IVector ode_solver::extract_invariants() {
map<Enode*, pair<double, double>> inv_map;
for (auto inv : m_invs) {
Enode * p = inv->getCdr()->getCdr()->getCdr()->getCdr()->getCar();
Enode * op = p->getCar();
bool pos = true;
// Handle Negation
if (op->getId() == ENODE_ID_NOT) {
p = p->getCdr()->getCar();
op = p->getCar();
pos = false;
}
switch (op->getId()) {
case ENODE_ID_GEQ:
case ENODE_ID_GT:
// Handle >= & >
pos = !pos;
case ENODE_ID_LEQ:
case ENODE_ID_LT: {
// Handle <= & <
Enode * lhs = pos ? p->getCdr()->getCar() : p->getCdr()->getCdr()->getCar();
Enode * rhs = pos ? p->getCdr()->getCdr()->getCar() : p->getCdr()->getCar();
if (lhs->isVar() && rhs->isConstant()) {
if (inv_map.find(lhs) != inv_map.end()) {
inv_map[lhs].second = rhs->getValue();
} else {
inv_map.emplace(lhs, make_pair(lhs->getLowerBound(), rhs->getValue()));
}
} else if (lhs->isConstant() && rhs->isVar()) {
if (inv_map.find(rhs) != inv_map.end()) {
inv_map[rhs].first = lhs->getValue();
} else {
inv_map.emplace(rhs, make_pair(lhs->getValue(), rhs->getUpperBound()));
}
} else {
cerr << "ode_solver::extract_invariant: error:" << p << endl;
}
}
break;
default:
cerr << "ode_solver::extract_invariant: error" << p << endl;
}
}
IVector ret (m_t_vars.size());
unsigned i = 0;
for (auto const & m_t_var : m_t_vars) {
if (inv_map.find(m_t_var) != inv_map.end()) {
auto inv = interval(inv_map[m_t_var].first, inv_map[m_t_var].second);
DREAL_LOG_INFO << "Invariant extracted from " << m_t_var << " = " << inv;
ret[i++] = inv;
} else {
auto inv = interval(m_t_var->getLowerBound(), m_t_var->getUpperBound());
DREAL_LOG_INFO << "Default Invariant set for " << m_t_var << " = " << inv;
ret[i++] = inv;
}
}
return ret;
}
void THandler::clearVar( Var v )
{
assert( var_to_enode[ v ] != NULL );
Enode * e = var_to_enode[ v ];
assert( e->getId( ) < static_cast< int >( enode_id_to_var.size( ) ) );
assert( enode_id_to_var[ e->getId( ) ] == v );
var_to_enode[ v ] = NULL;
enode_id_to_var[ e->getId( ) ] = var_Undef;
}
//
// Merge collected arguments for nodes
//
Enode * Cnfizer::mergeEnodeArgs( Enode * e
, map< enodeid_t, Enode * > & cache
, map< enodeid_t, int > & enodeid_to_incoming_edges )
{
assert( e->isAnd( ) || e->isOr( ) );
Enode * e_symb = e->getCar( );
vector< Enode * > new_args;
for ( Enode * list = e->getCdr( ) ;
!list->isEnil( ) ;
list = list->getCdr( ) )
{
Enode * arg = list->getCar( );
Enode * sub_arg = cache[ arg->getId( ) ];
Enode * sym = arg->getCar( );
if ( sym->getId( ) != e_symb->getId( ) )
{
new_args.push_back( sub_arg );
continue;
}
assert( enodeid_to_incoming_edges.find( arg->getId( ) ) != enodeid_to_incoming_edges.end( ) );
assert( enodeid_to_incoming_edges[ arg->getId( ) ] >= 1 );
if ( enodeid_to_incoming_edges[ arg->getId( ) ] > 1 )
{
new_args.push_back( sub_arg );
continue;
}
for ( Enode * sub_arg_list = sub_arg->getCdr( ) ;
!sub_arg_list->isEnil( ) ;
sub_arg_list = sub_arg_list->getCdr( ) )
new_args.push_back( sub_arg_list->getCar( ) );
}
Enode * new_list = const_cast< Enode * >(egraph.enil);
while ( !new_args.empty( ) )
{
new_list = egraph.cons( new_args.back( ), new_list );
new_args.pop_back( );
}
return egraph.cons( e_symb, new_list );
}
cgcolor_t CGraph::colorNodesRec( CNode * c, const uint64_t mask )
{
// Already done
if ( colored_nodes.find( c ) != colored_nodes.end( ) )
return c->color;
// Base case, color variables
if ( c->e->getArity( ) == 0 )
{
cgcolor_t color = CG_UNDEF;
// Belongs to B
if ( (egraph.getIPartitions( c->e ) & mask) != 0 )
color |= CG_B;
// Belongs to A
if ( (egraph.getIPartitions( c->e ) & ~mask) != 0 )
