (exp f)' = (exp f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return exp(f) * f_;
}
case ENODE_ID_LOG: {
// (log f)' = f' / f
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return f_ / f;
}
case ENODE_ID_POW: {
// (f^g)' = f^g (f' * g / f + g' * ln g)
assert(e->getArity() == 2);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
double const g = eval_enode(e->get2nd(), var_map);
double const g_ = deriv_enode(e->get2nd(), v, var_map);
return pow(f, g) * (f_ * g / f + g_ * log(g));
}
case ENODE_ID_ABS: {
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
if (f > 0) {
return f_;
} else {
return - f_;
}
}
case ENODE_ID_SIN: {
// (sin f)' = (cos f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return cos(f) * f_;
}
case ENODE_ID_COS: {
// (cos f)' = - (sin f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return - sin(f) * f_;
}
case ENODE_ID_TAN: {
// (tan f)' = (1 + tan^2 f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return (1 + tan(f) * tan(f)) * f_;
}
case ENODE_ID_SINH: {
// (sinh f)' = (e^f + e^(-f))/2 * f'
// = cosh(f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return cosh(f) * f_;
}
case ENODE_ID_COSH: {
// (cosh f)' = (e^f - e^(-f))/2 * f'
// = sinh(f) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return sinh(f) * f_;
}
case ENODE_ID_TANH: {
// (tanh f)' = (sech^2 f) * f'
// = (1 - tanh(f) ^ 2) * f'
assert(e->getArity() == 1);
double const f = eval_enode(e->get1st(), var_map);
double const f_ = deriv_enode(e->get1st(), v, var_map);
return (1 - tanh(f) * tanh(f)) * f_;
}
default:
throw runtime_error("deriv_enode: Unknown Term");
}
} else if (e->isList()) {
throw runtime_error("deriv_enode: List");
} else if (e->isDef()) {
throw runtime_error("deriv_enode: Def");
} else if (e->isEnil()) {
throw runtime_error("deriv_enode: Nil");
} else {
throw runtime_error("deriv_enode: unknown case");
}
throw runtime_error("Not implemented yet: deriv_enode");
}
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;
}
//
// Performs the actual cnfization
//
bool Tseitin::cnfize( Enode * formula, map< enodeid_t, Enode * > & cnf_cache )
{
(void)cnf_cache;
assert( formula );
assert( !formula->isAnd( ) );
Enode * arg_def = egraph.valDupMap1( formula );
if ( arg_def != NULL )
{
vector< Enode * > clause;
clause.push_back( arg_def );
#ifdef PRODUCE_PROOF
if ( config.produce_inter > 0 )
return solver.addSMTClause( clause, egraph.getIPartitions( formula ) );
#endif
return solver.addSMTClause( clause );
}
vector< Enode * > unprocessed_enodes; // Stack for unprocessed enodes
unprocessed_enodes.push_back( formula ); // formula needs to be processed
//
// 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 ( egraph.valDupMap1( enode ) != NULL )
{
unprocessed_enodes.pop_back( );
continue;
}
bool unprocessed_children = false;
Enode * arg_list;
for ( arg_list = enode->getCdr( ) ;
arg_list != egraph.enil ;
arg_list = arg_list->getCdr( ) )
{
Enode * arg = arg_list->getCar( );
assert( arg->isTerm( ) );
//
// Push only if it is an unprocessed boolean operator
//
if ( enode->isBooleanOperator( )
&& egraph.valDupMap1( arg ) == NULL )
{
unprocessed_enodes.push_back( arg );
unprocessed_children = true;
}
//
// If it is an atom (either boolean or theory) just
// store it in the cache
//
else if ( arg->isAtom( ) )
{
egraph.storeDupMap1( arg, arg );
}
}
//
// SKip if unprocessed_children
//
if ( unprocessed_children )
continue;
unprocessed_enodes.pop_back( );
Enode * result = NULL;
//
// At this point, every child has been processed
//
//
// Do the actual cnfization, according to the node type
//
char def_name[ 32 ];
if ( enode->isLit( ) )
{
result = enode;
}
else if ( enode->isNot( ) )
{
Enode * arg_def = egraph.valDupMap1( enode->get1st( ) );
assert( arg_def );
result = egraph.mkNot( egraph.cons( arg_def ) ); // Toggle the literal
}
else
{
Enode * arg_def = NULL;
Enode * new_arg_list = egraph.copyEnodeEtypeListWithCache( enode->getCdr( ) );
//
// If the enode is not top-level it needs a definition
//
if ( formula != enode )
{
sprintf( def_name, CNF_STR, formula->getId( ), enode->getId( ) );
