// For debugging: there are missing cases: user-defined types, symbols inside of quantifiers, etc.
void VCCmd::printSymbols(Expr e, ExprMap<bool>& cache)
{
if (cache.find(e) != cache.end()) return;
switch (e.getKind()) {
case SKOLEM_VAR:
case UCONST: {
cout << e << " : ";
ExprStream os(d_vc->getEM());
os.dagFlag(false);
os << e.getType().getExpr();
cout << ";" << endl;
break;
}
case APPLY: {
Expr op = e.getOpExpr();
if ((op.getKind() == UFUNC) && (cache.find(op) == cache.end())) {
cout << op << " : ";
ExprStream os(d_vc->getEM());
os.dagFlag(false);
os << op.getType().getExpr();
cout << ";" << endl;
cache[op] = true;
}
// fall through
}
default: {
Expr::iterator i = e.begin(), iend = e.end();
for (; i != iend; ++i) {
printSymbols(*i, cache);
}
break;
}
}
cache[e] = true;
}
unsigned compute_degree(ExprManager& exprManager, const Expr& term) {
unsigned n = term.getNumChildren();
unsigned degree = 0;
// boolean stuff
if (term.getType() == exprManager.booleanType()) {
for (unsigned i = 0; i < n; ++ i) {
degree = std::max(degree, compute_degree(exprManager, term[i]));
}
return degree;
}
// terms
if (n == 0) {
if (term.getKind() == kind::CONST_RATIONAL) {
return 0;
} else {
return 1;
}
} else {
unsigned degree = 0;
if (term.getKind() == kind::MULT) {
for (unsigned i = 0; i < n; ++ i) {
degree += std::max(degree, compute_degree(exprManager, term[i]));
}
} else {
for (unsigned i = 0; i < n; ++ i) {
degree = std::max(degree, compute_degree(exprManager, term[i]));
}
}
return degree;
}
}
//! find all bound variables in e and maps them to true in boundVars
void QuantTheoremProducer::recFindBoundVars(const Expr& e,
ExprMap<bool> & boundVars, ExprMap<bool> &visited)
{
if(visited.count(e)>0)
return;
else
visited[e] = true;
if(e.getKind() == BOUND_VAR)
boundVars[e] = true;
if(e.getKind() == EXISTS || e.getKind() == FORALL)
recFindBoundVars(e.getBody(), boundVars, visited);
for(Expr::iterator it = e.begin(); it!=e.end(); ++it)
recFindBoundVars(*it, boundVars, visited);
}
void Tptp::checkLetBinding(const std::vector<Expr>& bvlist, Expr lhs, Expr rhs,
bool formula) {
if (lhs.getKind() != CVC4::kind::APPLY_UF) {
parseError("malformed let: LHS must be a flat function application");
}
const std::multiset<CVC4::Expr> vars{lhs.begin(), lhs.end()};
if(formula && !lhs.getType().isBoolean()) {
parseError("malformed let: LHS must be formula");
}
for (const CVC4::Expr& var : vars) {
if (var.hasOperator()) {
parseError("malformed let: LHS must be flat, illegal child: " +
var.toString());
}
}
// ensure all let-bound variables appear on the LHS, and appear only once
for (const Expr& bound_var : bvlist) {
const size_t count = vars.count(bound_var);
if (count == 0) {
parseError(
"malformed let: LHS must make use of all quantified variables, "
"missing `" +
bound_var.toString() + "'");
} else if (count >= 2) {
parseError("malformed let: LHS cannot use same bound variable twice: " +
bound_var.toString());
}
}
}
bool TheoryArith::isSyntacticRational(const Expr& e, Rational& r)
{
if (e.getKind() == REAL_CONST) {
r = e[0].getRational();
return true;
}
else if (e.isRational()) {
r = e.getRational();
return true;
}
else if (isUMinus(e)) {
if (isSyntacticRational(e[0], r)) {
r = -r;
return true;
}
}
else if (isDivide(e)) {
Rational num;
if (isSyntacticRational(e[0], num)) {
Rational den;
if (isSyntacticRational(e[1], den)) {
if (den != 0) {
r = num / den;
return true;
}
}
}
}
return false;
}
// returns 0 if b is structurally equal to *this
int Expr::compare(const Expr &b, ExprEquivSet &equivs) const {
if (this == &b) return 0;
const Expr *ap, *bp;
if (this < &b) {
ap = this; bp = &b;
} else {
ap = &b; bp = this;
}
if (equivs.count(std::make_pair(ap, bp)))
return 0;
Kind ak = getKind(), bk = b.getKind();
if (ak!=bk)
return (ak < bk) ? -1 : 1;
if (hashValue != b.hashValue)
return (hashValue < b.hashValue) ? -1 : 1;
if (int res = compareContents(b))
return res;
unsigned aN = getNumKids();
for (unsigned i=0; i<aN; i++)
if (int res = getKid(i)->compare(*b.getKid(i), equivs))
return res;
equivs.insert(std::make_pair(ap, bp));
return 0;
}
bool TheoryArith::isAtomicArithTerm(const Expr& e)
{
switch (e.getKind()) {
case RATIONAL_EXPR:
return true;
case ITE:
return false;
case UMINUS:
case PLUS:
case MINUS:
case MULT:
case DIVIDE:
case POW:
case INTDIV:
case MOD: {
int i=0, iend=e.arity();
for(; i!=iend; ++i) {
if (!isAtomicArithTerm(e[i])) return false;
}
break;
}
default:
break;
}
return true;
}
Expr ExprManager::mkExpr(Expr opExpr, const std::vector<Expr>& children) {
const unsigned n = children.size();
Kind kind = NodeManager::operatorToKind(opExpr.getNode());
CheckArgument(opExpr.getKind() == kind::BUILTIN || kind::metaKindOf(kind) == kind::metakind::PARAMETERIZED, opExpr,
"This Expr constructor is for parameterized kinds only");
CheckArgument(n >= minArity(kind) && n <= maxArity(kind), kind,
"Exprs with kind %s must have at least %u children and "
"at most %u children (the one under construction has %u)",
kind::kindToString(kind).c_str(),
minArity(kind), maxArity(kind), n);
NodeManagerScope nms(d_nodeManager);
vector<Node> nodes;
vector<Expr>::const_iterator it = children.begin();
vector<Expr>::const_iterator it_end = children.end();
while(it != it_end) {
nodes.push_back(it->getNode());
++it;
}
try {
INC_STAT(kind);
return Expr(this,d_nodeManager->mkNodePtr(opExpr.getNode(), nodes));
} catch (const TypeCheckingExceptionPrivate& e) {
throw TypeCheckingException(this, &e);
}
}
ExprVisitor::Action ExprEvaluator::visitExprPost(const Expr& e) {
// When evaluating an assignment we should fold NotOptimizedExpr
// nodes so we can fully evaluate.
