(*  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.

*)

signature RES_CLAUSE =

  sig

  exception CLAUSE of string * term

  type clause and arityClause and classrelClause

  type fol_type

  type typ_var

  type type_literal

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

  val arity_clause_thy: theory -> arityClause list 

  val ascii_of : string -> string

  val bracket_pack : string list -> string

  val check_var_pairs: ''a * ''b -> (''a * ''b) list -> int

  val classrel_clauses_thy: theory -> classrelClause list 

  val clause_eq : clause * clause -> bool

  val clause_prefix : string 

  val clause2tptp : clause -> string * string list

  val const_prefix : string

  val dfg_write_file: thm list -> string -> (clause list * classrelClause list * arityClause list) -> unit

  val fixed_var_prefix : string

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

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

  val get_axiomName : clause ->  string

  val hash_clause : clause -> int

  val init : theory -> unit

  val isMeta : string -> bool

  val isTaut : clause -> bool

  val keep_types : bool ref

  val list_ord : ('a * 'b -> order) -> 'a list * 'b list -> order

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

  val make_conjecture_clauses : term list -> clause list

  val make_fixed_const : string -> string		

  val make_fixed_type_const : string -> string   

  val make_fixed_type_var : string -> string

  val make_fixed_var : string -> string

  val make_schematic_type_var : string * int -> string

  val make_schematic_var : string * int -> string

  val make_type_class : string -> string

  val mk_fol_type: string * string * fol_type list -> fol_type

  val mk_typ_var_sort : Term.typ -> typ_var * sort

  val paren_pack : string list -> string

  val schematic_var_prefix : string

  val special_equal : bool ref

  val string_of_fol_type : fol_type -> string

  val tconst_prefix : string 

  val tfree_prefix : string

  val tptp_arity_clause : arityClause -> string

  val tptp_classrelClause : classrelClause -> string

  val tptp_of_typeLit : type_literal -> string

  val tptp_tfree_clause : string -> string

  val tptp_write_file: thm list -> string -> (clause list * classrelClause list * arityClause list) -> unit

  val tvar_prefix : string

  val types_eq: fol_type list * fol_type list -> (string*string) list * (string*string) list -> bool * ((string*string) list * (string*string) list)

  val types_ord : fol_type list * fol_type list -> order

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

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

  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"),

		   ("Divides.op div", "div"),

		   ("HOL.divide", "divide"),

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

		   ("{}", "emptyset"),

		   ("op :", "in"),

		   ("op Un", "union"),

		   ("op Int", "inter"),

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

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.*)

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 lookup_const c =

    case Symtab.lookup const_trans_table c of

        SOME c' => c'

      | NONE => ascii_of c;

fun lookup_type_const c = 

    case Symtab.lookup type_const_trans_table c of

        SOME c' => c'

      | NONE => 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. *****)

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;

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

type tag = bool; 

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

val tagged = ref false;

type pred_name = string;

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));

fun mk_fol_type ("Var",x,_) = AtomV(x)

  | mk_fol_type ("Fixed",x,_) = AtomF(x)

  | mk_fol_type ("Comp",con,args) = Comp(con,args)

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

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

datatype fol_term = UVar of string * fol_type

                 | Fun of string * fol_type list * fol_term list;

datatype predicate = Predicate of pred_name * fol_type list * fol_term 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);

(*A clause has first-order literals and other, type-related literals*)

datatype clause = 

	 Clause of {clause_id: clause_id,

		    axiom_name: axiom_name,

		    kind: kind,

		    literals: literal list,

		    types_sorts: (typ_var * sort) list};

fun get_axiomName (Clause cls) = #axiom_name cls;

exception CLAUSE of string * term;

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

      (pol andalso pname = "c_False") orelse

      (not pol andalso pname = "c_True")

  | isFalse _ = false;

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

      (pol andalso pname = "c_True") orelse

      (not pol andalso pname = "c_False")

  | isTrue _ = false;

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

fun make_clause (clause_id, axiom_name, kind, literals, types_sorts) =

  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};

(*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) = 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;

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)) = (make_fixed_const c, const_types_of (c,T))

  | 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(c,T)) args = (make_fixed_const c, const_types_of (c,T))

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

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

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

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

(*Convert a term to a fol_term while accumulating sort constraints on the TFrees and

  TVars it contains.*)    

fun term_of (Var(ind_nm,T)) = 

      let val (folType,ts) = type_of T

      in (UVar(make_schematic_var ind_nm, folType), ts) end

  | term_of (Free(x,T)) = 

      let val (folType, ts) = type_of T

      in

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

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

      end

  | term_of app = 

      let val (f,args) = strip_comb app

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

	  val (args',ts2) = terms_of args

      in

	  (Fun(funName,contys,args'), union_all (ts1::ts2))

      end

and terms_of ts = ListPair.unzip (map term_of ts)

(*Create a predicate value, again accumulating sort constraints.*)    

