Theorem
QuantTheoremProducer::normalizeQuant(const Expr& quant) {
if(CHECK_PROOFS) {
CHECK_SOUND(quant.isForall()||quant.isExists(),
"normalizeQuant: expr must be FORALL or EXISTS\n"
+quant.toString());
}
std::map<Expr,int>::iterator typeIter;
std::string base("_BD");
int counter(0);
vector<Expr> newVars;
const std::vector<Expr>& cur_vars = quant.getVars();
for(size_t j =0; j<cur_vars.size(); j++){
Type t = cur_vars[j].getType();
int typeIndex ;
typeIter = d_typeFound.find(t.getExpr());
if(d_typeFound.end() == typeIter){
typeIndex = d_typeFound.size();
d_typeFound[t.getExpr()] = typeIndex;
}
else{
typeIndex = typeIter->second;
}
counter++;
std::stringstream stringType;
stringType << counter << "TY" << typeIndex ;
std::string out_str = base + stringType.str();
Expr newExpr = d_theoryQuant->getEM()->newBoundVarExpr(out_str, int2string(counter));
newExpr.setType(t);
newVars.push_back(newExpr);
}
vector<vector<Expr> > trigs = quant.getTriggers();
for(size_t i = 0 ; i < trigs.size(); i++){
for(size_t j = 0 ; j < trigs[i].size(); j++){
trigs[i][j] = trigs[i][j].substExpr(cur_vars,newVars);
}
}
Expr normBody = quant.getBody().substExpr(cur_vars,newVars);
Expr normQuant = d_theoryQuant->getEM()->newClosureExpr(quant.isForall()?FORALL:EXISTS, newVars, normBody, trigs);
Proof pf;
if(withProof())
pf = newPf("normalizeQuant", quant, normQuant);
return newRWTheorem(quant, normQuant, Assumptions::emptyAssump(), pf);
}
/*! @brief From T|- QUANTIFIER (vars): e we get T|-QUANTIFIER(vars') e
* where vars' is obtained from vars by removing all bound variables
* not used in e. If vars' is empty the produced theorem is just T|-e
*/
Theorem QuantTheoremProducer::boundVarElim(const Theorem& t1)
{
const Expr e=t1.getExpr();
const Expr body = e.getBody();
if(CHECK_PROOFS) {
CHECK_SOUND(e.isForall() || e.isExists(),
"bound var elimination: "
+e.toString());
}
ExprMap<bool> boundVars; //a mapping of bound variables in the body to true
ExprMap<bool> visited; //to make sure expressions aren't traversed
//multiple times
recFindBoundVars(body, boundVars, visited);
vector<Expr> quantVars;
const vector<Expr>& origVars = e.getVars();
for(vector<Expr>::const_iterator it = origVars.begin(),
iend=origVars.end(); it!=iend; ++it)
{
if(boundVars.count(*it) > 0)
quantVars.push_back(*it);
}
// If all variables are used, just return the original theorem
if(quantVars.size() == origVars.size())
return t1;
Proof pf;
if(withProof()) {
vector<Expr> es;
vector<Proof> pfs;
es.push_back(e);
es.insert(es.end(), quantVars.begin(), quantVars.end());
pfs.push_back(t1.getProof());
pf= newPf("bound_variable_elimination", es, pfs);
}
if(quantVars.size() == 0)
return(newTheorem(e.getBody(), t1.getAssumptionsRef(), pf));
Expr newQuantExpr;
if(e.isForall())
newQuantExpr = d_theoryQuant->getEM()->newClosureExpr(FORALL, quantVars, body);
else
newQuantExpr = d_theoryQuant->getEM()->newClosureExpr(EXISTS, quantVars, body);
return(newTheorem(newQuantExpr, t1.getAssumptionsRef(), pf));
}
//! convert (forall (x) ... forall (y)) into (forall (x y)...)
//! convert (exists (x) ... exists (y)) into (exists (x y)...)
