(*  Author: Jia Meng, Cambridge University Computer Laboratory

    ID: $Id$

    Copyright 2004 University of Cambridge

Storing/printing FOL clauses and arity clauses.

Typed equality is treated differently.

*)

(*FIXME: combine with res_hol_clause!*)

signature RES_CLAUSE =

sig

  val schematic_var_prefix: string

  val fixed_var_prefix: string

  val tvar_prefix: string

  val tfree_prefix: string

  val clause_prefix: string

  val const_prefix: string

  val tconst_prefix: string

  val class_prefix: string

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

  val const_trans_table: string Symtab.table

  val type_const_trans_table: string Symtab.table

  val ascii_of: string -> string

  val undo_ascii_of: string -> string

  val paren_pack : string list -> string

  val make_schematic_var : string * int -> string

  val make_fixed_var : string -> string

  val make_schematic_type_var : string * int -> string

  val make_fixed_type_var : string -> string

  val dfg_format: bool ref

  val make_fixed_const : string -> string

  val make_fixed_type_const : string -> string

  val make_type_class : string -> string

  datatype kind = Axiom | Conjecture

  val name_of_kind : kind -> string

  type axiom_name = string

  datatype typ_var = FOLTVar of indexname | FOLTFree of string

  datatype fol_type =

      AtomV of string

    | AtomF of string

    | Comp of string * fol_type list

  val string_of_fol_type : fol_type -> string

  datatype type_literal = LTVar of string * string | LTFree of string * string

  val mk_typ_var_sort: typ -> typ_var * sort

  exception CLAUSE of string * term

  val init : theory -> unit

  val isMeta : string -> bool

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

  val get_tvar_strs: (typ_var * sort) list -> string list

  datatype arLit =

      TConsLit of class * string * string list

    | TVarLit of class * string

  datatype arityClause = ArityClause of

   {axiom_name: axiom_name,

    kind: kind,

    conclLit: arLit,

    premLits: arLit list}

  datatype classrelClause = ClassrelClause of

   {axiom_name: axiom_name,

    subclass: class,

    superclass: class}

  val make_classrel_clauses: theory -> class list -> class list -> classrelClause list

  val make_arity_clauses: theory -> string list -> class list -> class list * arityClause list

  val add_type_sort_preds: (typ_var * string list) * int Symtab.table -> int Symtab.table

  val add_classrelClause_preds : classrelClause * int Symtab.table -> int Symtab.table

