コード例 #1
0
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);

}
コード例 #2
0
/*! @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));
}
コード例 #3
0
//! 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; 
}