/*********************                                                        */
/*! \file quantifiers_rewriter.cpp
 ** \verbatim
 ** Original author: Morgan Deters
 ** Major contributors: Andrew Reynolds
 ** Minor contributors (to current version): Tim King
 ** This file is part of the CVC4 project.
 ** Copyright (c) 2009-2014  New York University and The University of Iowa
 ** See the file COPYING in the top-level source directory for licensing
 ** information.\endverbatim
 **
 ** \brief Implementation of QuantifiersRewriter class
 **/

#include "theory/quantifiers/quantifiers_rewriter.h"

#include "options/quantifiers_options.h"
#include "theory/datatypes/datatypes_rewriter.h"
#include "theory/quantifiers/term_database.h"
#include "theory/quantifiers/trigger.h"

using namespace std;
using namespace CVC4;
using namespace CVC4::kind;
using namespace CVC4::context;
using namespace CVC4::theory;
using namespace CVC4::theory::quantifiers;

bool QuantifiersRewriter::isClause( Node n ){
  if( isLiteral( n ) ){
    return true;
  }else if( n.getKind()==NOT ){
    return isCube( n[0] );
  }else if( n.getKind()==OR ){
    for( int i=0; i<(int)n.getNumChildren(); i++ ){
      if( !isClause( n[i] ) ){
        return false;
      }
    }
    return true;
  }else if( n.getKind()==IMPLIES ){
    return isCube( n[0] ) && isClause( n[1] );
  }else{
    return false;
  }
}

bool QuantifiersRewriter::isLiteral( Node n ){
  switch( n.getKind() ){
  case NOT:
    return isLiteral( n[0] );
    break;
  case OR:
  case AND:
  case IMPLIES:
  case XOR:
  case ITE:
  case IFF:
    return false;
    break;
  case EQUAL:
    return n[0].getType()!=NodeManager::currentNM()->booleanType();
    break;
  default:
    break;
  }
  return true;
}

bool QuantifiersRewriter::isCube( Node n ){
  if( isLiteral( n ) ){
    return true;
  }else if( n.getKind()==NOT ){
    return isClause( n[0] );
  }else if( n.getKind()==AND ){
    for( int i=0; i<(int)n.getNumChildren(); i++ ){
      if( !isCube( n[i] ) ){
        return false;
      }
    }
    return true;
  }else{
    return false;
  }
}

int QuantifiersRewriter::getPurifyId( Node n ){
  if( !TermDb::hasBoundVarAttr( n ) ){
    return 0;
  }else if( inst::Trigger::isAtomicTriggerKind( n.getKind() ) ){
    return 1;
  }else if( TermDb::isBoolConnective( n.getKind() ) || n.getKind()==EQUAL || n.getKind()==BOUND_VARIABLE ){
    return 0;
  }else{
    return -1;
  }
}

int QuantifiersRewriter::getPurifyIdLit2( Node n, std::map< Node, int >& visited ) {
  std::map< Node, int >::iterator it = visited.find( n );
  if( visited.find( n )==visited.end() ){
    int ret = 0;
    if( TermDb::hasBoundVarAttr( n ) ){
      ret = getPurifyId( n );
      for( unsigned i=0; i<n.getNumChildren(); i++ ){
        int cid = getPurifyIdLit2( n[i], visited );
        if( cid!=0 ){
          if( ret==0 ){
            ret = cid;
          }else if( cid!=ret ){
            ret = -2;
            break;
          }
        }
      }
    }
    visited[n] = ret;
    return ret;
  }else{
    return it->second;
  }
}

int QuantifiersRewriter::getPurifyIdLit( Node n ) {
  std::map< Node, int > visited;
  return getPurifyIdLit2( n, visited );
}

void QuantifiersRewriter::addNodeToOrBuilder( Node n, NodeBuilder<>& t ){
  if( n.getKind()==OR ){
    for( int i=0; i<(int)n.getNumChildren(); i++ ){
      t << n[i];
    }
  }else{
    t << n;
  }
}

void QuantifiersRewriter::computeArgs( std::vector< Node >& args, std::map< Node, bool >& activeMap, Node n, std::map< Node, bool >& visited ){
  if( visited.find( n )==visited.end() ){
    visited[n] = true;
    if( n.getKind()==BOUND_VARIABLE ){
      if( std::find( args.begin(), args.end(), n )!=args.end() ){
        activeMap[ n ] = true;
      }
    }else{
      for( int i=0; i<(int)n.getNumChildren(); i++ ){
        computeArgs( args, activeMap, n[i], visited );
      }
    }
  }
}

void QuantifiersRewriter::computeArgVec( std::vector< Node >& args, std::vector< Node >& activeArgs, Node n ) {
  Assert( activeArgs.empty() );
  std::map< Node, bool > activeMap;
  std::map< Node, bool > visited;
  computeArgs( args, activeMap, n, visited );
  if( !activeMap.empty() ){
    for( unsigned i=0; i<args.size(); i++ ){
      if( activeMap.find( args[i] )!=activeMap.end() ){
        activeArgs.push_back( args[i] );
      }
    }
  }
}

void QuantifiersRewriter::computeArgVec2( std::vector< Node >& args, std::vector< Node >& activeArgs, Node n, Node ipl ) {
  Assert( activeArgs.empty() );
  std::map< Node, bool > activeMap;
  std::map< Node, bool > visited;
  computeArgs( args, activeMap, n, visited );
  if( !activeMap.empty() ){
    //collect variables in inst pattern list only if we cannot eliminate quantifier
    computeArgs( args, activeMap, ipl, visited );
    for( unsigned i=0; i<args.size(); i++ ){
      if( activeMap.find( args[i] )!=activeMap.end() ){
        activeArgs.push_back( args[i] );
      }
    }
  }
}

RewriteResponse QuantifiersRewriter::preRewrite(TNode in) {
  if( in.getKind()==kind::EXISTS || in.getKind()==kind::FORALL ){
    Trace("quantifiers-rewrite-debug") << "pre-rewriting " << in << std::endl;
    std::vector< Node > args;
    for( int i=0; i<(int)in[0].getNumChildren(); i++ ){
      args.push_back( in[0][i] );
    }
    Node body = in[1];
    bool doRewrite = false;
    std::vector< Node > ipl;
    while( body.getNumChildren()>=2 && body.getKind()==in.getKind() ){
      if( body.getNumChildren()==3 ){
        for( unsigned i=0; i<body[2].getNumChildren(); i++ ){
          ipl.push_back( body[2][i] );
        }
      }
      for( int i=0; i<(int)body[0].getNumChildren(); i++ ){
        args.push_back( body[0][i] );
      }
      body = body[1];
      doRewrite = true;
    }
    if( doRewrite ){
      std::vector< Node > children;
      children.push_back( NodeManager::currentNM()->mkNode(kind::BOUND_VAR_LIST,args) );
      children.push_back( body );
      if( in.getNumChildren()==3 ){
        for( unsigned i=0; i<in[2].getNumChildren(); i++ ){
          ipl.push_back( in[2][i] );
        }
      }
      if( !ipl.empty() ){
        children.push_back( NodeManager::currentNM()->mkNode( INST_PATTERN_LIST, ipl ) );
      }
      Node n = NodeManager::currentNM()->mkNode( in.getKind(), children );
      if( in!=n ){
        Trace("quantifiers-pre-rewrite") << "*** pre-rewrite " << in << std::endl;
        Trace("quantifiers-pre-rewrite") << " to " << std::endl;
        Trace("quantifiers-pre-rewrite") << n << std::endl;
      }
      return RewriteResponse(REWRITE_DONE, n);
    }
  }
  return RewriteResponse(REWRITE_DONE, in);
}

RewriteResponse QuantifiersRewriter::postRewrite(TNode in) {
  Trace("quantifiers-rewrite-debug") << "post-rewriting " << in << std::endl;
  RewriteStatus status = REWRITE_DONE;
  Node ret = in;
  //get the body
  if( in.getKind()==EXISTS ){
    std::vector< Node > children;
    children.push_back( in[0] );
    children.push_back( in[1].negate() );
    if( in.getNumChildren()==3 ){
      children.push_back( in[2] );
    }
    ret = NodeManager::currentNM()->mkNode( FORALL, children );
    ret = ret.negate();
    status = REWRITE_AGAIN_FULL;
  }else if( in.getKind()==FORALL ){
    //compute attributes
    QAttributes qa;
    TermDb::computeQuantAttributes( in, qa );
    if( !qa.isRewriteRule() ){
      for( int op=0; op<COMPUTE_LAST; op++ ){
        if( doOperation( in, op, qa ) ){
          ret = computeOperation( in, op, qa );
          if( ret!=in ){
            status = REWRITE_AGAIN_FULL;
            break;
          }
        }
      }
    }
  }
  //print if changed
  if( in!=ret ){
    Trace("quantifiers-rewrite") << "*** rewrite " << in << std::endl;
    Trace("quantifiers-rewrite") << " to " << std::endl;
    Trace("quantifiers-rewrite") << ret << std::endl;
  }
  return RewriteResponse( status, ret );
}

Node QuantifiersRewriter::computeElimSymbols( Node body ) {
  if( isLiteral( body ) ){
    return body;
  }else{
    bool childrenChanged = false;
    Kind k = body.getKind();
    if( body.getKind()==IMPLIES ){
      k = OR;
      childrenChanged = true;
    }else if( body.getKind()==XOR ){
      k = IFF;
      childrenChanged = true;
    }
    std::vector< Node > children;
    std::map< Node, bool > lit_pol;
    for( unsigned i=0; i<body.getNumChildren(); i++ ){
      Node c = computeElimSymbols( body[i] );
      if( i==0 && ( body.getKind()==IMPLIES || body.getKind()==XOR ) ){
        c = c.negate();
      }
      if( ( k==OR || k==AND ) && options::elimTautQuant() ){
        Node lit = c.getKind()==NOT ? c[0] : c;
        bool pol = c.getKind()!=NOT;
        std::map< Node, bool >::iterator it = lit_pol.find( lit );
        if( it==lit_pol.end() ){
          lit_pol[lit] = pol;
          children.push_back( c );
        }else{
          childrenChanged = true;
          if( it->second!=pol ){
            return NodeManager::currentNM()->mkConst( k==OR );
          }
        }
      }else{
        children.push_back( c );
      }
      childrenChanged = childrenChanged || c!=body[i];
    }
    //if( body.getKind()==ITE && isLiteral( body[0] ) ){
    //  ret = NodeManager::currentNM()->mkNode( AND, NodeManager::currentNM()->mkNode( OR, body[0].negate(), body[1] ), 
    //                                               NodeManager::currentNM()->mkNode( OR, body[0], body[2] ) );
    //}
    if( childrenChanged ){
      return ( children.size()==1 && k!=NOT ) ? children[0] : NodeManager::currentNM()->mkNode( k, children );
    }else{
      return body;
    }
  }
}

