/*-----------------------------------------------------------------------

  File  : cte_termfunc.c

  Author: Stephan Schulz

  Contents

  Most of the user-level functionality for unshared terms.

  Copyright 1998-2021 by the author.
  This code is released under the GNU General Public Licence and
  the GNU Lesser General Public License.
  See the file COPYING in the main E directory for details..
  Run "eprover -h" for contact information.


  Created: Wed Feb 25 16:50:36 MET 1998 (Ripped from cte_terms.c)

-----------------------------------------------------------------------*/


#include "cte_termfunc.h"
#include "cte_typecheck.h"
#include "clb_plocalstacks.h"
#include <cte_termpos.h>
#include <ccl_tformulae.h>
#include <cte_lambda.h>
#include <cte_pattern_match_mgu.h>

/*---------------------------------------------------------------------*/
/*                        Global Variables                             */
/*---------------------------------------------------------------------*/

bool      TermPrintLists = true;
bool      TermPrintTypes = false;

/*---------------------------------------------------------------------*/
/*                      Forward Declarations                           */
/*---------------------------------------------------------------------*/
void do_fool_print(FILE* out, Sig_p sig, TFormula_p form, int depth);

/*---------------------------------------------------------------------*/
/*                         Internal Functions                          */
/*---------------------------------------------------------------------*/


/*-----------------------------------------------------------------------
//
// Function: print_cons_list()
//
//   Print a list of $cons'ed terms, terminated with $nil. Abort on
//   not well-formed lists (no cons pairs!).
//
// Global Variables: -
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/

static void print_cons_list(FILE* out, Term_p list, Sig_p sig, DerefType deref)
{
   assert(SigSupportLists);
   putc('[', out);
   if(list->f_code == SIG_CONS_CODE)
   {
      assert(list->args);
      TermPrint(out, list->args[0], sig, deref);
      list = list->args[1];
      while(list->f_code == SIG_CONS_CODE)
      {
         putc(',', out);
         /* putc(' ', out); */
         assert(list->args);
         TermPrint(out, list->args[0], sig, deref);
         list = list->args[1];
      }
      assert(list->f_code == SIG_NIL_CODE);
   }
   putc(']', out);
}


/*-----------------------------------------------------------------------
//
// Function: parse_cons_list()
//
//   Parse a LOP list into an internal $cons list.
//
// Global Variables: -
//
// Side Effects    : Input, Memory operations
//
/----------------------------------------------------------------------*/

static Term_p parse_cons_list(Scanner_p in, Sig_p sig, VarBank_p vars)
{
   Term_p handle;
   Term_p current;

   assert(SigSupportLists);

   AcceptInpTok(in, OpenSquare);

   handle = TermDefaultCellArityAlloc(2);
   current = handle;

   if(!TestInpTok(in, CloseSquare))
   {

      current->f_code = SIG_CONS_CODE;
      current->type = SigDefaultSort(sig);
      current->args[0] = TermParse(in, sig, vars);
      current->args[1] = TermDefaultCellArityAlloc(2);
      current = current->args[1];

      while(TestInpTok(in, Comma))
      {
         NextToken(in);
         current->f_code = SIG_CONS_CODE;
         current->type = SigDefaultSort(sig);
         current->args[0] = TermParse(in, sig, vars);
         TermCellDelProp(current->args[0], TPTopPos);
         current->args[1] = TermDefaultCellArityAlloc(2);
         current = current->args[1];
      }
   }
   AcceptInpTok(in, CloseSquare);
   current->f_code = SIG_NIL_CODE;

   return handle;
}

/*-----------------------------------------------------------------------
//
// Function: term_check_consistency_rek()
//
//   Traverse a tree and check if any one term cell occurs more than
//   once on any branch (which would make the term cyclic). Return the
//   first inconsistency found or NULL.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

static Term_p term_check_consistency_rek(Term_p term, PTree_p *branch,
                                         DerefType deref)
{
   int      i;
   Term_p   res = NULL;

   const int limit = DEREF_LIMIT(term, deref);
   term = TermDeref(term, &deref);
   putc('.', stdout);

   if(!PTreeStore(branch, term))
   {
      return term;
   }
   for(i=0; i<term->arity; i++)
   {
      if((res = term_check_consistency_rek(term->args[i], branch,
                                           CONVERT_DEREF(i, limit, deref))))
      {
         break;
      }
   }
   PTreeDeleteEntry(branch, term);
   return res;
}

/*-----------------------------------------------------------------------
//
// Function: discard_last()
//
//   Returns the term where the last argument is left out.
//   Assumes that there is at least one argument!
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

Term_p discard_last(Term_p term)
{
   assert(ARG_NUM(term));
   return TermCreatePrefix(term, ARG_NUM(term)-1);
}

/*-----------------------------------------------------------------------
//
// Function: create_var_renaming_de_bruin()
//
// Traverse a term and create alpha-normalizing variable renaming.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

NumTree_p create_var_renaming_de_bruin(VarBank_p vars, Term_p term)
{
   int i;
   NumTree_p node;
   NumTree_p root;
   PStack_p open;
   long fresh_var_code;

   open = PStackAlloc();
   fresh_var_code = -2;
   root = NULL;

   PStackPushP(open, term);
   while(!PStackEmpty(open))
   {
      term = PStackPopP(open);
      if(TermIsFreeVar(term))
      {
         if (!NumTreeFind(&root, term->f_code)) {
            node = NumTreeCellAllocEmpty();
            node->key = term->f_code;
            node->val1.p_val = VarBankVarAssertAlloc(vars, fresh_var_code, term->type);
            //node->val1.p_val = VarBankVarAssertAlloc(vars, fresh_var_code, STIndividuals);
            fresh_var_code -= 2;

            NumTreeInsert(&root, node);
         }
      }
      else
      {
         for(i=0; i<term->arity; i++)
         {
            PStackPushP(open, term->args[term->arity-1-i]);
         }
      }
   }
   PStackFree(open);

   return root;
}

/*-----------------------------------------------------------------------
//
// Function: print_let()
//
//    Prints let term
//
// Global Variables: TermPrintLists
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/
void print_let(FILE* out, Term_p term, Sig_p sig, DerefType deref)
{
   fputs("$let(", out);
   long n_decls = term->arity - 1;

   if(n_decls > 1)
   {
      fputs("[", out);
   }
   for(int i=0; i<n_decls; i++)
   {
      assert(term->args[i]->f_code == sig->eqn_code);
      FunCode id = term->args[i]->args[0]->f_code;
      fputs(SigFindName(sig, id), out);
      fputs( " : ", out);
      TypePrintTSTP(out, sig->type_bank, SigGetType(sig, id));
      if(i!=n_decls-1)
      {
         fputs( ", ", out);
      }
   }

   if(n_decls > 1)
   {
      fputs("]", out);
   }
   fputs(", ", out);

   if(n_decls > 1)
   {
      fputs("[", out);
   }
   for(int i=0; i<n_decls; i++)
   {
      TermPrintFO(out, term->args[i]->args[0], sig, deref);
      fputs(" := ", out);
      TermPrintFO(out, term->args[i]->args[1], sig, deref);
      if(i!=n_decls-1)
      {
         fputs( ", ", out);
      }
   }
   if(n_decls > 1)
   {
      fputs("]", out);
   }

   fputs(", ", out);
   TermPrintFO(out, term->args[n_decls], sig, deref);
   fputs(")", out);
}


/*-----------------------------------------------------------------------
//
// Function: do_is_db_closed()
//
//    Does the actual closeness check.
//
// Global Variables: TermPrintLists
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/
bool do_is_db_closed(Term_p t,  long depth)
{
   if(!TermHasDBSubterm(t))
   {
      return true;
   }
   if(TermIsDBVar(t))
   {
      return t->f_code < depth;
   }
   if(TermIsLambda(t))
   {
      return do_is_db_closed(t->args[1], depth+1);
   }
   else
   {
      bool closed = true;
      for(long i=0; closed && i<t->arity; i++)
      {
         closed = closed && do_is_db_closed(t->args[i], depth);
      }
      return closed;
   }
}

/*-----------------------------------------------------------------------
//
// Function: do_fool_print()
//
//    Inner function
//
// Global Variables: TermPrintLists
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/
void do_ho_print(FILE* out, TFormula_p term, Sig_p sig, DerefType deref, int depth)
{
   if (problemType == PROBLEM_FO)
   {
      TermPrintFO(out, term, sig, deref);
      return;
   }

   assert(term);
   assert(sig||TermIsFreeVar(term));

   const int limit = DEREF_LIMIT(term, deref);
   term = TermDeref(term, &deref);

   if((!TermIsAnyVar(term) &&
       !(TFormulaIsQuantified(sig, term) && term->arity == 1) &&
      ((SigIsLogicalSymbol(sig, term->f_code) && TypeIsBool(term->type)) ||
      TermIsLambda(term)) &&
      term->f_code != SIG_TRUE_CODE &&
      term->f_code != SIG_FALSE_CODE))
   {
      do_fool_print(out, sig, term, depth);
      return;
   }
   if(term->f_code == SIG_ITE_CODE)
   {
      assert(term->arity==3);
      fprintf(out, "$ite(");
      do_ho_print(out, term->args[0], sig, deref, depth);
      fprintf(out, ", ");
      do_ho_print(out, term->args[1], sig, deref, depth);
      fprintf(out, ", ");
      do_ho_print(out, term->args[2], sig, deref, depth);
      fprintf(out, ")");
      return;
   }


   if(TermIsDBVar(term))
   {
      fprintf(out, "Z%d", depth - (int)term->f_code - 1);
   }
   else if(!TermIsTopLevelAnyVar(term))
   {
      if(TermIsPhonyApp(term))
      {
         if(TermIsLambda(term->args[0]))
         {
            fputs("( ", out);
         }
         do_ho_print(out, term->args[0], sig, deref, depth);
         if(TermIsLambda(term->args[0]))
         {
            fputs(" )", out);
         }
      }
      else
      {
         fputs(SigFindName(sig, term->f_code), out);
      }
   }
   else
   {
      Term_p var = TermIsAnyVar(term) ? term : term->args[0];
      if (TermIsFreeVar(var))
      {
         VarPrint(out, var->f_code);
      }
      else
      {
         fprintf(out, "Z%d", depth - (int)var->f_code - 1);
      }