if (e.getKind() == Expr::NotOptimized) {
return Action::changeTo(static_cast<const NotOptimizedExpr&>(e).src);
}
return Action::skipChildren();
}
Theorem CNF_Manager::replaceITErec(const Expr& e, Var v, bool translateOnly)
{
// Quick exit for atomic expressions
if (e.isAtomic()) return d_commonRules->reflexivityRule(e);
// Check cache
Theorem thm;
bool foundInCache = false;
ExprHashMap<Theorem>::iterator iMap = d_iteMap.find(e);
if (iMap != d_iteMap.end()) {
thm = (*iMap).second;
foundInCache = true;
}
if (e.getKind() == ITE) {
// Replace non-Bool ITE expressions
DebugAssert(!e.getType().isBool(), "Expected non-Bool ITE");
// generate e = x for new x
if (!foundInCache) thm = d_commonRules->varIntroSkolem(e);
Theorem thm2 = d_commonRules->symmetryRule(thm);
thm2 = d_commonRules->iffMP(thm2, d_rules->ifLiftRule(thm2.getExpr(), 1));
d_translateQueueVars.push_back(v);
d_translateQueueThms.push_back(thm2);
d_translateQueueFlags.push_back(translateOnly);
}
else {
// Recursively traverse, replacing ITE's
vector<Theorem> thms;
vector<unsigned> changed;
unsigned index = 0;
Expr::iterator i, iend;
if (foundInCache) {
for(i = e.begin(), iend = e.end(); i!=iend; ++i, ++index) {
replaceITErec(*i, v, translateOnly);
}
}
else {
for(i = e.begin(), iend = e.end(); i!=iend; ++i, ++index) {
thm = replaceITErec(*i, v, translateOnly);
if (!thm.isRefl()) {
thms.push_back(thm);
changed.push_back(index);
}
}
if(changed.size() > 0) {
thm = d_commonRules->substitutivityRule(e, changed, thms);
}
else thm = d_commonRules->reflexivityRule(e);
}
}
// Update cache and return
if (!foundInCache) d_iteMap[e] = thm;
return thm;
}
bool TheoryArith::isAtomicArithFormula(const Expr& e)
{
switch (e.getKind()) {
case LT:
case GT:
case LE:
case GE:
case EQ:
return isAtomicArithTerm(e[0]) && isAtomicArithTerm(e[1]);
}
return false;
}
Expr ExprManager::mkExpr(Expr opExpr, Expr child1) {
const unsigned n = 1;
Kind kind = NodeManager::operatorToKind(opExpr.getNode());
CheckArgument(opExpr.getKind() == kind::BUILTIN || kind::metaKindOf(kind) == kind::metakind::PARAMETERIZED, opExpr,
"This Expr constructor is for parameterized kinds only");
CheckArgument(n >= minArity(kind) && n <= maxArity(kind), kind,
"Exprs with kind %s must have at least %u children and "
"at most %u children (the one under construction has %u)",
kind::kindToString(kind).c_str(),
minArity(kind), maxArity(kind), n);
NodeManagerScope nms(d_nodeManager);
try {
INC_STAT(kind);
return Expr(this, d_nodeManager->mkNodePtr(opExpr.getNode(), child1.getNode()));
} catch (const TypeCheckingExceptionPrivate& e) {
throw TypeCheckingException(this, &e);
}
}
// returns 0 if b is structurally equal to *this
int Expr::compare(const Expr &b) const {
if (this == &b) return 0;
Kind ak = getKind(), bk = b.getKind();
if (ak!=bk)
return (ak < bk) ? -1 : 1;
if (hashValue != b.hashValue)
return (hashValue < b.hashValue) ? -1 : 1;
if (int res = compareContents(b))
return res;
unsigned aN = getNumKids();
for (unsigned i=0; i<aN; i++)
if (int res = getKid(i).compare(b.getKid(i)))
return res;
return 0;
}
Expr collectSortsExpr(Expr e)
{
if(substitutions.find(e) != substitutions.end()) {
return substitutions[e];
}
++depth;
Expr old_e = e;
for(unsigned i = 0; i < e.getNumChildren(); ++i) {
collectSortsExpr(e[i]);
}
e = e.substitute(substitutions);
// cout << "[debug] " << e << " " << e.getKind() << " " << theory::kindToTheoryId(e.getKind()) << endl;
if(theory::kindToTheoryId(e.getKind()) == theory::THEORY_SETS) {
SetType t = SetType(e.getType().isBoolean() ? e[1].getType() : e.getType());
substitutions[e] = add(t, e);
e = e.substitute(substitutions);
}
substitutions[old_e] = e;
// cout << ";"; for(int i = 0; i < depth; ++i) cout << " "; cout << old_e << " => " << e << endl;
--depth;
return e;
}
void translate_to_redlog(const map<Expr, unsigned>& variables, const Expr& assertion) {
bool first;
unsigned n = assertion.getNumChildren();
if (n == 0) {
if (assertion.isConst()) {
if (assertion.getConst<bool>()) {
cout << "(1 > 0)";
} else {
cout << "(1 < 0)";
}
} else {
assert(false);
}
} else {
std::string op;
bool binary = false;
bool theory = false;
switch (assertion.getKind()) {
case kind::NOT:
cout << "(not ";
translate_to_redlog(variables, assertion[0]);
cout << ")";
break;
case kind::OR:
first = true;
cout << "(";
for (unsigned i = 0; i < n; ++ i) {
if (!first) {
cout << " or ";
}
first = false;
translate_to_redlog(variables, assertion[i]);
}
cout << ")";
break;
case kind::AND:
first = true;
cout << "(";
for (unsigned i = 0; i < n; ++ i) {
if (!first) {
cout << " and ";
}
first = false;
translate_to_redlog(variables, assertion[i]);
}
cout << ")";
break;
case kind::IMPLIES:
cout << "(";
translate_to_redlog(variables, assertion[0]);
cout << " impl ";
translate_to_redlog(variables, assertion[1]);
cout << ")";
break;
case kind::IFF:
cout << "(";
translate_to_redlog(variables, assertion[0]);
cout << " equiv ";
translate_to_redlog(variables, assertion[1]);
cout << ")";
break;
case kind::EQUAL:
op = "=";
theory = true;
break;
case kind::LT:
op = "<";
theory = true;
break;
case kind::LEQ:
op = "<=";
theory = true;
break;
case kind::GT:
op = ">";
theory = true;
break;
case kind::GEQ:
op = ">=";
theory = true;
break;
default:
assert(false);
break;
}
if (binary) {
cout << "(";
translate_to_redlog(variables, assertion[0]);
cout << " " << op << " ";
translate_to_redlog(variables, assertion[1]);
cout << ")";
}
if (theory) {
cout << "(";
translate_to_redlog_term(variables, assertion[0]);
cout << " " << op << " ";
translate_to_redlog_term(variables, assertion[1]);
cout << ")";
}
}
}
void translate_to_redlog_term(const map<Expr, unsigned>& variables, const Expr& term) {
bool first;
unsigned n = term.getNumChildren();
if (n == 0) {
if (term.getKind() == kind::CONST_RATIONAL) {
cout << term.getConst<Rational>();
} else {
assert(variables.find(term) != variables.end());
cout << "x" << variables.find(term)->second;
}
} else {
switch (term.getKind()) {
case kind::PLUS:
cout << "(";
first = true;
for (unsigned i = 0; i < n; ++ i) {
if (!first) {
cout << " + ";
}
first = false;
translate_to_redlog_term(variables, term[i]);
}
cout << ")";
break;
case kind::MULT:
cout << "(";
first = true;
for (unsigned i = 0; i < n; ++ i) {
if (!first) {
cout << " * ";
}
first = false;
translate_to_redlog_term(variables, term[i]);
}
cout << ")";
break;
case kind::MINUS:
cout << "(";
translate_to_redlog_term(variables, term[0]);
cout << " - ";
translate_to_redlog_term(variables, term[1]);
cout << ")";
break;
case kind::DIVISION:
cout << "(";
translate_to_redlog_term(variables, term[0]);
cout << " / ";
translate_to_redlog_term(variables, term[1]);
cout << ")";
break;
case kind::UMINUS:
cout << "(-(";
translate_to_redlog_term(variables, term[0]);
cout << "))";
break;
default:
assert(false);
break;
}
}
}
LFSCProof* LFSCProof::Make_CNF( const Expr& form, const Expr& reason, int pos )
{
Expr ec = cascade_expr( form );
#ifdef PRINT_MAJOR_METHODS
cout << ";[M] CNF " << reason << " " << pos << std::endl;
#endif
int m = queryM( ec );
if( m>0 )
{
ostringstream os1;
ostringstream os2;
RefPtr< LFSCProof > p;
if( reason==d_or_final_s )
{
#if 0
//this is the version that cascades
//make the proof for the or
p = LFSCPfVar::Make( "@v", abs(m) );
//clausify the or statement
p = LFSCClausify::Make( ec, p.get(), true );
//return
return LFSCAssume::Make( m, p.get(), true );
#else
//this is the version that does not expand the last
ostringstream oss1, oss2;
p = LFSCPfVar::Make( "@v", abs(m) );
for( int a=(form.arity()-2); a>=0; a-- ){
int m1 = queryM( form[a] );
oss1 << "(or_elim_1 _ _ ";
oss1 << ( m1<0 ? "(not_not_intro _ " : "" );
oss1 << "@v" << abs( m1 );
oss1 << ( m1<0 ? ") " : " " );
oss2 << ")";
}
p = LFSCProofGeneric::Make( oss1.str(), p.get(), oss2.str() );
//p = LFSCClausify::Make( form[form.arity()-1], p.get() );
p = LFSCClausify::Make( queryM( form[form.arity()-1] ), p.get() );
for( int a=0; a<(form.arity()-1); a++ ){
p = LFSCAssume::Make( queryM( form[a] ), p.get(), false );
}
return LFSCAssume::Make( m, p.get() );
#endif
}
else if( reason==d_and_final_s )
{
#if 1
//this is the version that does not expand the last
p = LFSCPfVar::Make( "@v", abs(m) );
os1 << "(contra _ ";
for( int a=0; a<form.arity(); a++ ){
if( a<(form.arity()-1))
os1 << "(and_intro _ _ ";
os1 << "@v" << abs( queryM( form[a] ) );
if( a<(form.arity()-1)){
os1 << " ";
os2 << ")";
}
}
os2 << " @v" << abs(m) << ")";
os1 << os2.str();
p = LFSCProofGeneric::MakeStr( os1.str().c_str() );
for( int a=0; a<form.arity(); a++ ){
p = LFSCAssume::Make( queryM( form[a] ), p.get() );