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

      let val arg_typ = eq_arg_type typ 

	  val (args',ts) = terms_of args

	  val equal_name = make_fixed_const "op ="

      in

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

	   union_all ts)

      end

  | pred_of (pred,args) = 

      let val (pname, (predType,ts1)) = pred_name_type pred

	  val (args',ts2) = terms_of args

      in

	  (Predicate(pname,predType,args'), union_all (ts1::ts2))

      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 (Const("op |",_) $ P $ Q) = 

      literals_of_term1 (literals_of_term1 args P) Q

  | literals_of_term1 (lits, ts) P =

      let val ((pred, ts'), polarity, tag) = predicate_of (P,true,false)

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

      in

	  (lits', ts union ts')

      end;

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

fun list_ord _ ([],[]) = EQUAL

  | list_ord _ ([],_) = LESS

  | list_ord _ (_,[]) = GREATER

  | list_ord ord (x::xs, y::ys) =

    let val xy_ord = ord(x,y)

    in

	case xy_ord of EQUAL => list_ord ord (xs,ys)

		     | _ => xy_ord

    end;

fun type_ord (AtomV(_),AtomV(_)) = EQUAL

  | type_ord (AtomV(_),_) = LESS

  | type_ord (AtomF(_),AtomV(_)) = GREATER

  | type_ord (AtomF(f1),AtomF(f2)) = string_ord (f1,f2)

  | type_ord (AtomF(_),_) = LESS

  | type_ord (Comp(_,_),AtomV(_)) = GREATER

  | type_ord (Comp(_,_),AtomF(_)) = GREATER

  | type_ord (Comp(con1,args1),Comp(con2,args2)) = 

    let val con_ord = string_ord(con1,con2)

    in

	case con_ord of EQUAL => types_ord (args1,args2)

		      | _ => con_ord

    end

and

    types_ord ([],[]) = EQUAL

  | types_ord (tps1,tps2) = list_ord type_ord (tps1,tps2);

fun term_ord (UVar _, UVar _) = EQUAL

  | term_ord (UVar _, _) = LESS

  | term_ord (Fun _, UVar _) = GREATER

  | term_ord (Fun(f1,tps1,tms1),Fun(f2,tps2,tms2)) = 

     (case string_ord (f1,f2) of

         EQUAL => 

	   (case terms_ord (tms1,tms2) of EQUAL => types_ord (tps1,tps2)

	      | tms_ord => tms_ord)

       | fn_ord => fn_ord)

and

      terms_ord ([],[]) = EQUAL

    | terms_ord (tms1,tms2) = list_ord term_ord (tms1,tms2);

fun predicate_ord (Predicate(pname1,ftyps1,ftms1),Predicate(pname2,ftyps2,ftms2)) = 

  case string_ord (pname1,pname2) of

       EQUAL => (case terms_ord(ftms1,ftms2) of EQUAL => types_ord(ftyps1,ftyps2)

				              | ftms_ord => ftms_ord)

     | pname_ord => pname_ord

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;

(********** clause equivalence ******************)

fun check_var_pairs (x,y) [] = 0 

  | check_var_pairs (x,y) ((u,v)::w) =

    if (x,y) = (u,v) then 1 

    else

	if (x = u) orelse (y = v) then 2 (*conflict*)

	else check_var_pairs (x,y) w;

fun type_eq (AtomV(v1),AtomV(v2)) (vars,tvars) =

    (case check_var_pairs (v1,v2) tvars of 0 => (true,(vars,(v1,v2)::tvars))

					 | 1 => (true,(vars,tvars))

					 | 2 => (false,(vars,tvars)))

  | type_eq (AtomV(_),_) vtvars = (false,vtvars)

  | type_eq (AtomF(f1),AtomF(f2)) vtvars = (f1=f2,vtvars)

  | type_eq (AtomF(_),_) vtvars = (false,vtvars)

  | type_eq (Comp(con1,args1),Comp(con2,args2)) vtvars =

      let val (eq1,vtvars1) = 

	      if con1 = con2 then types_eq (args1,args2) vtvars

	      else (false,vtvars)

      in

	  (eq1,vtvars1)

      end

  | type_eq (Comp(_,_),_) vtvars = (false,vtvars)

and

    types_eq ([],[]) vtvars = (true,vtvars)

  | types_eq (tp1::tps1,tp2::tps2) vtvars =

      let val (eq1,vtvars1) = type_eq (tp1,tp2) vtvars

	  val (eq2,vtvars2) = if eq1 then types_eq (tps1,tps2) vtvars1

			      else (eq1,vtvars1)

      in

	  (eq2,vtvars2)

      end;

fun term_eq (UVar(v1,tp1),UVar(v2,tp2)) (vars,tvars) =

    (case check_var_pairs (v1,v2) vars of 0 => type_eq (tp1,tp2) (((v1,v2)::vars),tvars)

					| 1 => type_eq (tp1,tp2) (vars,tvars)

					| 2 => (false,(vars,tvars)))

  | term_eq (UVar _,_) vtvars = (false,vtvars)