color |= CG_A;
c->color = color;
}
else
{
// Function symbol: color depending on the arguments
// Decide color of term as intersection
cgcolor_t color = CG_AB;
Enode * args = c->e->getCdr( );
for ( args = c->e->getCdr( )
; !args->isEnil( )
; args = args->getCdr( ) )
{
Enode * arg = args->getCar( );
// Not necessairly an argument is needed in the graph
if ( cnodes_store.find( arg->getId( ) ) != cnodes_store.end( ) )
color &= colorNodesRec( cnodes_store[ arg->getId( ) ], mask );
}
c->color = color;
}
assert( colored_nodes.find( c ) == colored_nodes.end( ) );
colored_nodes.insert( c );
return c->color;
}
// a != b → R( a, i_{a,b} ) = R( b, i_{a,b} )
void Egraph::ExtAxiom( Enode * a, Enode * b )
{
assert( isDynamic( a ) );
assert( isDynamic( b ) );
Enode * as = dynamicToStatic( a );
Enode * bs = dynamicToStatic( b );
assert( isStatic( as ) );
assert( isStatic( bs ) );
assert( as->isDTypeArray( ) );
assert( bs->isDTypeArray( ) );
// create fresh index i_a,b for pair a,b
char def_name[ 48 ];
sprintf( def_name, IND_STR, as->getId( ), bs->getId( ) );
const unsigned type = DTYPE_ARRAY_INDEX;
if ( lookupSymbol( def_name ) == NULL )
newSymbol( def_name, type );
// Create new variable
Enode * i = mkVar( def_name );
// Create two new selections
Enode * select1 = mkSelect( as, i );
Enode * select2 = mkSelect( bs, i );
// Create new literals
Enode * lit1 = mkEq( cons( as, cons( bs ) ) );
Enode * lit2_pos = mkEq( cons( select1, cons( select2 ) ) );
Enode * lit2 = mkNot( cons( lit2_pos ) );
#ifdef PRODUCE_PROOF
if ( config.gconfig.print_inter > 0 )
{
const uint64_t shared = getIPartitions( as )
& getIPartitions( bs );
// Mixed can't be one at this point
assert( shared != 1 );
// Set AB-mixed partition if no intersection
if ( shared == 0 )
{
setIPartitions( i, 1 );
setIPartitions( select1, 1 );
setIPartitions( select2, 1 );
setIPartitions( lit1, 1 );
setIPartitions( lit2_pos, 1 );
setIPartitions( lit2, 1 );
}
// Otherwise they share something
else
{
setIPartitions( i, shared );
setIPartitions( select1, shared );
setIPartitions( select2, shared );
setIPartitions( lit1, shared );
setIPartitions( lit2_pos, shared );
setIPartitions( lit2, shared );
}
}
#endif
vector< Enode * > v;
v.push_back( lit1 );
v.push_back( lit2 );
#ifdef ARR_VERB
cout << "Axiom Ext -> " << "( or " << lit1 << " " << lit2 << " )" << endl;
#endif
splitOnDemand( v, id );
handleArrayAssertedAtomTerm( select1 );
handleArrayAssertedAtomTerm( select2 );
// New contexts to propagate info about new index
// Given R(a,new) look for all store users W(a,i,e)
// and instantiate RoW over R(W(a,i,e),new)
vector< Enode * > sela;
vector< Enode * > stoa;
vector< Enode * > selb;
vector< Enode * > stob;
Enode * select3 = NULL;
// Act over a
getUsers( a, sela, stoa );
for( size_t j = 0 ; j < stoa.size( ) ; j++ )
{
assert( isDynamic( stoa[ j ] ) );
Enode * ss = dynamicToStatic( stoa[ j ] );
assert( isStatic( ss ) );
// Creation new select for each store user of a
select3 = mkSelect( ss, i );
// RoW over new select
handleArrayAssertedAtomTerm( select3 );
#ifdef PRODUCE_PROOF
if ( config.gconfig.print_inter > 0 )
{
const uint64_t shared = getIPartitions( ss )
& getIPartitions( i );
// Mixed can't be one at this point
assert( shared != 1 );
// Set AB-mixed partition if no intersection
if ( shared == 0 )
setIPartitions( select3, 1 );
// Otherwise they share something
else
setIPartitions( select3, shared );
}
#endif
}
// Act over b
getUsers( b, selb, stob );
for ( size_t j = 0 ; j < stob.size( ) ; j++ )
{
