(*  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;

datatype typ_var = FOLTVar of indexname | FOLTFree of string;

datatype fol_type = AtomV of string

		  | AtomF of string

		  | Comp of string * fol_type list;

fun string_of_fol_type (AtomV x) = x

  | string_of_fol_type (AtomF x) = x

  | string_of_fol_type (Comp(tcon,tps)) = 

    let val tstrs = map string_of_fol_type tps

    in

	tcon ^ (paren_pack tstrs)

    end;

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;

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;

fun get_literals (c as Clause(cls)) = #literals cls;

fun components_of_literal (Literal (pol,pred,tag)) = ((pol,pred),tag);

fun predicate_name (Predicate(predname,_,_)) = predname;

(*** 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 fol_type 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    

	  (Comp(t,folTyps), (ts, (t, length Ts)::funcs))

      end

  | type_of (TFree (a,s)) = 

      let val t = make_fixed_type_var a

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

  | type_of (TVar (v, s)) = (AtomV(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 ([],[],[],[]);

fun predicate_ord (Predicate(predname1,_,_),Predicate(predname2,_,_)) = string_ord (predname1,predname2);

fun literal_ord (Literal(false,_,_),Literal(true,_,_)) = LESS

  | literal_ord (Literal(true,_,_),Literal(false,_,_)) = GREATER

  | literal_ord (Literal(_,pred1,_),Literal(_,pred2,_)) = predicate_ord(pred1,pred2);

fun sort_lits lits = sort literal_ord lits;

(* 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 lits' = sort_lits lits

	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 lits' = sort_lits lits

	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

	  val typ' = string_of_fol_type typ

      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 map string_of_fol_type 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 map string_of_fol_type 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 =