Node QuantifiersRewriter::computeNNF( Node body ){
  if( body.getKind()==NOT ){
    if( body[0].getKind()==NOT ){
      return computeNNF( body[0][0] );
    }else if( isLiteral( body[0] ) ){
      return body;
    }else{
      std::vector< Node > children;
      Kind k = body[0].getKind();

      if( body[0].getKind()==OR || body[0].getKind()==AND ){
        k = body[0].getKind()==AND ? OR : AND;
        for( int i=0; i<(int)body[0].getNumChildren(); i++ ){
          Node nc = computeNNF( body[0][i].notNode() );
          if( nc.getKind()==k ){
            for( unsigned j=0; j<nc.getNumChildren(); j++ ){
              children.push_back( nc[j] );
            }
          }else{
            children.push_back( nc );
          }
        }
      }else if( body[0].getKind()==IFF ){
        for( int i=0; i<2; i++ ){
          Node nn = i==0 ? body[0][i] : body[0][i].notNode();
          children.push_back( computeNNF( nn ) );
        }
      }else if( body[0].getKind()==ITE ){
        for( int i=0; i<3; i++ ){
          Node nn = i==0 ? body[0][i] : body[0][i].notNode();
          children.push_back( computeNNF( nn ) );
        }
      }else{
        Notice() << "Unhandled Quantifiers NNF: " << body << std::endl;
        return body;
      }
      return NodeManager::currentNM()->mkNode( k, children );
    }
  }else if( isLiteral( body ) ){
    return body;
  }else{
    std::vector< Node > children;
    bool childrenChanged = false;
    bool isAssoc = body.getKind()==AND || body.getKind()==OR;
    for( int i=0; i<(int)body.getNumChildren(); i++ ){
      Node nc = computeNNF( body[i] );
      if( isAssoc && nc.getKind()==body.getKind() ){
        for( unsigned j=0; j<nc.getNumChildren(); j++ ){
          children.push_back( nc[j] );
        }
        childrenChanged = true;
      }else{
        children.push_back( nc );
        childrenChanged = childrenChanged || nc!=body[i];
      }
    }
    if( childrenChanged ){
      return NodeManager::currentNM()->mkNode( body.getKind(), children );
    }else{
      return body;
    }
  }
}


void QuantifiersRewriter::computeDtTesterIteSplit( Node n, std::map< Node, Node >& pcons, std::map< Node, std::map< int, Node > >& ncons,
                                                   std::vector< Node >& conj ){
  if( n.getKind()==ITE && n[0].getKind()==APPLY_TESTER && n[1].getType().isBoolean() ){
    Trace("quantifiers-rewrite-ite-debug") << "Split tester condition : " << n << std::endl;
    Node x = n[0][0];
    std::map< Node, Node >::iterator itp = pcons.find( x );
    if( itp!=pcons.end() ){
      Trace("quantifiers-rewrite-ite-debug") << "...condition already set " << itp->second << std::endl;
      computeDtTesterIteSplit( n[ itp->second==n[0] ? 1 : 2 ], pcons, ncons, conj );
    }else{
      Expr testerExpr = n[0].getOperator().toExpr();
      int index = Datatype::indexOf( testerExpr );
      std::map< int, Node >::iterator itn = ncons[x].find( index );
      if( itn!=ncons[x].end() ){
        Trace("quantifiers-rewrite-ite-debug") << "...condition negated " << itn->second << std::endl;
        computeDtTesterIteSplit( n[ 2 ], pcons, ncons, conj );
      }else{
        for( unsigned i=0; i<2; i++ ){
          if( i==0 ){
            pcons[x] = n[0];
          }else{
            pcons.erase( x );
            ncons[x][index] = n[0].negate();
          }
          computeDtTesterIteSplit( n[i+1], pcons, ncons, conj );
        }
        ncons[x].erase( index );
      }
    }
  }else{
    Trace("quantifiers-rewrite-ite-debug") << "Return value : " << n << std::endl;
    std::vector< Node > children;
    children.push_back( n );
    std::vector< Node > vars;
    //add all positive testers
    for( std::map< Node, Node >::iterator it = pcons.begin(); it != pcons.end(); ++it ){
      children.push_back( it->second.negate() );
      vars.push_back( it->first );
    }
    //add all negative testers
    for( std::map< Node, std::map< int, Node > >::iterator it = ncons.begin(); it != ncons.end(); ++it ){
      Node x = it->first;
      //only if we haven't settled on a positive tester
      if( std::find( vars.begin(), vars.end(), x )==vars.end() ){
        //check if we have exhausted all options but one
        const Datatype& dt = DatatypeType(x.getType().toType()).getDatatype();
        std::vector< Node > nchildren;
        int pos_cons = -1;
        for( int i=0; i<(int)dt.getNumConstructors(); i++ ){
          std::map< int, Node >::iterator itt = it->second.find( i );
          if( itt==it->second.end() ){
            pos_cons = pos_cons==-1 ? i : -2;
          }else{
            nchildren.push_back( itt->second.negate() );
          }
        }
        if( pos_cons>=0 ){
          const DatatypeConstructor& c = dt[pos_cons];
          Expr tester = c.getTester();
          children.push_back( NodeManager::currentNM()->mkNode( kind::APPLY_TESTER, Node::fromExpr( tester ), x ).negate() );
        }else{
          children.insert( children.end(), nchildren.begin(), nchildren.end() );
        }
      }
    }
    //make condition/output pair
    Node c = children.size()==1 ? children[0] : NodeManager::currentNM()->mkNode( OR, children );
    conj.push_back( c );
  }
}

int getEntailedCond( Node n, std::map< Node, bool >& currCond ){
  std::map< Node, bool >::iterator it = currCond.find( n );
  if( it!=currCond.end() ){
    return it->second ? 1 : -1;
  }else if( n.getKind()==AND || n.getKind()==OR ){
    bool hasZero = false;
    for( unsigned i=0; i<n.getNumChildren(); i++ ){
      int res = getEntailedCond( n[i], currCond );
      if( res==0 ){
        hasZero = true;
      }else if( n.getKind()==AND && res==-1 ){
        return -1;
      }else if( n.getKind()==OR && res==1 ){
        return 1;
      }
    }
    return hasZero ? 0 : ( n.getKind()==AND ? 1 : -1 );
  }else if( n.getKind()==ITE ){
    int res = getEntailedCond( n[0], currCond );
    if( res==1 ){
      return getEntailedCond( n[1], currCond );
    }else if( res==-1 ){
      return getEntailedCond( n[2], currCond );
    }
  }
  if( n.getKind()==IFF || n.getKind()==ITE ){
    unsigned start = n.getKind()==IFF ? 0 : 1;
    int res1 = 0;
    for( unsigned j=start; j<=(start+1); j++ ){
      int res = getEntailedCond( n[j], currCond );
      if( res==0 ){
        return 0;
      }else if( j==start ){
        res1 = res;
      }else{
        Assert( res!=0 );
        if( n.getKind()==ITE ){
          return res1==res ? res : 0;
        }else if( n.getKind()==IFF ){
          return res1==res ? 1 : -1;
        }
      }
    }
  }
  return 0;
}

bool addEntailedCond( Node n, bool pol, std::map< Node, bool >& currCond, std::vector< Node >& new_cond, bool& conflict ) {
  std::map< Node, bool >::iterator it = currCond.find( n );
  if( it==currCond.end() ){
    Trace("quantifiers-rewrite-term-debug") << "cond : " << n << " -> " << pol << std::endl;
    new_cond.push_back( n );
    currCond[n] = pol;
    return true;
  }else{
    if( it->second!=pol ){
      Trace("quantifiers-rewrite-term-debug") << "CONFLICTING cond : " << n << " -> " << pol << std::endl;
      conflict = true;
    }
    return false;
  }
}

void setEntailedCond( Node n, bool pol, std::map< Node, bool >& currCond, std::vector< Node >& new_cond, bool& conflict ) {
  if( ( n.getKind()==AND && pol ) || ( n.getKind()==OR && !pol ) ){
    for( unsigned i=0; i<n.getNumChildren(); i++ ){
      setEntailedCond( n[i], pol, currCond, new_cond, conflict );
      if( conflict ){
        break;
      }
    }
  }else if( n.getKind()==NOT ){
    setEntailedCond( n[0], !pol, currCond, new_cond, conflict );
    return;
  }else if( n.getKind()==ITE ){
    int pol = getEntailedCond( n, currCond );
    if( pol==1 ){
      setEntailedCond( n[1], pol, currCond, new_cond, conflict );
    }else if( pol==-1 ){
      setEntailedCond( n[2], pol, currCond, new_cond, conflict );
    }
  }
  if( addEntailedCond( n, pol, currCond, new_cond, conflict ) ){
    if( n.getKind()==APPLY_TESTER ){
      const Datatype& dt = Datatype::datatypeOf(n.getOperator().toExpr());
      unsigned index = Datatype::indexOf(n.getOperator().toExpr());
      Assert( dt.getNumConstructors()>1 );
      if( pol ){
        for( unsigned i=0; i<dt.getNumConstructors(); i++ ){
          if( i!=index ){
            Node t = NodeManager::currentNM()->mkNode( APPLY_TESTER, Node::fromExpr( dt[i].getTester() ), n[0] );
            addEntailedCond( t, false, currCond, new_cond, conflict );
          }
        }
      }else{
        if( dt.getNumConstructors()==2 ){
          int oindex = 1-index;
          Node t = NodeManager::currentNM()->mkNode( APPLY_TESTER, Node::fromExpr( dt[oindex].getTester() ), n[0] );
          addEntailedCond( t, true, currCond, new_cond, conflict );
        }
      }
    }
  }
}

void removeEntailedCond( std::map< Node, bool >& currCond, std::vector< Node >& new_cond, std::map< Node, Node >& cache ) {
  if( !new_cond.empty() ){
    for( unsigned j=0; j<new_cond.size(); j++ ){
      currCond.erase( new_cond[j] );
    }
    new_cond.clear();
    cache.clear();
  }
}