}
return LFSCAssume::Make( m, p.get(), false );
#else
//this is the version that cascades
std::vector< Expr > assumes;
Expr ce = cascade_expr( form );
Expr curr = ce;
os1 << "(contra _ ";
while( curr.getKind()==AND ){
os1 << "(and_intro _ _ ";
os1 << "@v" << abs( queryM( curr[0] ) ) << " ";
os2 << ")";
assumes.push_back( curr[0] );
curr = curr[1];
}
os2 << " @v" << abs(m) << ")";
p = LFSCProofGeneric::Make( os1.str(), p.get(), os2.str() );
for( int a=0; a<(int)assumes.size(); a++ ){
p = LFSCAssume::Make( queryM( assumes[a] ), p.get() );
}
return LFSCAssume::Make( m, p.get(), false );
#endif
}
else if( reason==d_imp_s )
{
int m1 = queryM( ec[0] );
int m2 = queryM( ec[1] );
switch( pos )
{
case 0:
break;
case 1:
break;
case 2:
{
//make a proof of the RHS
ostringstream os;
os << "(impl_elim _ _ @v" << abs( m1 ) << " @v" << abs( m ) << ")";
p = LFSCProofGeneric::MakeStr( os.str().c_str() );
//clausify the RHS
p = LFSCClausify::Make( form[1], p.get() ); //cascadeOr?
p = LFSCAssume::Make( queryM( ec[0] ), p.get() );
return LFSCAssume::Make( queryM( ec ), p.get() );
}
break;
}
}
else if( reason==d_ite_s )
{
int m1 = queryM( ec[0] );
int m2 = queryM( ec[1] );
switch( pos )
{
case 1:
{
ostringstream os;
os << "(ite_elim_2" << (m1<0 ? "n" : "" );
os << " _ _ _ @v" << abs( m1 ) << " @v" << abs( m ) << ")";
p = LFSCProofGeneric::MakeStr( os.str().c_str() );
p = LFSCClausify::Make( form[2], p.get() );
p = LFSCAssume::Make( queryM( ec[0] ), p.get(), false );
return LFSCAssume::Make( queryM( ec ), p.get() );
}
break;
case 2:
{
ostringstream os;
os << "(not_ite_elim_2 _ _ _ @v" << (m1<0 ? "n" : "" );
os << abs( m1 ) << " @v" << abs( m ) << ")";
p = LFSCProofGeneric::MakeStr( os.str().c_str() );
Expr e = Expr( NOT, form[2] );
p = LFSCClausify::Make( e, p.get() );
p = LFSCAssume::Make( queryM( ec[0] ), p.get(), false );
return LFSCAssume::Make( queryM( ec ), p.get(), false );
}
break;
case 3:
{
ostringstream os;
os << "(not_ite_elim_1 _ _ _ @v" << abs( m1 ) << " @v" << abs( m ) << ")";
p = LFSCProofGeneric::MakeStr( os.str().c_str() );
Expr e = Expr( NOT, form[1] );
p = LFSCClausify::Make( e, p.get() );
p = LFSCAssume::Make( queryM( ec[0] ), p.get() );
return LFSCAssume::Make( queryM( ec ), p.get(), false );
}
break;
case 4:
{
ostringstream os;
os << "(ite_elim_1";// << (m1<0 ? "n" : "" );
os << " _ _ _ @v" << abs( m1 ) << " @v" << abs( m ) << ")";
p = LFSCProofGeneric::MakeStr( os.str().c_str() );
p = LFSCClausify::Make( form[1], p.get() );
p = LFSCAssume::Make( queryM( ec[0] ), p.get() );
return LFSCAssume::Make( queryM( ec ), p.get() );
}
break;
case 5:
{
ostringstream os;
os << "(not_ite_elim_3 _ _ _ @v" << abs( m2 ) << " @v" << abs( m ) << ")";
p = LFSCProofGeneric::MakeStr( os.str().c_str() );
Expr e = Expr( NOT, form[2] );
p = LFSCClausify::Make( e, p.get() );
p = LFSCAssume::Make( queryM( ec[1] ), p.get() );
return LFSCAssume::Make( queryM( ec ), p.get(), false );
}
break;
case 6:
{
ostringstream os;
os << "(ite_elim_3";// << (m1<0 ? "n" : "" );
os << " _ _ _ @v" << abs( m2 ) << " @v" << abs( m ) << ")";
p = LFSCProofGeneric::MakeStr( os.str().c_str() );
p = LFSCClausify::Make( form[2], p.get() );
p = LFSCAssume::Make( queryM( ec[1] ), p.get(), false );
return LFSCAssume::Make( queryM( ec ), p.get() );
}
break;
}
}
else if( reason==d_iff_s )
{
int m1 = queryM( ec[0] );
int m2 = queryM( ec[1] );
switch( pos )
{
case 0:
{
ostringstream os;
os << "(not_iff_elim_1 _ _ @v" << abs( m1 ) << " @v" << abs( m ) << ")";
p = LFSCProofGeneric::MakeStr( os.str().c_str() );
p = LFSCClausify::Make( form[1], p.get() );
p = LFSCAssume::Make( queryM( ec[0] ), p.get(), false );
return LFSCAssume::Make( queryM( ec ), p.get(), false );
}
break;
case 1:
{
ostringstream os;
os << "(not_iff_elim_2 _ _ @v" << abs( m1 ) << " @v" << abs( m ) << ")";
p = LFSCProofGeneric::MakeStr( os.str().c_str() );
p = LFSCClausify::Make( Expr( NOT, form[1] ), p.get() );
p = LFSCAssume::Make( queryM( ec[0] ), p.get() );
return LFSCAssume::Make( queryM( ec ), p.get(), false );
}
break;
case 2:
{
ostringstream os;
os << "(impl_elim _ _ @v" << abs( m1 ) << "(iff_elim_1 _ _ @v" << abs( m ) << "))";
p = LFSCProofGeneric::MakeStr( os.str().c_str() );
//clausify the RHS
p = LFSCClausify::Make( form[1], p.get() ); //cascadeOr?
