(*  Author: Jia Meng, Cambridge University Computer Laboratory

     ID: $Id$

     Copyright 2004 University of Cambridge

 ML data structure for storing/printing FOL clauses and arity clauses.

 Typed equality is treated differently.

 *)

 (* works for writeoutclasimp on typed *)

 signature RES_CLAUSE =

   sig

   val keep_types : bool ref

   val special_equal : bool ref

   val tagged : bool ref

   exception ARCLAUSE of string

   exception CLAUSE of string * term

   type arityClause 

   type classrelClause

   type clause

   val init : theory -> unit

   val make_axiom_clause : Term.term -> string * int -> clause

   val make_conjecture_clauses : term list -> clause list

   val get_axiomName : clause ->  string

   val isTaut : clause -> bool

   val num_of_clauses : clause -> int

   val clause2dfg : clause -> string * string list

   val clauses2dfg : clause list -> string -> clause list -> clause list ->

 	   (string * int) list -> (string * int) list -> string

   val tfree_dfg_clause : string -> string

   val arity_clause_thy: theory -> arityClause list 

   val classrel_clauses_thy: theory -> classrelClause list 

   val tptp_arity_clause : arityClause -> string

   val tptp_classrelClause : classrelClause -> string

   val tptp_clause : clause -> string list

   val clause2tptp : clause -> string * string list

   val tfree_clause : string -> string

   val schematic_var_prefix : string

   val fixed_var_prefix : string

   val tvar_prefix : string

   val tfree_prefix : string

   val clause_prefix : string 

   val arclause_prefix : string

   val const_prefix : string

   val tconst_prefix : string 

   val class_prefix : string 

   val union_all : ''a list list -> ''a list

   val ascii_of : String.string -> String.string

   val paren_pack : string list -> string

   val bracket_pack : string list -> string

   val make_schematic_var : String.string * int -> string

   val make_fixed_var : String.string -> string

   val make_schematic_type_var : string * int -> string

   val make_fixed_type_var : string -> string

   val make_fixed_const : String.string -> string		

   val make_fixed_type_const : String.string -> string   

   val make_type_class : String.string -> string

   val isMeta : String.string -> bool

   type typ_var

   val mk_typ_var_sort : Term.typ -> typ_var * sort

   type type_literal

   val add_typs_aux2 : (typ_var * string list) list -> type_literal list * type_literal list

   val gen_tptp_cls : int * string * string * string -> string

   val gen_tptp_type_cls : int * string * string * string * int -> string

   val tptp_of_typeLit : type_literal -> string

   end;

 structure ResClause: RES_CLAUSE =

 struct

 (* Added for typed equality *)

 val special_equal = ref false; (* by default,equality does not carry type information *)

 val eq_typ_wrapper = "typeinfo"; (* default string *)

 val schematic_var_prefix = "V_";

 val fixed_var_prefix = "v_";

 val tvar_prefix = "T_";

 val tfree_prefix = "t_";

 val clause_prefix = "cls_"; 

 val arclause_prefix = "clsarity_" 

 val clrelclause_prefix = "clsrel_";

 val const_prefix = "c_";

 val tconst_prefix = "tc_"; 

 val class_prefix = "class_"; 

 fun union_all xss = foldl (op union) [] xss;

 (*Provide readable names for the more common symbolic functions*)

 val const_trans_table =

       Symtab.make [("op =", "equal"),

 	  	   ("op <=", "lessequals"),

 		   ("op <", "less"),

 		   ("op &", "and"),

 		   ("op |", "or"),

 		   ("op +", "plus"),

 		   ("op -", "minus"),

 		   ("op *", "times"),

 		   ("op -->", "implies"),

 		   ("{}", "emptyset"),

 		   ("op :", "in"),

 		   ("op Un", "union"),

 		   ("op Int", "inter"),

 		   ("List.op @", "append")];

 val type_const_trans_table =

       Symtab.make [("*", "t_prod"),

 	  	   ("+", "t_sum"),

 		   ("~=>", "t_map")];

 (*Escaping of special characters.

   Alphanumeric characters are left unchanged.

   The character _ goes to __

   Characters in the range ASCII space to / go to _A to _P, respectively.

   Other printing characters go to _NNN where NNN is the decimal ASCII code.*)

 local

 val A_minus_space = Char.ord #"A" - Char.ord #" ";

 fun ascii_of_c c =

   if Char.isAlphaNum c then String.str c

   else if c = #"_" then "__"

   else if #" " <= c andalso c <= #"/" 

        then "_" ^ String.str (Char.chr (Char.ord c + A_minus_space))

   else if Char.isPrint c then ("_" ^ Int.toString (Char.ord c))

   else ""

 in

 val ascii_of = String.translate ascii_of_c;

 end;

 (* convert a list of strings into one single string; surrounded by brackets *)

 fun paren_pack [] = ""   (*empty argument list*)

   | paren_pack strings = "(" ^ commas strings ^ ")";

 fun bracket_pack strings = "[" ^ commas strings ^ "]";

 (*Remove the initial ' character from a type variable, if it is present*)

 fun trim_type_var s =

   if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)

   else error ("trim_type: Malformed type variable encountered: " ^ s);

 fun ascii_of_indexname (v,0) = ascii_of v

   | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ Int.toString i;

 fun make_schematic_var v = schematic_var_prefix ^ (ascii_of_indexname v);

 fun make_fixed_var x = fixed_var_prefix ^ (ascii_of x);

 fun make_schematic_type_var (x,i) = 

       tvar_prefix ^ (ascii_of_indexname (trim_type_var x,i));