Node QuantifiersRewriter::computeProcessTerms( Node body, std::vector< Node >& new_vars, std::vector< Node >& new_conds, Node q, QAttributes& qa ){
  std::map< Node, bool > curr_cond;
  std::map< Node, Node > cache;
  std::map< Node, Node > icache;
  if( qa.isFunDef() ){
    Node h = TermDb::getFunDefHead( q );
    Assert( !h.isNull() );
    // if it is a function definition, rewrite the body independently
    Node fbody = TermDb::getFunDefBody( q );
    Assert( !body.isNull() );
    Trace("quantifiers-rewrite-debug") << "Decompose " << h << " / " << fbody << " as function definition for " << q << "." << std::endl;
    Node r = computeProcessTerms2( fbody, true, true, curr_cond, 0, cache, icache, new_vars, new_conds );
    return Rewriter::rewrite( NodeManager::currentNM()->mkNode( h.getType().isBoolean() ? IFF : EQUAL, h, r ) );
  }else{
    return computeProcessTerms2( body, true, true, curr_cond, 0, cache, icache, new_vars, new_conds );
  }
}

Node QuantifiersRewriter::computeProcessTerms2( Node body, bool hasPol, bool pol, std::map< Node, bool >& currCond, int nCurrCond,
                                                std::map< Node, Node >& cache, std::map< Node, Node >& icache,
                                                std::vector< Node >& new_vars, std::vector< Node >& new_conds ) {
  Trace("quantifiers-rewrite-term-debug2") << "computeProcessTerms " << body << " " << hasPol << " " << pol << std::endl;
  Node ret;
  std::map< Node, Node >::iterator iti = cache.find( body );
  if( iti!=cache.end() ){
    ret = iti->second;
    Trace("quantifiers-rewrite-term-debug2") << "Return (cached) " << ret << " for " << body << std::endl;
  }else{
    //only do context dependent processing up to depth 8
    bool doCD = nCurrCond<8;
    bool changed = false;
    std::vector< Node > children;
    //set entailed conditions based on OR/AND
    std::map< int, std::vector< Node > > new_cond_children;
    if( doCD && ( body.getKind()==OR || body.getKind()==AND ) ){
      nCurrCond = nCurrCond + 1;
      bool conflict = false;
      bool use_pol = body.getKind()==AND;
      for( unsigned j=0; j<body.getNumChildren(); j++ ){
        setEntailedCond( body[j], use_pol, currCond, new_cond_children[j], conflict );
      }
      if( conflict ){
        Trace("quantifiers-rewrite-term-debug") << "-------conflict, return " << !use_pol << std::endl;
        ret = NodeManager::currentNM()->mkConst( !use_pol );
      }
    }
    if( ret.isNull() ){
      for( size_t i=0; i<body.getNumChildren(); i++ ){
      
        //set/update entailed conditions
        std::vector< Node > new_cond;
        bool conflict = false;
        if( doCD ){
          if( Trace.isOn("quantifiers-rewrite-term-debug") ){
            if( ( body.getKind()==ITE && i>0 ) || body.getKind()==OR || body.getKind()==AND ){
              Trace("quantifiers-rewrite-term-debug") << "---rewrite " << body[i] << " under conditions:----" << std::endl;
            }
          }
          if( body.getKind()==ITE && i>0 ){
            if( i==1 ){
              nCurrCond = nCurrCond + 1;
            }
            setEntailedCond( children[0], i==1, currCond, new_cond, conflict );
            //should not conflict (entailment check failed) 
            Assert( !conflict );
          }
          if( body.getKind()==OR || body.getKind()==AND ){
            bool use_pol = body.getKind()==AND;
            //remove the current condition
            removeEntailedCond( currCond, new_cond_children[i], cache );
            if( i>0 ){
              //add the previous condition
              setEntailedCond( children[i-1], use_pol, currCond, new_cond_children[i-1], conflict );
            }
            if( conflict ){
              Trace("quantifiers-rewrite-term-debug") << "-------conflict, return " << !use_pol << std::endl;
              ret = NodeManager::currentNM()->mkConst( !use_pol );
            }
          }
          if( !new_cond.empty() ){
            cache.clear();
          }
          if( Trace.isOn("quantifiers-rewrite-term-debug") ){
            if( ( body.getKind()==ITE && i>0 ) || body.getKind()==OR || body.getKind()==AND ){      
              Trace("quantifiers-rewrite-term-debug") << "-------" << std::endl;
            }
          }
        }
        
        //do the recursive call on children
        if( !conflict ){
          bool newHasPol;
          bool newPol;
          QuantPhaseReq::getPolarity( body, i, hasPol, pol, newHasPol, newPol );
          Node nn = computeProcessTerms2( body[i], newHasPol, newPol, currCond, nCurrCond, cache, icache, new_vars, new_conds );
          if( body.getKind()==ITE && i==0 ){
            int res = getEntailedCond( nn, currCond );
            Trace("quantifiers-rewrite-term-debug") << "Condition for " << body << " is " << nn << ", entailment check=" << res << std::endl;
            if( res==1 ){
              ret = computeProcessTerms2( body[1], hasPol, pol, currCond, nCurrCond, cache, icache, new_vars, new_conds );
            }else if( res==-1 ){
              ret = computeProcessTerms2( body[2], hasPol, pol, currCond, nCurrCond, cache, icache, new_vars, new_conds );
            }
          }
          children.push_back( nn );
          changed = changed || nn!=body[i];
        }
        
        //clean up entailed conditions
        removeEntailedCond( currCond, new_cond, cache );
        
        if( !ret.isNull() ){
          break;
        }
      }
      
      //make return value
      if( ret.isNull() ){
        if( changed ){
          if( body.getMetaKind() == kind::metakind::PARAMETERIZED ){
            children.insert( children.begin(), body.getOperator() );
          }
          ret = NodeManager::currentNM()->mkNode( body.getKind(), children );
        }else{
          ret = body;
        }
      }
    }
    
    //clean up entailed conditions
    if( body.getKind()==OR || body.getKind()==AND ){
      for( unsigned j=0; j<body.getNumChildren(); j++ ){
        removeEntailedCond( currCond, new_cond_children[j], cache );
      }
    }
    
    Trace("quantifiers-rewrite-term-debug2") << "Returning " << ret << " for " << body << std::endl;
    cache[body] = ret;
  }

  //do context-independent rewriting
  iti = icache.find( ret );
  if( iti!=icache.end() ){
    return iti->second;
  }else{
    Node prev = ret;
    if( ret.getKind()==EQUAL && options::iteLiftQuant()!=ITE_LIFT_QUANT_MODE_NONE ){
      for( size_t i=0; i<2; i++ ){
        if( ret[i].getKind()==ITE ){
          Node no = i==0 ? ret[1] : ret[0];
          if( no.getKind()!=ITE ){
            bool doRewrite = options::iteLiftQuant()==ITE_LIFT_QUANT_MODE_ALL;
            std::vector< Node > children;
            children.push_back( ret[i][0] );
            for( size_t j=1; j<=2; j++ ){
              //check if it rewrites to a constant
              Node nn = NodeManager::currentNM()->mkNode( EQUAL, no, ret[i][j] );
              nn = Rewriter::rewrite( nn );
              children.push_back( nn );
              if( nn.isConst() ){
                doRewrite = true;
              }
            }
            if( doRewrite ){
              ret = NodeManager::currentNM()->mkNode( ITE, children );
              break;
            }
          }
        }
      }
    /* ITE lifting
    if( ret.getKind()==ITE ){
      TypeNode ite_t = ret[1].getType();
      if( !ite_t.isBoolean() ){
        ite_t = TypeNode::leastCommonTypeNode( ite_t, ret[2].getType() );
        Node ite_v = NodeManager::currentNM()->mkBoundVar(ite_t);
        new_vars.push_back( ite_v );
        Node cond = NodeManager::currentNM()->mkNode(kind::ITE, ret[0], ite_v.eqNode( ret[1] ), ite_v.eqNode( ret[2] ) );
        new_conds.push_back( cond.negate() );
        ret = ite_v;
      }
      */
    }else if( options::elimExtArithQuant() ){
      if( ret.getKind()==INTS_DIVISION_TOTAL || ret.getKind()==INTS_MODULUS_TOTAL ){
        Node num = ret[0];
        Node den = ret[1];
        if(den.isConst()) {
          const Rational& rat = den.getConst<Rational>();
          Assert(!num.isConst());
          if(rat != 0) {
            Node intVar = NodeManager::currentNM()->mkBoundVar(NodeManager::currentNM()->integerType());
            new_vars.push_back( intVar );
            Node cond;
            if(rat > 0) {
              cond = NodeManager::currentNM()->mkNode(kind::AND,
                       NodeManager::currentNM()->mkNode(kind::LEQ, NodeManager::currentNM()->mkNode(kind::MULT, den, intVar), num),
                       NodeManager::currentNM()->mkNode(kind::LT, num,
                         NodeManager::currentNM()->mkNode(kind::MULT, den, NodeManager::currentNM()->mkNode(kind::PLUS, intVar, NodeManager::currentNM()->mkConst(Rational(1))))));
            } else {
              cond = NodeManager::currentNM()->mkNode(kind::AND,
                       NodeManager::currentNM()->mkNode(kind::LEQ, NodeManager::currentNM()->mkNode(kind::MULT, den, intVar), num),
                       NodeManager::currentNM()->mkNode(kind::LT, num,
                         NodeManager::currentNM()->mkNode(kind::MULT, den, NodeManager::currentNM()->mkNode(kind::PLUS, intVar, NodeManager::currentNM()->mkConst(Rational(-1))))));
            }
            new_conds.push_back( cond.negate() );
            if( ret.getKind()==INTS_DIVISION_TOTAL ){
              ret = intVar;
            }else{
              ret = NodeManager::currentNM()->mkNode(kind::MINUS, num, NodeManager::currentNM()->mkNode(kind::MULT, den, intVar));
            }
          }
        }
      }else if( ret.getKind()==TO_INTEGER || ret.getKind()==IS_INTEGER ){
        Node intVar = NodeManager::currentNM()->mkBoundVar(NodeManager::currentNM()->integerType());
        new_vars.push_back( intVar );
        new_conds.push_back(NodeManager::currentNM()->mkNode(kind::AND,
                              NodeManager::currentNM()->mkNode(kind::LT,
                                NodeManager::currentNM()->mkNode(kind::MINUS, ret[0], NodeManager::currentNM()->mkConst(Rational(1))), intVar),
                              NodeManager::currentNM()->mkNode(kind::LEQ, intVar, ret[0])).negate());
        if( ret.getKind()==TO_INTEGER ){
          ret = intVar;
        }else{
          ret = ret[0].eqNode( intVar );
        }
      }
    }
    icache[prev] = ret;
    return ret;
  }
}


