path: root/src/util/sort_inference.cpp

/*********************                                                        */
/*! \file sort_inference.cpp
 ** \verbatim
 ** Original author: Andrew Reynolds
 ** Major contributors: Morgan Deters
 ** Minor contributors (to current version): Kshitij Bansal
 ** 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 Sort inference module
 **
 ** This class implements sort inference, based on a simple algorithm:
 ** First, we assume all functions and predicates have distinct uninterpreted types.
 ** One pass is made through the input assertions, while a union-find data structure
 ** maintains necessary information regarding constraints on these types.
 **/

#include <vector>

#include "util/sort_inference.h"
#include "theory/uf/options.h"
#include "smt/options.h"
#include "theory/rewriter.h"

using namespace CVC4;
using namespace std;

namespace CVC4 {

void SortInference::UnionFind::print(const char * c){
  for( std::map< int, int >::iterator it = d_eqc.begin(); it != d_eqc.end(); ++it ){
    Trace(c) << "s_" << it->first << " = s_" << it->second << ", ";
  }
  for( unsigned i=0; i<d_deq.size(); i++ ){
    Trace(c) << "s_" << d_deq[i].first << " != s_" << d_deq[i].second << ", ";
  }
  Trace(c) << std::endl;
}
void SortInference::UnionFind::set( UnionFind& c ) {
  clear();
  for( std::map< int, int >::iterator it = c.d_eqc.begin(); it != c.d_eqc.end(); ++it ){
    d_eqc[ it->first ] = it->second;
  }
  d_deq.insert( d_deq.end(), c.d_deq.begin(), c.d_deq.end() );
}
int SortInference::UnionFind::getRepresentative( int t ){
  std::map< int, int >::iterator it = d_eqc.find( t );
  if( it==d_eqc.end() || it->second==t ){
    return t;
  }else{
    int rt = getRepresentative( it->second );
    d_eqc[t] = rt;
    return rt;
  }
}
void SortInference::UnionFind::setEqual( int t1, int t2 ){
  if( t1!=t2 ){
    int rt1 = getRepresentative( t1 );
    int rt2 = getRepresentative( t2 );
    if( rt1>rt2 ){
      d_eqc[rt1] = rt2;
    }else{
      d_eqc[rt2] = rt1;
    }
  }
}
bool SortInference::UnionFind::isValid() {
  for( unsigned i=0; i<d_deq.size(); i++ ){
    if( areEqual( d_deq[i].first, d_deq[i].second ) ){
      return false;
    }
  }
  return true;
}


void SortInference::recordSubsort( TypeNode tn, int s ){
  s = d_type_union_find.getRepresentative( s );
  if( std::find( d_sub_sorts.begin(), d_sub_sorts.end(), s )==d_sub_sorts.end() ){
    d_sub_sorts.push_back( s );
    d_type_sub_sorts[tn].push_back( s );
  }
}

void SortInference::printSort( const char* c, int t ){
  int rt = d_type_union_find.getRepresentative( t );
  if( d_type_types.find( rt )!=d_type_types.end() ){
    Trace(c) << d_type_types[rt];
  }else{
    Trace(c) << "s_" << rt;
  }
}

void SortInference::reset() {
  d_sub_sorts.clear();
  d_non_monotonic_sorts.clear();
  d_type_sub_sorts.clear();
  //reset info
  sortCount = 1;
  d_type_union_find.clear();
  d_type_types.clear();
  d_id_for_types.clear();
  d_op_return_types.clear();
  d_op_arg_types.clear();
  d_var_types.clear();
  //for rewriting
  d_symbol_map.clear();
  d_const_map.clear();
}