 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x));

 fun make_fixed_const c =

     case Symtab.lookup const_trans_table c of

         SOME c' => c'

       | NONE =>  const_prefix ^ ascii_of c;

 fun make_fixed_type_const c = 

     case Symtab.lookup type_const_trans_table c of

         SOME c' => c'

       | NONE =>  tconst_prefix ^ ascii_of c;

 fun make_type_class clas = class_prefix ^ ascii_of clas;

 (***** definitions and functions for FOL clauses, prepared for conversion into TPTP format or SPASS format. *****)

 val keep_types = ref true;

 datatype kind = Axiom | Hypothesis | Conjecture;

 fun name_of_kind Axiom = "axiom"

   | name_of_kind Hypothesis = "hypothesis"

   | name_of_kind Conjecture = "conjecture";

 type clause_id = int;

 type axiom_name = string;

 type polarity = bool;

 type indexname = Term.indexname;

 (* "tag" is used for vampire specific syntax  *)

 type tag = bool; 

 (**** Isabelle FOL clauses ****)

 val tagged = ref false;

 type pred_name = string;

 type sort = Term.sort;

 type fol_type = string;

 datatype type_literal = LTVar of string | LTFree of string;

 datatype folTerm = UVar of string * fol_type

                  | Fun of string * fol_type list * folTerm list;

 datatype predicate = Predicate of pred_name * fol_type list * folTerm list;

 datatype literal = Literal of polarity * predicate * tag;

 datatype typ_var = FOLTVar of indexname | FOLTFree of string;

 fun mk_typ_var_sort (TFree(a,s)) = (FOLTFree a,s)

   | mk_typ_var_sort (TVar(v,s)) = (FOLTVar v,s);

 (* ML datatype used to repsent one single clause: disjunction of literals. *)

 datatype clause = 

 	 Clause of {clause_id: clause_id,

 		    axiom_name: axiom_name,

 		    kind: kind,

 		    literals: literal list,

 		    types_sorts: (typ_var * sort) list, 

                     tvar_type_literals: type_literal list, 

                     tfree_type_literals: type_literal list ,

                     tvars: string list,

                     predicates: (string*int) list,

                     functions: (string*int) list};

 exception CLAUSE of string * term;

 (*** make clauses ***)

 fun isFalse (Literal (pol,Predicate(a,_,[]),_)) =

       (pol andalso a = "c_False") orelse

       (not pol andalso a = "c_True")

   | isFalse _ = false;

 fun isTrue (Literal (pol,Predicate(a,_,[]),_)) =

       (pol andalso a = "c_True") orelse

       (not pol andalso a = "c_False")

   | isTrue _ = false;

 fun isTaut (Clause {literals,...}) = exists isTrue literals;  

 fun make_clause (clause_id,axiom_name,kind,literals,

                  types_sorts,tvar_type_literals,

                  tfree_type_literals,tvars, predicates, functions) =

   if forall isFalse literals 

   then error "Problem too trivial for resolution (empty clause)"

   else

      Clause {clause_id = clause_id, axiom_name = axiom_name, kind = kind, 

              literals = literals, types_sorts = types_sorts,

              tvar_type_literals = tvar_type_literals,

              tfree_type_literals = tfree_type_literals,

              tvars = tvars, predicates = predicates, 

              functions = functions};

 (** Some Clause destructor functions **)

 fun string_of_kind (Clause cls) = name_of_kind (#kind cls);

 fun get_axiomName (Clause cls) = #axiom_name cls;

 fun get_clause_id (Clause cls) = #clause_id cls;

 fun funcs_of_cls (Clause cls) = #functions cls;

 fun preds_of_cls (Clause cls) = #predicates cls;

 (*Declarations of the current theory--to allow suppressing types.*)

 val const_typargs = ref (Library.K [] : (string*typ -> typ list));

 fun num_typargs(s,T) = if !keep_types then length (!const_typargs (s,T)) else 0;

 (*Initialize the type suppression mechanism with the current theory before

     producing any clauses!*)

 fun init thy = (const_typargs := Sign.const_typargs thy);

 (*Flatten a type to a string while accumulating sort constraints on the TFrees and

   TVars it contains.*)    

 fun type_of (Type (a, Ts)) = 

       let val (folTyps, (ts, funcs)) = types_of Ts 

 	  val t = make_fixed_type_const a

       in    

 	  ((t ^ paren_pack folTyps), (ts, (t, length Ts)::funcs))

       end

   | type_of (TFree (a,s)) = 

       let val t = make_fixed_type_var a

       in (t, ([((FOLTFree a),s)], [(t,0)])) end

   | type_of (TVar (v, s)) = (make_schematic_type_var v, ([((FOLTVar v),s)], []))

 and types_of Ts =

       let val foltyps_ts = map type_of Ts 

 	  val (folTyps,ts_funcs) = ListPair.unzip foltyps_ts

 	  val (ts, funcslist) = ListPair.unzip ts_funcs

       in    

 	  (folTyps, (union_all ts, union_all funcslist))

       end;

 fun const_types_of (c,T) = types_of (!const_typargs (c,T));