bool QuantifiersRewriter::isConditionalVariableElim( Node n, int pol ){
  if( n.getKind()==NOT ){
    return isConditionalVariableElim( n[0], -pol );
  }else if( ( n.getKind()==AND && pol>=0 ) || ( n.getKind()==OR && pol<=0 ) ){
    pol = n.getKind()==AND ? 1 : -1;
    for( unsigned i=0; i<n.getNumChildren(); i++ ){
      if( isConditionalVariableElim( n[i], pol ) ){
        return true;
      }
    }
  }else if( n.getKind()==EQUAL ){
    for( unsigned i=0; i<2; i++ ){
      if( n[i].getKind()==BOUND_VARIABLE ){
        if( !TermDb::containsTerm( n[1-i], n[i] ) ){
          return true;
        }
      }
    }
  }else if( n.getKind()==BOUND_VARIABLE ){
    return true;
  }
  return false;
}

Node QuantifiersRewriter::computeCondSplit( Node body, QAttributes& qa ){
  if( options::iteDtTesterSplitQuant() && body.getKind()==ITE ){
    Trace("quantifiers-rewrite-ite-debug") << "DTT split : " << body << std::endl;
    std::map< Node, Node > pcons;
    std::map< Node, std::map< int, Node > > ncons;
    std::vector< Node > conj;
    computeDtTesterIteSplit( body, pcons, ncons, conj );
    Assert( !conj.empty() );
    if( conj.size()>1 ){
      Trace("quantifiers-rewrite-ite") << "*** Split ITE (datatype tester) " << body << " into : " << std::endl;
      for( unsigned i=0; i<conj.size(); i++ ){
        Trace("quantifiers-rewrite-ite") << "   " << conj[i] << std::endl;
      }
      return NodeManager::currentNM()->mkNode( AND, conj );
    }
  }
  if( options::condVarSplitQuant() ){
    if( body.getKind()==ITE || ( body.getKind()==IFF && options::condVarSplitQuantAgg() ) ){
      Assert( !qa.isFunDef() );
      Trace("quantifiers-rewrite-debug") << "Conditional var elim split " << body << "?" << std::endl;
      bool do_split = false;
      unsigned index_max = body.getKind()==ITE ? 0 : 1;
      for( unsigned index=0; index<=index_max; index++ ){
        if( isConditionalVariableElim( body[index] ) ){
          do_split = true;
          break;
        }
      }
      if( do_split ){
        Node pos;
        Node neg;
        if( body.getKind()==ITE ){
          pos = NodeManager::currentNM()->mkNode( OR, body[0].negate(), body[1] );
          neg = NodeManager::currentNM()->mkNode( OR, body[0], body[2] );
        }else{
          pos = NodeManager::currentNM()->mkNode( OR, body[0].negate(), body[1] );
          neg = NodeManager::currentNM()->mkNode( OR, body[0], body[1].negate() );
        }
        Trace("quantifiers-rewrite-debug") << "*** Split (conditional variable eq) " << body << " into : " << std::endl;
        Trace("quantifiers-rewrite-debug") << "   " << pos << std::endl;
        Trace("quantifiers-rewrite-debug") << "   " << neg << std::endl;
        return NodeManager::currentNM()->mkNode( AND, pos, neg );
      }
    }else if( body.getKind()==OR && options::condVarSplitQuantAgg() ){
      std::vector< Node > bchildren;
      std::vector< Node > nchildren;
      for( unsigned i=0; i<body.getNumChildren(); i++ ){
        bool split = false;
        if( nchildren.empty() ){
          if( body[i].getKind()==AND ){
            std::vector< Node > children;
            for( unsigned j=0; j<body[i].getNumChildren(); j++ ){
              if( ( body[i][j].getKind()==NOT && body[i][j][0].getKind()==EQUAL && isConditionalVariableElim( body[i][j][0] ) ) ||
                  body[i][j].getKind()==BOUND_VARIABLE ){
                nchildren.push_back( body[i][j] );
              }else{
                children.push_back( body[i][j] );
              }
            }
            if( !nchildren.empty() ){
              if( !children.empty() ){
                nchildren.push_back( children.size()==1 ? children[0] : NodeManager::currentNM()->mkNode( AND, children ) );
              }
              split = true;
            }
          }
        }
        if( !split ){
          bchildren.push_back( body[i] );
        }
      }
      if( !nchildren.empty() ){
        Trace("quantifiers-rewrite-debug") << "*** Split (conditional variable eq) " << body << " into : " << std::endl;
        for( unsigned i=0; i<nchildren.size(); i++ ){
          bchildren.push_back( nchildren[i] );
          nchildren[i] = NodeManager::currentNM()->mkNode( OR, bchildren );
          Trace("quantifiers-rewrite-debug") << "   " << nchildren[i] << std::endl;
          bchildren.pop_back();
        }
        return NodeManager::currentNM()->mkNode( AND, nchildren );
      }
    }
  }
  return body;
}

bool QuantifiersRewriter::isVariableElim( Node v, Node s, std::map< Node, std::vector< int > >& var_parent ) {
  if( TermDb::containsTerm( s, v ) || !s.getType().isSubtypeOf( v.getType() ) ){
    return false;
  }else{
    if( !var_parent.empty() ){
      std::map< Node, std::vector< int > >::iterator it = var_parent.find( v );
      if( it!=var_parent.end() ){
        Assert( !it->second.empty() );
        int id = getPurifyId( s );
        return it->second.size()==1 && it->second[0]==id;
      }
    }
    return true;
  }
}

bool QuantifiersRewriter::computeVariableElimLit( Node lit, bool pol, std::vector< Node >& args, std::vector< Node >& vars, std::vector< Node >& subs,
                                                  std::map< Node, std::vector< int > >& var_parent ) {
  if( lit.getKind()==EQUAL && pol ){
    for( unsigned i=0; i<2; i++ ){
      std::vector< Node >::iterator ita = std::find( args.begin(), args.end(), lit[i] );
      if( ita!=args.end() ){
        if( isVariableElim( lit[i], lit[1-i], var_parent ) ){
          Trace("var-elim-quant") << "Variable eliminate based on equality : " << lit[i] << " -> " << lit[1-i] << std::endl;
          vars.push_back( lit[i] );
          subs.push_back( lit[1-i] );
          args.erase( ita );
          return true;
        }
      }
    }
    //for arithmetic, solve the equality
    if( lit[0].getType().isReal() ){
      std::map< Node, Node > msum;
      if( QuantArith::getMonomialSumLit( lit, msum ) ){
        for( std::map< Node, Node >::iterator itm = msum.begin(); itm != msum.end(); ++itm ){
          std::vector< Node >::iterator ita = std::find( args.begin(), args.end(), itm->first );
          if( ita!=args.end() ){
            Node veq_c;
            Node val;
            int ires = QuantArith::isolate( itm->first, msum, veq_c, val, EQUAL );
            if( ires!=0 && veq_c.isNull() && isVariableElim( itm->first, val, var_parent ) ){
              Trace("var-elim-quant") << "Variable eliminate based on solved equality : " << itm->first << " -> " << val << std::endl;
              vars.push_back( itm->first );
              subs.push_back( val );
              args.erase( ita );
              return true;
            }
          }
        }
      }
    }
  }else if( lit.getKind()==APPLY_TESTER && pol && lit[0].getKind()==BOUND_VARIABLE ){
    Trace("var-elim-dt") << "Expand datatype variable based on : " << lit << std::endl;
    std::vector< Node >::iterator ita = std::find( args.begin(), args.end(), lit[0] );
    if( ita!=args.end() ){
      vars.push_back( lit[0] );
      Expr testerExpr = lit.getOperator().toExpr();
      int index = Datatype::indexOf( testerExpr );
      const Datatype& dt = Datatype::datatypeOf(testerExpr);
      const DatatypeConstructor& c = dt[index];
      std::vector< Node > newChildren;
      newChildren.push_back( Node::fromExpr( c.getConstructor() ) );
      std::vector< Node > newVars;
      for( unsigned j=0; j<c.getNumArgs(); j++ ){
        TypeNode tn = TypeNode::fromType( c[j].getRangeType() );
        Node v = NodeManager::currentNM()->mkBoundVar( tn );
        newChildren.push_back( v );
        newVars.push_back( v );
      }
      subs.push_back( NodeManager::currentNM()->mkNode( APPLY_CONSTRUCTOR, newChildren ) );
      Trace("var-elim-dt") << "...apply substitution " << subs[0] << "/" << vars[0] << std::endl;
      args.erase( ita );
      args.insert( args.end(), newVars.begin(), newVars.end() );
      return true;
    }
  }else if( lit.getKind()==BOUND_VARIABLE ){
    std::vector< Node >::iterator ita = std::find( args.begin(), args.end(), lit );
    if( ita!=args.end() ){
      Trace("var-elim-bool") << "Variable eliminate : " << lit << std::endl;
      vars.push_back( lit );
      subs.push_back( NodeManager::currentNM()->mkConst( pol ) );
      args.erase( ita );
      return true;
    }
  }
  return false;
}