bool SortInference::simplify( std::vector< Node >& assertions ){
  Trace("sort-inference") << "Calculating sort inference..." << std::endl;
  //process all assertions
  for( unsigned i=0; i<assertions.size(); i++ ){
    Trace("sort-inference-debug") << "Process " << assertions[i] << std::endl;
    std::map< Node, Node > var_bound;
    process( assertions[i], var_bound );
  }
  for( std::map< Node, int >::iterator it = d_op_return_types.begin(); it != d_op_return_types.end(); ++it ){
    Trace("sort-inference") << it->first << " : ";
    TypeNode retTn = it->first.getType();
    if( !d_op_arg_types[ it->first ].empty() ){
      Trace("sort-inference") << "( ";
      for( size_t i=0; i<d_op_arg_types[ it->first ].size(); i++ ){
        recordSubsort( retTn[i], d_op_arg_types[ it->first ][i] );
        printSort( "sort-inference", d_op_arg_types[ it->first ][i] );
        Trace("sort-inference") << " ";
      }
      Trace("sort-inference") << ") -> ";
      retTn = retTn[(int)retTn.getNumChildren()-1];
    }
    recordSubsort( retTn, it->second );
    printSort( "sort-inference", it->second );
    Trace("sort-inference") << std::endl;
  }
  for( std::map< Node, std::map< Node, int > >::iterator it = d_var_types.begin(); it != d_var_types.end(); ++it ){
    Trace("sort-inference") << "Quantified formula : " << it->first << " : " << std::endl;
    for( unsigned i=0; i<it->first[0].getNumChildren(); i++ ){
      recordSubsort( it->first[0][i].getType(), it->second[it->first[0][i]] );
      printSort( "sort-inference", it->second[it->first[0][i]] );
      Trace("sort-inference") << std::endl;
    }
    Trace("sort-inference") << std::endl;
  }

  if( !options::ufssSymBreak() ){
    bool rewritten = false;
    //determine monotonicity of sorts
    for( unsigned i=0; i<assertions.size(); i++ ){
      Trace("sort-inference-debug") << "Process monotonicity for " << assertions[i] << std::endl;
      std::map< Node, Node > var_bound;
      processMonotonic( assertions[i], true, true, var_bound );
    }

    Trace("sort-inference") << "We have " << d_sub_sorts.size() << " sub-sorts : " << std::endl;
    for( unsigned i=0; i<d_sub_sorts.size(); i++ ){
      printSort( "sort-inference", d_sub_sorts[i] );
      if( d_type_types.find( d_sub_sorts[i] )!=d_type_types.end() ){
        Trace("sort-inference") << " is interpreted." << std::endl;
      }else if( d_non_monotonic_sorts.find( d_sub_sorts[i] )==d_non_monotonic_sorts.end() ){
        Trace("sort-inference") << " is monotonic." << std::endl;
      }else{
        Trace("sort-inference") << " is not monotonic." << std::endl;
      }
    }

    //simplify all assertions by introducing new symbols wherever necessary
    for( unsigned i=0; i<assertions.size(); i++ ){
      Node prev = assertions[i];
      std::map< Node, Node > var_bound;
      assertions[i] = simplify( assertions[i], var_bound );
      if( prev!=assertions[i] ){
        assertions[i] = theory::Rewriter::rewrite( assertions[i] );
        rewritten = true;
        Trace("sort-inference-rewrite") << prev << std::endl;
        Trace("sort-inference-rewrite") << " --> " << assertions[i] << std::endl;
      }
    }
    //now, ensure constants are distinct
    for( std::map< TypeNode, std::map< Node, Node > >::iterator it = d_const_map.begin(); it != d_const_map.end(); ++it ){
      std::vector< Node > consts;
      for( std::map< Node, Node >::iterator it2 = it->second.begin(); it2 != it->second.end(); ++it2 ){
        consts.push_back( it2->second );
      }
      //TODO: add lemma enforcing introduced constants to be distinct
    }