 (* Any variables created via the METAHYPS tactical should be treated as

    universal vars, although it is represented as "Free(...)" by Isabelle *)

 val isMeta = String.isPrefix "METAHYP1_"

 fun pred_name_type (Const(c,T)) = 

       let val (contys,(folTyps,funcs)) = const_types_of (c,T)

       in (make_fixed_const c, (contys,folTyps), funcs) end

   | pred_name_type (Free(x,T))  = 

       if isMeta x then raise CLAUSE("Predicate Not First Order 1", Free(x,T)) 

       else (make_fixed_var x, ([],[]), [])

   | pred_name_type (v as Var _) = raise CLAUSE("Predicate Not First Order 2", v)

   | pred_name_type t        = raise CLAUSE("Predicate input unexpected", t);

 (* For typed equality *)

 (* here "arg_typ" is the type of "="'s argument's type, not the type of the equality *)

 (* Find type of equality arg *)

 fun eq_arg_type (Type("fun",[T,_])) = 

     let val (folT,_) = type_of T;

     in  folT  end;

 fun fun_name_type (Const("op =",T)) args =   (*FIXME: Is this special treatment of = needed??*)

       let val t = make_fixed_const "op ="

       in (t, ([eq_arg_type T], []), [(t,2)]) end

   | fun_name_type (Const(c,T)) args = 

       let val t = make_fixed_const c

 	  val (contys, (folTyps,funcs)) = const_types_of (c,T)

 	  val arity = num_typargs(c,T) + length args

       in

 	  (t, (contys,folTyps), ((t,arity)::funcs))

       end

  | fun_name_type (Free(x,T)) args  = 

       let val t = make_fixed_var x

       in  (t, ([],[]), [(t, length args)]) end

   | fun_name_type f args = raise CLAUSE("Function Not First Order 1", f);

 fun term_of (Var(ind_nm,T)) = 

       let val (folType,(ts,funcs)) = type_of T

       in

 	  (UVar(make_schematic_var ind_nm, folType), (ts, funcs))

       end

   | term_of (Free(x,T)) = 

       let val (folType, (ts,funcs)) = type_of T

       in

 	  if isMeta x then (UVar(make_schematic_var(x,0),folType),

 			    (ts, ((make_schematic_var(x,0)),0)::funcs))

 	  else

 	      (Fun(make_fixed_var x, [folType], []), 

 	       (ts, ((make_fixed_var x),0)::funcs))

       end

   | term_of (Const(c,T)) =  (* impossible to be equality *)

       let val (contys, (folTyps,funcs)) = const_types_of (c,T)

       in

 	  (Fun(make_fixed_const c, contys, []),

 	   (folTyps, ((make_fixed_const c),0)::funcs))

       end    

   | term_of app = 

       let val (f,args) = strip_comb app

           val _ = case f of Const(_,_) => ()

 			  | Free(s,_)  => 

 			      if isMeta s 

 			      then raise CLAUSE("Function Not First Order 2", f)

 			      else ()

 			  | _ => raise CLAUSE("Function Not First Order 3", f);

 	  val (funName,(contys,ts1),funcs) = fun_name_type f args

 	  val (args',(ts2,funcs')) = terms_of args

       in

 	  (Fun(funName,contys,args'), 

 	   (union_all (ts1::ts2), 

 	    union_all(funcs::funcs')))

       end

   | term_of t = raise CLAUSE("Function Not First Order 4", t)

 and terms_of ts =  

       let val (args, ts_funcs) = ListPair.unzip (map term_of ts)

       in

 	  (args, ListPair.unzip ts_funcs)

       end

 fun pred_of (Const("op =", typ), args) =

       let val arg_typ = eq_arg_type typ 

 	  val (args',(ts,funcs)) = terms_of args

 	  val equal_name = make_fixed_const "op ="

       in

 	  (Predicate(equal_name,[arg_typ],args'),

 	   union_all ts, 

 	   [((make_fixed_var equal_name), 2)], 

 	   union_all funcs)

       end

   | pred_of (pred,args) = 

       let val (predName,(predType,ts1), pfuncs) = pred_name_type pred

 	  val (args',(ts2,ffuncs)) = terms_of args

 	  val ts3 = union_all (ts1::ts2)

 	  val ffuncs' = union_all ffuncs

 	  val newfuncs = pfuncs union ffuncs'

 	  val arity = 

 	    case pred of

 		Const (c,T) => num_typargs(c,T) + length args

 	      | _ => length args

       in

 	  (Predicate(predName,predType,args'), ts3, 

 	   [(predName, arity)], newfuncs)

       end;

 (*Treatment of literals, possibly negated or tagged*)

 fun predicate_of ((Const("Not",_) $ P), polarity, tag) =

       predicate_of (P, not polarity, tag)

   | predicate_of ((Const("HOL.tag",_) $ P), polarity, tag) =

       predicate_of (P, polarity, true)

   | predicate_of (term,polarity,tag) =

         (pred_of (strip_comb term), polarity, tag);

 fun literals_of_term1 args (Const("Trueprop",_) $ P) = literals_of_term1 args P

   | literals_of_term1 (args as (lits, ts, preds, funcs)) (Const("op |",_) $ P $ Q) = 

       let val (lits', ts', preds', funcs') = literals_of_term1 args P

       in

 	  literals_of_term1 (lits', ts', preds' union preds, funcs' union funcs) Q

       end

   | literals_of_term1 (lits, ts, preds, funcs) P =

       let val ((pred, ts', preds', funcs'), pol, tag) = predicate_of (P,true,false)

 	  val lits' = Literal(pol,pred,tag) :: lits

       in

 	  (lits', ts union ts', preds' union preds, funcs' union funcs)

       end;

 val literals_of_term = literals_of_term1 ([],[],[],[]);