Node QuantifiersRewriter::computeVarElimination2( Node body, std::vector< Node >& args, QAttributes& qa, std::map< Node, std::vector< int > >& var_parent ){
  Trace("var-elim-quant-debug") << "Compute var elimination for " << body << std::endl;
  QuantPhaseReq qpr( body );
  std::vector< Node > vars;
  std::vector< Node > subs;
  for( std::map< Node, bool >::iterator it = qpr.d_phase_reqs.begin(); it != qpr.d_phase_reqs.end(); ++it ){
    //Notice() << "   " << it->first << " -> " << ( it->second ? "true" : "false" ) << std::endl;
    if( ( it->first.getKind()==EQUAL && it->second && options::varElimQuant() ) ||
        ( it->first.getKind()==APPLY_TESTER && it->second && it->first[0].getKind()==BOUND_VARIABLE && options::dtVarExpandQuant() ) ||
        ( it->first.getKind()==BOUND_VARIABLE && options::varElimQuant() ) ){
      if( computeVariableElimLit( it->first, it->second, args, vars, subs, var_parent ) ){
        break;
      }
    }
  }
  if( !vars.empty() ){
    Trace("var-elim-quant-debug") << "VE " << vars.size() << "/" << args.size() << std::endl;
    //remake with eliminated nodes
    body = body.substitute( vars.begin(), vars.end(), subs.begin(), subs.end() );
    body = Rewriter::rewrite( body );
    if( !qa.d_ipl.isNull() ){
      qa.d_ipl = qa.d_ipl.substitute( vars.begin(), vars.end(), subs.begin(), subs.end() );
    }
    Trace("var-elim-quant") << "Return " << body << std::endl;
  }
  return body;
}

Node QuantifiersRewriter::computeVarElimination( Node body, std::vector< Node >& args, QAttributes& qa ){
  //the parent id's for each variable, if using purifyQuant
  std::map< Node, std::vector< int > > var_parent;
  if( options::purifyQuant() ){
    body = computePurify( body, args, var_parent );
  }
  if( options::varElimQuant() || options::dtVarExpandQuant() ){
    Node prev;
    do{
      prev = body;
      body = computeVarElimination2( body, args, qa, var_parent );
    }while( prev!=body && !args.empty() );
  }
  return body;
}

Node QuantifiersRewriter::computeClause( Node n ){
  Assert( isClause( n ) );
  if( isLiteral( n ) ){
    return n;
  }else{
    NodeBuilder<> t(OR);
    if( n.getKind()==NOT ){
      if( n[0].getKind()==NOT ){
        return computeClause( n[0][0] );
      }else{
        //De-Morgan's law
        Assert( n[0].getKind()==AND );
        for( int i=0; i<(int)n[0].getNumChildren(); i++ ){
          Node nn = computeClause( n[0][i].notNode() );
          addNodeToOrBuilder( nn, t );
        }
      }
    }else{
      for( int i=0; i<(int)n.getNumChildren(); i++ ){
        Node nn = computeClause( n[i] );
        addNodeToOrBuilder( nn, t );
      }
    }
    return t.constructNode();
  }
}

Node QuantifiersRewriter::computeCNF( Node n, std::vector< Node >& args, NodeBuilder<>& defs, bool forcePred ){
  if( isLiteral( n ) ){
    return n;
  }else if( !forcePred && isClause( n ) ){
    return computeClause( n );
  }else{
    Kind k = n.getKind();
    NodeBuilder<> t(k);
    for( int i=0; i<(int)n.getNumChildren(); i++ ){
      Node nc = n[i];
      Node ncnf = computeCNF( nc, args, defs, k!=OR );
      if( k==OR ){
        addNodeToOrBuilder( ncnf, t );
      }else{
        t << ncnf;
      }
    }
    if( !forcePred && k==OR ){
      return t.constructNode();
    }else{
      //compute the free variables
      Node nt = t;
      std::vector< Node > activeArgs;
      computeArgVec( args, activeArgs, nt );
      std::vector< TypeNode > argTypes;
      for( int i=0; i<(int)activeArgs.size(); i++ ){
        argTypes.push_back( activeArgs[i].getType() );
      }
      //create the predicate
      Assert( argTypes.size()>0 );
      TypeNode typ = NodeManager::currentNM()->mkFunctionType( argTypes, NodeManager::currentNM()->booleanType() );
      std::stringstream ss;
      ss << "cnf_" << n.getKind() << "_" << n.getId();
      Node op = NodeManager::currentNM()->mkSkolem( ss.str(), typ, "was created by the quantifiers rewriter" );
      std::vector< Node > predArgs;
      predArgs.push_back( op );
      predArgs.insert( predArgs.end(), activeArgs.begin(), activeArgs.end() );
      Node pred = NodeManager::currentNM()->mkNode( APPLY_UF, predArgs );
      Trace("quantifiers-rewrite-cnf-debug") << "Made predicate " << pred << " for " << nt << std::endl;
      //create the bound var list
      Node bvl = NodeManager::currentNM()->mkNode( BOUND_VAR_LIST, activeArgs );
      //now, look at the structure of nt
      if( nt.getKind()==NOT ){
        //case for NOT
        for( int i=0; i<2; i++ ){
          NodeBuilder<> tt(OR);
          tt << ( i==0 ? nt[0].notNode() : nt[0] );
          tt << ( i==0 ? pred.notNode() : pred );
          defs << NodeManager::currentNM()->mkNode( FORALL, bvl, tt.constructNode() );
        }
      }else if( nt.getKind()==OR ){
        //case for OR
        for( int i=0; i<(int)nt.getNumChildren(); i++ ){
          NodeBuilder<> tt(OR);
          tt << nt[i].notNode() << pred;
          defs << NodeManager::currentNM()->mkNode( FORALL, bvl, tt.constructNode() );
        }
        NodeBuilder<> tt(OR);
        for( int i=0; i<(int)nt.getNumChildren(); i++ ){
          tt << nt[i];
        }
        tt << pred.notNode();
        defs << NodeManager::currentNM()->mkNode( FORALL, bvl, tt.constructNode() );
      }else if( nt.getKind()==AND ){
        //case for AND
        for( int i=0; i<(int)nt.getNumChildren(); i++ ){
          NodeBuilder<> tt(OR);
          tt << nt[i] << pred.notNode();
          defs << NodeManager::currentNM()->mkNode( FORALL, bvl, tt.constructNode() );
        }
        NodeBuilder<> tt(OR);
        for( int i=0; i<(int)nt.getNumChildren(); i++ ){
          tt << nt[i].notNode();
        }
        tt << pred;
        defs << NodeManager::currentNM()->mkNode( FORALL, bvl, tt.constructNode() );
      }else if( nt.getKind()==IFF ){
        //case for IFF
        for( int i=0; i<4; i++ ){
          NodeBuilder<> tt(OR);
          tt << ( ( i==0 || i==3 ) ? nt[0].notNode() : nt[0] );
          tt << ( ( i==1 || i==3 ) ? nt[1].notNode() : nt[1] );
          tt << ( ( i==0 || i==1 ) ? pred.notNode() : pred );
          defs << NodeManager::currentNM()->mkNode( FORALL, bvl, tt.constructNode() );
        }
      }else if( nt.getKind()==ITE ){
        //case for ITE
        for( int j=1; j<=2; j++ ){
          for( int i=0; i<2; i++ ){
            NodeBuilder<> tt(OR);
            tt << ( ( j==1 ) ? nt[0].notNode() : nt[0] );
            tt << ( ( i==1 ) ? nt[j].notNode() : nt[j] );
            tt << ( ( i==0 ) ? pred.notNode() : pred );
            defs << NodeManager::currentNM()->mkNode( FORALL, bvl, tt.constructNode() );
          }
        }
        for( int i=0; i<2; i++ ){
          NodeBuilder<> tt(OR);
          tt << ( i==0 ? nt[1].notNode() : nt[1] );
          tt << ( i==0 ? nt[2].notNode() : nt[2] );
          tt << ( i==1 ? pred.notNode() : pred );
          defs << NodeManager::currentNM()->mkNode( FORALL, bvl, tt.constructNode() );
        }
      }else{
        Notice() << "Unhandled Quantifiers CNF: " << nt << std::endl;
      }
      return pred;
    }
  }
}

Node QuantifiersRewriter::computePrenex( Node body, std::vector< Node >& args, bool pol ){
  if( body.getKind()==FORALL ){
    if( pol && ( options::prenexQuant()==PRENEX_ALL || body.getNumChildren()==2 ) ){
      std::vector< Node > terms;
      std::vector< Node > subs;
      //for doing prenexing of same-signed quantifiers
      //must rename each variable that already exists
      for( int i=0; i<(int)body[0].getNumChildren(); i++ ){
        //if( std::find( args.begin(), args.end(), body[0][i] )!=args.end() ){
        terms.push_back( body[0][i] );
        subs.push_back( NodeManager::currentNM()->mkBoundVar( body[0][i].getType() ) );
      }
      args.insert( args.end(), subs.begin(), subs.end() );
      Node newBody = body[1];
      newBody = newBody.substitute( terms.begin(), terms.end(), subs.begin(), subs.end() );
      Debug("quantifiers-substitute-debug") << "Did substitute have an effect" << (body[1] != newBody) << body[1] << " became " << newBody << endl;
      return newBody;
    }else{
      return body;
    }
  }else{
    Assert( body.getKind()!=EXISTS );
    bool childrenChanged = false;
    std::vector< Node > newChildren;
    for( int i=0; i<(int)body.getNumChildren(); i++ ){
      bool newHasPol;
      bool newPol;
      QuantPhaseReq::getPolarity( body, i, true, pol, newHasPol, newPol );
      if( newHasPol ){
        Node n = computePrenex( body[i], args, newPol );
        newChildren.push_back( n );
        if( n!=body[i] ){
          childrenChanged = true;
        }
      }else{
        newChildren.push_back( body[i] );
      }
    }
    if( childrenChanged ){
      if( body.getKind()==NOT && newChildren[0].getKind()==NOT ){
        return newChildren[0][0];
      }else{
        return NodeManager::currentNM()->mkNode( body.getKind(), newChildren );
      }
    }else{
      return body;
    }
  }
}

