// ∀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 (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);
}
}
// ∀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 );
}
}
// 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 );
}
}