egraph.newSymbol( def_name, sstore.mkBool( ) );
arg_def = egraph.mkVar( def_name );
#ifdef PRODUCE_PROOF
if ( config.produce_inter > 0 )
{
// Tag Positive and negative literals
egraph.tagIFormula( arg_def
, egraph.getIPartitions( enode ) );
egraph.tagIFormula( egraph.mkNot( egraph.cons( arg_def ) )
, egraph.getIPartitions( enode ) );
}
#endif
}
#ifdef PRODUCE_PROOF
uint64_t partitions = 0;
if ( config.produce_inter > 0 )
{
partitions = egraph.getIPartitions( enode );
assert( partitions != 0 );
}
#endif
//
// Handle boolean operators
//
if ( enode->isAnd( ) )
cnfizeAnd( new_arg_list, arg_def
#ifdef PRODUCE_PROOF
, partitions
#endif
);
else if ( enode->isOr( ) )
cnfizeOr( new_arg_list, arg_def
#ifdef PRODUCE_PROOF
, partitions
#endif
);
else if ( enode->isIff( ) )
cnfizeIff( new_arg_list, arg_def
#ifdef PRODUCE_PROOF
, partitions
#endif
);
else if ( enode->isXor( ) )
cnfizeXor( new_arg_list, arg_def
#ifdef PRODUCE_PROOF
, partitions
#endif
);
else
{
opensmt_error2( "operator not handled ", enode->getCar( ) );
}
if ( arg_def != NULL )
result = arg_def;
}
assert( egraph.valDupMap1( enode ) == NULL );
egraph.storeDupMap1( enode, result );
}
if ( formula->isNot( ) )
{
// Retrieve definition of argument
Enode * arg_def = egraph.valDupMap1( formula->get1st( ) );
assert( arg_def );
vector< Enode * > clause;
clause.push_back( toggleLit( arg_def ) );
#ifdef PRODUCE_PROOF
if ( config.produce_inter > 0 )
return solver.addSMTClause( clause, egraph.getIPartitions( formula ) );
#endif
return solver.addSMTClause( clause );
}
return true;
}
// Translate an Enode e into ibex::ExprNode.
// Note: As a side-effect, update var_map : string -> ibex::Variable
// Note: Use subst map (Enode ->ibex::Interval)
ExprNode const * translate_enode_to_exprnode(map<string, Variable const> & var_map, Enode * const e, unordered_map<Enode*, ibex::Interval> const & subst) {
// TODO(soonhok): for the simple case such as 0 <= x or x <= 10.
// Handle it as a domain specification instead of constraints.
if (e->isVar()) {
auto const subst_it = subst.find(e);
if (subst_it != subst.cend()) {
auto const i = subst_it->second;
return &ExprConstant::new_scalar(i);
}
string const & var_name = e->getCar()->getNameFull();
auto const it = var_map.find(var_name);
if (it == var_map.cend()) {
// The variable is new, we need to make one.
Variable v(var_name.c_str());
// double const lb = e->getLowerBound();
// double const ub = e->getUpperBound();
var_map.emplace(var_name, v);
return v.symbol;
} else {
// Variable is found in var_map
Variable const & v = it->second;
return v.symbol;
}
} else if (e->isConstant()) {
double const lb = e->getValueLowerBound();
double const ub = e->getValueUpperBound();
return &ExprConstant::new_scalar(ibex::Interval(lb, ub));
} else if (e->isSymb()) {
throw logic_error("translateEnodeExprNode: Symb");
} else if (e->isNumb()) {
throw logic_error("translateEnodeExprNode: Numb");
} else if (e->isTerm()) {
assert(e->getArity() >= 1);
enodeid_t id = e->getCar()->getId();
ExprNode const * ret = nullptr;
Enode * tmp = e;
switch (id) {
case ENODE_ID_PLUS:
ret = translate_enode_to_exprnode(var_map, tmp->get1st(), subst);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = &(*ret + *translate_enode_to_exprnode(var_map, tmp->getCar(), subst));
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_MINUS:
ret = translate_enode_to_exprnode(var_map, tmp->get1st(), subst);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = &(*ret - *translate_enode_to_exprnode(var_map, tmp->getCar(), subst));
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_UMINUS:
ret = translate_enode_to_exprnode(var_map, tmp->get1st(), subst);
assert(tmp->getArity() == 1);
return &(- *ret);
case ENODE_ID_TIMES:
ret = translate_enode_to_exprnode(var_map, tmp->get1st(), subst);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = &(*ret * *translate_enode_to_exprnode(var_map, tmp->getCar(), subst));
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_DIV:
ret = translate_enode_to_exprnode(var_map, tmp->get1st(), subst);