    //enforce constraints based on monotonicity
    for( std::map< TypeNode, std::vector< int > >::iterator it = d_type_sub_sorts.begin(); it != d_type_sub_sorts.end(); ++it ){
      int nmonSort = -1;
      for( unsigned i=0; i<it->second.size(); i++ ){
        if( d_non_monotonic_sorts.find( it->second[i] )!=d_non_monotonic_sorts.end() ){
          nmonSort = it->second[i];
          break;
        }
      }
      if( nmonSort!=-1 ){
        std::vector< Node > injections;
        TypeNode base_tn = getOrCreateTypeForId( nmonSort, it->first );
        for( unsigned i=0; i<it->second.size(); i++ ){
          if( it->second[i]!=nmonSort ){
            TypeNode new_tn = getOrCreateTypeForId( it->second[i], it->first );
            //make injection to nmonSort
            Node a1 = mkInjection( new_tn, base_tn );
            injections.push_back( a1 );
            if( d_non_monotonic_sorts.find( it->second[i] )!=d_non_monotonic_sorts.end() ){
              //also must make injection from nmonSort to this
              Node a2 = mkInjection( base_tn, new_tn );
              injections.push_back( a2 );
            }
          }
        }
        Trace("sort-inference-rewrite") << "Add the following injections for " << it->first << " to ensure consistency wrt non-monotonic sorts : " << std::endl;
        for( unsigned j=0; j<injections.size(); j++ ){
          Trace("sort-inference-rewrite") << "   " << injections[j] << std::endl;
        }
        assertions.insert( assertions.end(), injections.begin(), injections.end() );
        if( !injections.empty() ){
          rewritten = true;
        }
      }
    }
    //no sub-sort information is stored
    reset();
    return rewritten;
  }
  /*
  else if( !options::ufssSymBreak() ){
    //just add the unit lemmas between constants
    std::map< TypeNode, std::map< int, Node > > constants;
    for( std::map< Node, int >::iterator it = d_op_return_types.begin(); it != d_op_return_types.end(); ++it ){
      int rt = d_type_union_find.getRepresentative( it->second );
      if( d_op_arg_types[ it->first ].empty() ){
        TypeNode tn = it->first.getType();
        if( constants[ tn ].find( rt )==constants[ tn ].end() ){
          constants[ tn ][ rt ] = it->first;
        }
      }
    }
    //add unit lemmas for each constant
    for( std::map< TypeNode, std::map< int, Node > >::iterator it = constants.begin(); it != constants.end(); ++it ){
      Node first_const;
      for( std::map< int, Node >::iterator it2 = it->second.begin(); it2 != it->second.end(); ++it2 ){
        if( first_const.isNull() ){
          first_const = it2->second;
        }else{
          Node eq = first_const.eqNode( it2->second );
          //eq = Rewriter::rewrite( eq );
          Trace("sort-inference-lemma") << "Sort inference lemma : " << eq << std::endl;
          assertions.push_back( eq );
        }
      }
    }
  }
  */
  initialSortCount = sortCount;
  return false;
}

void SortInference::setEqual( int t1, int t2 ){
  if( t1!=t2 ){
    int rt1 = d_type_union_find.getRepresentative( t1 );
    int rt2 = d_type_union_find.getRepresentative( t2 );
    if( rt1!=rt2 ){
      Trace("sort-inference-debug") << "Set equal : ";
      printSort( "sort-inference-debug", rt1 );
      Trace("sort-inference-debug") << " ";
      printSort( "sort-inference-debug", rt2 );
      Trace("sort-inference-debug") << std::endl;
      /*
      d_type_eq_class[rt1].insert( d_type_eq_class[rt1].end(), d_type_eq_class[rt2].begin(), d_type_eq_class[rt2].end() );
      d_type_eq_class[rt2].clear();
      Trace("sort-inference-debug") << "EqClass : { ";
      for( int i=0; i<(int)d_type_eq_class[rt1].size(); i++ ){
        Trace("sort-inference-debug") << d_type_eq_class[rt1][i] << ", ";
      }
      Trace("sort-inference-debug") << "}" << std::endl;
      */
      if( rt2>rt1 ){
        //swap
        int swap = rt1;
        rt1 = rt2;
        rt2 = swap;
      }
      d_type_union_find.d_eqc[rt1] = rt2;
      std::map< int, TypeNode >::iterator it1 = d_type_types.find( rt1 );
      if( it1!=d_type_types.end() ){
        Assert( d_type_types.find( rt2 )==d_type_types.end() );
        d_type_types[rt2] = it1->second;
        d_type_types.erase( rt1 );
      }
    }
  }
}