p = LFSCAssume::Make( queryM( ec[0] ), p.get() );
return LFSCAssume::Make( queryM( ec ), p.get() );
}
break;
case 3:
{
ostringstream os;
os << "(impl_elim _ _ @v" << abs( m2 ) << "(iff_elim_2 _ _ @v" << abs( m ) << "))";
p = LFSCProofGeneric::MakeStr( os.str().c_str() );
//clausify the RHS
p = LFSCClausify::Make( form[0], p.get() ); //cascadeOr?
p = LFSCAssume::Make( queryM( ec[1] ), p.get() );
return LFSCAssume::Make( m, p.get() );
}
break;
}
}
else if( reason==d_or_mid_s )
{
ostringstream os1, os2;
if( form[pos].isNot() )
os1 << "(not_not_elim _ ";
os1 << "(or_elim" << ( (pos==form.arity()) ? "_end" : "" );
os1 << " _ _ " << pos << " ";
os2 << ")";
if( form[pos].isNot() )
os2 << ")";
p = LFSCPfVar::Make( "@v", abs( m ) );
p = LFSCProofGeneric::Make( os1.str(), p.get(), os2.str() );
Expr ea = Expr( NOT, form[pos] );
p = LFSCClausify::Make( ea, p.get() );
return LFSCAssume::Make( m, p.get(), false );
}
else if( reason==d_and_mid_s )
{
//make a proof of the pos-th statement
p = LFSCPfVar::Make( "@v", abs( m ) );
p = LFSCProof::Make_and_elim( form, p.get(), pos, form[pos] );
p = LFSCClausify::Make( form[pos], p.get() );
return LFSCAssume::Make( m, p.get() );
}
}
ostringstream ose;
ose << "CNF, " << reason << " unknown position = " << pos << std::endl;
print_error( ose.str().c_str(), cout );
return NULL;
}
Expr add(SetType t, Expr e) {
if(setTypes.find(t) == setTypes.end() ) {
// mark as processed
setTypes.insert(t);
Type elementType = t.getElementType();
ostringstream oss_type;
oss_type << language::SetLanguage(language::output::LANG_SMTLIB_V2)
<< elementType;
string elementTypeAsString = oss_type.str();
elementTypeAsString.erase(
remove_if(elementTypeAsString.begin(), elementTypeAsString.end(), nonsense),
elementTypeAsString.end());
// define-sort
ostringstream oss_name;
oss_name << language::SetLanguage(language::output::LANG_SMTLIB_V2)
<< "(Set " << elementType << ")";
string name = oss_name.str();
Type newt = em->mkArrayType(t.getElementType(), em->booleanType());
mapTypes[t] = newt;
// diffent types
vector<Type> t_t;
t_t.push_back(t);
t_t.push_back(t);
vector<Type> elet_t;
elet_t.push_back(elementType);
elet_t.push_back(t);
if(!enableAxioms)
sout << "(define-fun emptyset" << elementTypeAsString << " "
<< " ()"
<< " " << name
<< " ( (as const " << name << ") false ) )" << endl;
setoperators[ make_pair(t, kind::EMPTYSET) ] =
em->mkVar( std::string("emptyset") + elementTypeAsString,
t);
if(!enableAxioms)
sout << "(define-fun singleton" << elementTypeAsString << " "
<< " ( (x " << elementType << ") )"
<< " " << name << ""
<< " (store emptyset" << elementTypeAsString << " x true) )" << endl;
setoperators[ make_pair(t, kind::SINGLETON) ] =
em->mkVar( std::string("singleton") + elementTypeAsString,
em->mkFunctionType( elementType, t ) );
if(!enableAxioms)
sout << "(define-fun union" << elementTypeAsString << " "
<< " ( (s1 " << name << ") (s2 " << name << ") )"
<< " " << name << ""
<< " ((_ map or) s1 s2))" << endl;
setoperators[ make_pair(t, kind::UNION) ] =
em->mkVar( std::string("union") + elementTypeAsString,
em->mkFunctionType( t_t, t ) );
if(!enableAxioms)
sout << "(define-fun intersection" << elementTypeAsString << ""
<< " ( (s1 " << name << ") (s2 " << name << ") )"
<< " " << name << ""
<< " ((_ map and) s1 s2))" << endl;
setoperators[ make_pair(t, kind::INTERSECTION) ] =
em->mkVar( std::string("intersection") + elementTypeAsString,
em->mkFunctionType( t_t, t ) );
if(!enableAxioms)
sout << "(define-fun setminus" << elementTypeAsString << " "
<< " ( (s1 " << name << ") (s2 " << name << ") )"
<< " " << name << ""
<< " (intersection" << elementTypeAsString << " s1 ((_ map not) s2)))" << endl;
setoperators[ make_pair(t, kind::SETMINUS) ] =
em->mkVar( std::string("setminus") + elementTypeAsString,
em->mkFunctionType( t_t, t ) );
if(!enableAxioms)
sout << "(define-fun member" << elementTypeAsString << " "
<< " ( (x " << elementType << ")" << " (s " << name << "))"
<< " Bool"
<< " (select s x) )" << endl;
setoperators[ make_pair(t, kind::MEMBER) ] =
em->mkVar( std::string("member") + elementTypeAsString,
em->mkPredicateType( elet_t ) );
if(!enableAxioms)
sout << "(define-fun subset" << elementTypeAsString << " "
<< " ( (s1 " << name << ") (s2 " << name << ") )"
<< " Bool"
<<" (= emptyset" << elementTypeAsString << " (setminus" << elementTypeAsString << " s1 s2)) )" << endl;