   }

   for(int i = TermIsPhonyApp(term) ? 1 : 0; i < term->arity; ++i)
   {
      fputs(" @ ", out);
      DerefType c_deref = CONVERT_DEREF(i, limit, deref);
      if(term->args[i]->arity ||
         (c_deref != DEREF_NEVER &&
          term->args[i]->binding && term->args[i]->binding->arity))
      {
         fputs("(", out);
         if(TypeIsBool(term->args[i]->type))
         {
            do_fool_print(out, sig, term->args[i], depth);
         }
         else
         {
            do_ho_print(out, term->args[i], sig, c_deref, depth);
         }
         fputs(")", out);
      }
      else
      {
         do_ho_print(out, term->args[i], sig, c_deref, depth);
      }
   }
}

/*-----------------------------------------------------------------------
//
// Function: do_fool_print()
//
//    Inner function
//
// Global Variables: TermPrintLists
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/
void do_fool_print(FILE* out, Sig_p sig, TFormula_p form, int depth)
{
   assert(form);

   if(TermIsDBVar(form))
   {
      fprintf(out, "Z%d", depth - (int)form->f_code - 1);
   }
   else if((form->f_code == sig->eqn_code || form->f_code == sig->neqn_code)
           && TypeIsBool(form->type))
   {
      if(form->args[1]->f_code == SIG_TRUE_CODE)
      {
         if(form->f_code == sig->neqn_code)
         {
           fputs("~", out);
         }
         PRINT_HO_PAREN(out, '(');
         do_ho_print(out, form->args[0], sig, DEREF_NEVER, depth);
         PRINT_HO_PAREN(out, ')');
      }
      else
      {
         PRINT_HO_PAREN(out, '(');
         PRINT_HO_PAREN(out, '(');
         do_ho_print(out, form->args[0], sig, DEREF_NEVER, depth);
         PRINT_HO_PAREN(out, ')');
         if(form->f_code == sig->neqn_code)
         {
            fputc('!', out);
         }
         fputc('=', out);
         PRINT_HO_PAREN(out, '(');
         do_ho_print(out, form->args[1], sig, DEREF_NEVER, depth);
         PRINT_HO_PAREN(out, ')');
         PRINT_HO_PAREN(out, ')');
      }

   }
   else if((form->f_code == sig->qex_code || form->f_code == sig->qall_code ||
           TermIsLambda(form)) && form->arity == 2)
   {
      FunCode quantifier = form->f_code;
      if(form->f_code == sig->qex_code)
      {
         fputs("?[", out);
      }
      else if (form->f_code == sig->qall_code)
      {
         fputs("![", out);
      }
      else
      {
         fputs("^[", out);
      }

      if(form->f_code == SIG_DB_LAMBDA_CODE)
      {
         fprintf(out, "Z%d", depth);
         fprintf(out, "/* %ld */", form->args[1]->f_code);
         depth++;
      }
      else
      {
         do_ho_print(out, form->args[0], sig, DEREF_NEVER, depth);
      }

      if(problemType == PROBLEM_HO || !TypeIsIndividual(form->args[0]->type))
      {
         fputs(":", out);
         TypePrintTSTP(out, sig->type_bank, form->args[0]->type);
      }
      while(form->args[1]->f_code == quantifier)
      {
         form = form->args[1];
         fputs(", ", out);
         if(form->f_code == SIG_DB_LAMBDA_CODE)
         {
            fprintf(out, "Z%d", depth);
            depth++;
         }
         else
         {
            do_ho_print(out, form->args[0], sig, DEREF_NEVER, depth);
         }
         if(problemType == PROBLEM_HO || !TypeIsIndividual(form->args[0]->type))
         {
            fputs(":", out);
            TypePrintTSTP(out, sig->type_bank, form->args[0]->type);
         }
      }
      fputs("]:(", out);
      do_fool_print(out, sig, form->args[1], depth);
      fputs(")", out);
   }
   else if(form->f_code == sig->not_code)
   {
      assert(form->f_code == sig->not_code);
      fputs("~(", out);
      do_fool_print(out, sig, form->args[0], depth);
      fputs(")", out);
   }
   else
   {
      char* oprep = "XXX";
      // does not print or chain now
      if(!TermIsFreeVar(form) && SigQueryFuncProp(sig, form->f_code, FPFOFOp) && form->arity == 2)
      {
         fputs("(", out);
         do_fool_print(out, sig, form->args[0], depth);
         if(form->f_code == sig->and_code)
         {
            oprep = "&";
         }
         else if(form->f_code == sig->or_code)
         {
            oprep = "|";
         }
         else if(form->f_code == sig->impl_code)
         {
            oprep = "=>";
         }
         else if(form->f_code == sig->equiv_code)
         {
            oprep = "<=>";
         }
         else if(form->f_code == sig->nand_code)
         {
            oprep = "~&";
         }
         else if(form->f_code == sig->nor_code)
         {
         oprep = "~|";
         }
         else if(form->f_code == sig->bimpl_code)
         {
            oprep = "<=";
         }
         else if(form->f_code == sig->xor_code)
         {
            oprep = "<~>";
         }
         fputs(oprep, out);
         do_fool_print(out, sig, form->args[1], depth);
         fputs(")", out);
      }
      else
      {
         do_ho_print(out, form, sig, DEREF_NEVER, depth);
      }
   }
}

/*---------------------------------------------------------------------*/
/*                         Exported Functions                          */
/*---------------------------------------------------------------------*/


/*-----------------------------------------------------------------------
//
// Function: VarPrint()
//
//   Print a variable with FunCode var out.
//
// Global Variables: -
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/

void VarPrint(FILE* out, FunCode var)
{
   char id;
   assert(var<0);

   id = 'X';
   if(var%2)
   {
      id = 'Y';
   }
   fprintf(out, "%c%ld", id, -((var-1)/2));
}


/*-----------------------------------------------------------------------
//
// Function: TermPrintFO()
//
//   Print a FO term to the given stream.
//
// Global Variables: TermPrintLists
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/
void TermPrintFO(FILE* out, Term_p term, Sig_p sig, DerefType deref)
{
   assert(term);
   assert(sig||TermIsFreeVar(term));
   // no need to change derefs here -- FOL

   term = TermDeref(term, &deref);

   if(term->f_code == SIG_LET_CODE)
   {
      print_let(out, term, sig, deref);
      return;
   }
   if(!TermIsFreeVar(term) &&
      SigIsLogicalSymbol(sig, term->f_code) &&
      term->f_code != SIG_TRUE_CODE &&
      term->f_code != SIG_FALSE_CODE)
   {
      TermFOOLPrint(out, sig, term);
      return;
   }

#ifdef NEVER_DEFINED
   if(TermCellQueryProp(term, TPRestricted))
   {
      fprintf(out, "*");
   }
   if(TermCellQueryProp(term, TPIsRewritten))
   {
      if(TermIsTopRewritten(term))
      {
         fprintf(out, "=");
      }
      else
      {
         fprintf(out, "+");
      }
   }
#endif
   if(SigSupportLists && TermPrintLists &&
      ((term->f_code == SIG_NIL_CODE)||
       (term->f_code == SIG_CONS_CODE)))
   {
      print_cons_list(out, term, sig, deref);
   }
   else
   {
      if(TermIsFreeVar(term))
      {
         VarPrint(out, term->f_code);
      }
      else
      {
         fputs(SigFindName(sig, term->f_code), out);
         // fprintf(out, "(%ld)", term->f_code);
         if(!TermIsConst(term))
         {
            assert(term->args);
            TermPrintArgList(out, term->args, term->arity, sig, deref);
         }
      }
   }

   if(TermPrintTypes)
   {
      fputc(':', out);
      TypePrintTSTP(out, sig->type_bank, term->type);
   }
}


#define PRINT_AT

#ifdef ENABLE_LFHO

/*-----------------------------------------------------------------------
//
// Function: TermPrintHO()
//
//   Print a HO term to the given stream. If PRINT_AT is defined
//   terms will be delimited by @, otherwise " ".
//
// Global Variables: TermPrintLists
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/

void TermPrintHO(FILE* out, Term_p term, Sig_p sig, DerefType deref)
{
   do_ho_print(out, term, sig, deref, 0);
}


/*-----------------------------------------------------------------------
//
// Function: TermPrintDbgHO()
//
//   Prints the term as is, with no pretty printing of interpreted
//   symbols.
//
// Global Variables: TermPrintLists
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/

void TermPrintDbgHO(FILE* out, Term_p term, Sig_p sig, DerefType deref)
{
   assert(term);
   assert(sig||TermIsFreeVar(term));

   const int limit = DEREF_LIMIT(term, deref);
   term = TermDeref(term, &deref);

   if(TermIsDBVar(term))
   {
      // assert(term->arity == 0);
      fprintf(out, "db(%ld)", term->f_code);
   }
   else if(!TermIsFreeVar(term))
   {
      fputs(SigFindName(sig, term->f_code), out);
   }
   else
   {
      VarPrint(out, (TermIsFreeVar(term) ? term : term->args[0])->f_code);
      // fputs(" : ", out);
      // TypePrintTSTP(stderr, sig->type_bank, (TermIsFreeVar(term) ? term : term->args[0])->type);
   }


   for(int i = 0; i < term->arity; ++i)
   {
#ifdef PRINT_AT
      fputs(" @ ", out);
#else
      fputs(" ", out);
#endif
      DerefType c_deref = CONVERT_DEREF(i, limit, deref);
      if(term->args[i]->arity ||
         (c_deref != DEREF_NEVER && term->args[i]->binding && term->args[i]->binding->arity))
      {
         fputs("(", out);
         TermPrintDbgHO(out, term->args[i], sig, c_deref);
         fputs(")", out);
      }
      else
      {
         TermPrintDbgHO(out, term->args[i], sig, c_deref);
      }
   }
}