int SortInference::getIdForType( TypeNode tn ){
  //register the return type
  std::map< TypeNode, int >::iterator it = d_id_for_types.find( tn );
  if( it==d_id_for_types.end() ){
    int sc = sortCount;
    d_type_types[ sortCount ] = tn;
    d_id_for_types[ tn ] = sortCount;
    sortCount++;
    return sc;
  }else{
    return it->second;
  }
}

int SortInference::process( Node n, std::map< Node, Node >& var_bound ){
  Trace("sort-inference-debug") << "...Process " << n << std::endl;
  //add to variable bindings
  if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
    if( d_var_types.find( n )!=d_var_types.end() ){
      return getIdForType( n.getType() );
    }else{
      for( size_t i=0; i<n[0].getNumChildren(); i++ ){
        //apply sort inference to quantified variables
        d_var_types[n][ n[0][i] ] = sortCount;
        sortCount++;

        //type of the quantified variable must be the same
        var_bound[ n[0][i] ] = n;
      }
    }
  }

  //process children
  std::vector< Node > children;
  std::vector< int > child_types;
  for( size_t i=0; i<n.getNumChildren(); i++ ){
    bool processChild = true;
    if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
      processChild = i==1;
    }
    if( processChild ){
      children.push_back( n[i] );
      child_types.push_back( process( n[i], var_bound ) );
    }
  }

  //remove from variable bindings
  if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
    //erase from variable bound
    for( size_t i=0; i<n[0].getNumChildren(); i++ ){
      var_bound.erase( n[0][i] );
    }
  }

  int retType;
  if( n.getKind()==kind::EQUAL ){
    //we only require that the left and right hand side must be equal
    setEqual( child_types[0], child_types[1] );
    //int eqType = getIdForType( n[0].getType() );
    //setEqual( child_types[0], eqType );
    //setEqual( child_types[1], eqType );
    retType = getIdForType( n.getType() );
  }else if( n.getKind()==kind::APPLY_UF ){
    Node op = n.getOperator();
    if( d_op_return_types.find( op )==d_op_return_types.end() ){
      if( n.getType().isBoolean() ){
        //use booleans
        d_op_return_types[op] = getIdForType( n.getType() );
      }else{
        //assign arbitrary sort for return type
        d_op_return_types[op] = sortCount;
        sortCount++;
      }
      //d_type_eq_class[sortCount].push_back( op );
      //assign arbitrary sort for argument types
      for( size_t i=0; i<n.getNumChildren(); i++ ){
        d_op_arg_types[op].push_back( sortCount );
        sortCount++;
      }
    }
    for( size_t i=0; i<n.getNumChildren(); i++ ){
      //the argument of the operator must match the return type of the subterm
      setEqual( child_types[i], d_op_arg_types[op][i] );
    }
    //return type is the return type
    retType = d_op_return_types[op];
  }else{
    std::map< Node, Node >::iterator it = var_bound.find( n );
    if( it!=var_bound.end() ){
      Trace("sort-inference-debug") << n << " is a bound variable." << std::endl;
      //the return type was specified while binding
      retType = d_var_types[it->second][n];
    }else if( n.getKind() == kind::VARIABLE || n.getKind()==kind::SKOLEM ){
      Trace("sort-inference-debug") << n << " is a variable." << std::endl;
      if( d_op_return_types.find( n )==d_op_return_types.end() ){
        //assign arbitrary sort
        d_op_return_types[n] = sortCount;
        sortCount++;
        //d_type_eq_class[sortCount].push_back( n );
      }
      retType = d_op_return_types[n];
    //}else if( n.isConst() ){
    //  Trace("sort-inference-debug") << n << " is a constant." << std::endl;
      //can be any type we want
    //  retType = sortCount;
    //  sortCount++;
    }else{
      Trace("sort-inference-debug") << n << " is a interpreted symbol." << std::endl;
      //it is an interpretted term
      for( size_t i=0; i<children.size(); i++ ){
        Trace("sort-inference-debug") << children[i] << " forced to have " << children[i].getType() << std::endl;
        //must enforce the actual type of the operator on the children
        int ct = getIdForType( children[i].getType() );
        setEqual( child_types[i], ct );
      }
      //return type must be the actual return type
      retType = getIdForType( n.getType() );
    }
  }
  Trace("sort-inference-debug") << "...Type( " << n << " ) = ";
  printSort("sort-inference-debug", retType );
  Trace("sort-inference-debug") << std::endl;
  return retType;
}

