//! ==> NOT EXISTS (vars): e IFF FORALL (vars) NOT e
Theorem QuantTheoremProducer::rewriteNotExists(const Expr& e) {
if(CHECK_PROOFS) {
CHECK_SOUND(e.isNot() && e[0].isExists(),
"rewriteNotExists: expr must be NOT FORALL:\n"
+e.toString());
}
Proof pf;
if(withProof())
pf = newPf("rewrite_not_exists", e);
return newRWTheorem(e, e.getEM()->newClosureExpr(FORALL, e[0].getVars(),
!e[0].getBody()),
Assumptions::emptyAssump(), pf);
}
Theorem QuantTheoremProducer::partialUniversalInst(const Theorem& t1, const vector<Expr>& terms, int quantLevel){
cout<<"error in partial inst" << endl;
Expr e = t1.getExpr();
const vector<Expr>& boundVars = e.getVars();
if(CHECK_PROOFS) {
CHECK_SOUND(boundVars.size() >= terms.size(),
"Universal instantiation: size of terms array does "
"not match quanitfied variables array size");
CHECK_SOUND(e.isForall(),
"universal instantiation: expr must be FORALL:\n"
+e.toString());
for(unsigned int i=0; i<terms.size(); i++){
CHECK_SOUND(d_theoryQuant->getBaseType(boundVars[i]) ==
d_theoryQuant->getBaseType(terms[i]),
"partial Universal instantiation: type mismatch");
}
}
//build up a conjunction of type predicates for expression
Expr tr = e.getEM()->trueExpr();
Expr typePred = tr;
for(unsigned int i=0; i<terms.size(); i++) {
Expr p = d_theoryQuant->getTypePred(boundVars[i].getType(),terms[i]);
if(p!=tr) {
if(typePred==tr)
typePred = p;
else
typePred = typePred.andExpr(p);
}
}
Proof pf;
if(withProof()) {
vector<Proof> pfs;
vector<Expr> es;
pfs.push_back(t1.getProof());
es.push_back(e);
es.insert(es.end(), terms.begin(), terms.end());
pf= newPf("partial_universal_instantiation", es, pfs);
}
if(terms.size() == boundVars.size()){
Expr inst = e.getBody().substExpr(e.getVars(), terms);
Expr imp;
if(typePred == tr)
imp = inst;
else
imp = typePred.impExpr(inst);
return(newTheorem(imp, t1.getAssumptionsRef(), pf));
}
else{
vector<Expr> newBoundVars;
for(size_t i=0; i<terms.size(); i++) {
newBoundVars.push_back(boundVars[i]);
}
vector<Expr>leftBoundVars;
for(size_t i=terms.size(); i<boundVars.size(); i++) {
leftBoundVars.push_back(boundVars[i]);
}
Expr tempinst = e.getBody().substExpr(newBoundVars, terms);
Expr inst = d_theoryQuant->getEM()->newClosureExpr(FORALL, leftBoundVars, tempinst);
Expr imp;
if(typePred == tr)
imp = inst;
else
imp = typePred.impExpr(inst);
Theorem res = (newTheorem(imp, t1.getAssumptionsRef(), pf));
int thmLevel = t1.getQuantLevel();
if(quantLevel >= thmLevel) {
res.setQuantLevel(quantLevel+1);
}
else{
//k ret.setQuantLevel(thmLevel+1);
res.setQuantLevel(thmLevel);
}
return res;
}
}
Theorem QuantTheoremProducer::universalInst(const Theorem& t1, const vector<Expr>& terms){
Expr e = t1.getExpr();
const vector<Expr>& boundVars = e.getVars();
if(CHECK_PROOFS) {
CHECK_SOUND(boundVars.size() == terms.size(),
"Universal instantiation: size of terms array does "
"not match quanitfied variables array size");
CHECK_SOUND(e.isForall(),
"universal instantiation: expr must be FORALL:\n"
+e.toString());
for(unsigned int i=0; i<terms.size(); i++)
CHECK_SOUND(d_theoryQuant->getBaseType(boundVars[i]) ==
d_theoryQuant->getBaseType(terms[i]),
"Universal instantiation: type mismatch");
}
//build up a conjunction of type predicates for expression
Expr tr = e.getEM()->trueExpr();
Expr typePred = tr;
unsigned qlevel=0, qlevelMax = 0;
for(unsigned int i=0; i<terms.size(); i++) {
Expr p = d_theoryQuant->getTypePred(boundVars[i].getType(),terms[i]);
if(p!=tr) {
if(typePred==tr)
typePred = p;
else
typePred = typePred.andExpr(p);
}
qlevel = d_theoryQuant->theoryCore()->getQuantLevelForTerm(terms[i]);
if (qlevel > qlevelMax) qlevel = qlevelMax;
}
Expr inst = e.getBody().substExpr(e.getVars(), terms);
// Expr inst = e.getBody().substExprQuant(e.getVars(), terms);
// Expr inst = e.getBody().substExpr(e.getVars(), terms);
Proof pf;
if(withProof()) {
vector<Proof> pfs;
vector<Expr> es;
pfs.push_back(t1.getProof());
es.push_back(e);
es.push_back(Expr(RAW_LIST,terms));
// es.insert(es.end(), terms.begin(), terms.end());
es.push_back(inst);
pf= newPf("universal_elimination3", es, pfs);
}
// Expr inst = e.getBody().substExpr(e.getVars(), terms);
Expr imp;
if( typePred == tr ) //just for easy life, yeting, change this asap
imp = inst;
else
imp = typePred.impExpr(inst);
Theorem ret = newTheorem(imp, t1.getAssumptionsRef(), pf);
unsigned thmLevel = t1.getQuantLevel();
if(qlevel >= thmLevel) {
ret.setQuantLevel(qlevel+1);
}
else{
// ret.setQuantLevel(thmLevel+1);
ret.setQuantLevel(thmLevel+1);
}
// ret.setQuantLevel(qlevel+1);
return ret;
}