 (* FIX: not sure what to do with these funcs *)

 (*Make literals for sorted type variables*) 

 fun sorts_on_typs (_, [])   = ([]) 

   | sorts_on_typs (v, "HOL.type" :: s) =

       sorts_on_typs (v,s)   (*Ignore sort "type"*)

   | sorts_on_typs ((FOLTVar indx), (s::ss)) =

       LTVar((make_type_class s) ^ 

         "(" ^ (make_schematic_type_var indx) ^ ")") :: 

       (sorts_on_typs ((FOLTVar indx), ss))

   | sorts_on_typs ((FOLTFree x), (s::ss)) =

       LTFree((make_type_class s) ^ "(" ^ (make_fixed_type_var x) ^ ")") :: 

       (sorts_on_typs ((FOLTFree x), ss));

 (*UGLY: seems to be parsing the "show sorts" output, removing anything that

   starts with a left parenthesis.*)

 fun remove_type str = hd (String.fields (fn c => c = #"(") str);

 fun pred_of_sort (LTVar x) = ((remove_type x),1)

 |   pred_of_sort (LTFree x) = ((remove_type x),1)

 (*Given a list of sorted type variables, return two separate lists.

   The first is for TVars, the second for TFrees.*)

 fun add_typs_aux [] preds  = ([],[], preds)

   | add_typs_aux ((FOLTVar indx,s)::tss) preds = 

       let val vs = sorts_on_typs (FOLTVar indx, s)

           val preds' = (map pred_of_sort vs)@preds

 	  val (vss,fss, preds'') = add_typs_aux tss preds'

       in

 	  (vs union vss, fss, preds'')

       end

   | add_typs_aux ((FOLTFree x,s)::tss) preds  =

       let val fs = sorts_on_typs (FOLTFree x, s)

           val preds' = (map pred_of_sort fs)@preds

 	  val (vss,fss, preds'') = add_typs_aux tss preds'

       in

 	  (vss, fs union fss, preds'')

       end;

 fun add_typs_aux2 [] = ([],[])

   | add_typs_aux2 ((FOLTVar indx,s)::tss) =

     let val vs = sorts_on_typs (FOLTVar indx,s)

 	val (vss,fss) = add_typs_aux2 tss

     in

 	(vs union vss,fss)

     end

   | add_typs_aux2 ((FOLTFree x,s)::tss) =

     let val fs = sorts_on_typs (FOLTFree x,s)

 	val (vss,fss) = add_typs_aux2 tss

     in

 	(vss,fs union fss)

     end;

 fun add_typs (Clause cls) preds  = add_typs_aux (#types_sorts cls) preds 

 (** make axiom clauses, hypothesis clauses and conjecture clauses. **)

 fun get_tvar_strs [] = []

   | get_tvar_strs ((FOLTVar indx,s)::tss) = 

       let val vstr = make_schematic_type_var indx

       in

 	  vstr ins (get_tvar_strs tss)

       end

   | get_tvar_strs((FOLTFree x,s)::tss) = distinct (get_tvar_strs tss)

 (* FIX add preds and funcs to add typs aux here *)

 fun make_axiom_clause_thm thm (ax_name,cls_id) =

     let val (lits,types_sorts, preds, funcs) = literals_of_term (prop_of thm)

 	val (tvar_lits,tfree_lits, preds) = add_typs_aux types_sorts preds 

         val tvars = get_tvar_strs types_sorts

     in 

 	make_clause(cls_id,ax_name,Axiom,

 	            lits,types_sorts,tvar_lits,tfree_lits,

 	            tvars, preds, funcs)

     end;

 (* check if a clause is FOL first*)

 fun make_conjecture_clause n t =

     let val _ = check_is_fol_term t

 	    handle TERM("check_is_fol_term",_) => raise CLAUSE("Goal is not FOL",t)

 	val (lits,types_sorts, preds, funcs) = literals_of_term t

 	val (tvar_lits,tfree_lits, preds) = add_typs_aux types_sorts preds 

         val tvars = get_tvar_strs types_sorts

     in

 	make_clause(n,"conjecture",Conjecture,

 	            lits,types_sorts,tvar_lits,tfree_lits,

 	            tvars, preds, funcs)

     end;

 fun make_conjecture_clauses_aux _ [] = []

   | make_conjecture_clauses_aux n (t::ts) =

       make_conjecture_clause n t :: make_conjecture_clauses_aux (n+1) ts

 val make_conjecture_clauses = make_conjecture_clauses_aux 0

 (*before converting an axiom clause to "clause" format, check if it is FOL*)

 fun make_axiom_clause term (ax_name,cls_id) =

     let val _ = check_is_fol_term term 

 	    handle TERM("check_is_fol_term",_) => raise CLAUSE("Axiom is not FOL", term) 

 	val (lits,types_sorts, preds,funcs) = literals_of_term term

 	val (tvar_lits,tfree_lits, preds) = add_typs_aux types_sorts preds

         val tvars = get_tvar_strs types_sorts	

     in 

 	make_clause(cls_id,ax_name,Axiom,

 	            lits,types_sorts,tvar_lits,tfree_lits,

 	            tvars, preds,funcs)

     end;