Node QuantifiersRewriter::computeSplit( Node f, std::vector< Node >& args, Node body ) {
  Assert( body.getKind()==OR );
  size_t var_found_count = 0;
  size_t eqc_count = 0;
  size_t eqc_active = 0;
  std::map< Node, int > var_to_eqc;
  std::map< int, std::vector< Node > > eqc_to_var;
  std::map< int, std::vector< Node > > eqc_to_lit;

  std::vector<Node> lits;

  for( unsigned i=0; i<body.getNumChildren(); i++ ){
    //get variables contained in the literal
    Node n = body[i];
    std::vector< Node > lit_args;
    computeArgVec( args, lit_args, n );
    if (lit_args.empty()) {
      lits.push_back(n);
    }else {
      //collect the equivalence classes this literal belongs to, and the new variables it contributes
      std::vector< int > eqcs;
      std::vector< Node > lit_new_args;
      //for each variable in literal
      for( unsigned j=0; j<lit_args.size(); j++) {
        //see if the variable has already been found
        if (var_to_eqc.find(lit_args[j])!=var_to_eqc.end()) {
          int eqc = var_to_eqc[lit_args[j]];
          if (std::find(eqcs.begin(), eqcs.end(), eqc)==eqcs.end()) {
            eqcs.push_back(eqc);
          }
        }else{
          var_found_count++;
          lit_new_args.push_back(lit_args[j]);
        }
      }
      if (eqcs.empty()) {
        eqcs.push_back(eqc_count);
        eqc_count++;
        eqc_active++;
      }

      int eqcz = eqcs[0];
      //merge equivalence classes with eqcz
      for (unsigned j=1; j<eqcs.size(); j++) {
        int eqc = eqcs[j];
        //move all variables from equivalence class
        for (unsigned k=0; k<eqc_to_var[eqc].size(); k++) {
          Node v = eqc_to_var[eqc][k];
          var_to_eqc[v] = eqcz;
          eqc_to_var[eqcz].push_back(v);
        }
        eqc_to_var.erase(eqc);
        //move all literals from equivalence class
        for (unsigned k=0; k<eqc_to_lit[eqc].size(); k++) {
          Node l = eqc_to_lit[eqc][k];
          eqc_to_lit[eqcz].push_back(l);
        }
        eqc_to_lit.erase(eqc);
        eqc_active--;
      }
      //add variables to equivalence class
      for (unsigned j=0; j<lit_new_args.size(); j++) {
        var_to_eqc[lit_new_args[j]] = eqcz;
        eqc_to_var[eqcz].push_back(lit_new_args[j]);
      }
      //add literal to equivalence class
      eqc_to_lit[eqcz].push_back(n);
    }
  }
  if ( eqc_active>1 || !lits.empty() ){
    Trace("clause-split-debug") << "Split clause " << f << std::endl;
    Trace("clause-split-debug") << "   Ground literals: " << std::endl;
    for( size_t i=0; i<lits.size(); i++) {
      Trace("clause-split-debug") << "      " << lits[i] << std::endl;
    }
    Trace("clause-split-debug") << std::endl;
    Trace("clause-split-debug") << "Equivalence classes: " << std::endl;
    for (std::map< int, std::vector< Node > >::iterator it = eqc_to_lit.begin(); it != eqc_to_lit.end(); ++it ){
      Trace("clause-split-debug") << "   Literals: " << std::endl;
      for (size_t i=0; i<it->second.size(); i++) {
        Trace("clause-split-debug") << "      " << it->second[i] << std::endl;
      }
      int eqc = it->first;
      Trace("clause-split-debug") << "   Variables: " << std::endl;
      for (size_t i=0; i<eqc_to_var[eqc].size(); i++) {
        Trace("clause-split-debug") << "      " << eqc_to_var[eqc][i] << std::endl;
      }
      Trace("clause-split-debug") << std::endl;
      Node bvl = NodeManager::currentNM()->mkNode( BOUND_VAR_LIST, eqc_to_var[eqc]);
      Node body = it->second.size()==1 ? it->second[0] : NodeManager::currentNM()->mkNode( OR, it->second );
      Node fa = NodeManager::currentNM()->mkNode( FORALL, bvl, body );
      lits.push_back(fa);
    }
    Assert( lits.size()>1 );
    Node nf = NodeManager::currentNM()->mkNode(OR,lits);
    Trace("clause-split-debug") << "Made node : " << nf << std::endl;
    return nf;
  }
  return f;
}

Node QuantifiersRewriter::mkForAll( std::vector< Node >& args, Node body, QAttributes& qa ){
  std::vector< Node > activeArgs;
  //if cegqi is on, may be synthesis conjecture, in which case we want to keep all variables
  if( options::ceGuidedInst() && qa.d_sygus ){
    activeArgs.insert( activeArgs.end(), args.begin(), args.end() );
  }else{
    computeArgVec2( args, activeArgs, body, qa.d_ipl );
  }
  if( activeArgs.empty() ){
    return body;
  }else{
    std::vector< Node > children;
    children.push_back( NodeManager::currentNM()->mkNode(kind::BOUND_VAR_LIST, activeArgs ) );
    children.push_back( body );
    if( !qa.d_ipl.isNull() ){
      children.push_back( qa.d_ipl );
    }
    return NodeManager::currentNM()->mkNode( kind::FORALL, children );
  }
}

Node QuantifiersRewriter::computeMiniscoping( Node f, std::vector< Node >& args, Node body, QAttributes& qa ){
  if( body.getKind()==FORALL ){
    //combine arguments
    std::vector< Node > newArgs;
    for( int i=0; i<(int)body[0].getNumChildren(); i++ ){
      newArgs.push_back( body[0][i] );
    }
    newArgs.insert( newArgs.end(), args.begin(), args.end() );
    return mkForAll( newArgs, body[ 1 ], qa );
  }else{
    if( body.getKind()==NOT ){
      //push not downwards
      if( body[0].getKind()==NOT ){
        return computeMiniscoping( f, args, body[0][0], qa );
      }else if( body[0].getKind()==AND ){
        if( options::miniscopeQuantFreeVar() ){
          NodeBuilder<> t(kind::OR);
          for( int i=0; i<(int)body[0].getNumChildren(); i++ ){
            t <<  ( body[0][i].getKind()==NOT ? body[0][i][0] : body[0][i].notNode() );
          }
          return computeMiniscoping( f, args, t.constructNode(), qa );
        }
      }else if( body[0].getKind()==OR ){
        if( options::miniscopeQuant() ){
          NodeBuilder<> t(kind::AND);
          for( int i=0; i<(int)body[0].getNumChildren(); i++ ){
            Node trm = body[0][i].negate();
            t << computeMiniscoping( f, args, trm, qa );
          }
          return t.constructNode();
        }
      }
    }else if( body.getKind()==AND ){
      if( options::miniscopeQuant() ){
        //break apart
        NodeBuilder<> t(kind::AND);
        for( unsigned i=0; i<body.getNumChildren(); i++ ){
          t << computeMiniscoping( f, args, body[i], qa );
        }
        Node retVal = t;
        return retVal;
      }
    }else if( body.getKind()==OR ){
      if( options::quantSplit() ){
        //splitting subsumes free variable miniscoping, apply it with higher priority
        Node nf = computeSplit( f, args, body );
        if( nf!=f ){
          return nf;
        }
      }else if( options::miniscopeQuantFreeVar() ){
        Node newBody = body;
        NodeBuilder<> body_split(kind::OR);
        NodeBuilder<> tb(kind::OR);
        for( unsigned i=0; i<body.getNumChildren(); i++ ){
          Node trm = body[i];
          if( TermDb::containsTerms( body[i], args ) ){
            tb << trm;
          }else{
            body_split << trm;
          }
        }
        if( tb.getNumChildren()==0 ){
          return body_split;
        }else if( body_split.getNumChildren()>0 ){
          newBody = tb.getNumChildren()==1 ? tb.getChild( 0 ) : tb;
          body_split << mkForAll( args, newBody, qa );
          return body_split.getNumChildren()==1 ? body_split.getChild( 0 ) : body_split;
        }
      }
    }
  }
  //if( body==f[1] ){
  //  return f;
  //}else{
  return mkForAll( args, body, qa );
  //}
}