  val class_of_arityLit: arLit -> class

  val add_arityClause_preds: arityClause * int Symtab.table -> int Symtab.table

  val add_foltype_funcs: fol_type * int Symtab.table -> int Symtab.table

  val add_arityClause_funcs: arityClause * int Symtab.table -> int Symtab.table

  val init_functab: int Symtab.table

  val writeln_strs: TextIO.outstream -> string list -> unit

  val dfg_sign: bool -> string -> string

  val dfg_of_typeLit: type_literal -> string

  val gen_dfg_cls: int * string * string * string * string list -> string

  val string_of_preds: (string * Int.int) list -> string

  val string_of_funcs: (string * int) list -> string

  val string_of_symbols: string -> string -> string

  val string_of_start: string -> string

  val string_of_descrip : string -> string

  val dfg_tfree_clause : string -> string

  val dfg_classrelClause: classrelClause -> string

  val dfg_arity_clause: arityClause -> string

  val tptp_sign: bool -> string -> string

  val tptp_of_typeLit : type_literal -> string

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

  val tptp_tfree_clause : string -> string

  val tptp_arity_clause : arityClause -> string

  val tptp_classrelClause : classrelClause -> string

end

structure ResClause: RES_CLAUSE =

struct

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"),

                   (@{const_name HOL.less_eq}, "lessequals"),

                   (@{const_name HOL.less}, "less"),

                   ("op &", "and"),

                   ("op |", "or"),

                   (@{const_name HOL.plus}, "plus"),

                   (@{const_name HOL.minus}, "minus"),

                   (@{const_name HOL.times}, "times"),

                   (@{const_name Divides.div}, "div"),

                   (@{const_name HOL.divide}, "divide"),

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

                   ("{}", "emptyset"),

                   ("op :", "in"),

                   ("op Un", "union"),

                   ("op Int", "inter"),

                   ("List.append", "append"),

                   ("ATP_Linkup.fequal", "fequal"),

                   ("ATP_Linkup.COMBI", "COMBI"),

                   ("ATP_Linkup.COMBK", "COMBK"),

                   ("ATP_Linkup.COMBB", "COMBB"),

                   ("ATP_Linkup.COMBC", "COMBC"),

                   ("ATP_Linkup.COMBS", "COMBS"),

                   ("ATP_Linkup.COMBB'", "COMBB_e"),

                   ("ATP_Linkup.COMBC'", "COMBC_e"),

                   ("ATP_Linkup.COMBS'", "COMBS_e")];

val type_const_trans_table =

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

                   ("+", "sum"),

                   ("~=>", "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.*)

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

fun stringN_of_int 0 _ = ""

  | stringN_of_int k n = stringN_of_int (k-1) (n div 10) ^ Int.toString (n mod 10);

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 ("_" ^ stringN_of_int 3 (Char.ord c))  (*fixed width, in case more digits follow*)

  else ""

val ascii_of = String.translate ascii_of_c;

(** Remove ASCII armouring from names in proof files **)

(*We don't raise error exceptions because this code can run inside the watcher.

  Also, the errors are "impossible" (hah!)*)

fun undo_ascii_aux rcs [] = String.implode(rev rcs)

  | undo_ascii_aux rcs [#"_"] = undo_ascii_aux (#"_"::rcs) []  (*ERROR*)

      (*Three types of _ escapes: __, _A to _P, _nnn*)

  | undo_ascii_aux rcs (#"_" :: #"_" :: cs) = undo_ascii_aux (#"_"::rcs) cs

  | undo_ascii_aux rcs (#"_" :: c :: cs) =

      if #"A" <= c andalso c<= #"P"  (*translation of #" " to #"/"*)

      then undo_ascii_aux (Char.chr(Char.ord c - A_minus_space) :: rcs) cs

      else

        let val digits = List.take (c::cs, 3) handle Subscript => []

        in

            case Int.fromString (String.implode digits) of

                NONE => undo_ascii_aux (c:: #"_"::rcs) cs  (*ERROR*)

              | SOME n => undo_ascii_aux (Char.chr n :: rcs) (List.drop (cs, 2))

        end

  | undo_ascii_aux rcs (c::cs) = undo_ascii_aux (c::rcs) cs;

val undo_ascii_of = undo_ascii_aux [] o String.explode;

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

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

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

(*TSTP format uses (...) rather than the old [...]*)

fun tptp_pack strings = "(" ^ space_implode " | " 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));

(*HACK because SPASS truncates identifiers to 63 characters :-(( *)

val dfg_format = ref false;

(*32-bit hash,so we expect no collisions unless there are around 65536 long identifiers...*)

fun controlled_length s =

  if size s > 60 andalso !dfg_format

  then Word.toString (Polyhash.hashw_string(s,0w0))

  else s;

fun lookup_const c =

    case Symtab.lookup const_trans_table c of

        SOME c' => c'

      | NONE => controlled_length (ascii_of c);

fun lookup_type_const c =

    case Symtab.lookup type_const_trans_table c of

        SOME c' => c'

      | NONE => controlled_length (ascii_of c);

fun make_fixed_const "op =" = "equal"   (*MUST BE "equal" because it's built-in to ATPs*)

  | make_fixed_const c      = const_prefix ^ lookup_const c;

fun make_fixed_type_const c = tconst_prefix ^ lookup_type_const c;

fun make_type_class clas = class_prefix ^ ascii_of clas;

(***** definitions and functions for FOL clauses, for conversion to TPTP or DFG format. *****)

datatype kind = Axiom | Conjecture;

fun name_of_kind Axiom = "axiom"

  | name_of_kind Conjecture = "negated_conjecture";

type axiom_name = string;

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

datatype typ_var = FOLTVar of indexname | FOLTFree of string;

(*FIXME: give the constructors more sensible names*)