#endif


/*--------------------------------------------------------------------
//
// Function: TermPrintArgList()
//
//   Print an argument list (i.e. an array with at least one term
//   element) to the given stream.
//
// Global Variables: -
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/

void TermPrintArgList(FILE* out, Term_p *args, int arity, Sig_p sig,
                      DerefType deref)
{
   int i;

   assert(arity>=1);
   putc('(', out);

   TermPrintFO(out, args[0], sig, deref);

   for(i=1; i<arity; i++)
   {
      putc(',', out);
      /* putc(' ', out); */
      TermPrintFO(out, args[i], sig, deref);
   }
   putc(')', out);
}



/*-----------------------------------------------------------------------
//
// Function: TermPrintSimple()
//
//   Print a FO term without giving any special semantics to
//   symbols -- basically prints the serialized syntax tree.
//
// Global Variables:
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/

void TermPrintSimple(FILE* out, Term_p term, Sig_p sig)
{
   assert(term);
   assert(sig||TermIsAnyVar(term));
   // no need to change derefs here -- FOL

   if(TermIsFreeVar(term))
   {
      VarPrint(out, term->f_code);
   }
   else
   {
      fputs(SigFindName(sig, term->f_code), out);
      if(!TermIsConst(term))
      {
         assert(term->args);
         int i;

         assert(term->arity>=1);
         putc('(', out);

         TermPrintSimple(out, term->args[0], sig);

         for(i=1; i<term->arity; i++)
         {
            putc(',', out);
            /* putc(' ', out); */
            TermPrintSimple(out, term->args[i], sig);
         }
         putc(')', out);
      }
   }
}

/*-----------------------------------------------------------------------
//
// Function: TermIsFlat()
//
//   Return true if the term has no nested subterms.
//
// Global Variables: -
//
// Side Effects    : -
//
----------------------------------------------------------------------*/

bool TermIsFlat(Term_p t)
{
   int i;

   if(TermIsConst(t) || TermIsFreeVar(t))
   {
      return true;
   }
   for(i=0; i<t->arity; i++)
   {
      if(!TermIsConst(t->args[i]) && !TermIsFreeVar(t->args[i]))
      {
         return false;
      }
   }
   return true;
}

/*-----------------------------------------------------------------------
//
// Function: TermPrettyPrintSimple()
//
//   Print a FO term without giving any special semantics to
//   symbols -- basically prints the serialized syntax tree in a
//   nicely formatted manner.
//
// Global Variables:
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/

void TermPrettyPrintSimple(FILE* out, Term_p term, Sig_p sig, int level)
{
   int i;
   assert(term);
   assert(sig||TermIsAnyVar(term));
   // no need to change derefs here -- FOL

   for(i=0; i<level; i++)
   {
      fputs("  ", out);
   }

   TypePrintTSTP(out, sig->type_bank, term->type);
   fprintf(out, ":");
   if(TermIsFreeVar(term))
   {
      VarPrint(out, term->f_code);
      fputs(":", out);
      TypePrintTSTP(out, sig->type_bank, term->type);

   }
   else
   {
      fputs(SigFindName(sig, term->f_code), out);
      if(term->arity)
      {
         //assert(term->args);
         assert(term->arity>=1);
         if(TermIsFlat(term))
         {
            fputc('(', out);

            TermPrettyPrintSimple(out, term->args[0], sig, 0);

            for(i=1; i<term->arity; i++)
            {
               fputc(',', out);
               TermPrettyPrintSimple(out, term->args[i], sig, 0);
            }
            fputc(')', out);
         }
         else
         {
            fputs("(\n", out);

            TermPrettyPrintSimple(out, term->args[0], sig, level+1);

            for(i=1; i<term->arity; i++)
            {
               fputs(",\n", out);
               TermPrettyPrintSimple(out, term->args[i], sig, level+1);
            }
            fputc('\n', out);
            for(i=0; i<level; i++)
            {
               fputs("  ", out);
            }
            putc(')', out);
         }
      }
   }
}





/*-----------------------------------------------------------------------
//
// Function: TermParseOperator()
//
//   Parse an operator (i.e. an optional $, followed by an
//   identifier), store the representation into id and determine
//   the type.using the following rules:
//   - If it starts with a $, it's a TermIdentInterpreted (LOP global
//     variables are treated as interpreted constants).
//   - If it is a PosInt, it is a TermIdentNumber
//   - If its a String, it is a TermIdentObject
//   - If it is an upper-case or underscore Ident and no opening
//     bracket follows, its a TermIdentVariable
//   - Otherwise its a free function symbol (cases are SQString and
//     Identifier starting with lower-case letter.
//
//   Return value is the type
//
// Global Variables: SigIdentStartToken
//
// Side Effects    : Read input
//
/----------------------------------------------------------------------*/

FuncSymbType TermParseOperator(Scanner_p in, DStr_p id)
{
   FuncSymbType res = FuncSymbParse(in, id);

#ifndef STRICT_TPTP
   if((isupper(DStrView(id)[0])
       ||
       (DStrView(id)[0] == '_'))
      &&
      TestInpTok(in,OpenBracket))
   {
      res = FSIdentFreeFun;
   }
#endif

   return res;
}

/*-----------------------------------------------------------------------
//
// Function: TermSigInsert()
//
//   Thin wrapper around SigInsertId that also sets corresponding
//   properties for different identifier types.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

FunCode TermSigInsert(Sig_p sig, const char* name, int arity, bool
                      special_id, FuncSymbType type)
{
   FunCode res;

   res = SigInsertId(sig, name, arity, special_id);
   switch(type)
   {
   case FSIdentInt:
         SigSetFuncProp(sig, res, FPIsInteger);
         break;
   case FSIdentFloat:
         SigSetFuncProp(sig, res, FPIsFloat);
         break;
   case FSIdentRational:
         SigSetFuncProp(sig, res, FPIsRational);
         break;
   case FSIdentObject:
         SigSetFuncProp(sig, res, FPIsObject);
         break;
   case FSIdentInterpreted:
         SigSetFuncProp(sig, res, FPInterpreted);
         break;
   default:
         /* Nothing */
         break;
   }
   return res;
}


/*-----------------------------------------------------------------------
//
// Function: TermParse()
//
//   Parse a term from the given scanner object into the internal term
//   representation.
//
// Global Variables: -
//
// Side Effects    : Input, memory operations, may extend signature
//
/----------------------------------------------------------------------*/

Term_p TermParse(Scanner_p in, Sig_p sig, VarBank_p vars)
{
   Term_p        handle;
   DStr_p        id;
   FuncSymbType id_type;
   DStr_p        source_name, errpos;
   Type_p        type;
   long          line, column;
   StreamType    type_stream;

   if(SigSupportLists && TestInpTok(in, OpenSquare))
   {
      handle =  parse_cons_list(in, sig, vars);
   }
   else
   {
      id = DStrAlloc();
      line = AktToken(in)->line;
      column = AktToken(in)->column;
      source_name = DStrGetRef(AktToken(in)->source);
      type_stream = AktToken(in)->stream_type;

      if((id_type = TermParseOperator(in, id))==FSIdentVar)
      {
         /* A variable may be annotated with a type */
         if(TestInpTok(in, Colon))
         {
            AcceptInpTok(in, Colon);
            type = TypeBankParseType(in, vars->sort_table);
            handle = VarBankExtNameAssertAllocSort(vars,
                                                   DStrView(id), type);
         }
         else
         {
            handle = VarBankExtNameAssertAlloc(vars, DStrView(id));
         }
      }
      else
      {
         handle = NULL;

         if(TestInpTok(in, OpenBracket))
         {
            if((id_type == FSIdentInt)
               &&(sig->distinct_props & FPIsInteger))
            {
               AktTokenError(in,
                             "Number cannot have argument list (consider --free-numbers)",
                             false);
            }
            if((id_type == FSIdentObject)
               &&(sig->distinct_props & FPIsObject))
            {
               AktTokenError(in,
                             "Object cannot have argument list (consider --free-objects)",
                             false);
            }

            handle = TermParseArgList(in, sig, vars);
         }
         else
         {
            handle->arity = 0;
         }
         handle->f_code = TermSigInsert(sig, DStrView(id),
                                        handle->arity, false, id_type);
         if(!handle->f_code)
         {
            errpos = DStrAlloc();

            DStrAppendStr(errpos, PosRep(type_stream, source_name, line, column));
            DStrAppendChar(errpos, ' ');
            DStrAppendStr(errpos, DStrView(id));
            DStrAppendStr(errpos, " used with arity ");
            DStrAppendInt(errpos, (long)handle->arity);
            DStrAppendStr(errpos, " but registered with arity ");
            DStrAppendInt(errpos,
                          (long)SigFindArity(sig, SigFindFCode(sig, DStrView(id))));
            Error(DStrView(errpos), SYNTAX_ERROR);
            DStrFree(errpos);
         }
      }
      DStrReleaseRef(source_name);
      DStrFree(id);
   }
   return handle;
}


/*-----------------------------------------------------------------------
//
// Function: TermParseArgList()
//
//   Parse a list of terms (comma-separated and enclosed in brackets)
//   into an array of term pointers. Return the actual term containing
//   the terms parsed. Note: The array has to have exactly the right
//   size, as it will be handled by Size[Malloc|Free] for efficiency
//   reasons and may otherwise lead to a memory leak.
//   This leads to some complexity...
//   If the arglist is empty, return a default term containing no
//   arguments.
//
// Global Variables: -
//
// Side Effects    : Input, memory operations
//
/----------------------------------------------------------------------*/