 (**** Isabelle arities ****)

 exception ARCLAUSE of string;

 type class = string; 

 type tcons = string; 

 datatype arLit = TConsLit of bool * (class * tcons * string list) | TVarLit of bool * (class * string);

 datatype arityClause =  

 	 ArityClause of {clause_id: clause_id,

 	  	         axiom_name: axiom_name,

 			 kind: kind,

 			 conclLit: arLit,

 			 premLits: arLit list};

 fun get_TVars 0 = []

   | get_TVars n = ("T_" ^ (Int.toString n)) :: get_TVars (n-1);

 fun pack_sort(_,[])  = raise ARCLAUSE("Empty Sort Found") 

   | pack_sort(tvar, [cls]) = [(make_type_class cls, tvar)] 

   | pack_sort(tvar, cls::srt) =  (make_type_class cls,tvar) :: (pack_sort(tvar, srt));

 fun make_TVarLit (b,(cls,str)) = TVarLit(b,(cls,str));

 fun make_TConsLit (b,(cls,tcons,tvars)) = TConsLit(b,(make_type_class cls,make_fixed_type_const tcons,tvars));

 fun make_axiom_arity_clause (tcons,n,(res,args)) =

    let val nargs = length args

        val tvars = get_TVars nargs

        val tvars_srts = ListPair.zip (tvars,args)

        val tvars_srts' = union_all(map pack_sort tvars_srts)

        val false_tvars_srts' = map (pair false) tvars_srts'

    in

       ArityClause {clause_id = n, kind = Axiom, 

                    axiom_name = tcons,

                    conclLit = make_TConsLit(true,(res,tcons,tvars)), 

                    premLits = map make_TVarLit false_tvars_srts'}

    end;

 (*The number of clauses generated from cls, including type clauses*)

 fun num_of_clauses (Clause cls) =

     let val num_tfree_lits = 

 	      if !keep_types then length (#tfree_type_literals cls)

 	      else 0

     in 	1 + num_tfree_lits  end;

 (**** Isabelle class relations ****)

 datatype classrelClause = 

 	 ClassrelClause of {clause_id: clause_id,

 			    subclass: class,

 			    superclass: class option};

 fun make_axiom_classrelClause n subclass superclass =

   ClassrelClause {clause_id = n,

                   subclass = subclass, superclass = superclass};

 fun classrelClauses_of_aux n sub [] = []

   | classrelClauses_of_aux n sub (sup::sups) =

       make_axiom_classrelClause n sub (SOME sup) :: classrelClauses_of_aux (n+1) sub sups;

 fun classrelClauses_of (sub,sups) = 

     case sups of [] => [make_axiom_classrelClause 0 sub NONE]

 	       | _ => classrelClauses_of_aux 0 sub sups;

 (***** Isabelle arities *****)

 fun arity_clause _ (tcons, []) = []

   | arity_clause n (tcons, ar::ars) =

       make_axiom_arity_clause (tcons,n,ar) :: 

       arity_clause (n+1) (tcons,ars);

 fun multi_arity_clause [] = []

   | multi_arity_clause (tcon_ar :: tcons_ars)  =

       arity_clause 0 tcon_ar  @  multi_arity_clause tcons_ars 

 fun arity_clause_thy thy =

   let val arities = #arities (Type.rep_tsig (Sign.tsig_of thy))

   in multi_arity_clause (Symtab.dest arities) end;

 (* Isabelle classes *)

 type classrelClauses = classrelClause list Symtab.table;

 val classrel_of = #2 o #classes o Type.rep_tsig o Sign.tsig_of;

 fun classrel_clauses_classrel (C: Sorts.classes) = map classrelClauses_of (Graph.dest C);

 val classrel_clauses_thy = List.concat o classrel_clauses_classrel o classrel_of;

 (****!!!! Changed for typed equality !!!!****)

 fun wrap_eq_type typ t = eq_typ_wrapper ^"(" ^ t ^ "," ^ typ ^ ")";

 (*Only need to wrap equality's arguments with "typeinfo" if the output clauses are typed 

  and if we specifically ask for types to be included.   *)

 fun string_of_equality (typ,terms) =

       let val [tstr1,tstr2] = map string_of_term terms

       in

 	  if !keep_types andalso !special_equal 

 	  then "equal(" ^ (wrap_eq_type typ tstr1) ^ "," ^ 

 		 	  (wrap_eq_type typ tstr2) ^ ")"

 	  else "equal(" ^ tstr1 ^ "," ^ tstr2 ^ ")"

       end

 and string_of_term (UVar(x,_)) = x

   | string_of_term (Fun("equal",[typ],terms)) = string_of_equality(typ,terms)

   | string_of_term (Fun (name,typs,[])) = name (*Overloaded consts like 0 don't get types!*)

   | string_of_term (Fun (name,typs,terms)) = 

       let val terms_as_strings = map string_of_term terms

 	  val typs' = if !keep_types then typs else []

       in  name ^ (paren_pack (terms_as_strings @ typs'))  end

   | string_of_term _ = error "string_of_term";      