void SortInference::processMonotonic( Node n, bool pol, bool hasPol, std::map< Node, Node >& var_bound ) {
  Trace("sort-inference-debug") << "...Process monotonic " << pol << " " << hasPol << " " << n << std::endl;
  if( n.getKind()==kind::FORALL ){
    for( unsigned i=0; i<n[0].getNumChildren(); i++ ){
      var_bound[n[0][i]] = n;
    }
    processMonotonic( n[1], pol, hasPol, var_bound );
    for( unsigned i=0; i<n[0].getNumChildren(); i++ ){
      var_bound.erase( n[0][i] );
    }
  }else if( n.getKind()==kind::EQUAL ){
    if( !hasPol || pol ){
      for( unsigned i=0; i<2; i++ ){
        if( var_bound.find( n[i] )!=var_bound.end() ){
          int sid = getSortId( var_bound[n[i]], n[i] );
          d_non_monotonic_sorts[sid] = true;
          break;
        }
      }
    }
  }
  for( unsigned i=0; i<n.getNumChildren(); i++ ){
    bool npol = pol;
    bool nhasPol = hasPol;
    if( n.getKind()==kind::NOT || ( n.getKind()==kind::IMPLIES && i==0 ) ){
      npol = !npol;
    }
    if( ( n.getKind()==kind::ITE && i==0 ) || n.getKind()==kind::XOR || n.getKind()==kind::IFF ){
      nhasPol = false;
    }
    processMonotonic( n[i], npol, nhasPol, var_bound );
  }
}


TypeNode SortInference::getOrCreateTypeForId( int t, TypeNode pref ){
  int rt = d_type_union_find.getRepresentative( t );
  if( d_type_types.find( rt )!=d_type_types.end() ){
    return d_type_types[rt];
  }else{
    TypeNode retType;
    //see if we can assign pref
    if( !pref.isNull() && d_id_for_types.find( pref )==d_id_for_types.end() ){
      retType = pref;
    }else{
      //must create new type
      std::stringstream ss;
      ss << "it_" << t << "_" << pref;
      retType = NodeManager::currentNM()->mkSort( ss.str() );
    }
    Trace("sort-inference") << "-> Make type " << retType << " to correspond to ";
    printSort("sort-inference", t );
    Trace("sort-inference") << std::endl;
    d_id_for_types[ retType ] = rt;
    d_type_types[ rt ] = retType;
    return retType;
  }
}

TypeNode SortInference::getTypeForId( int t ){
  int rt = d_type_union_find.getRepresentative( t );
  if( d_type_types.find( rt )!=d_type_types.end() ){
    return d_type_types[rt];
  }else{
    return TypeNode::null();
  }
}

Node SortInference::getNewSymbol( Node old, TypeNode tn ){
  if( tn==old.getType() ){
    return old;
  }else if( old.isConst() ){
    //must make constant of type tn
    if( d_const_map[tn].find( old )==d_const_map[tn].end() ){
      std::stringstream ss;
      ss << "ic_" << tn << "_" << old;
      d_const_map[tn][ old ] = NodeManager::currentNM()->mkSkolem( ss.str(), tn, "constant created during sort inference" );  //use mkConst???
    }
    return d_const_map[tn][ old ];
  }else if( old.getKind()==kind::BOUND_VARIABLE ){
    std::stringstream ss;
    ss << "b_" << old;
    return NodeManager::currentNM()->mkBoundVar( ss.str(), tn );
  }else{
    std::stringstream ss;
    ss << "i_" << old;
    return NodeManager::currentNM()->mkSkolem( ss.str(), tn, "created during sort inference" );
  }
}