Term_p TermParseArgList(Scanner_p in, Sig_p sig, VarBank_p vars)
{
   Term_p   tmp;
   Term_p result;
   PStackPointer i, arity;
   PStack_p args;

   AcceptInpTok(in, OpenBracket);
   if(TestInpTok(in, CloseBracket))
   {
      NextToken(in);
      result = TermDefaultCellAlloc();

      return result;
   }
   args = PStackAlloc();
   tmp = TermParse(in, sig, vars);
   PStackPushP(args, tmp);

   while(TestInpTok(in, Comma))
   {
      NextToken(in);
      tmp = TermParse(in, sig, vars);
      PStackPushP(args, tmp);
   }
   AcceptInpTok(in, CloseBracket);
   arity = PStackGetSP(args);
   result = TermDefaultCellArityAlloc(arity);

   for(i=0;i<arity;i++)
   {
      result->args[i] = PStackElementP(args,i);
   }
   PStackFree(args);

   return result;
}


/*-----------------------------------------------------------------------
//
// Function: TermCopy()
//
//   Return a copy of a given term. The new term will be unshared
//   (except, of coure, for the variables) even if the original term
//   was shared. Variable cells will be allocated from the VarBank
//   given to the function.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

Term_p TermCopy(Term_p source, VarBank_p vars, DBVarBank_p dbvars, DerefType deref)
{
   Term_p handle;
   int i;

   assert(source);

   const int limit = DEREF_LIMIT(source, deref);
   source = TermDeref(source, &deref);

   if(TermIsFreeVar(source))
   {
      handle = VarBankVarAssertAlloc(vars, source->f_code, source->type);
   }
   else if (TermIsDBVar(source))
   {
      if(!dbvars)
      {
         handle = source;
      }
      else
      {
         handle = _RequestDBVar(dbvars, source->type, source->f_code);
         TermSetBank(handle, vars->term_bank);
      }
   }
   else
   {
      handle = TermTopCopyWithoutArgs(source);

      for(i=0; i<handle->arity; i++)
      {
         handle->args[i] = TermCopy(source->args[i], vars, dbvars,
                                    CONVERT_DEREF(i, limit, deref));
      }
   }

   TermSetBank(handle, TermGetBank(source));
   return handle;
}


/*-----------------------------------------------------------------------
//
// Function: TermCopyKeepVars()
//
//   Return a copy of a given term. The new term will be unshared
//   (except, of coure, for the variables) even if the original term
//   was shared. Variable cells will not be copied. Note that printing
//   such a term might be confusing, since two variables with the same
//   f_code may indeed be different!
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

Term_p TermCopyKeepVars(Term_p source, DerefType deref)
{
   Term_p handle;
   int i;

   assert(source);

   const int limit = DEREF_LIMIT(source, deref);
   source = TermDeref(source, &deref);

   if(TermIsAnyVar(source))
   {
      return source;
   }

   handle = TermTopCopy(source);

   for(i=0; i<handle->arity; i++) /* Hack: Loop will not be entered if
                                     arity = 0 */
   {
      handle->args[i] = TermCopyKeepVars(handle->args[i],
                                         CONVERT_DEREF(i, limit, deref));
   }
   return handle;
}


/*-----------------------------------------------------------------------
//
// Function: TermStructEqual()
//
//   Return true if the two terms have the same structure. Follows
//   bindings.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

bool TermStructEqual(Term_p t1, Term_p t2)
{
   return TermStructEqualDeref(t1, t2, DEREF_ALWAYS, DEREF_ALWAYS);
}


/*-----------------------------------------------------------------------
//
// Function: TermStructEqualNoDeref()
//
//   Return true if the two terms have the same structures. Ignores
//   bindings.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/


bool TermStructEqualNoDeref(Term_p t1, Term_p t2)
{
   if(t1==t2)
   {
      return true;
   }

   if(TermIsDBVar(t1) != TermIsDBVar(t2))
   {
      return false;
   }

   if(t1->f_code != t2->f_code)
   {
      return false;
   }

   if(t1->type != t2->type)
   {
      // in HO case, it is posible for term
      // to have same head but different arities.
      // in that case the type must be different.
      assert(problemType == PROBLEM_HO);
      assert(TermIsPhonyApp(t1) || TermIsDBVar(t1) ||  TermIsLambda(t1) || t1->arity != t2->arity);
      return false;
   }

   //old asserts
   assert(problemType == PROBLEM_HO || t1->type == t2->type);
   assert(problemType == PROBLEM_HO || t1->arity == t2->arity);

   for(int i=0; i<t1->arity; i++)
   {
      if(!TermStructEqualNoDeref(t1->args[i], t2->args[i]))
      {
         return false;
      }
   }
   return true;
}

/*-----------------------------------------------------------------------
//
// Function: TermStructEqualDeref()
//
//   Return true if the two terms have the same
//   structures. Dereference both terms as designated by deref_1,
//   deref_2.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

// to make sure that we terminate, we do not eta-expand the variables
// and constants.
bool TermStructEqualDeref(Term_p t1, Term_p t2, DerefType deref_1, DerefType deref_2)
{

   int limit_1 = DEREF_LIMIT(t1, deref_1);
   int limit_2 = DEREF_LIMIT(t2, deref_2);

   TB_p bank = TermGetBank(t1) ? TermGetBank(t1) : TermGetBank(t2);

   if(problemType == PROBLEM_HO)
   {
      if(deref_1 == DEREF_ALWAYS)
      {
         t1 = WHNF_deref(t1);
      }
      else
      {
         t1 =
            deref_1 == DEREF_ONCE ?
               (TermIsFreeVar(t1) ? t1->binding : TBInsertInstantiatedDeref(bank, t1, deref_1)) : t1;
         t1 = BetaNormalizeDB(bank, t1);
         limit_1 = INT_MAX;
         deref_1 = DEREF_NEVER;
      }
   }
   else
   {
      t1 = TermDeref(t1, &deref_1);
   }

   if(problemType == PROBLEM_HO)
   {
      if(deref_2 == DEREF_ALWAYS)
      {
         t2 = WHNF_deref(t2);
      }
      else
      {
         t2 =
            deref_2 == DEREF_ONCE ?
               (TermIsFreeVar(t2) ? t2->binding : TBInsertInstantiatedDeref(bank, t2, deref_2)) : t2;
         t2 = BetaNormalizeDB(bank, t2);
         limit_2 = INT_MAX;
         deref_2 = DEREF_NEVER;
      }
   }
   else
   {
      t2 = TermDeref(t2, &deref_2);
   }

   if(t1->type != t2->type)
   {
      return false;
   }
   PruneLambdaPrefix(bank, &t1, &t2);

   if(deref_1 == DEREF_NEVER && deref_2 == DEREF_NEVER)
   {
      return t1 == t2;
   }

   if((t1==t2) && (deref_1==deref_2))
   {
      return true;
   }

   if(TermIsDBVar(t1) != TermIsDBVar(t2))
   {
      return false;
   }

   if(t1->f_code != t2->f_code)
   {
      return false;
   }

   if(t1->type != t2->type)
   {
      // in HO case, it is posible for term
      // to have same head but different arities.
      // in that case the type must be different.
      assert(problemType == PROBLEM_HO);
      assert(TermIsPhonyApp(t1) || TermIsLambda(t1) || t1->arity != t2->arity);
      return false;
   }

   //old asserts
   assert(problemType == PROBLEM_HO || t1->type == t2->type);
   assert(problemType == PROBLEM_HO || t1->arity == t2->arity);
   for(int i=TermIsLambda(t1) ? 1 : 0; i<t1->arity; i++)
   {
      if(!TermStructEqualDeref(t1->args[i], t2->args[i],
                               CONVERT_DEREF(i, limit_1, deref_1),
                               CONVERT_DEREF(i, limit_2, deref_2)))
      {
         return false;
      }
   }
   return true;
}

/*-----------------------------------------------------------------------
//
// Function: TermStructPrefixEqual()
//
//   Return true if the two terms have the same
//   structures except there are trailing arguments in r.
//   Dereference both terms as designated by deref_1, deref_2.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

bool TermStructPrefixEqual(Term_p l, Term_p r, DerefType d_l, DerefType d_r,
                           int remaining, Sig_p sig)
{
   bool res = true;
   if(remaining == 0)
   {
      res = TermStructEqualDeref(l, r, d_l, d_r);
   }
   else
   {
      const int limit_l = DEREF_LIMIT(l, d_l);
      const int limit_r = DEREF_LIMIT(r, d_r);
      l = TermDeref(l, &d_l);
      r = TermDeref(r, &d_r);

      if(TermIsAppliedAnyVar(r) && (r->arity - remaining == 1))
      {
         // f-code comparisons would fail without this hack.
         r = r->args[0];
      }

      if(l->f_code != r->f_code || (!TermIsAnyVar(r) && r->arity < remaining))
      {
         res = false;
      }
      else
      {
         assert((TermIsAnyVar(l) && TermIsAnyVar(r)) || l->arity == r->arity-remaining);

         for(int i=0; i<l->arity; i++)
         {
            if(!TermStructEqualDeref(l->args[i], r->args[i],
                                      CONVERT_DEREF(i, limit_l, d_l),
                                      CONVERT_DEREF(i, limit_r, d_r)))
            {
               res = false;
               break;
            }
         }
      }
   }

   return res;
}
/*-----------------------------------------------------------------------
//
// Function: TermStructWeightCompare()
//
//   Compare two terms based on just structural criteria: First
//   compare standard-weight, then compare top-symbol arity, then
//   compare subterms lexicographically. $true is always minimal.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

long TermStructWeightCompare(Term_p t1, Term_p t2)
{
   assert(t1);
   assert(t2);

   if(t1->f_code == SIG_TRUE_CODE)
   {
      assert(t1->arity == 0);
      if(t2->f_code == SIG_TRUE_CODE)
      {
         assert(t2->arity == 0);
         return 0;
      }
      return -1;
   }

   if(t2->f_code == SIG_TRUE_CODE)
   {
      assert(t2->arity == 0);
      return 1;
   }

   long res = TermStandardWeight(t1) - TermStandardWeight(t2);
   if(res)
   {
      return res;
   }

   if(TermIsFreeVar(t1))
   { /* Then t2 also is a variable due to equal weights! */
      assert(problemType == PROBLEM_HO || TermIsFreeVar(t2));
      return TypesCmp(t1->type, t2->type);
   }