 (* before output the string of the predicate, check if the predicate corresponds to an equality or not. *)

 fun string_of_predicate (Predicate("equal",[typ],terms)) = string_of_equality(typ,terms)

   | string_of_predicate (Predicate(name,typs,terms)) = 

       let val terms_as_strings = map string_of_term terms

 	  val typs' = if !keep_types then typs else []

       in  name ^ (paren_pack (terms_as_strings @ typs'))  end

   | string_of_predicate _ = error "string_of_predicate";      

 fun string_of_clausename (cls_id,ax_name) = 

     clause_prefix ^ ascii_of ax_name ^ "_" ^ Int.toString cls_id;

 fun string_of_type_clsname (cls_id,ax_name,idx) = 

     string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);

 (********************************)

 (* Code for producing DFG files *)

 (********************************)

 fun dfg_literal (Literal(pol,pred,tag)) =

     let val pred_string = string_of_predicate pred

     in

 	if pol then pred_string else "not(" ^pred_string ^ ")"  

     end;

 (* FIX: what does this mean? *)

 (*fun dfg_of_typeLit (LTVar x) = "not(" ^ x ^ ")"

   | dfg_of_typeLit (LTFree x) = "(" ^ x ^ ")";*)

 fun dfg_of_typeLit (LTVar x) =  x 

   | dfg_of_typeLit (LTFree x) = x ;

 (*Make the string of universal quantifiers for a clause*)

 fun forall_open ([],[]) = ""

   | forall_open (vars,tvars) = "forall([" ^ (commas (tvars@vars))^ "],\n"

 fun forall_close ([],[]) = ""

   | forall_close (vars,tvars) = ")"

 fun gen_dfg_cls (cls_id,ax_name,knd,lits,tvars,vars) = 

     "clause( %(" ^ knd ^ ")\n" ^ forall_open(vars,tvars) ^ 

     "or(" ^ lits ^ ")" ^ forall_close(vars,tvars) ^ ",\n" ^ 

     string_of_clausename (cls_id,ax_name) ^  ").";

 fun gen_dfg_type_cls (cls_id,ax_name,knd,tfree_lit,idx,tvars,vars) = 

     "clause( %(" ^ knd ^ ")\n" ^ forall_open(vars,tvars) ^ 

     "or( " ^ tfree_lit ^ ")" ^ forall_close(vars,tvars) ^ ",\n" ^ 

     string_of_type_clsname (cls_id,ax_name,idx) ^  ").";

 fun dfg_clause_aux (Clause cls) = 

   let val lits = map dfg_literal (#literals cls)

       val tvar_lits_strs = 

 	  if !keep_types then map dfg_of_typeLit (#tvar_type_literals cls) 

 	  else []

       val tfree_lits =

           if !keep_types then map dfg_of_typeLit (#tfree_type_literals cls)

           else []

   in

       (tvar_lits_strs @ lits, tfree_lits)

   end; 

 fun dfg_folterms (Literal(pol,pred,tag)) = 

   let val Predicate (predname, _, folterms) = pred

   in  folterms  end

 fun get_uvars (UVar(a,typ)) = [a] 

 |   get_uvars (Fun (_,typ,tlist)) = union_all(map get_uvars tlist)

 fun is_uvar (UVar _) = true

 |   is_uvar (Fun _) = false;

 fun uvar_name (UVar(a,_)) = a

 |   uvar_name (Fun (a,_,_)) = raise CLAUSE("Not a variable", Const(a,dummyT));

 fun dfg_vars (Clause cls) =

     let val lits = #literals cls

         val folterms = List.concat (map dfg_folterms lits)

     in 

         union_all(map get_uvars folterms)

     end

 fun dfg_tvars (Clause cls) =(#tvars cls)

 (* make this return funcs and preds too? *)

 fun string_of_predname (Predicate("equal",_,terms)) = "EQUALITY"

   | string_of_predname (Predicate(name,_,terms)) = name

 fun concat_with sep []  = ""

   | concat_with sep [x] = "(" ^ x ^ ")"

   | concat_with sep (x::xs) = "(" ^ x ^ ")" ^  sep ^ (concat_with sep xs);

 fun dfg_pred (Literal(pol,pred,tag)) ax_name = 

     (string_of_predname pred) ^ " " ^ ax_name

 fun dfg_clause cls =

     let val (lits,tfree_lits) = dfg_clause_aux cls 

              (*"lits" includes the typing assumptions (TVars)*)

         val vars = dfg_vars cls

         val tvars = dfg_tvars cls

 	val knd = string_of_kind cls

 	val lits_str = commas lits

 	val cls_id = get_clause_id cls

 	val axname = get_axiomName cls

 	val cls_str = gen_dfg_cls(cls_id,axname,knd,lits_str,tvars, vars) 			

         fun typ_clss k [] = []

           | typ_clss k (tfree :: tfrees) = 

               (gen_dfg_type_cls(cls_id,axname,knd,tfree,k, tvars,vars)) :: 