Node QuantifiersRewriter::computeAggressiveMiniscoping( std::vector< Node >& args, Node body ){
  std::map< Node, std::vector< Node > > varLits;
  std::map< Node, std::vector< Node > > litVars;
  if( body.getKind()==OR ){
    Trace("ag-miniscope") << "compute aggressive miniscoping on " << body << std::endl;
    for( size_t i=0; i<body.getNumChildren(); i++ ){
      std::vector< Node > activeArgs;
      computeArgVec( args, activeArgs, body[i] );
      for (unsigned j=0; j<activeArgs.size(); j++ ){
        varLits[activeArgs[j]].push_back( body[i] );
      }
      litVars[body[i]].insert( litVars[body[i]].begin(), activeArgs.begin(), activeArgs.end() );
    }
    //find the variable in the least number of literals
    Node bestVar;
    for( std::map< Node, std::vector< Node > >::iterator it = varLits.begin(); it != varLits.end(); ++it ){
      if( bestVar.isNull() || varLits[bestVar].size()>it->second.size() ){
        bestVar = it->first;
      }
    }
    Trace("ag-miniscope-debug") << "Best variable " << bestVar << " occurs in " << varLits[bestVar].size() << "/ " << body.getNumChildren() << " literals." << std::endl;
    if( !bestVar.isNull() && varLits[bestVar].size()<body.getNumChildren() ){
      //we can miniscope
      Trace("ag-miniscope") << "Miniscope on " << bestVar << std::endl;
      //make the bodies
      std::vector< Node > qlit1;
      qlit1.insert( qlit1.begin(), varLits[bestVar].begin(), varLits[bestVar].end() );
      std::vector< Node > qlitt;
      //for all literals not containing bestVar
      for( size_t i=0; i<body.getNumChildren(); i++ ){
        if( std::find( qlit1.begin(), qlit1.end(), body[i] )==qlit1.end() ){
          qlitt.push_back( body[i] );
        }
      }
      //make the variable lists
      std::vector< Node > qvl1;
      std::vector< Node > qvl2;
      std::vector< Node > qvsh;
      for( unsigned i=0; i<args.size(); i++ ){
        bool found1 = false;
        bool found2 = false;
        for( size_t j=0; j<varLits[args[i]].size(); j++ ){
          if( !found1 && std::find( qlit1.begin(), qlit1.end(), varLits[args[i]][j] )!=qlit1.end() ){
            found1 = true;
          }else if( !found2 && std::find( qlitt.begin(), qlitt.end(), varLits[args[i]][j] )!=qlitt.end() ){
            found2 = true;
          }
          if( found1 && found2 ){
            break;
          }
        }
        if( found1 ){
          if( found2 ){
            qvsh.push_back( args[i] );
          }else{
            qvl1.push_back( args[i] );
          }
        }else{
          Assert(found2);
          qvl2.push_back( args[i] );
        }
      }
      Assert( !qvl1.empty() );
      Assert( !qvl2.empty() || !qvsh.empty() );
      //check for literals that only contain shared variables
      std::vector< Node > qlitsh;
      std::vector< Node > qlit2;
      for( size_t i=0; i<qlitt.size(); i++ ){
        bool hasVar2 = false;
        for( size_t j=0; j<litVars[qlitt[i]].size(); j++ ){
          if( std::find( qvl2.begin(), qvl2.end(), litVars[qlitt[i]][j] )!=qvl2.end() ){
            hasVar2 = true;
            break;
          }
        }
        if( hasVar2 ){
          qlit2.push_back( qlitt[i] );
        }else{
          qlitsh.push_back( qlitt[i] );
        }
      }
      varLits.clear();
      litVars.clear();
      Trace("ag-miniscope-debug") << "Split into literals : " << qlit1.size() << " / " << qlit2.size() << " / " << qlitsh.size();
      Trace("ag-miniscope-debug") << ", variables : " << qvl1.size() << " / " << qvl2.size() << " / " << qvsh.size() << std::endl;
      Node n1 = qlit1.size()==1 ? qlit1[0] : NodeManager::currentNM()->mkNode( OR, qlit1 );
      n1 = computeAggressiveMiniscoping( qvl1, n1 );
      qlitsh.push_back( n1 );
      if( !qlit2.empty() ){
        Node n2 = qlit2.size()==1 ? qlit2[0] : NodeManager::currentNM()->mkNode( OR, qlit2 );
        n2 = computeAggressiveMiniscoping( qvl2, n2 );
        qlitsh.push_back( n2 );
      }
      Node n = NodeManager::currentNM()->mkNode( OR, qlitsh );
      if( !qvsh.empty() ){
        Node bvl = NodeManager::currentNM()->mkNode(kind::BOUND_VAR_LIST, qvsh);
        n = NodeManager::currentNM()->mkNode( FORALL, bvl, n );
      }
      Trace("ag-miniscope") << "Return " << n << " for " << body << std::endl;
      return n;
    }
  }
  QAttributes qa;
  return mkForAll( args, body, qa );
}

bool QuantifiersRewriter::doOperation( Node f, int computeOption, QAttributes& qa ){
  bool is_std = !qa.d_sygus && !qa.d_quant_elim && !qa.isFunDef();
  if( computeOption==COMPUTE_ELIM_SYMBOLS ){
    return true;
  }else if( computeOption==COMPUTE_MINISCOPING ){
    return is_std;
  }else if( computeOption==COMPUTE_AGGRESSIVE_MINISCOPING ){
    return options::aggressiveMiniscopeQuant() && is_std;
  }else if( computeOption==COMPUTE_NNF ){
    return options::nnfQuant();
  }else if( computeOption==COMPUTE_PROCESS_TERMS ){
    return true;
    //return options::iteLiftQuant()!=ITE_LIFT_QUANT_MODE_NONE || options::iteCondVarSplitQuant();
  }else if( computeOption==COMPUTE_COND_SPLIT ){
    return ( options::iteDtTesterSplitQuant() || options::condVarSplitQuant() ) && is_std;
  }else if( computeOption==COMPUTE_PRENEX ){
    return options::prenexQuant()!=PRENEX_NONE && !options::aggressiveMiniscopeQuant();
  }else if( computeOption==COMPUTE_VAR_ELIMINATION ){
    return ( options::varElimQuant() || options::dtVarExpandQuant() || options::purifyQuant() ) && is_std;
  //}else if( computeOption==COMPUTE_CNF ){
  //  return options::cnfQuant();
  }else if( computeOption==COMPUTE_PURIFY_EXPAND ){
    return options::purifyQuant();
  }else{
    return false;
  }
}

//general method for computing various rewrites
Node QuantifiersRewriter::computeOperation( Node f, int computeOption, QAttributes& qa ){
  Trace("quantifiers-rewrite-debug") << "Compute operation " << computeOption << " on " << f << std::endl;
  std::vector< Node > args;
  for( unsigned i=0; i<f[0].getNumChildren(); i++ ){
    args.push_back( f[0][i] );
  }
  Node n = f[1];
  if( computeOption==COMPUTE_ELIM_SYMBOLS ){
    n = computeElimSymbols( n );
  }else if( computeOption==COMPUTE_MINISCOPING ){
    //return directly
    return computeMiniscoping( f, args, n, qa );
  }else if( computeOption==COMPUTE_AGGRESSIVE_MINISCOPING ){
    return computeAggressiveMiniscoping( args, n );
  }else if( computeOption==COMPUTE_NNF ){
    n = computeNNF( n );
  }else if( computeOption==COMPUTE_PROCESS_TERMS ){
    std::vector< Node > new_conds;
    n = computeProcessTerms( n, args, new_conds, f, qa );
    if( !new_conds.empty() ){
      new_conds.push_back( n );
      n = NodeManager::currentNM()->mkNode( OR, new_conds );
    }
  }else if( computeOption==COMPUTE_COND_SPLIT ){
    n = computeCondSplit( n, qa );
  }else if( computeOption==COMPUTE_PRENEX ){
    n = computePrenex( n, args, true );
  }else if( computeOption==COMPUTE_VAR_ELIMINATION ){
    n = computeVarElimination( n, args, qa );
  //}else if( computeOption==COMPUTE_CNF ){
    //n = computeCNF( n, args, defs, false );
    //ipl = Node::null();
  }else if( computeOption==COMPUTE_PURIFY_EXPAND ){
    std::vector< Node > conj;
    computePurifyExpand( n, conj, args, qa );
    if( !conj.empty() ){
      return conj.size()==1 ? conj[0] : NodeManager::currentNM()->mkNode( AND, conj );
    }else{
      return f;
    }
  }
  Trace("quantifiers-rewrite-debug") << "Compute Operation: return " << n << ", " << args.size() << std::endl;
  if( f[1]==n && args.size()==f[0].getNumChildren() ){
    return f;
  }else{
    if( args.empty() ){
      return n;
    }else{
      std::vector< Node > children;
      children.push_back( NodeManager::currentNM()->mkNode(kind::BOUND_VAR_LIST, args ) );
      children.push_back( n );
      if( !qa.d_ipl.isNull() ){
        children.push_back( qa.d_ipl );
      }
      return NodeManager::currentNM()->mkNode(kind::FORALL, children );
    }
  }
}


Node QuantifiersRewriter::rewriteRewriteRule( Node r ) {
  Kind rrkind = r[2].getKind();

  //guards, pattern, body

  //   Replace variables by Inst_* variable and tag the terms that contain them
  std::vector<Node> vars;
  vars.reserve(r[0].getNumChildren());
  for( Node::const_iterator v = r[0].begin(); v != r[0].end(); ++v ){
    vars.push_back(*v);
  };

  // Body/Remove_term/Guards/Triggers
  Node body = r[2][1];
  TNode new_terms = r[2][1];
  std::vector<Node> guards;
  std::vector<Node> pattern;
  Node true_node = NodeManager::currentNM()->mkConst(true);
  // shortcut
  TNode head = r[2][0];
  switch(rrkind){
  case kind::RR_REWRITE:
    // Equality
    pattern.push_back( head );
    if( head.getType().isBoolean() ){
      body = head.iffNode(body);
    }else{
      body = head.eqNode(body);
    }
    break;
  case kind::RR_REDUCTION:
  case kind::RR_DEDUCTION:
    // Add head to guards and pattern
    switch(head.getKind()){
    case kind::AND:
      for( unsigned i = 0; i<head.getNumChildren(); i++ ){
        guards.push_back(head[i]);
        pattern.push_back(head[i]);
      }
      break;
    default:
      if( head!=true_node ){
        guards.push_back(head);
        pattern.push_back( head );
      }
      break;
    }
    break;
  default:
    Unreachable("RewriteRules can be of only three kinds");
    break;
  }
  // Add the other guards
  TNode g = r[1];
  switch(g.getKind()){
  case kind::AND:
    for( unsigned i = 0; i<g.getNumChildren(); i++ ){
      guards.push_back(g[i]);
    }
    break;
  default:
    if( g != true_node ){
      guards.push_back( g );
    }
    break;
  }
  // Add the other triggers
  if( r[2].getNumChildren() >= 3 ){
    for( unsigned i=0; i<r[2][2][0].getNumChildren(); i++ ) {
      pattern.push_back( r[2][2][0][i] );
    }
  }

  Trace("rr-rewrite") << "Rule is " << r << std::endl;
  Trace("rr-rewrite") << "Head is " << head << std::endl;
  Trace("rr-rewrite") << "Patterns are ";
  for( unsigned i=0; i<pattern.size(); i++ ){
    Trace("rr-rewrite") << pattern[i] << " ";
  }
  Trace("rr-rewrite") << std::endl;

  NodeBuilder<> forallB(kind::FORALL);
  forallB << r[0];
  Node gg = guards.size()==0 ? true_node : ( guards.size()==1 ? guards[0] : NodeManager::currentNM()->mkNode( AND, guards ) );
  gg = NodeManager::currentNM()->mkNode( OR, gg.negate(), body );
  gg = Rewriter::rewrite( gg );
  forallB << gg;
  NodeBuilder<> patternB(kind::INST_PATTERN);
  patternB.append(pattern);
  NodeBuilder<> patternListB(kind::INST_PATTERN_LIST);
  //the entire rewrite rule is the first pattern
  if( options::quantRewriteRules() ){
    patternListB << NodeManager::currentNM()->mkNode( INST_ATTRIBUTE, r );
  }
  patternListB << static_cast<Node>(patternB);
  forallB << static_cast<Node>(patternListB);
  Node rn = (Node) forallB;

  return rn;
}

struct ContainsQuantAttributeId {};
typedef expr::Attribute<ContainsQuantAttributeId, uint64_t> ContainsQuantAttribute;