   // DB var is smaller than fcode
   res = CMP(!TermIsDBVar(t1), !TermIsDBVar(t2));
   if(res)
   {
      return res;
   }

   if(TermIsDBVar(t1))
   {
      assert(TermIsDBVar(t2));
      return TypesCmp(t1->type, t2->type);
   }


   res = t1->arity - t2->arity;
   if(res)
   {
      return res;
   }

   //This is a non-valid assert... check with Stephan
   //  (reason: compares terms from different equations.)
   //assert(t1->type == t2->type);
   assert(t1->arity == t2->arity);
   for(int i=0; i<t1->arity; i++)
   {
      res = TermStructWeightCompare(t1->args[i], t2->args[i]);
      if(res)
      {
         return res;
      }
   }

   return 0;
}


/*-----------------------------------------------------------------------
//
// Function: TermLexCompare()
//
//   Compare two terms lexicographically by f_codes.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

long TermLexCompare(Term_p t1, Term_p t2)
{
   int i;

   long res = t1->f_code - t2->f_code;
   if(res)
   {
      return res;
   }

   if(t1->arity != t2->arity)
   {
      // in HO case, it is posible for term
      // to have same head but different arities.
      // in that case the type must be different.
      assert(problemType == PROBLEM_HO);
      assert(t1->type != t2->type);
      return t1->arity - t2->arity; //asume length-lexicographic
   }

   //old asserts
   assert(problemType == PROBLEM_HO || t1->type == t2->type);
   assert(problemType == PROBLEM_HO || t1->arity == t2->arity);
   for(i=0; i<t1->arity; i++)
   {
      res = TermLexCompare(t1->args[i], t2->args[i]);
      if(res)
      {
         return res;
      }
   }
   return res;
}


/*-----------------------------------------------------------------------
//
// Function: TermIsSubterm()
//
//   Return true if test is a subterm to super.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

bool TermIsSubterm(Term_p super, Term_p test, DerefType deref)
{
   int i;

   const int limit = DEREF_LIMIT(super, deref);
   super = TermDeref(super, &deref);

   if(super == test)
   {
      return true;
   }
   for(i=0; i<super->arity; i++)
   {
      if(TermIsSubterm(super->args[i], test, CONVERT_DEREF(i, limit, deref)))
      {
         return true;
      }
   }
   return false;
}


/*-----------------------------------------------------------------------
//
// Function: TermIsSubtermDeref()
//
//   Return true if test is a subterm to super. Uses
//   TermStructEqualDeref() for equal test.
//    NB: Deref is not changed since the function is not used.
//
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

bool TermIsSubtermDeref(Term_p super, Term_p test, DerefType
                        deref_super, DerefType deref_test)
{
   int i;

   super = TermDeref(super, &deref_super);
   if(TermStructEqualDeref(super, test, deref_super, deref_test))
   {
      return true;
   }
   for(i=0; i<super->arity; i++)
   {
      if(TermIsSubtermDeref(super->args[i], test, deref_super, deref_test))
      {
         return true;
      }
   }
   return false;
}


/*-----------------------------------------------------------------------
//
// Function: TermWeightCompute()
//
//   Compute the weight of a term, counting variables as vweight and
//   function symbols as fweight.
//
// Global Variables: -
//
// Side Effects    : Memory operations for the stack used.
//
/----------------------------------------------------------------------*/

long TermWeightCompute(Term_p term, long vweight, long fweight)
{
   long res = 0;

   if(TermIsFreeVar(term) ||
     (TermIsAppliedFreeVar(term) && NormalizePatternAppVar(TermGetBank(term), term)))
   {
      // if variable is of the form X xn where xn are bound variables -->
      // then it is counted as a simple variable
      res += vweight;
   }
   else
   {
      // lambdas (and corresponding bound var) are ignored.
      res += fweight*((TermIsPhonyApp(term) || TermIsDBLambda(term)) ? 0 : 1);
      for(int i=(TermIsDBLambda(term)?1:0); i<term->arity; i++)
      {
         res += TermWeight(term->args[i], vweight, fweight);
      }
   }

   return res;
}


/*-----------------------------------------------------------------------
//
// Function: TermFsumWeight()
//
//   Return a weighted sum of the function symbols weights (and
//   variable weights) in the term.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

long TermFsumWeight(Term_p term, long vweight, long flimit,
                    long *fweights, long default_fweight,
                    long* typefreqs)
{
   long res = 0;

   if(TermIsFreeVar(term))
   {
      res += vweight;
   }
   else
   {
      if(term->f_code < flimit)
      {
         if(!TermIsPhonyApp(term))
         {
            res += TermIsDBVar(term) ? default_fweight : fweights[term->f_code];
         }
         else
         {
            assert(problemType == PROBLEM_HO);
            if(typefreqs && typefreqs[term->args[0]->type->type_uid])
            {
               assert(typefreqs[term->args[0]->type->type_uid] > 0);
               res += typefreqs[term->args[0]->type->type_uid];
            }
         }
      }
      else
      {
         if(!TermIsPhonyApp(term))
         {
            res += default_fweight;
         }
         else
         {
            assert(problemType == PROBLEM_HO);
         }

      }

      for(int i = 0; i < term->arity; i++)
      {
         res += TermFsumWeight(term->args[i], vweight, flimit, fweights, default_fweight,
                               typefreqs);
      }
   }

   return res;

}



/*-----------------------------------------------------------------------
//
// Function: TermNonLinearWeight()
//
//   Compute the weight of a term, counting variables that occur for
//   the first time as vlweight, varaibes that reoccur as vweight, and
//   function symbols as fweight.
//
// Global Variables: -
//
// Side Effects    : Memory operations for the stack used.
//
/----------------------------------------------------------------------*/

long TermNonLinearWeight(Term_p term, long vlweight, long vweight,
                         long fweight)
{
   long     res = 0;
   PStack_p stack = PStackAlloc();
   Term_p   handle;

   assert(term);

   TermDelProp(term, DEREF_NEVER, TPOpFlag);

   PStackPushP(stack, term);

   while(!PStackEmpty(stack))
   {
      handle = PStackPopP(stack);
      if(TermIsFreeVar(handle))
      {
         if(TermCellQueryProp(handle, TPOpFlag))
         {
            res += vweight;
         }
         else
         {
            TermCellSetProp(handle, TPOpFlag);
            res += vlweight;
         }
      }
      else
      {
         int i;

         res += fweight * (TermIsPhonyApp(handle) ? 0 : 1);

         for(i=0; i<handle->arity; i++)
         {
            PStackPushP(stack, handle->args[i]);
         }
      }
   }
   PStackFree(stack);

   return res;
}


/*-----------------------------------------------------------------------
//
// Function: TermSymTypeWeight()
//
//   Compute the weight of a term, giving different weight to
//   variables, constants, function symbols and predicates.
//
// Global Variables: -
//
// Side Effects    : Memory operations for the stack.
//
/----------------------------------------------------------------------*/

long TermSymTypeWeight(Term_p term, long vweight, long fweight, long
                       cweight, long pweight)
{
   long     res = 0;
   PStack_p stack = PStackAlloc();
   Term_p   handle;

   assert(term);

   PStackPushP(stack, term);

   while(!PStackEmpty(stack))
   {
      handle = PStackPopP(stack);
      if(TermIsFreeVar(handle))
      {
         res += vweight;
      }
      else
      {
         int i;

         if(TermCellQueryProp(handle,TPPredPos))
         {
            res += pweight;
         }
         else if(handle->arity==0)
         {
            res += cweight;
         }
         else
         {
            res += fweight * (TermIsPhonyApp(handle) ? 0 : 1);
         }
         for(i=0; i<handle->arity; i++)
         {
            PStackPushP(stack, handle->args[i]);
         }
      }
   }
   PStackFree(stack);

   return res;
}

/*-----------------------------------------------------------------------
//
// Function: TermDepth()
//
//   Return the depth of a term.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

long TermDepth(Term_p term)
{
   long maxdepth = 0, ldepth;
   int  i;

   for(i=0; i<term->arity; i++)
   {
      ldepth = TermDepth(term->args[i]);
      maxdepth = MAX(maxdepth, ldepth);
   }
   return maxdepth+1;
}

/*-----------------------------------------------------------------------
//
// Function: TermIsDefTerm()
//
//   Return true if t is of the form f(X1...Xn) with n>=arity.
//
// Global Variables: -
//
// Side Effects    : Sets TPOpFlag
//
/----------------------------------------------------------------------*/

bool TermIsDefTerm(Term_p term, int min_arity)
{
   int i;

   assert(term);

   if(TermIsAnyVar(term) || TermIsPhonyApp(term) || TermIsLambda(term))
   {
      return false;
   }
   if(term->arity<min_arity)
   {
      return false;
   }
   if(TermStandardWeight(term)!=(DEFAULT_FWEIGHT+term->arity*DEFAULT_VWEIGHT))
   {
      return false;
   }
   for(i=0; i<term->arity; i++)
   {
      TermCellDelProp(term->args[i], TPOpFlag);
   }
   for(i=0; i<term->arity; i++)
   {
      if(!TermIsFreeVar(term->args[i]) || TermCellQueryProp(term->args[i], TPOpFlag))
      {
         return false;
      }
      TermCellSetProp(term->args[i], TPOpFlag);
   }
   return true;
}