               (typ_clss (k+1) tfrees)

     in 

 	cls_str :: (typ_clss 0 tfree_lits)

     end;

 fun string_of_arity (name, num) =  name ^ "," ^ (Int.toString num) 

 fun string_of_preds preds = 

   "predicates[" ^ (concat_with ", " (map string_of_arity preds)) ^ "].\n";

 fun string_of_funcs funcs =

   "functions[" ^ (concat_with ", " (map string_of_arity funcs)) ^ "].\n" ;

 fun string_of_symbols predstr funcstr = 

   "list_of_symbols.\n" ^ predstr  ^ funcstr  ^ "end_of_list.\n\n";

 fun string_of_axioms axstr = 

   "list_of_clauses(axioms,cnf).\n" ^ axstr ^ "end_of_list.\n\n";

 fun string_of_conjectures conjstr = 

   "list_of_clauses(conjectures,cnf).\n" ^ conjstr ^ "end_of_list.\n\n";

 fun string_of_descrip () = 

   "list_of_descriptions.\nname({*[ File     : ],[ Names    :]*}).\nauthor({*[ Source   :]*}).\nstatus(unknown).\ndescription({*[ Refs     :]*}).\nend_of_list.\n\n"

 fun string_of_start name = "%------------------------------------------------------------------------------\nbegin_problem(" ^ name ^ ").\n\n";

 fun string_of_end () = "end_problem.\n%------------------------------------------------------------------------------";

 fun clause2dfg cls =

     let val (lits,tfree_lits) = dfg_clause_aux cls 

             (*"lits" includes the typing assumptions (TVars)*)

 	val cls_id = get_clause_id cls

 	val ax_name = get_axiomName cls

         val vars = dfg_vars cls

         val tvars = dfg_tvars cls

         val funcs = funcs_of_cls cls

         val preds = preds_of_cls cls

 	val knd = string_of_kind cls

 	val lits_str = commas lits

 	val cls_str = gen_dfg_cls(cls_id,ax_name,knd,lits_str,tvars,vars) 

     in

 	(cls_str,tfree_lits) 

     end;

 fun tfree_dfg_clause tfree_lit =

   "clause( %(conjecture)\n" ^ "or( " ^ tfree_lit ^ "),\n" ^ "tfree_tcs" ^ ")."

 fun gen_dfg_file probname axioms conjectures funcs preds = 

     let val axstrs_tfrees = (map clause2dfg axioms)

 	val (axstrs, atfrees) = ListPair.unzip axstrs_tfrees

         val axstr = (space_implode "\n" axstrs) ^ "\n\n"

         val conjstrs_tfrees = (map clause2dfg conjectures)

 	val (conjstrs, atfrees) = ListPair.unzip conjstrs_tfrees

         val tfree_clss = map tfree_dfg_clause (union_all atfrees) 

         val conjstr = (space_implode "\n" (tfree_clss@conjstrs)) ^ "\n\n"

         val funcstr = string_of_funcs funcs

         val predstr = string_of_preds preds

     in

        (string_of_start probname) ^ (string_of_descrip ()) ^ 

        (string_of_symbols funcstr predstr) ^  

        (string_of_axioms axstr) ^

        (string_of_conjectures conjstr) ^ (string_of_end ())

     end;

 fun clauses2dfg [] probname axioms conjectures funcs preds = 

       let val funcs' = (union_all(map funcs_of_cls axioms)) @ funcs

 	  val preds' = (union_all(map preds_of_cls axioms)) @ preds

       in

 	 gen_dfg_file probname axioms conjectures funcs' preds' 

       end

  | clauses2dfg (cls::clss) probname axioms conjectures funcs preds = 

      let val (lits,tfree_lits) = dfg_clause_aux cls

 	       (*"lits" includes the typing assumptions (TVars)*)

 	 val cls_id = get_clause_id cls

 	 val ax_name = get_axiomName cls

 	 val vars = dfg_vars cls

 	 val tvars = dfg_tvars cls

 	 val funcs' = (funcs_of_cls cls) union funcs

 	 val preds' = (preds_of_cls cls) union preds

 	 val knd = string_of_kind cls

 	 val lits_str = concat_with ", " lits

 	 val axioms' = if knd = "axiom" then (cls::axioms) else axioms

 	 val conjectures' = 

 	     if knd = "conjecture" then (cls::conjectures) else conjectures

      in

 	 clauses2dfg clss probname axioms' conjectures' funcs' preds' 

      end;

 fun string_of_arClauseID (ArityClause {clause_id,axiom_name,...}) =

     arclause_prefix ^ ascii_of axiom_name ^ "_" ^ Int.toString clause_id;

 fun string_of_arKind (ArityClause arcls) = name_of_kind(#kind arcls);

 (*FIXME!!! currently is TPTP format!*)

 fun dfg_of_arLit (TConsLit(b,(c,t,args))) =

       let val pol = if b then "++" else "--"

 	  val arg_strs = paren_pack args

       in 

 	  pol ^ c ^ "(" ^ t ^ arg_strs ^ ")"

       end

   | dfg_of_arLit (TVarLit(b,(c,str))) =

       let val pol = if b then "++" else "--"

       in

 	  pol ^ c ^ "(" ^ str ^ ")"

       end;

 fun dfg_of_conclLit (ArityClause arcls) = dfg_of_arLit (#conclLit arcls);

 fun dfg_of_premLits (ArityClause arcls) = map dfg_of_arLit (#premLits arcls);