assert( isDynamic( stoa[ j ] ) );
Enode * ss = dynamicToStatic( stob[ j ] );
assert( isStatic( ss ) );
// Creation new select for each store user of b
select3 = mkSelect( ss, i );
#ifdef PRODUCE_PROOF
if ( config.gconfig.print_inter > 0 )
{
const uint64_t shared = getIPartitions( ss )
& getIPartitions( i );
// Mixed can't be one at this point
assert( shared != 1 );
// Set AB-mixed partition if no intersection
if ( shared == 0 )
setIPartitions( select3, 1 );
// Otherwise they share something
else
setIPartitions( select3, shared );
}
#endif
// RoW over new select
handleArrayAssertedAtomTerm( select3 );
}
}
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 ) );
}
//
// 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;
}
//
// Rewrite formula with maximum arity for operators
//
Enode * Cnfizer::rewriteMaxArity( Enode * formula, map< enodeid_t, int > & enodeid_to_incoming_edges )
{
assert( formula );
vector< Enode * > unprocessed_enodes; // Stack for unprocessed enodes
unprocessed_enodes.push_back( formula ); // formula needs to be processed
map< enodeid_t, Enode * > cache; // Cache of processed nodes
//
// 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 ( cache.find( enode->getId( ) ) != cache.end( ) )
{
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 ( arg->isBooleanOperator( )
&& cache.find( arg->getId( ) ) == cache.end( ) )
{
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( ) )
{
cache.insert( make_pair( arg->getId( ), arg ) );
}
}
//
// SKip if unprocessed_children
//
if ( unprocessed_children )
continue;
unprocessed_enodes.pop_back( );
Enode * result = NULL;
//
// At this point, every child has been processed
//
assert ( enode->isBooleanOperator( ) );
if ( enode->isAnd( )
|| enode->isOr ( ) )
{
assert( enode->isAnd( ) || enode->isOr( ) );
//
// Construct the new lists for the operators
//
result = mergeEnodeArgs( enode, cache, enodeid_to_incoming_edges );
}
else
{
result = enode;
}
assert( result );
assert( cache.find( enode->getId( ) ) == cache.end( ) );
cache[ enode->getId( ) ] = result;
}
Enode * top_enode = cache[ formula->getId( ) ];
return top_enode;
}
//
// Compute the number of incoming edges for e and children
//
void Cnfizer::computeIncomingEdges( Enode * e
, map< enodeid_t, int > & enodeid_to_incoming_edges )
{
assert( e );
vector< Enode * > unprocessed_enodes; // Stack for unprocessed enodes
unprocessed_enodes.push_back( e ); // 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
//
map< enodeid_t, int >::iterator it = enodeid_to_incoming_edges.find( enode->getId( ) );
if ( it != enodeid_to_incoming_edges.end( ) )
{
it->second++;
unprocessed_enodes.pop_back( );
continue;
}
bool unprocessed_children = false;
if ( enode->isBooleanOperator( ) )
{
for ( Enode * arg_list = enode->getCdr( )
; !arg_list->isEnil( )
; arg_list = arg_list->getCdr( ) )
{
Enode * arg = arg_list->getCar( );
//
// Push only if it is an unprocessed boolean operator
//
map< enodeid_t, int >::iterator it = enodeid_to_incoming_edges.find( arg->getId( ) );
if ( it == enodeid_to_incoming_edges.end( ) )
{
unprocessed_enodes.push_back( arg );
unprocessed_children = true;
}
else
{
it->second ++;
}
}
}
//
// SKip if unprocessed_children
//
if ( unprocessed_children )
continue;
unprocessed_enodes.pop_back( );
//
// At this point, every child has been processed
//
assert ( enode->isBooleanOperator( ) || enode->isAtom( ) );
assert ( enodeid_to_incoming_edges.find( enode->getId( ) ) == enodeid_to_incoming_edges.end( ) );
enodeid_to_incoming_edges[ enode->getId( ) ] = 1;
}
}