Theorem QuantTheoremProducer::pullVarOut(const Theorem& t1){
const Expr thm_expr=t1.getExpr();
if(CHECK_PROOFS) {
CHECK_SOUND(thm_expr.isForall() || thm_expr.isExists(),
"pullVarOut: "
+thm_expr.toString());
}
const Expr outBody = thm_expr.getBody();
// if(((outBody.isAnd() && outBody[1].isForall()) ||
// (outBody.isImpl() && outBody[1].isForall()) ||
// (outBody.isNot() && outBody[0].isAnd() && outBody[0][1].isExists()) )){
// return t1;
// }
if (thm_expr.isForall()){
if((outBody.isNot() && outBody[0].isAnd() && outBody[0][1].isExists())){
vector<Expr> bVarsOut = thm_expr.getVars();
const Expr innerExists =outBody[0][1];
const Expr innerBody = innerExists.getBody();
vector<Expr> bVarsIn = innerExists.getVars();
for(vector<Expr>::iterator i=bVarsIn.begin(), iend=bVarsIn.end(); i!=iend; i++){
bVarsOut.push_back(*i);
}
Proof pf;
if(withProof()) {
vector<Expr> es;
vector<Proof> pfs;
es.push_back(thm_expr);
es.insert(es.end(), bVarsIn.begin(), bVarsIn.end());
pfs.push_back(t1.getProof());
pf= newPf("pullVarOut", es, pfs);
}
Expr newbody;
newbody=(outBody[0][0].notExpr()).orExpr(innerBody.notExpr());
Expr newQuantExpr;
newQuantExpr = d_theoryQuant->getEM()->newClosureExpr(FORALL, bVarsOut, newbody);
return(newTheorem(newQuantExpr, t1.getAssumptionsRef(), pf));
}
else if ((outBody.isAnd() && outBody[1].isForall()) ||
(outBody.isImpl() && outBody[1].isForall())){
vector<Expr> bVarsOut = thm_expr.getVars();
const Expr innerForall=outBody[1];
const Expr innerBody = innerForall.getBody();
vector<Expr> bVarsIn = innerForall.getVars();
for(vector<Expr>::iterator i=bVarsIn.begin(), iend=bVarsIn.end(); i!=iend; i++){
bVarsOut.push_back(*i);
}
Proof pf;
if(withProof()) {
vector<Expr> es;
vector<Proof> pfs;
es.push_back(thm_expr);
es.insert(es.end(), bVarsIn.begin(), bVarsIn.end());
pfs.push_back(t1.getProof());
pf= newPf("pullVarOut", es, pfs);
}
Expr newbody;
if(outBody.isAnd()){
newbody=outBody[0].andExpr(innerBody);
}
else if(outBody.isImpl()){
newbody=outBody[0].impExpr(innerBody);
}
Expr newQuantExpr;
newQuantExpr = d_theoryQuant->getEM()->newClosureExpr(FORALL, bVarsOut, newbody);
return(newTheorem(newQuantExpr, t1.getAssumptionsRef(), pf));
}
return t1; // case cannot be handled now.
}
else if (thm_expr.isExists()){
if ((outBody.isAnd() && outBody[1].isExists()) ||
(outBody.isImpl() && outBody[1].isExists())){
vector<Expr> bVarsOut = thm_expr.getVars();
const Expr innerExists = outBody[1];
const Expr innerBody = innerExists.getBody();
vector<Expr> bVarsIn = innerExists.getVars();
for(vector<Expr>::iterator i=bVarsIn.begin(), iend=bVarsIn.end(); i!=iend; i++){
bVarsOut.push_back(*i);
}
Proof pf;
if(withProof()) {
vector<Expr> es;
vector<Proof> pfs;
es.push_back(thm_expr);
es.insert(es.end(), bVarsIn.begin(), bVarsIn.end());
pfs.push_back(t1.getProof());
pf= newPf("pullVarOut", es, pfs);
}
Expr newbody;
if(outBody.isAnd()){
newbody=outBody[0].andExpr(innerBody);
}
else if(outBody.isImpl()){
newbody=outBody[0].impExpr(innerBody);
}
Expr newQuantExpr;
newQuantExpr = d_theoryQuant->getEM()->newClosureExpr(EXISTS, bVarsOut, newbody);
return(newTheorem(newQuantExpr, t1.getAssumptionsRef(), pf));
}
}
return t1;
}