Node SortInference::simplify( Node n, std::map< Node, Node >& var_bound ){
  std::vector< Node > children;
  if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
    //recreate based on types of variables
    std::vector< Node > new_children;
    for( size_t i=0; i<n[0].getNumChildren(); i++ ){
      TypeNode tn = getOrCreateTypeForId( d_var_types[n][ n[0][i] ], n[0][i].getType() );
      Node v = getNewSymbol( n[0][i], tn );
      new_children.push_back( v );
      var_bound[ n[0][i] ] = v;
    }
    children.push_back( NodeManager::currentNM()->mkNode( n[0].getKind(), new_children ) );
  }

  //process children
  if( n.getMetaKind() == kind::metakind::PARAMETERIZED ){
    children.push_back( n.getOperator() );
  }
  for( size_t i=0; i<n.getNumChildren(); i++ ){
    bool processChild = true;
    if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
      processChild = i>=1;
    }
    if( processChild ){
      children.push_back( simplify( n[i], var_bound ) );
    }
  }

  //remove from variable bindings
  if( n.getKind()==kind::FORALL || n.getKind()==kind::EXISTS ){
    //erase from variable bound
    for( size_t i=0; i<n[0].getNumChildren(); i++ ){
      var_bound.erase( n[0][i] );
    }
    return NodeManager::currentNM()->mkNode( n.getKind(), children );
  }else if( n.getKind()==kind::EQUAL ){
    if( children[0].getType()!=children[1].getType() ){
      if( children[0].isConst() ){
        children[0] = getNewSymbol( children[0], children[1].getType() );
      }else if( children[1].isConst() ){
        children[1] = getNewSymbol( children[1], children[0].getType() );
      }else{
        Trace("sort-inference-warn") << "Sort inference created bad equality: " << children[0] << " = " << children[1] << std::endl;
        Trace("sort-inference-warn") << "  Types : " << children[0].getType() << " " << children[1].getType() << std::endl;
        Assert( false );
      }
    }
    return NodeManager::currentNM()->mkNode( kind::EQUAL, children );
  }else if( n.getKind()==kind::APPLY_UF ){
    Node op = n.getOperator();
    if( d_symbol_map.find( op )==d_symbol_map.end() ){
      //make the new operator if necessary
      bool opChanged = false;
      std::vector< TypeNode > argTypes;
      for( size_t i=0; i<n.getNumChildren(); i++ ){
        TypeNode tn = getOrCreateTypeForId( d_op_arg_types[op][i], n[i].getType() );
        argTypes.push_back( tn );
        if( tn!=n[i].getType() ){
          opChanged = true;
        }
      }
      TypeNode retType = getOrCreateTypeForId( d_op_return_types[op], n.getType() );
      if( retType!=n.getType() ){
        opChanged = true;
      }
      if( opChanged ){
        std::stringstream ss;
        ss << "io_" << op;
        TypeNode typ = NodeManager::currentNM()->mkFunctionType( argTypes, retType );
        d_symbol_map[op] = NodeManager::currentNM()->mkSkolem( ss.str(), typ, "op created during sort inference" );
        Trace("setp-model") << "Function " << op << " is replaced with " << d_symbol_map[op] << std::endl;
        d_model_replace_f[op] = d_symbol_map[op];
      }else{
        d_symbol_map[op] = op;
      }
    }
    children[0] = d_symbol_map[op];
    //make sure all children have been taken care of
    for( size_t i=0; i<n.getNumChildren(); i++ ){
      TypeNode tn = children[i+1].getType();
      TypeNode tna = getTypeForId( d_op_arg_types[op][i] );
      if( tn!=tna ){
        if( n[i].isConst() ){
          children[i+1] = getNewSymbol( n[i], tna );
        }else{
          Trace("sort-inference-warn") << "Sort inference created bad child: " << n[i] << " " << tn << " " << tna << std::endl;
          Assert( false );
        }
      }
    }
    return NodeManager::currentNM()->mkNode( kind::APPLY_UF, children );
  }else{
    std::map< Node, Node >::iterator it = var_bound.find( n );
    if( it!=var_bound.end() ){
      return it->second;
    }else if( n.getKind() == kind::VARIABLE || n.getKind() == kind::SKOLEM ){
      if( d_symbol_map.find( n )==d_symbol_map.end() ){
        TypeNode tn = getOrCreateTypeForId( d_op_return_types[n], n.getType() );
        d_symbol_map[n] = getNewSymbol( n, tn );
      }
      return d_symbol_map[n];
    }else if( n.isConst() ){
      //just return n, we will fix at higher scope
      return n;
    }else{
      return NodeManager::currentNM()->mkNode( n.getKind(), children );
    }
  }