/*-----------------------------------------------------------------------
//
// Function: TermHasFCode()
//
//   Return true if f occurs in term, false otherwise.
//   NB: DeBruijn variables are ignored.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

bool TermHasFCode(Term_p term, FunCode f)
{
   int i;

   assert(term);

   if(TermIsDBVar(term))
   {
      return false;
   }

   if(term->f_code == f)
   {
      return true;
   }
   for(i=0; i<term->arity; i++)
   {
      if(TermHasFCode(term->args[i], f))
      {
         return true;
      }
   }
   return false;
}

/*-----------------------------------------------------------------------
//
// Function: TermHasUnboundVariables()
//
//   Return if the term contains unbound variables.
//   Does not follow bindings.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

bool TermHasUnboundVariables(Term_p term)
{
   bool res = false;

   if(TermIsFreeVar(term))
   {
      if(!term->binding)
      {
         res = true;
      }
   }
   else
   {
      for(int i=0; i < term->arity; i++)
      {
         if(TermHasUnboundVariables(term->args[i]))
         {
            res = true;
            break;
         }
      }
   }

   return res;
}

/*-----------------------------------------------------------------------
//
// Function: TermIsGroundCompute()
//
//   Return if the term contains no variables.
//   Does not follow bindings.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

bool TermIsGroundCompute(Term_p term)
{
   bool res = true;

   if(TermIsFreeVar(term))
   {
      res = false;
   }
   else
   {
      for(int i=0; i < term->arity; i++)
      {
         if(!TermIsGroundCompute(term->args[i]))
         {
            res = false;
            break;
         }
      }
   }

   return res;
}

/*-----------------------------------------------------------------------
//
// Function: TermFindMaxVarCode()
//
//   Return largest (absolute, i.e. largest negative) f_code of any
//   variable in term.
//
// Global Variables:
//
// Side Effects    :
//
/----------------------------------------------------------------------*/

FunCode TermFindMaxVarCode(Term_p term)
{
   int i;
   long res, tmp;

   if(TermIsFreeVar(term))
   {
      return term->f_code;
   }
   else
   {
      res = 0;
      if(!TermIsGround(term))
      {
         for(i=0; i<term->arity; i++)
         {
            tmp = TermFindMaxVarCode(term->args[i]);
            res = MIN(res, tmp);
         }
      }
   }
   return res;
}

/*-----------------------------------------------------------------------
//
// Function: TermFindIteSubterm()
//
//   Returns true if it finds an $ite subterm in t. pos is the position
//   corresponding to this subterm if it is found, empty otherwise.
//
// Global Variables:
//
// Side Effects    :
//
/----------------------------------------------------------------------*/

bool TermFindIteSubterm(Term_p t, TermPos_p pos)
{
   assert(t);
   PStackPushP(pos, t);
   bool found = false;

   for(long i=0; !TermIsLambda(t) && !found && i<t->arity; i++)
   {
      PStackPushInt(pos, i);
      found = found ||
              (t->args[i]->f_code == SIG_ITE_CODE) ||
              TermFindIteSubterm(t->args[i], pos);
      if(!found)
      {
         PStackDiscardTop(pos);
      }
   }

   if(!found)
   {
      // did not find formula subterm
      PStackDiscardTop(pos);
      return false;
   }
   else
   {
      return true;
   }
}

/*-----------------------------------------------------------------------
//
// Function: VarBankCheckBindings()
//
//   For all variables in bank, check if they are bound. If sig!=0,
//   print the variable and binding as a comment, otherwise just print
//   variable number. Return number of bound variables.
//
// Global Variables: -
//
// Side Effects    : Output, Memory
//
/----------------------------------------------------------------------*/

FunCode VarBankCheckBindings(FILE* out, VarBank_p bank, Sig_p sig)
{
   Term_p    term;
   long      res = 0;
   int       i;

   fprintf(out, "#  VarBankCheckBindings() started...\n");
   for(i=1; i<PDArraySize(bank->variables); i++)
   {
      term = PDArrayElementP(bank->variables, i);
      if(term)
      {
         assert(TermIsFreeVar(term));
         if(term->binding)
         {
            res++;
            if(sig)
            {
               fprintf(out, "# %ld: ", term->f_code);
               TermPrint(out, term, sig, DEREF_NEVER);
               fprintf(out, " <--- ");
               TermPrint(out, term, sig, DEREF_ONCE);
               fprintf(out, "\n");
            }
            else
            {
               fprintf(out, "# Var%ld <---- %p\n",
                       term->f_code,
                       (void*)term->binding);
            }
         }
      }
   }
   fprintf(out, "#  ...VarBankCheckBindings() completed\n");
   return res;
}


/*-----------------------------------------------------------------------
//
// Function: TermAddSymbolDistributionLimited()
//
//   Count occurences of function symbols with f_code<limit in
//   dist_array. Terms are not dereferenced!
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

void TermAddSymbolDistributionLimited(Term_p term, long *dist_array, long limit)
{
   PStack_p stack = PStackAlloc();
   assert(term);

   PStackPushP(stack, term);

   while(!PStackEmpty(stack))
   {
      term = PStackPopP(stack);
      assert(term);

      if(!TermIsAnyVar(term))
      {
         int i;

         assert(term->f_code > 0);
         if(term->f_code < limit)
         {
            dist_array[term->f_code]++;
         }
         for(i=0; i<term->arity; i++)
         {
            assert(term->args);
            PStackPushP(stack, term->args[i]);
         }
      }
   }
   PStackFree(stack);
}

/*-----------------------------------------------------------------------
//
// Function: TermAddTypeDistribution()
//
//   Count occurences of types of symbols in term and store them
//   in type_arr
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

void  TermAddTypeDistribution(Term_p term, Sig_p sig, long* type_arr)
{
   PStack_p stack = PStackAlloc();
   Type_p ty = NULL;
   assert(term);
   assert(sig);

   PStackPushP(stack, term);

   while(!PStackEmpty(stack))
   {
      term = PStackPopP(stack);
      assert(term);
      ty = GetHeadType(sig, term);
      if(ty) // some polymorphic symbols have no type
      {
         type_arr[ty->type_uid]++;
      }


      int i;
      for(i=TermIsPhonyApp(term) ? 1 : 0; i<term->arity; i++)
      {
         PStackPushP(stack, term->args[i]);
      }
   }
   PStackFree(stack);
}

/*-----------------------------------------------------------------------
//
// Function: TermAddSymbolDistribExist()
//
//   Compute the distribution of symbols in term. Push all occuring
//   symbols onto exists (once ;-).
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

void TermAddSymbolDistExist(Term_p term, long *dist_array,
                            PStack_p exists)
{
   PStack_p stack = PStackAlloc();
   assert(term);

   PStackPushP(stack, term);

   while(!PStackEmpty(stack))
   {
      term = PStackPopP(stack);
      assert(term);

      if(!TermIsAnyVar(term))
      {
         int i;

         assert(term->f_code > 0);
         if(!dist_array[term->f_code] && !TermIsPhonyApp(term) && !TermIsLambda(term))
         {
            PStackPushInt(exists, term->f_code);
         }
         dist_array[term->f_code] += (TermIsPhonyApp(term) || TermIsLambda(term)) ? 0 : 1;

         for(i=0; i<term->arity; i++)
         {
            assert(term->args);
            PStackPushP(stack, term->args[i]);
         }
      }
   }
   PStackFree(stack);
}


/*-----------------------------------------------------------------------
//
// Function: TermAddSymbolFeaturesLimited()
//
//   Add function symbol frequencies and deepest depth of a function
//   symbol to the two arrays. This is an extension of the function
//   above, this one does the extendet task in a single term
//   traversal. Note that function symbols >=limit are counted in
//   array[0] for both depth and frequency.
//
// Global Variables: -
//
// Side Effects    : Changes the arrays.
//
/----------------------------------------------------------------------*/

void TermAddSymbolFeaturesLimited(Term_p term, long depth,
                                  long *freq_array, long* depth_array,
                                  long limit)
{
   if(!TermIsAnyVar(term))
   {
      int i;

      if(term->f_code < limit && !TermIsPhonyApp(term))
      {
         freq_array[term->f_code]++;
         depth_array[term->f_code] = MAX(depth, depth_array[term->f_code]);
      }
      else
      {
         freq_array[0] += TermIsPhonyApp(term) ? 0 : 1;
         depth_array[0] = MAX(depth, depth_array[0]);
      }
      for(i=0; i<term->arity; i++)
      {
         TermAddSymbolFeaturesLimited(term->args[i], depth + 1,
                                      freq_array, depth_array,
                                      limit);
      }
   }
}


/*-----------------------------------------------------------------------
//
// Function: TermAddSymbolFeatures()
//
//   Add function symbol frequencies and deepest depth of a function
//   symbol to the array. offset should be 0 for positive literals, 2
//   for negative literals. Thus, the 4 features for a given f
//   are stored at indices follows:
//   - 4*f_code:   |C^+|_f
//   - 4*f_code+1: d_f(C^+)
//   - 4*f_code+2: |C^-|_f
//   - 4*f_code+3: d_f(C^-)
//
// Global Variables: -
//
// Side Effects    : Changes the arrays.
//
/----------------------------------------------------------------------*/

void TermAddSymbolFeatures(Term_p term, PStack_p mod_stack, long depth,
                           long *feature_array, long offset)
{
   if(!TermIsAnyVar(term))
   {
      int i;
      if(!TermIsPhonyApp(term))
      {
         long findex = 4*term->f_code+offset;

         if(feature_array[findex] == 0)
         {
            PStackPushInt(mod_stack, findex);
         }

         feature_array[findex]++;
         feature_array[findex+1] = MAX(depth, feature_array[findex+1]);
      }
      for(i=0; i<term->arity; i++)
      {
         TermAddSymbolFeatures(term->args[i], mod_stack, depth + 1,
                               feature_array, offset);
      }
   }
}