tmp = tmp->getCdr()->getCdr(); // e is pointing to the 2nd arg
while (!tmp->isEnil()) {
ret = &(*ret / *translate_enode_to_exprnode(var_map, tmp->getCar(), subst));
tmp = tmp->getCdr();
}
return ret;
case ENODE_ID_ACOS:
assert(e->getArity() == 1);
return &acos(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_ASIN:
assert(e->getArity() == 1);
return &asin(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_ATAN:
assert(e->getArity() == 1);
return &atan(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_ATAN2:
assert(e->getArity() == 2);
return &atan2(*translate_enode_to_exprnode(var_map, e->get1st(), subst), *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
case ENODE_ID_MIN:
assert(e->getArity() == 2);
return &min(*translate_enode_to_exprnode(var_map, e->get1st(), subst), *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
case ENODE_ID_MAX:
assert(e->getArity() == 2);
return &max(*translate_enode_to_exprnode(var_map, e->get1st(), subst), *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
case ENODE_ID_MATAN:
// TODO(soonhok): MATAN
throw logic_error("translateEnodeExprNode: MATAN");
case ENODE_ID_SAFESQRT:
// TODO(soonhok): SAFESQRT
throw logic_error("translateEnodeExprNode: SAFESQRT");
case ENODE_ID_SQRT:
assert(e->getArity() == 1);
return &sqrt(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_EXP:
assert(e->getArity() == 1);
return &exp(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_LOG:
assert(e->getArity() == 1);
return &log(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_POW: {
assert(e->getArity() == 2);
bool is_1st_constant = false;
bool is_1st_int = false;
bool is_2nd_constant = false;
bool is_2nd_int = false;
double dbl_1st = 0.0;
int int_1st = 0;
double dbl_2nd = 0.0;
int int_2nd = 0;
if (e->get1st()->isConstant()) {
dbl_1st = e->get1st()->getValue();
is_1st_constant = true;
double tmp;
if (modf(dbl_1st, &tmp) == 0.0) {
is_1st_int = true;
int_1st = static_cast<int>(tmp);
}
}
if (e->get2nd()->isConstant()) {
dbl_2nd = e->get2nd()->getValue();
is_2nd_constant = true;
double tmp;
if (modf(dbl_2nd, &tmp) == 0.0) {
is_2nd_int = true;
int_2nd = static_cast<int>(tmp);
}
}
if (is_1st_constant && is_2nd_constant) {
// Both of them are constant, just compute and return a number
return &ExprConstant::new_scalar(pow(dbl_1st, dbl_2nd));
}
// Now, either of them is non-constant.
if (is_1st_int) {
return &pow(int_1st, *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
}
if (is_1st_constant) {
return &pow(dbl_1st, *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
}
if (is_2nd_int) {
return &pow(*translate_enode_to_exprnode(var_map, e->get1st(), subst), int_2nd);
}
if (is_2nd_constant) {
return &pow(*translate_enode_to_exprnode(var_map, e->get1st(), subst), dbl_2nd);
}
return &pow(*translate_enode_to_exprnode(var_map, e->get1st(), subst), *translate_enode_to_exprnode(var_map, e->get2nd(), subst));
}
case ENODE_ID_ABS:
assert(e->getArity() == 1);
return &abs(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_SIN:
assert(e->getArity() == 1);
return &sin(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_COS:
assert(e->getArity() == 1);
return &cos(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_TAN:
assert(e->getArity() == 1);
return &tan(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_SINH:
assert(e->getArity() == 1);
return &sinh(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_COSH:
assert(e->getArity() == 1);
return &cosh(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
case ENODE_ID_TANH:
assert(e->getArity() == 1);
return &tanh(*translate_enode_to_exprnode(var_map, e->get1st(), subst));
default:
throw logic_error("translateEnodeExprNode: Unknown Term");
}
} else if (e->isList()) {
throw logic_error("translateEnodeExprNode: List");
} else if (e->isDef()) {
throw logic_error("translateEnodeExprNode: Def");
} else if (e->isEnil()) {
throw logic_error("translateEnodeExprNode: Nil");
} else {
throw logic_error("translateEnodeExprNode: unknown case");
}
throw logic_error("Not implemented yet: translateEnodeExprNode");
}