setoperators[ make_pair(t, kind::SUBSET) ] =
em->mkVar( std::string("subset") + elementTypeAsString,
em->mkPredicateType( t_t ) );
if(enableAxioms) {
int N = sizeof(setaxioms) / sizeof(setaxioms[0]);
for(int i = 0; i < N; ++i) {
string s = setaxioms[i];
ostringstream oss;
oss << language::SetLanguage(language::output::LANG_SMTLIB_V2) << elementType;
boost::replace_all(s, "HOLDA", elementTypeAsString);
boost::replace_all(s, "HOLDB", oss.str());
if( s == "" ) continue;
sout << s << endl;
}
}
}
Expr ret;
if(e.getKind() == kind::EMPTYSET) {
ret = setoperators[ make_pair(t, e.getKind()) ];
} else {
vector<Expr> children = e.getChildren();
children.insert(children.begin(), setoperators[ make_pair(t, e.getKind()) ]);
ret = em->mkExpr(kind::APPLY, children);
}
// cout << "returning " << ret << endl;
return ret;
}
Lit CNF_Manager::translateExprRec(const Expr& e, CNF_Formula& cnf, const Theorem& thmIn)
{
if (e.isFalse()) return Lit::getFalse();
if (e.isTrue()) return Lit::getTrue();
if (e.isNot()) return !translateExprRec(e[0], cnf, thmIn);
ExprHashMap<Var>::iterator iMap = d_cnfVars.find(e);
if (e.isTranslated()) {
DebugAssert(iMap != d_cnfVars.end(), "Translated expr should be in map");
return Lit((*iMap).second);
}
else e.setTranslated(d_bottomScope);
Var v(int(d_varInfo.size()));
bool translateOnly = false;
if (iMap != d_cnfVars.end()) {
v = (*iMap).second;
translateOnly = true;
d_varInfo[v].fanouts.clear();
}
else {
d_varInfo.resize(v+1);
d_varInfo.back().expr = e;
d_cnfVars[e] = v;
}
Expr::iterator i, iend;
bool isAnd = false;
switch (e.getKind()) {
case AND:
isAnd = true;
case OR: {
vector<Lit> lits;
unsigned idx;
for (i = e.begin(), iend = e.end(); i != iend; ++i) {
lits.push_back(translateExprRec(*i, cnf, thmIn));
}
// DebugAssert(concreteExpr(e,Lit(v)) == e,"why here");
for (idx = 0; idx < lits.size(); ++idx) {
cnf.newClause();
cnf.addLiteral(Lit(v),isAnd);
cnf.addLiteral(lits[idx], !isAnd);
// DebugAssert(concreteExpr(e[idx],lits[idx]) == e[idx], "why here");
std::string reasonStr = (isAnd ? "and_mid" : "or_mid");
Expr after = e[idx] ;
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, after, reasonStr, idx)); // by yeting
}
cnf.newClause();
cnf.addLiteral(Lit(v),!isAnd);
for (idx = 0; idx < lits.size(); ++idx) {
cnf.addLiteral(lits[idx], isAnd);
}
std::string reasonStr = (isAnd ? "and_final" : "or_final") ;
Expr after = e ;
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, after, reasonStr, 0)); // by yeting
break;
}
case IMPLIES: {
Lit arg0 = translateExprRec(e[0], cnf, thmIn);
Lit arg1 = translateExprRec(e[1], cnf, thmIn);
// DebugAssert(concreteExpr(e, Lit(v)) == e, "why here");
// DebugAssert(concreteExpr(e[0], arg0) == e[0], "why here");
// DebugAssert(concreteExpr(e[1], arg1) == e[1], "why here");
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0);
cnf.getCurrentClause().setClauseTheorem( d_rules->CNFtranslate(e, e, "imp", 0)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem( d_rules->CNFtranslate(e, e, "imp", 1)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem( d_rules->CNFtranslate(e, e, "imp", 2)); // by yeting
break;
}
case IFF: {
Lit arg0 = translateExprRec(e[0], cnf, thmIn);
Lit arg1 = translateExprRec(e[1], cnf, thmIn);
// DebugAssert(concreteExpr(e, Lit(v)) == e, "why here");
// DebugAssert(concreteExpr(e[0], arg0) == e[0], "why here");
// DebugAssert(concreteExpr(e[1], arg1) == e[1], "why here");
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "iff", 0)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "iff", 1)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "iff", 2)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0);
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "iff", 3)); // by yeting
break;
}
case XOR: {
Lit arg0 = translateExprRec(e[0], cnf, thmIn);
Lit arg1 = translateExprRec(e[1], cnf, thmIn);
// DebugAssert(concreteExpr(e, Lit(v)) == e, "why here");
// DebugAssert(concreteExpr(e[0], arg0) == e[0], "why here");
// DebugAssert(concreteExpr(e[1], arg1) == e[1], "why here");
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "xor", 0)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "xor", 1)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "xor", 2)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0);
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFtranslate(e, e, "xor", 3)); // by yeting
break;