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)) =

      tcon ^ (paren_pack (map string_of_fol_type tps));

(*First string is the type class; the second is a TVar or TFfree*)

datatype type_literal = LTVar of string * string | LTFree of string * string;

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

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

exception CLAUSE of string * term;

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

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

fun num_typargs(s,T) = length (!const_typargs (s,T));

(*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) = types_of Ts

          val t = make_fixed_type_const a

      in (Comp(t,folTyps), ts) end

  | type_of (TFree (a,s)) = (AtomF(make_fixed_type_var a), [(FOLTFree a, s)])

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

and types_of Ts =

      let val (folTyps,ts) = ListPair.unzip (map type_of Ts)

      in (folTyps, union_all ts) end;

(* 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_"

(*Make literals for sorted type variables*)

fun sorts_on_typs (_, [])   = []

  | sorts_on_typs (v,  s::ss) =

      let val sorts = sorts_on_typs (v, ss)

      in

          if s = "HOL.type" then sorts

          else case v of

              FOLTVar indx => LTVar(make_type_class s, make_schematic_type_var indx) :: sorts

            | FOLTFree x => LTFree(make_type_class s, make_fixed_type_var x) :: sorts

      end;

fun pred_of_sort (LTVar (s,ty)) = (s,1)

  | pred_of_sort (LTFree (s,ty)) = (s,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 [] = ([],[])

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

      let val vs = sorts_on_typs (FOLTVar indx, s)

          val (vss,fss) = add_typs_aux tss

      in  (vs union vss, fss)  end

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

      let val fs = sorts_on_typs (FOLTFree x, s)

          val (vss,fss) = add_typs_aux tss

      in  (vss, fs union fss)  end;

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

fun get_tvar_strs [] = []

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

      insert (op =) (make_schematic_type_var indx) (get_tvar_strs tss)

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

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

exception ARCLAUSE of string;

datatype arLit = TConsLit of class * string * string list

               | TVarLit of class * string;

datatype arityClause =

         ArityClause of {axiom_name: axiom_name,

                         kind: kind,

                         conclLit: arLit,

                         premLits: arLit list};

fun gen_TVars 0 = []

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

fun pack_sort(_,[])  = []

  | pack_sort(tvar, "HOL.type"::srt) = pack_sort(tvar, srt)   (*IGNORE sort "type"*)

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

(*Arity of type constructor tcon :: (arg1,...,argN)res*)

fun make_axiom_arity_clause (tcons, axiom_name, (cls,args)) =

   let val tvars = gen_TVars (length args)

       val tvars_srts = ListPair.zip (tvars,args)

   in

      ArityClause {axiom_name = axiom_name, kind = Axiom,

                   conclLit = TConsLit (cls, make_fixed_type_const tcons, tvars),

                   premLits = map TVarLit (union_all(map pack_sort tvars_srts))}

   end;

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

datatype classrelClause =

         ClassrelClause of {axiom_name: axiom_name,

                            subclass: class,

                            superclass: class};

(*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)

fun class_pairs thy [] supers = []

  | class_pairs thy subs supers =

      let val class_less = Sorts.class_less(Sign.classes_of thy)

          fun add_super sub (super,pairs) =

                if class_less (sub,super) then (sub,super)::pairs else pairs

          fun add_supers (sub,pairs) = foldl (add_super sub) pairs supers

      in  foldl add_supers [] subs  end;

fun make_classrelClause (sub,super) =

  ClassrelClause {axiom_name = clrelclause_prefix ^ ascii_of sub ^ "_" ^ ascii_of super,

                  subclass = make_type_class sub,

                  superclass = make_type_class super};

fun make_classrel_clauses thy subs supers =

  map make_classrelClause (class_pairs thy subs supers);

(** Isabelle arities **)

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

  | arity_clause seen n (tcons, ("HOL.type",_)::ars) =  (*ignore*)

      arity_clause seen n (tcons,ars)

  | arity_clause seen n (tcons, (ar as (class,_)) :: ars) =

      if class mem_string seen then (*multiple arities for the same tycon, class pair*)

          make_axiom_arity_clause (tcons, lookup_type_const tcons ^ "_" ^ class ^ "_" ^ Int.toString n, ar) ::