 (*FIXME: would this have variables in a forall? *)

 fun dfg_arity_clause arcls = 

   let val arcls_id = string_of_arClauseID arcls

       val concl_lit = dfg_of_conclLit arcls

       val prems_lits = dfg_of_premLits arcls

       val knd = string_of_arKind arcls

       val all_lits = concl_lit :: prems_lits

   in

       "clause( %(" ^ knd ^ ")\n" ^  "or( " ^ (bracket_pack all_lits) ^ ")),\n" ^

        arcls_id ^  ")."

   end;

 (********************************)

 (* code to produce TPTP files   *)

 (********************************)

 fun tptp_literal (Literal(pol,pred,tag)) =

     let val pred_string = string_of_predicate pred

 	val tagged_pol = 

 	      if (tag andalso !tagged) then (if pol then "+++" else "---")

 	      else (if pol then "++" else "--")

      in

 	tagged_pol ^ pred_string

     end;

 fun tptp_of_typeLit (LTVar x) = "--" ^ x

   | tptp_of_typeLit (LTFree x) = "++" ^ x;

 fun gen_tptp_cls (cls_id,ax_name,knd,lits) = 

     "input_clause(" ^ string_of_clausename (cls_id,ax_name) ^ "," ^ 

     knd ^ "," ^ lits ^ ").";

 fun gen_tptp_type_cls (cls_id,ax_name,knd,tfree_lit,idx) = 

     "input_clause(" ^ string_of_type_clsname (cls_id,ax_name,idx) ^ "," ^ 

     knd ^ ",[" ^ tfree_lit ^ "]).";

 fun tptp_type_lits (Clause cls) = 

     let val lits = map tptp_literal (#literals cls)

 	val tvar_lits_strs =

 	      if !keep_types 

 	      then (map tptp_of_typeLit (#tvar_type_literals cls)) 

 	      else []

 	val tfree_lits = 

 	      if !keep_types

 	      then (map tptp_of_typeLit (#tfree_type_literals cls)) 

 	      else []

     in

 	(tvar_lits_strs @ lits, tfree_lits)

     end; 

 fun tptp_clause cls =

     let val (lits,tfree_lits) = tptp_type_lits cls 

             (*"lits" includes the typing assumptions (TVars)*)

 	val cls_id = get_clause_id cls

 	val ax_name = get_axiomName cls

 	val knd = string_of_kind cls

 	val lits_str = bracket_pack lits

 	val cls_str = gen_tptp_cls(cls_id,ax_name,knd,lits_str) 			 

 	fun typ_clss k [] = []

           | typ_clss k (tfree :: tfrees) = 

               gen_tptp_type_cls(cls_id,ax_name,knd,tfree,k) :: 

               typ_clss (k+1) tfrees

     in 

 	cls_str :: (typ_clss 0 tfree_lits)

     end;

 fun clause2tptp cls =

     let val (lits,tfree_lits) = tptp_type_lits cls 

             (*"lits" includes the typing assumptions (TVars)*)

 	val cls_id = get_clause_id cls

 	val ax_name = get_axiomName cls

 	val knd = string_of_kind cls

 	val lits_str = bracket_pack lits

 	val cls_str = gen_tptp_cls(cls_id,ax_name,knd,lits_str) 

     in

 	(cls_str,tfree_lits) 

     end;

 fun tfree_clause tfree_lit =

     "input_clause(" ^ "tfree_tcs," ^ "conjecture" ^ ",[" ^ tfree_lit ^ "]).";

 fun tptp_of_arLit (TConsLit(b,(c,t,args))) =

       let val pol = if b then "++" else "--"

 	  val  arg_strs = paren_pack args

       in 

 	  pol ^ c ^ "(" ^ t ^ arg_strs ^ ")"

       end

   | tptp_of_arLit (TVarLit(b,(c,str))) =

       let val pol = if b then "++" else "--"

       in

 	  pol ^ c ^ "(" ^ str ^ ")"

       end;

 fun tptp_of_conclLit (ArityClause arcls) = tptp_of_arLit (#conclLit arcls);

 fun tptp_of_premLits (ArityClause arcls) = map tptp_of_arLit (#premLits arcls);

 fun tptp_arity_clause arcls = 

     let val arcls_id = string_of_arClauseID arcls

 	val concl_lit = tptp_of_conclLit arcls

 	val prems_lits = tptp_of_premLits arcls

 	val knd = string_of_arKind arcls

 	val all_lits = concl_lit :: prems_lits

     in

 	"input_clause(" ^ arcls_id ^ "," ^ knd ^ "," ^ 

 	(bracket_pack all_lits) ^ ")."

     end;

 fun tptp_classrelLits sub sup = 

     let val tvar = "(T)"

     in 

 	case sup of NONE => "[++" ^ sub ^ tvar ^ "]"

 		  | (SOME supcls) =>  "[--" ^ sub ^ tvar ^ ",++" ^ supcls ^ tvar ^ "]"

     end;

 fun tptp_classrelClause (ClassrelClause {clause_id,subclass,superclass,...}) =

     let val relcls_id = clrelclause_prefix ^ ascii_of subclass ^ "_" ^ 

                         Int.toString clause_id

 	val lits = tptp_classrelLits (make_type_class subclass) 

 	                (Option.map make_type_class superclass)

     in

 	"input_clause(" ^ relcls_id ^ ",axiom," ^ lits ^ ")."

     end; 

 end;