}
case ITE:
{
Lit arg0 = translateExprRec(e[0], cnf, thmIn);
Lit arg1 = translateExprRec(e[1], cnf, thmIn);
Lit arg2 = translateExprRec(e[2], cnf, thmIn);
Expr aftere0 = concreteExpr(e[0], arg0);
Expr aftere1 = concreteExpr(e[1], arg1);
Expr aftere2 = concreteExpr(e[2], arg2);
vector<Expr> after ;
after.push_back(aftere0);
after.push_back(aftere1);
after.push_back(aftere2);
Theorem e0thm;
Theorem e1thm;
Theorem e2thm;
{ e0thm = d_iteMap[e[0]];
if (e0thm.isNull()) e0thm = d_commonRules->reflexivityRule(e[0]);
e1thm = d_iteMap[e[1]];
if (e1thm.isNull()) e1thm = d_commonRules->reflexivityRule(e[1]);
e2thm = d_iteMap[e[2]];
if (e2thm.isNull()) e2thm = d_commonRules->reflexivityRule(e[2]);
}
vector<Theorem> thms ;
thms.push_back(e0thm);
thms.push_back(e1thm);
thms.push_back(e2thm);
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0);
cnf.addLiteral(arg2);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 1)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0);
cnf.addLiteral(arg2,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 2)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 3)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg0,true);
cnf.addLiteral(arg1);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 4)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v));
cnf.addLiteral(arg1,true);
cnf.addLiteral(arg2,true);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 5)); // by yeting
cnf.newClause();
cnf.addLiteral(Lit(v),true);
cnf.addLiteral(arg1);
cnf.addLiteral(arg2);
cnf.getCurrentClause().setClauseTheorem(d_rules->CNFITEtranslate(e, after,thms, 6)); // by yeting
break;
}
default:
{
DebugAssert(!e.isAbsAtomicFormula() || d_varInfo[v].expr == e,
"Corrupted Varinfo");
if (e.isAbsAtomicFormula()) {
registerAtom(e, thmIn);
return Lit(v);
}
Theorem thm = replaceITErec(e, v, translateOnly);
const Expr& e2 = thm.getRHS();
DebugAssert(e2.isAbsAtomicFormula(), "Expected AbsAtomicFormula");
if (e2.isTranslated()) {
// Ugly corner case: we happen to create an expression that has been
// created before. We remove the current variable and fix up the
// translation stack.
if (translateOnly) {
DebugAssert(v == d_cnfVars[e2], "Expected literal match");
}
else {
d_varInfo.resize(v);
while (!d_translateQueueVars.empty() &&
d_translateQueueVars.back() == v) {
d_translateQueueVars.pop_back();
}
DebugAssert(d_cnfVars.find(e2) != d_cnfVars.end(),
"Expected existing literal");
v = d_cnfVars[e2];
d_cnfVars[e] = v;
while (d_translateQueueVars.size() < d_translateQueueThms.size()) {
d_translateQueueVars.push_back(v);
}
}
}
else {
e2.setTranslated(d_bottomScope);
// Corner case: don't register reflexive equality
if (!e2.isEq() || e2[0] != e2[1]) registerAtom(e2, thmIn);
if (!translateOnly) {
if (d_cnfVars.find(e2) == d_cnfVars.end()) {
d_varInfo[v].expr = e2;
d_cnfVars[e2] = v;
}
else {
// Same corner case in an untranslated expr
d_varInfo.resize(v);
while (!d_translateQueueVars.empty() &&
d_translateQueueVars.back() == v) {
d_translateQueueVars.pop_back();
}
v = d_cnfVars[e2];
d_cnfVars[e] = v;
while (d_translateQueueVars.size() < d_translateQueueThms.size()) {
d_translateQueueVars.push_back(v);
}
}
}
}
return Lit(v);
}
}
// Record fanins / fanouts
Lit l;
for (i = e.begin(), iend = e.end(); i != iend; ++i) {
l = getCNFLit(*i);
DebugAssert(!l.isNull(), "Expected non-null literal");
if (!translateOnly) d_varInfo[v].fanins.push_back(l);
if (l.isVar()) d_varInfo[l.getVar()].fanouts.push_back(v);
}
return Lit(v);
}
void translate_to_mathematica(const map<Expr, unsigned>& variables, const Expr& assertion) {
bool first;
unsigned n = assertion.getNumChildren();
if (n == 0) {
assert(false);
} else {
std::string op;
bool binary = false;
bool theory = false;
switch (assertion.getKind()) {
case kind::NOT:
cout << "!";
translate_to_mathematica(variables, assertion[0]);
break;
case kind::OR:
first = true;
cout << "(";
for (unsigned i = 0; i < n; ++ i) {
if (!first) {
cout << " || ";
}
first = false;
translate_to_mathematica(variables, assertion[i]);
}
cout << ")";
break;
case kind::AND:
first = true;
cout << "(";
for (unsigned i = 0; i < n; ++ i) {
if (!first) {
cout << " && ";
}
first = false;
translate_to_mathematica(variables, assertion[i]);
}
cout << ")";
break;
case kind::IMPLIES:
cout << "Implies[";
translate_to_mathematica(variables, assertion[0]);
cout << ",";
