// ∀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 );
}
// ∀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 );
}
}
//
// Sort a term if it commutes.
// The following simplifications implemented
// (should be refactored to separate methods?):
// - `and':
// - drop constant true terms
// - convert an empty `and' to the constant term `true'
// - convert an `and' containing `false' to a replicate `false'
// - `or':
// - drop constant false terms
// - convert an empty `or' to a replicate `false' term
// - convert an `or' containing `true' to a replicate `true'
//
//
void Logic::simplify(SymRef& s, vec<PTRef>& args) {
// First sort it
#ifdef SORT_BOOLEANS
if (sym_store[s].commutes())
#else
if (sym_store[s].commutes() && !isAnd(s) && !isOr(s))
#endif
sort(args, LessThan_PTRef());
if (!isBooleanOperator(s) && !isEquality(s)) return;
int dropped_args = 0;
bool replace = false;
if (s == getSym_and()) {
int i, j;
PTRef p = PTRef_Undef;
for (i = j = 0; i < args.size(); i++) {
if (args[i] == getTerm_false()) {
args.clear();
s = getSym_false();
#ifdef SIMPLIFY_DEBUG
cerr << "and -> false" << endl;
#endif
return;
} else if (args[i] != getTerm_true() && args[i] != p) {
args[j++] = p = args[i];
} else {
#ifdef SIMPLIFY_DEBUG
cerr << "and -> drop" << endl;
#endif
}
}
dropped_args = i-j;
if (dropped_args == args.size()) {
s = getSym_true();
args.clear();
#ifdef SIMPLIFY_DEBUG
cerr << "and -> true" << endl;
#endif
return;
} else if (dropped_args == args.size() - 1)
replace = true;
else if (dropped_args > 0)
args.shrink(dropped_args);
}
if (s == getSym_or()) {
int i, j;
PTRef p = PTRef_Undef;
for (i = j = 0; i < args.size(); i++) {
if (args[i] == getTerm_true()) {
args.clear();
s = getSym_true();
#ifdef SIMPLIFY_DEBUG
cerr << "or -> true" << endl;
#endif
return;
} else if (args[i] != getTerm_false() && args[i] != p) {
args[j++] = p = args[i];
} else {
#ifdef SIMPLIFY_DEBUG
cerr << "or -> drop" << endl;
#endif
}
}
dropped_args = i-j;
if (dropped_args == args.size()) {
s = getSym_false();
args.clear();
#ifdef SIMPLIFY_DEBUG
cerr << "or -> false" << endl;
#endif
return;
}
else if (dropped_args == args.size() - 1)
replace = true;
else if (dropped_args > 0)
args.shrink(dropped_args);
}
if (isEquality(s)) {
assert(args.size() == 2);
if (isBooleanOperator(s) && (args[0] == getTerm_true())) {
Pterm& t = getPterm(args[1]);
s = t.symb();
args.clear();
for (int i = 0; i < t.size(); i++)
args.push(t[i]);
#ifdef SIMPLIFY_DEBUG
cerr << "eq -> second" << endl;
#endif
return;
} else if (isBooleanOperator(s) && (args[0] == getTerm_false())) {
PTRef old = args[1];
PTRef tr = mkNot(args[1]);
Pterm& t = getPterm(tr);
s = t.symb();
args.clear();
args.push(old);
#ifdef SIMPLIFY_DEBUG
cerr << "eq -> not second" << endl;
#endif
return;
} else if (isBooleanOperator(s) && (args[1] == getTerm_true())) {
args.clear();
Pterm& t = getPterm(args[0]);
s = t.symb();
args.clear();
for (int i = 0; i < t.size(); i++)
args.push(t[i]);
#ifdef SIMPLIFY_DEBUG
cerr << "eq -> first" << endl;
#endif
return;
} else if (isBooleanOperator(s) && (args[1] == getTerm_false())) {
PTRef old = args[0];
PTRef tr = mkNot(args[0]);
Pterm& t = getPterm(tr);
s = t.symb();
args.clear();
args.push(old);
#ifdef SIMPLIFY_DEBUG
cerr << "eq -> not first"<< endl;
#endif
return;
} else if (args[0] == args[1]) {
args.clear();
s = getSym_true();
#ifdef SIMPLIFY_DEBUG
cerr << "eq -> true" << endl;
#endif
return;
} else if (isBooleanOperator(s) && (args[0] == mkNot(args[1]))) {
args.clear();
s = getSym_false();
#ifdef SIMPLIFY_DEBUG
cerr << "eq -> false" << endl;
#endif
return;
}
}
if (isNot(s)) {
if (isTrue(args[0])) {
args.clear();
s = getSym_false();
#ifdef SIMPLIFY_DEBUG
cerr << "not -> false" << endl;
#endif
return;
}
if (isFalse(args[0])) {
args.clear();
s = getSym_true();
#ifdef SIMPLIFY_DEBUG
cerr << "not -> true" << endl;
#endif
return;
}
}
// Others, to be implemented:
// - distinct
// - implies
// - xor
// - ite
if (replace) {
// Return whatever is the sole argument
Pterm& t = getPterm(args[0]);
s = t.symb();
args.clear();
for (int i = 0; i < t.size(); i++)
args.push(t[i]);
#ifdef SIMPLIFY_DEBUG
cerr << " replace" << endl;
#endif
}
}
// 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 * 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->isIff( )
&& !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 );
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 );
Enode * lhs = e->get1st( );
Enode * rhs = e->get2nd( );
Enode * leq = mkLeq( cons( lhs, cons( rhs ) ) );
LAExpression b( leq );
leq = b.toEnode( *this );
Enode * geq = mkGeq( cons( lhs, cons( rhs ) ) );
LAExpression c( geq );
geq = c.toEnode( *this );
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 );
}
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;
}