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

      else

          make_axiom_arity_clause (tcons, lookup_type_const tcons ^ "_" ^ class, ar) ::

          arity_clause (class::seen) n (tcons,ars)

fun multi_arity_clause [] = []

  | multi_arity_clause ((tcons,ars) :: tc_arlists) =

      arity_clause [] 1 (tcons, ars)  @  multi_arity_clause tc_arlists

(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy

  provided its arguments have the corresponding sorts.*)

fun type_class_pairs thy tycons classes =

  let val alg = Sign.classes_of thy

      fun domain_sorts (tycon,class) = Sorts.mg_domain alg tycon [class]

      fun add_class tycon (class,pairs) =

            (class, domain_sorts(tycon,class))::pairs

            handle Sorts.CLASS_ERROR _ => pairs

      fun try_classes tycon = (tycon, foldl (add_class tycon) [] classes)

  in  map try_classes tycons  end;

(*Proving one (tycon, class) membership may require proving others, so iterate.*)

fun iter_type_class_pairs thy tycons [] = ([], [])

  | iter_type_class_pairs thy tycons classes =

      let val cpairs = type_class_pairs thy tycons classes

          val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs))) \\ classes \\ HOLogic.typeS

          val _ = if null newclasses then ()

                  else Output.debug (fn _ => "New classes: " ^ space_implode ", " newclasses)

          val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses

      in  (classes' union classes, cpairs' union cpairs)  end;

fun make_arity_clauses thy tycons classes =

  let val (classes', cpairs) = iter_type_class_pairs thy tycons classes

  in  (classes', multi_arity_clause cpairs)  end;

(**** Find occurrences of predicates in clauses ****)

(*FIXME: multiple-arity checking doesn't work, as update_new is the wrong

  function (it flags repeated declarations of a function, even with the same arity)*)

fun update_many (tab, keypairs) = foldl (uncurry Symtab.update) tab keypairs;

fun add_type_sort_preds ((FOLTVar indx,s), preds) =

      update_many (preds, map pred_of_sort (sorts_on_typs (FOLTVar indx, s)))

  | add_type_sort_preds ((FOLTFree x,s), preds) =

      update_many (preds, map pred_of_sort (sorts_on_typs (FOLTFree x, s)));

fun add_classrelClause_preds (ClassrelClause {subclass,superclass,...}, preds) =

  Symtab.update (subclass,1) (Symtab.update (superclass,1) preds);

fun class_of_arityLit (TConsLit (tclass, _, _)) = tclass

  | class_of_arityLit (TVarLit (tclass, _)) = tclass;

fun add_arityClause_preds (ArityClause {conclLit,premLits,...}, preds) =

  let val classes = map (make_type_class o class_of_arityLit) (conclLit::premLits)

      fun upd (class,preds) = Symtab.update (class,1) preds

  in  foldl upd preds classes  end;

(*** Find occurrences of functions in clauses ***)

fun add_foltype_funcs (AtomV _, funcs) = funcs

  | add_foltype_funcs (AtomF a, funcs) = Symtab.update (a,0) funcs

  | add_foltype_funcs (Comp(a,tys), funcs) =

      foldl add_foltype_funcs (Symtab.update (a, length tys) funcs) tys;

(*TFrees are recorded as constants*)

fun add_type_sort_funcs ((FOLTVar _, _), funcs) = funcs

  | add_type_sort_funcs ((FOLTFree a, _), funcs) =

      Symtab.update (make_fixed_type_var a, 0) funcs

fun add_arityClause_funcs (ArityClause {conclLit,...}, funcs) =

  let val TConsLit (_, tcons, tvars) = conclLit

  in  Symtab.update (tcons, length tvars) funcs  end;

(*This type can be overlooked because it is built-in...*)

val init_functab = Symtab.update ("tc_itself", 1) Symtab.empty;

(**** String-oriented operations ****)

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);

fun writeln_strs os = List.app (fn s => TextIO.output (os, s));

(**** Producing DFG files ****)