translate_to_mathematica(variables, assertion[1]);
cout << "]";
break;
case kind::IFF:
cout << "Equivalent[";
translate_to_mathematica(variables, assertion[0]);
cout << ",";
translate_to_mathematica(variables, assertion[1]);
cout << "]";
break;
case kind::EQUAL:
op = "==";
theory = true;
break;
case kind::LT:
op = "<";
theory = true;
break;
case kind::LEQ:
op = "<=";
theory = true;
break;
case kind::GT:
op = ">";
theory = true;
break;
case kind::GEQ:
op = ">=";
theory = true;
break;
default:
assert(false);
break;
}
if (binary) {
cout << "(";
translate_to_mathematica(variables, assertion[0]);
cout << " " << op << " ";
translate_to_mathematica(variables, assertion[1]);
cout << ")";
}
if (theory) {
cout << "(";
translate_to_mathematica_term(variables, assertion[0]);
cout << " " << op << " ";
translate_to_mathematica_term(variables, assertion[1]);
cout << ")";
}
}
}
Expr TheoryArith::rewriteToDiff(const Expr& e)
{
Expr tmp = e[0] - e[1];
tmp = canonRec(tmp).getRHS();
switch (tmp.getKind()) {
case RATIONAL_EXPR: {
Rational r = tmp.getRational();
switch (e.getKind()) {
case LT:
if (r < 0) return trueExpr();
else return falseExpr();
case LE:
if (r <= 0) return trueExpr();
else return falseExpr();
case GT:
if (r > 0) return trueExpr();
else return falseExpr();
case GE:
if (r >= 0) return trueExpr();
else return falseExpr();
case EQ:
if (r == 0) return trueExpr();
else return falseExpr();
}
}
case MULT:
DebugAssert(tmp[0].isRational(), "Unexpected term structure from canon");
if (tmp[0].getRational() != -1) return e;
return Expr(e.getOp(), theoryCore()->getTranslator()->zeroVar() - tmp[1], rat(0));
case PLUS: {
DebugAssert(tmp[0].isRational(), "Unexpected term structure from canon");
Rational c = tmp[0].getRational();
Expr x, y;
if (tmp.arity() == 2) {
if (tmp[1].getKind() == MULT) {
x = theoryCore()->getTranslator()->zeroVar();
y = tmp[1];
}
else {
x = tmp[1];
y = rat(-1) * theoryCore()->getTranslator()->zeroVar();
}
}
else if (tmp.arity() == 3) {
if (tmp[1].getKind() == MULT) {
x = tmp[2];
y = tmp[1];
}
else if (tmp[2].getKind() == MULT) {
x = tmp[1];
y = tmp[2];
}
else return e;
}
else return e;
if (x.getKind() == MULT) return e;
DebugAssert(y[0].isRational(), "Unexpected term structure from canon");
if (y[0].getRational() != -1) return e;
return Expr(e.getOp(), x - y[1], getEM()->newRatExpr(-c));
}
default:
return Expr(e.getOp(), tmp - theoryCore()->getTranslator()->zeroVar(), rat(0));
break;
}
return e;
}
void TheoryUF::assertFact(const Theorem& e)
{
const Expr& expr = e.getExpr();
switch (expr.getKind()) {
case NOT:
break;
case APPLY:
if (expr.getOpExpr().computeTransClosure()) {
enqueueFact(d_rules->relToClosure(e));
}
else if (expr.getOpKind() == TRANS_CLOSURE) {
// const Expr& rel = expr.getFun();
DebugAssert(expr.isApply(), "Should be apply");
Expr rel = resolveID(expr.getOpExpr().getName());
DebugAssert(!rel.isNull(), "Expected known identifier");
DebugAssert(rel.isSymbol() && rel.getKind()==UFUNC && expr.arity()==2,
"Unexpected use of transitive closure: "+expr.toString());
// Insert into transitive closure table
ExprMap<TCMapPair*>::iterator i = d_transClosureMap.find(rel);
TCMapPair* pTable;
if (i == d_transClosureMap.end()) {
pTable = new TCMapPair();
d_transClosureMap[rel] = pTable;
}
else {
pTable = (*i).second;
}
ExprMap<CDList<Theorem>*>::iterator i2 = pTable->appearsFirstMap.find(expr[0]);
CDList<Theorem>* pList;
if (i2 == pTable->appearsFirstMap.end()) {
pList = new(true) CDList<Theorem>(theoryCore()->getCM()->getCurrentContext());
pTable->appearsFirstMap[expr[0]] = pList;
}
else {
pList = (*i2).second;
}
pList->push_back(e);
i2 = pTable->appearsSecondMap.find(expr[1]);
if (i2 == pTable->appearsSecondMap.end()) {
pList = new(true) CDList<Theorem>(theoryCore()->getCM()->getCurrentContext());
pTable->appearsSecondMap[expr[1]] = pList;
}
else {
pList = (*i2).second;
}
pList->push_back(e);
// Compute transitive closure with existing relations
size_t s,l;
i2 = pTable->appearsFirstMap.find(expr[1]);
if (i2 != pTable->appearsFirstMap.end()) {
pList = (*i2).second;
s = pList->size();
for (l = 0; l < s; ++l) {
enqueueFact(d_rules->relTrans(e,(*pList)[l]));
}
}
i2 = pTable->appearsSecondMap.find(expr[0]);
if (i2 != pTable->appearsSecondMap.end()) {
pList = (*i2).second;
s = pList->size();
for (l = 0; l < s; ++l) {
enqueueFact(d_rules->relTrans((*pList)[l],e));
}
}
}
break;
default:
break;
}
}