/*-----------------------------------------------------------------------
//
// Function: TermComputeFunctionRanks()
//
//   Assign an occurrence rank to each symbol in term.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

void TermComputeFunctionRanks(Term_p term, long *rank_array, long *count)
{
   int i;

   if(TermIsAnyVar(term))
   {
      return;
   }
   for(i=0; i < term->arity; i++)
   {
      TermComputeFunctionRanks(term->args[i], rank_array, count);
   }
   if(!rank_array[term->f_code] && !TermIsPhonyApp(term))
   {
      rank_array[term->f_code] = (*count)++;
   }
}


/*-----------------------------------------------------------------------
//
// Function: TermCollectPropVariables()
//
//   Insert all variables with properties prop in term into
//   tree. Return number of new variables.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

long TermCollectPropVariables(Term_p term, PTree_p *tree,
                              TermProperties prop)
{
   long res = 0;
   PStack_p stack = PStackAlloc();
   int      i;

   PStackPushP(stack,term);

   while(!PStackEmpty(stack))
   {
      term = PStackPopP(stack);
      if(TermIsFreeVar(term) &&
         TermCellQueryProp(term,prop))
      {
         if(PTreeStore(tree, term))
         {
            res++;
         }
      }
      else
      {
         for(i=0; i<term->arity; i++)
         {
            PStackPushP(stack,term->args[i]);
         }
      }
   }
   PStackFree(stack);

   return res;
}

/*-----------------------------------------------------------------------
//
// Function: TermCollectVariables()
//
//   Insert all variables in term into
//   tree. Return number of new variables.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

long TermCollectVariables(Term_p term, PTree_p *tree)
{
   long res = 0;
   PStack_p stack = PStackAlloc();
   int      i;

   PStackPushP(stack,term);

   while(!PStackEmpty(stack))
   {
      term = PStackPopP(stack);
      if(TermIsFreeVar(term))
      {
         if(PTreeStore(tree, term))
         {
            res++;
         }
      }
      else
      {
         for(i=0; i<term->arity; i++)
         {
            if(!TermIsGround(term->args[i]))
            {
               PStackPushP(stack,term->args[i]);
            }
         }
      }
   }
   PStackFree(stack);

   return res;
}

/*-----------------------------------------------------------------------
//
// Function: TermCollectFCodes()
//
//   Insert all f_codes in term into
//   tree. Return number of new f_codes found
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

long TermCollectFCodes(Term_p term, NumTree_p *tree)
{
   long res = 0;
   PStack_p stack = PStackAlloc();
   int      i;
   IntOrP   dummy;

   dummy.i_val = 0;
   PStackPushP(stack,term);

   while(!PStackEmpty(stack))
   {
      term = PStackPopP(stack);
      if(term->f_code > 0)
      {
         if(NumTreeStore(tree, term->f_code, dummy, dummy))
         {
            res++;
         }
      }
      for(i=0; i<term->arity; i++)
      {
         PStackPushP(stack,term->args[i]);
      }
   }
   PStackFree(stack);

   return res;
}




/*-----------------------------------------------------------------------
//
// Function: TermCollectGroundTerms()
//
//   Add no-constant ground subterms of term to result. If top_only is
//   set, only add maximal (in the subterm relation sense) terms,
//   otherwise add all non-constant ground terms. Returns number of
//   terms newly added.
//
// Global Variables: -
//
// Side Effects    : Memory operations per PTreeInsert()
//
/----------------------------------------------------------------------*/

long TermCollectGroundTerms(Term_p term, PTree_p *result, bool top_only)
{
   PStack_p stack = PStackAlloc();
   long count = 0;
   int i;

   PStackPushP(stack, term);

   while(!PStackEmpty(stack))
   {
      term = PStackPopP(stack);
      if(!TermIsFreeVar(term))
      {
         if(TermIsGround(term))
         {
            if(!TermIsConst(term) && PTreeStore(result, term))
            {
               count++;
            }
         }
         if(!TermIsGround(term) || !top_only)
         {
            for(i=0; i<term->arity; i++)
            {
               PStackPushP(stack, term->args[i]);
            }
         }
      }
   }
   return count;
}


/*-----------------------------------------------------------------------
//
// Function: TermAddFunOcc()
//
//  Add all new occurences of function symbol to res_stack and mark
//  them as no-longer-new in f_occur. Return number of new function
//  symbols added.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

long TermAddFunOcc(Term_p term, PDArray_p f_occur, PStack_p res_stack)
{
   long res = 0;
   PStack_p stack = PStackAlloc();
   int      i;

   PStackPushP(stack,term);

   while(!PStackEmpty(stack))
   {
      term = PStackPopP(stack);
      if(!TermIsAnyVar(term))
      {
         if(!TermIsPhonyApp(term) && !PDArrayElementInt(f_occur, term->f_code))
         {
            res++;
            PStackPushInt(res_stack, term->f_code);
            PDArrayAssignInt(f_occur, term->f_code, 1);
         }
         for(i=0; i<term->arity; i++)
         {
            PStackPushP(stack,term->args[i]);
         }
      }
   }
   PStackFree(stack);

   return res;
}



/*-----------------------------------------------------------------------
//
// Function: TermArrayNoDuplicates()
//
//   Checks if there are no duplicates in the
//
// Global Variables: -
//
// Side Effects    : Changes stack
//
/----------------------------------------------------------------------*/

bool TermArrayNoDuplicates(Term_p* args, long size)
{
   if (size <= 1)
   {
      return true;
   }
   else
   {
      Term_p copy[size];
      memcpy(copy, args, sizeof(Term_p)*size);
      qsort(copy, size, sizeof(Term_p), PCmpFun);
      bool unique = true;
      for(long i=1; i<size && unique; i++)
      {
         unique = args[i] != args[i-1];
      }
      return unique;
   }

}


/*-----------------------------------------------------------------------
//
// Function: TermLinearize()
//
//   Put all subterms of term onto PStack in left-right preorder. Note
//   that for an empty stack, that makes the index of s on the stack
//   equal to its TermCPos. Returns number of subterms.
//
// Global Variables: -
//
// Side Effects    : Changes stack
//
/----------------------------------------------------------------------*/

long TermLinearize(PStack_p stack, Term_p term)
{
   long res = 1;
   int i;

   PStackPushP(stack, term);
   for(i = 0; i<term->arity; i++)
   {
      res += TermLinearize(stack, term->args[i]);
   }
   return res;
}


/*-----------------------------------------------------------------------
//
// Function: TermCheckConsistency()
//
//   Traverse a tree and check if any one term cell occurs more than
//   once on any branch (which would make the term cyclic). Return the
//   first inconsistency found or NULL.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

Term_p TermCheckConsistency(Term_p term, DerefType deref)
{
   Term_p   res;
   PTree_p  branch = NULL;

   printf("TermCheckConsistency...\n");
   res = term_check_consistency_rek(term, &branch, deref);
   assert(branch == 0);
   printf("...TermCheckConsistency\n");
   return res;
}


/*-----------------------------------------------------------------------
//
// Function: TermAssertSameSort
//
//  checks whether the two terms have the same sort. Prints a (verbose)
//  message if it's not the case and exit.
//
// Global Variables: -
//
// Side Effects    : May exit
//
/----------------------------------------------------------------------*/

void TermAssertSameSort(Sig_p sig, Term_p t1, Term_p t2)
{
   if(t1->type != t2->type)
   {
      fprintf(stderr, "# Error: terms ");
      TermPrintDbg(stderr, t1, sig, DEREF_NEVER);
      fprintf(stderr, ": ");
      TypePrintTSTP(stderr, sig->type_bank, t1->type);
      fprintf(stderr, " and ");
      TermPrintDbg(stderr, t2, sig, DEREF_NEVER);
      fprintf(stderr, ": ");
      TypePrintTSTP(stderr, sig->type_bank, t2->type);
      fprintf(stderr, " should have the same sort\n");
      assert(false);
      Error("Type error", SYNTAX_ERROR);
   }
}


/*-----------------------------------------------------------------------
//
// Function: TermIsUntyped
//
//   check whether all sorts occurring in the term are either
//   individual or boolean. In other words, whether the term
//   belongs to regular untyped logic.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

bool TermIsUntyped(Term_p term)
{
   bool res = true;

   PLocalStackInit(stack);

   PLocalStackPush(stack, term);

   while(!PLocalStackEmpty(stack))
   {
      term = PLocalStackPop(stack);

      if(TypeIsIndividual(term->type) || TypeIsBool(term->type))
      {
         PLocalStackPushTermArgs(stack, term);
      }
      else
      {
         res = false;
         break;
      }
   }

   PLocalStackFree(stack);

   return res;
}

/*-----------------------------------------------------------------------
//
// Function: TermAppEncode()
//
//   App-encodes the term.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

Term_p TermAppEncode(Term_p orig, Sig_p sig)
{
   if(orig->arity == 0)
   {
      return TermCopyKeepVars(orig, DEREF_NEVER);
   }

   assert(orig->arity > 0);
   Term_p orig_prefix = discard_last(orig);
   Term_p applied_to  = orig->args[orig->arity-1];

   assert(TermIsFreeVar(orig_prefix) || !orig_prefix->type);
   TypeInferSort(sig, orig_prefix, NULL);
   assert(orig_prefix->type);