(*Attach sign in DFG syntax: false means negate.*)

fun dfg_sign true s = s

  | dfg_sign false s = "not(" ^ s ^ ")"

fun dfg_of_typeLit (LTVar (s,ty)) = "not(" ^ s ^ "(" ^ ty ^ "))"

  | dfg_of_typeLit (LTFree (s,ty)) = s ^ "(" ^ ty ^ ")";

(*Enclose the clause body by quantifiers, if necessary*)

fun dfg_forall [] body = body

  | dfg_forall vars body = "forall([" ^ commas vars ^ "],\n" ^ body ^ ")"

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

    "clause( %(" ^ knd ^ ")\n" ^

    dfg_forall vars ("or(" ^ lits ^ ")") ^ ",\n" ^

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

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

fun string_of_preds [] = ""

  | string_of_preds preds = "predicates[" ^ commas(map string_of_arity preds) ^ "].\n";

fun string_of_funcs [] = ""

  | string_of_funcs funcs = "functions[" ^ commas(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_start name = "begin_problem(" ^ name ^ ").\n\n";

fun string_of_descrip name =

  "list_of_descriptions.\nname({*" ^ name ^

  "*}).\nauthor({*Isabelle*}).\nstatus(unknown).\ndescription({*auto-generated*}).\nend_of_list.\n\n"

fun dfg_tfree_clause tfree_lit =

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

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

      dfg_sign true (make_type_class c ^ "(" ^ t ^ paren_pack args ^ ")")

  | dfg_of_arLit (TVarLit (c,str)) =

      dfg_sign false (make_type_class c ^ "(" ^ str ^ ")")

fun dfg_classrelLits sub sup =  "not(" ^ sub ^ "(T)), " ^ sup ^ "(T)";

fun dfg_classrelClause (ClassrelClause {axiom_name,subclass,superclass,...}) =

  "clause(forall([T],\nor( " ^ dfg_classrelLits subclass superclass ^ ")),\n" ^

  axiom_name ^ ").\n\n";

fun string_of_ar axiom_name = arclause_prefix ^ ascii_of axiom_name;

fun dfg_arity_clause (ArityClause{axiom_name,kind,conclLit,premLits,...}) =

  let val TConsLit (_,_,tvars) = conclLit

      val lits = map dfg_of_arLit (conclLit :: premLits)

  in

      "clause( %(" ^ name_of_kind kind ^ ")\n" ^

      dfg_forall tvars ("or( " ^ commas lits ^ ")") ^ ",\n" ^

      string_of_ar axiom_name ^ ").\n\n"

  end;

(**** Produce TPTP files ****)

(*Attach sign in TPTP syntax: false means negate.*)

fun tptp_sign true s = s

  | tptp_sign false s = "~ " ^ s

fun tptp_of_typeLit (LTVar (s,ty))  = tptp_sign false (s ^ "(" ^ ty ^ ")")

  | tptp_of_typeLit (LTFree (s,ty)) = tptp_sign true  (s ^ "(" ^ ty ^ ")");

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

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

    name_of_kind knd ^ "," ^ tptp_pack lits ^ ").\n";

fun tptp_tfree_clause tfree_lit =

    "cnf(" ^ "tfree_tcs," ^ "negated_conjecture" ^ "," ^ tptp_pack[tfree_lit] ^ ").\n";

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

      tptp_sign true (make_type_class c ^ "(" ^ t ^ paren_pack args ^ ")")

  | tptp_of_arLit (TVarLit (c,str)) =

      tptp_sign false (make_type_class c ^ "(" ^ str ^ ")")

fun tptp_arity_clause (ArityClause{axiom_name,kind,conclLit,premLits,...}) =

  "cnf(" ^ string_of_ar axiom_name ^ "," ^ name_of_kind kind ^ "," ^

  tptp_pack (map tptp_of_arLit (conclLit :: premLits)) ^ ").\n";

fun tptp_classrelLits sub sup =

  let val tvar = "(T)"

  in  tptp_pack [tptp_sign false (sub^tvar), tptp_sign true (sup^tvar)]  end;

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

  "cnf(" ^ axiom_name ^ ",axiom," ^ tptp_classrelLits subclass superclass ^ ").\n"

end;