// check if the given node contains a universal quantifier
bool QuantifiersRewriter::containsQuantifiers(Node n) {
  if( n.hasAttribute(ContainsQuantAttribute()) ){
    return n.getAttribute(ContainsQuantAttribute())==1;
  } else if(n.getKind() == kind::FORALL) {
    return true;
  } else {
    bool cq = false;
    for( unsigned i = 0; i < n.getNumChildren(); ++i ){
      if( containsQuantifiers(n[i]) ){
        cq = true;
        break;
      }
    }
    ContainsQuantAttribute cqa;
    n.setAttribute(cqa, cq ? 1 : 0);
    return cq;
  }
}

Node QuantifiersRewriter::preSkolemizeQuantifiers( Node n, bool polarity, std::vector< TypeNode >& fvTypes, std::vector< TNode >& fvs ){
  Trace("pre-sk") << "Pre-skolem " << n << " " << polarity << " " << fvs.size() << endl;
  if( n.getKind()==kind::NOT ){
    Node nn = preSkolemizeQuantifiers( n[0], !polarity, fvTypes, fvs );
    return nn.negate();
  }else if( n.getKind()==kind::FORALL ){
    if( polarity ){
      if( options::preSkolemQuant() && options::preSkolemQuantNested() ){
        vector< Node > children;
        children.push_back( n[0] );
        //add children to current scope
        std::vector< TypeNode > fvt;
        std::vector< TNode > fvss;
        fvt.insert( fvt.begin(), fvTypes.begin(), fvTypes.end() );
        fvss.insert( fvss.begin(), fvs.begin(), fvs.end() );
        for( int i=0; i<(int)n[0].getNumChildren(); i++ ){
          fvt.push_back( n[0][i].getType() );
          fvss.push_back( n[0][i] );
        }
        //process body
        children.push_back( preSkolemizeQuantifiers( n[1], polarity, fvt, fvss ) );
        if( n.getNumChildren()==3 ){
          children.push_back( n[2] );
        }
        //return processed quantifier
        return NodeManager::currentNM()->mkNode( kind::FORALL, children );
      }
    }else{
      //process body
      Node nn = preSkolemizeQuantifiers( n[1], polarity, fvTypes, fvs );
      std::vector< Node > sk;
      Node sub;
      std::vector< unsigned > sub_vars;
      //return skolemized body
      return TermDb::mkSkolemizedBody( n, nn, fvTypes, fvs, sk, sub, sub_vars );
    }
  }else{
    //check if it contains a quantifier as a subterm
    //if so, we will write this node
    if( containsQuantifiers( n ) ){
      if( ( n.getKind()==kind::ITE && n.getType().isBoolean() ) || n.getKind()==kind::IFF ){
        if( options::preSkolemQuantAgg() ){
          Node nn;
          //must remove structure
          if( n.getKind()==kind::ITE ){
            nn = NodeManager::currentNM()->mkNode( kind::AND,
                  NodeManager::currentNM()->mkNode( kind::OR, n[0].notNode(), n[1] ),
                  NodeManager::currentNM()->mkNode( kind::OR, n[0], n[2] ) );
          }else if( n.getKind()==kind::IFF || n.getKind()==kind::XOR ){
            nn = NodeManager::currentNM()->mkNode( kind::AND,
                  NodeManager::currentNM()->mkNode( kind::OR, n[0].notNode(), n.getKind()==kind::XOR ? n[1].notNode() : n[1] ),
                  NodeManager::currentNM()->mkNode( kind::OR, n[0], n.getKind()==kind::XOR ? n[1] : n[1].notNode() ) );
          }else if( n.getKind()==kind::IMPLIES ){
            nn = NodeManager::currentNM()->mkNode( kind::OR, n[0].notNode(), n[1] );
          }
          return preSkolemizeQuantifiers( nn, polarity, fvTypes, fvs );
        }
      }else if( n.getKind()==kind::AND || n.getKind()==kind::OR ){
        vector< Node > children;
        for( int i=0; i<(int)n.getNumChildren(); i++ ){
          children.push_back( preSkolemizeQuantifiers( n[i], polarity, fvTypes, fvs ) );
        }
        return NodeManager::currentNM()->mkNode( n.getKind(), children );
      }
    }
  }
  return n;
}

Node QuantifiersRewriter::preprocess( Node n, bool isInst ) {
  Node prev = n;
  if( options::preSkolemQuant() ){
    if( !isInst || !options::preSkolemQuantNested() ){
      Trace("quantifiers-preprocess-debug") << "Pre-skolemize " << n << "..." << std::endl;
      //apply pre-skolemization to existential quantifiers
      std::vector< TypeNode > fvTypes;
      std::vector< TNode > fvs;
      n = quantifiers::QuantifiersRewriter::preSkolemizeQuantifiers( prev, true, fvTypes, fvs );
    }
  }
  if( n!=prev ){       
    Trace("quantifiers-preprocess") << "Preprocess " << prev<< std::endl;
    Trace("quantifiers-preprocess") << "..returned " << n << std::endl;
  }
  return n;
}

Node QuantifiersRewriter::computePurify2( Node body, std::vector< Node >& args, std::map< Node, Node >& visited, std::map< Node, Node >& var_to_term,
                                          std::map< Node, std::vector< int > >& var_parent, int parentId ){
  std::map< Node, Node >::iterator it = visited.find( body );
  if( it!=visited.end() ){
    return it->second;
  }else{
    Node ret = body;
    if( body.getNumChildren()>0 && body.getKind()!=FORALL && TermDb::hasBoundVarAttr( ret ) ){
      std::vector< Node > children;
      bool childrenChanged = false;
      int id = getPurifyId( body );
      for( unsigned i=0; i<body.getNumChildren(); i++ ){
        Node bi;
        if( body.getKind()==EQUAL && i==1 ){
          int cid = getPurifyId( children[0] );
          bi = computePurify2( body[i], args, visited, var_to_term, var_parent, cid );
          if( children[0].getKind()==BOUND_VARIABLE ){
            cid = getPurifyId( bi );
            if( cid!=0 && std::find( var_parent[children[0]].begin(), var_parent[children[0]].end(), cid )==var_parent[children[0]].end() ){
              var_parent[children[0]].push_back( id );
            }
          }
        }else{
          bi = computePurify2( body[i], args, visited, var_to_term, var_parent, id );
        }
        childrenChanged = childrenChanged || bi!=body[i];
        children.push_back( bi );
        if( id!=0 && bi.getKind()==BOUND_VARIABLE ){
          if( std::find( var_parent[bi].begin(), var_parent[bi].end(), id )==var_parent[bi].end() ){
            var_parent[bi].push_back( id );
          }
        }
      }
      if( childrenChanged ){
        if( body.getMetaKind() == kind::metakind::PARAMETERIZED ){
          children.insert( children.begin(), body.getOperator() );
        }
        ret = NodeManager::currentNM()->mkNode( body.getKind(), children );
      }
      if( parentId!=0 && parentId!=id ){
        Node v = NodeManager::currentNM()->mkBoundVar( ret.getType() );
        var_to_term[v] = Rewriter::rewrite( v.eqNode( ret ) );
        ret = v;
        args.push_back( v );
      }
    }
    visited[body] = ret;
    return ret;
  }
}

Node QuantifiersRewriter::computePurify( Node body, std::vector< Node >& args, std::map< Node, std::vector< int > >& var_parent ) {
  std::map< Node, Node > visited;
  std::map< Node, Node > var_to_term;
  Node pbody = computePurify2( body, args, visited, var_to_term, var_parent, 0 );
  if( pbody==body ){
    return body;
  }else{
    Trace("quantifiers-rewrite-purify") << "Purify : " << body << std::endl;
    Trace("quantifiers-rewrite-purify") << "   Got : " << pbody << std::endl;
    for( std::map< Node, Node >::iterator it = var_to_term.begin(); it != var_to_term.end(); ++it ){
      Trace("quantifiers-rewrite-purify") << "         " << it->first << " : " << it->second << std::endl;
    }
    Trace("quantifiers-rewrite-purify") << "Variable parents : " << std::endl;
    for( std::map< Node, std::vector< int > >::iterator it = var_parent.begin(); it != var_parent.end(); ++it ){
      Trace("quantifiers-rewrite-purify") << "  " << it->first << " -> ";
      for( unsigned i=0; i<it->second.size(); i++ ){
        Trace("quantifiers-rewrite-purify") << it->second[i] << " ";
      }
      Trace("quantifiers-rewrite-purify") << std::endl;
    }
    Trace("quantifiers-rewrite-purify") << std::endl;
    std::vector< Node > disj;
    for( std::map< Node, Node >::iterator it = var_to_term.begin(); it != var_to_term.end(); ++it ){
      disj.push_back( it->second.negate() );
    }
    Node res;
    if( disj.empty() ){
      res = pbody;
    }else{
      disj.push_back( pbody );
      res = NodeManager::currentNM()->mkNode( OR, disj );
    }
    Trace("quantifiers-rewrite-purify") << "Constructed : " << res << std::endl << std::endl;
    return res;
  }
}

void QuantifiersRewriter::computePurifyExpand( Node body, std::vector< Node >& conj, std::vector< Node >& args, QAttributes& qa ) {
  if( body.getKind()==OR ){
    Trace("quantifiers-rewrite-purify-exp") << "Purify expansion : " << body << std::endl;
    std::map< int, std::vector< Node > > disj;
    std::map< int, std::vector< Node > > fvs;
    for( unsigned i=0; i<body.getNumChildren(); i++ ){
      int pid CVC4_UNUSED = getPurifyIdLit( body[i] );
    }
    //mark as an attribute
    //Node attr = NodeManager::currentNM()->mkNode( INST_ATTRIBUTE, body );
  }
}