   Term_p app_encoded = TermTopAlloc(SigGetTypedApp(sig, orig_prefix->type, applied_to->type, orig->type), 2);
   app_encoded->args[0] = TermAppEncode(orig_prefix, sig);
   app_encoded->args[1] = TermAppEncode(applied_to, sig);

   if(!TermIsFreeVar(orig_prefix))
   {
      TermTopFree(orig_prefix);
   }

   return app_encoded;
}

/*-----------------------------------------------------------------------
//
// Function: TermCreatePrefix()
//
//    Create a prefix containing arg_num arguments of original term orig.
//    If orig was an applied variable and arg_num is 0, return the shared
//    variable that is the first argument.
//
//    NB: In case caller needs proper prefix, returned term will not be
//    shared (unless it is a variable head of applied variable)!
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

Term_p TermCreatePrefix(Term_p orig, int arg_num)
{
   assert(orig && arg_num >= 0 && orig->arity >= arg_num);
   assert(!TermIsPhonyApp(orig) || orig->arity != arg_num);

   Term_p prefix;

   if(arg_num == ARG_NUM(orig))
   {
      prefix = orig;
   }
   else if(TermIsPhonyApp(orig) && arg_num == 0)
   {
      // due to app-encoding of applied variables,
      // the term head is hidden in first argument
      prefix = orig->args[0];
   }
   else
   {
      assert(arg_num < ARG_NUM(orig));
      int pref_len = arg_num + (TermIsPhonyApp(orig) ? 1 : 0);
      prefix = TermTopAlloc(orig->f_code, pref_len);

      for(int i=0; i < pref_len; i++)
      {
         prefix->args[i] = orig->args[i];
      }

      assert(!TermIsShared(prefix));
   }

   return prefix;
}

/*-----------------------------------------------------------------------
//
// Function: TermFOOLPrint()
//
//   Print a formula using only signature (not bank). Prints
//   equations as infix.
//
// Global Variables:
//
// Side Effects    : Output
//
/----------------------------------------------------------------------*/

void TermFOOLPrint(FILE* out, Sig_p sig, TFormula_p form)
{
   do_fool_print(out, sig, form, 0);
}

/*----------------------------------------------------------------------*/
//
// Function: TermCopyRenameVars()
//
//   Create a term copy with variables renamed.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/*----------------------------------------------------------------------*/

Term_p TermCopyRenameVars(NumTree_p* renaming, Term_p term)
{
    int i;
    Term_p copy;
    NumTree_p entry;

    if (TermIsFreeVar(term))
    {
        entry = NumTreeFind(renaming, term->f_code);
        assert(entry);
        copy = (Term_p)(entry->val1.p_val);
    }
    else if (TermIsDBVar(term))
    {
        copy = term;
    }
    else
    {
        copy = TermTopCopy(term);
        copy->type = term->type;
        for (i=0; i<term->arity; i++)
        {
            copy->args[i] = TermCopyRenameVars(renaming, term->args[i]);
        }
    }

    assert(copy);
    return copy;
}

/*-----------------------------------------------------------------------
//
// Function: TermCopyNormalizeVarsAlpha()
//
//   Create an alpha-normalized term copy.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

Term_p TermCopyNormalizeVarsAlpha(VarBank_p vars, Term_p term)
{
    Term_p copy;
    NumTree_p renaming;

    renaming = create_var_renaming_de_bruin(vars, term);
    copy = TermCopyRenameVars(&renaming, term);
    NumTreeFree(renaming);

    return copy;
}

/*-----------------------------------------------------------------------
//
// Function: TermCopyUnifyVars()
//
//   Create a term copy with all the variables unified (to X0).
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

Term_p TermCopyUnifyVars(VarBank_p vars, Term_p term)
{
    int i;

    if (TermIsFreeVar(term))
    {
        return VarBankVarAssertAlloc(vars, -2, vars->sort_table->i_type);
    }
    else if (TermIsDBVar(term))
    {
        return term;
    }

    Term_p new = TermTopCopy(term);
    for (i=0; i<term->arity; i++)
    {
        new->args[i] = TermCopyUnifyVars(vars, term->args[i]);
    }

    return new;
}

/*-----------------------------------------------------------------------
//
// Function: TermCopyRenameVars()
//
//   Create a term copy using the specified variable normalization.
//
// Global Variables: -
//
// Side Effects    : Memory operations
//
/----------------------------------------------------------------------*/

Term_p TermCopyNormalizeVars(VarBank_p vars, Term_p term,
   VarNormStyle var_norm)
{
   switch (var_norm) {
   case NSUnivar:
      return TermCopyUnifyVars(vars,term);
   case NSAlpha:
      return TermCopyNormalizeVarsAlpha(vars,term);
   default:
      return TermCopy(term,vars,NULL,DEREF_NEVER);
   }
}


/*-----------------------------------------------------------------------
//
// Function: TermDAGWeight()
//
//    Compute the DAG weight of a term. More concretely: For each
//    occurrence of an already considered subterm, count
//    dup_weigth. For all new termcells count fweight for function
//    sybmbols and vweight for variables. The new_term parameter
//    indicates if the term shall be considered individually, or if
//    this is a continuation of a previous computation which already
//    might have seen some subterms.
//
// Global Variables: -
//
// Side Effects    : Memory operations, manipulates TPPOpFlag in term
//                   cells.
//
/----------------------------------------------------------------------*/

long TermDAGWeight(Term_p term, long fweight, long vweight,
                   long dup_weight, bool new_term)
{
   PStack_p stack;
   long res = 0;
   int i;

   assert(term);

   if(new_term)
   {
      TermDelPropOpt(term, TPOpFlag);
   }
   stack = PStackAlloc();
   PStackPushP(stack, term);

   // printf("(F%ld/V%ld)\n", fweight, vweight);

   while(!PStackEmpty(stack))
   {
      term = PStackPopP(stack);
      assert(term);
      if(TermCellQueryProp(term, TPOpFlag))
      {
         res += dup_weight;
      }
      else
      {
         TermCellSetProp(term, TPOpFlag);
         if(TermIsFreeVar(term))
         {
            res += vweight;
         }
         else
         {
            res += fweight;
            for(i=0; i< term->arity; i++)
            {
               PStackPushP(stack, term->args[i]);
            }
         }
      }
   }
   PStackFree(stack);
   return res;
}

/*-----------------------------------------------------------------------
//
// Function: TermIsDBClosed()
//
//    Checks if term has no leaky variables.
//
// Global Variables: -
//
// Side Effects    : Memory operations, manipulates TPPOpFlag in term
//                   cells.
//
/----------------------------------------------------------------------*/
bool TermIsDBClosed(Term_p term)
{
   return !TermHasDBSubterm(term) || do_is_db_closed(term, 0);
}

/*-----------------------------------------------------------------------
//
// Function: TermApplyArg()
//
//   Applies one term to the other. Performs rudimentary typechecking.
//   Term is UNSHARED.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

Term_p TermApplyArg(TypeBank_p tb, Term_p s, Term_p arg)
{
   assert(TypeIsArrow(s->type));
   assert(s->type->args[0] == arg->type);

   Term_p s_arg = NULL;
   if ((!TermIsAnyVar(s) && !TermIsLambda(s)))
   {
      s_arg = TermTopAlloc(s->f_code, s->arity+1);
      for(int i=0; i<s->arity; i++)
      {
         s_arg->args[i] = s->args[i];
      }
      s_arg->args[s->arity] = arg;
   }
   else
   {
      s_arg = TermTopAlloc(SIG_PHONY_APP_CODE, 2);
      s_arg->args[0] = s;
      s_arg->args[1] = arg;
   }

   s_arg->type = TypeBankInsertTypeShared(tb, TypeDropFirstArg(s->type));

   return s_arg;
}

/*-----------------------------------------------------------------------
//
// Function: TermComputeOrder()
//
//   Computes the maximal order of the symbols that appear in the term.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

int TermComputeOrder(Sig_p sig, Term_p term)
{
   PStack_p subterms = PStackAlloc();
   PStackPushP(subterms, term);
   int ord = VAR_ORDER(term->type);

   while(!PStackEmpty(subterms))
   {
      Term_p subterm = PStackPopP(subterms);
      ord = MAX(ord, VAR_ORDER(subterm->type));

      for(int i=TermIsLambda(subterm) ? 1 : 0; i<subterm->arity; i++)
      {
         PStackPushP(subterms, subterm->args[i]);
      }
   }

   PStackFree(subterms);
   return ord;
}

/*-----------------------------------------------------------------------
//
// Function: TermPrintVarBinds()
//
//   Prints all the variables and their bindings from the term t
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

void visitor(void* sig, void* tp)
{
   Term_p t = tp;
   DBG_PRINT(stderr, "", TermPrintDbg(stderr, t, sig, DEREF_NEVER), " <- ");
   if(t->binding)
   {
      DBG_PRINT(stderr, "", TermPrintDbg(stderr, t->binding, sig, DEREF_NEVER), ";");
   }
   else
   {
      fprintf(stderr, "/;");
   }
}

void TermPrintDbgVarBinds(Sig_p sig, Term_p t)
{
   PTree_p vars = NULL;
   TermCollectVariables(t, &vars);
   PTreeVisitInOrder(vars, visitor, sig);
   PTreeFree(vars);
}

/*-----------------------------------------------------------------------
//
// Function: TermTrimImplications()
//
//   Consider only the conclusion part of the implication for
//   considering the symbols in SinE.
//
// Global Variables: -
//
// Side Effects    : -
//
/----------------------------------------------------------------------*/

#define TRIM_THRESHOLD 10
Term_p TermTrimImplications(Sig_p sig, Term_p f)
{
   Term_p orig_f = f;
   while(TFormulaIsQuantified(sig, f) && f->arity == 2)
   {
      f = f->args[1];
   }

   int num_impls = 0;
   while(f->f_code == sig->impl_code && f->arity == 2)
   {
      num_impls++;
      f = f->args[1];
   }
   return num_impls >= TRIM_THRESHOLD ? f : orig_f;
}

/*---------------------------------------------------------------------*/
/*                        End of File                                  */
/*---------------------------------------------------------------------*/