}

Node SortInference::mkInjection( TypeNode tn1, TypeNode tn2 ) {
  std::vector< TypeNode > tns;
  tns.push_back( tn1 );
  TypeNode typ = NodeManager::currentNM()->mkFunctionType( tns, tn2 );
  Node f = NodeManager::currentNM()->mkSkolem( "inj", typ, "injection for monotonicity constraint" );
  Trace("sort-inference") << "-> Make injection " << f << " from " << tn1 << " to " << tn2 << std::endl;
  Node v1 = NodeManager::currentNM()->mkBoundVar( "?x", tn1 );
  Node v2 = NodeManager::currentNM()->mkBoundVar( "?y", tn1 );
  Node ret = NodeManager::currentNM()->mkNode( kind::FORALL,
               NodeManager::currentNM()->mkNode( kind::BOUND_VAR_LIST, v1, v2 ),
               NodeManager::currentNM()->mkNode( kind::OR,
                 NodeManager::currentNM()->mkNode( kind::APPLY_UF, f, v1 ).eqNode( NodeManager::currentNM()->mkNode( kind::APPLY_UF, f, v2 ) ).negate(),
                 v1.eqNode( v2 ) ) );
  ret = theory::Rewriter::rewrite( ret );
  return ret;
}

int SortInference::getSortId( Node n ) {
  Node op = n.getKind()==kind::APPLY_UF ? n.getOperator() : n;
  if( d_op_return_types.find( op )!=d_op_return_types.end() ){
    return d_type_union_find.getRepresentative( d_op_return_types[op] );
  }else{
    return 0;
  }
}

int SortInference::getSortId( Node f, Node v ) {
  if( d_var_types.find( f )!=d_var_types.end() ){
    return d_type_union_find.getRepresentative( d_var_types[f][v] );
  }else{
    return 0;
  }
}

void SortInference::setSkolemVar( Node f, Node v, Node sk ){
  Trace("sort-inference-temp") << "Set skolem var for " << f << ", variable " << v << std::endl;
  if( isWellSortedFormula( f ) && d_var_types.find( f )==d_var_types.end() ){
    //calculate the sort for variables if not done so already
    std::map< Node, Node > var_bound;
    process( f, var_bound );
  }
  d_op_return_types[sk] = getSortId( f, v );
  Trace("sort-inference-temp") << "Set skolem sort id for " << sk << " to " << d_op_return_types[sk] << std::endl;
}

bool SortInference::isWellSortedFormula( Node n ) {
  if( n.getType().isBoolean() && n.getKind()!=kind::APPLY_UF ){
    for( unsigned i=0; i<n.getNumChildren(); i++ ){
      if( !isWellSortedFormula( n[i] ) ){
        return false;
      }
    }
    return true;
  }else{
    return isWellSorted( n );
  }
}

bool SortInference::isWellSorted( Node n ) {
  if( getSortId( n )==0 ){
    return false;
  }else{
    if( n.getKind()==kind::APPLY_UF ){
      for( unsigned i=0; i<n.getNumChildren(); i++ ){
        int s1 = getSortId( n[i] );
        int s2 = d_type_union_find.getRepresentative( d_op_arg_types[ n.getOperator() ][i] );
        if( s1!=s2 ){
          return false;
        }
        if( !isWellSorted( n[i] ) ){
          return false;
        }
      }
    }
    return true;
  }
}

void SortInference::getSortConstraints( Node n, UnionFind& uf ) {
  if( n.getKind()==kind::APPLY_UF ){
    for( unsigned i=0; i<n.getNumChildren(); i++ ){
      getSortConstraints( n[i], uf );
      uf.setEqual( getSortId( n[i] ), d_type_union_find.getRepresentative( d_op_arg_types[ n.getOperator() ][i] ) );
    }
  }
}

}/* CVC4 namespace */