  | term_eq (Fun(f1,tps1,tms1),Fun(f2,tps2,tms2)) vtvars =

      let val (eq1,vtvars1) = 

	      if f1 = f2 then terms_eq (tms1,tms2) vtvars

	      else (false,vtvars)

	  val (eq2,vtvars2) =

	      if eq1 then types_eq (tps1,tps2) vtvars1

	      else (eq1,vtvars1)

      in

	  (eq2,vtvars2)

      end

  | term_eq (Fun(_,_,_),_) vtvars = (false,vtvars)

and

    terms_eq ([],[]) vtvars = (true,vtvars)

  | terms_eq (tm1::tms1,tm2::tms2) vtvars =

      let val (eq1,vtvars1) = term_eq (tm1,tm2) vtvars

	  val (eq2,vtvars2) = if eq1 then terms_eq (tms1,tms2) vtvars1

				     else (eq1,vtvars1)

      in

	  (eq2,vtvars2)

      end;

fun pred_eq (Predicate(pname1,tps1,tms1),Predicate(pname2,tps2,tms2)) vtvars =

    let val (eq1,vtvars1) = 

	    if (pname1 = pname2) then terms_eq (tms1,tms2) vtvars

	    else (false,vtvars)

	val (eq2,vtvars2) = 

	    if eq1 then types_eq (tps1,tps2) vtvars1

	    else (eq1,vtvars1)

    in

	(eq2,vtvars2)

    end;

fun lit_eq (Literal(pol1,pred1,_),Literal(pol2,pred2,_)) vtvars =

    if (pol1 = pol2) then pred_eq (pred1,pred2) vtvars

    else (false,vtvars);

(*must have the same number of literals*)

fun lits_eq ([],[]) vtvars = (true,vtvars)

  | lits_eq (l1::ls1,l2::ls2) vtvars = 

    let val (eq1,vtvars1) = lit_eq (l1,l2) vtvars

    in

	if eq1 then lits_eq (ls1,ls2) vtvars1

	else (false,vtvars1)

    end;

(*Equality of two clauses up to variable renaming*)

fun clause_eq (Clause{literals=lits1,...}, Clause{literals=lits2,...}) =

  length lits1 = length lits2 andalso #1 (lits_eq (lits1,lits2) ([],[]));

(*** Hash function for clauses ***)

val xor_words = List.foldl Word.xorb 0w0;

fun hashw_term (UVar _, w) = w

  | hashw_term (Fun(f,tps,args), w) = 

      List.foldl hashw_term (Polyhash.hashw_string (f,w)) args;

fun hashw_pred (Predicate(pn,_,args), w) = 

    List.foldl hashw_term (Polyhash.hashw_string (pn,w)) args;

fun hash1_literal (Literal(true,pred,_)) = hashw_pred (pred, 0w0)

  | hash1_literal (Literal(false,pred,_)) = Word.notb (hashw_pred (pred, 0w0));

fun hash_clause (Clause{literals,...}) =

  Word.toIntX (xor_words (map hash1_literal literals));

(*Make literals for sorted type variables.  FIXME: can it use map?*) 

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);

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) = 

      (make_schematic_type_var indx) ins (get_tvar_strs tss)

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

(* check if a clause is first-order before making a conjecture clause*)

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) = literals_of_term t

    in

	make_clause(n, "conjecture", Conjecture, lits, types_sorts)

    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

(** Too general means, positive equality literal with a variable X as one operand,

  when X does not occur properly in the other operand. This rules out clearly

  inconsistent clauses such as V=a|V=b, though it by no means guarantees soundness. **)

fun occurs a (UVar(b,_)) = a=b

  | occurs a (Fun (_,_,ts)) = exists (occurs a) ts

(*Is the first operand a variable that does not properly occur in the second operand?*)

fun too_general_terms (UVar _, UVar _) = false

  | too_general_terms (Fun _, _) = false

  | too_general_terms (UVar (a,_), t) = not (occurs a t);

fun too_general_lit (Literal (true,Predicate("equal",_,[x,y]),_)) =

      too_general_terms (x,y) orelse too_general_terms(y,x)

  | too_general_lit _ = false;

(*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) = literals_of_term term

    in 

	if forall too_general_lit lits then

	   (Output.debug ("Omitting " ^ ax_name ^ ": equalities are too general"); 

	    NONE)

	else SOME (make_clause(cls_id, ax_name, Axiom, sort_lits lits, types_sorts))

    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 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) =  (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));

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

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

   let val nargs = length args

       val tvars = gen_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 = lookup_type_const tcons,

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

                   premLits = map make_TVarLit false_tvars_srts'}

   end;

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

datatype classrelClause = 

	 ClassrelClause of {axiom_name: axiom_name,

			    subclass: class,

			    superclass: class};

fun make_axiom_classrelClause n subclass superclass =

  ClassrelClause {axiom_name = clrelclause_prefix ^ ascii_of subclass ^ 

                                "_" ^ Int.toString n,

                  subclass = make_type_class subclass, 

                  superclass = make_type_class superclass};

fun classrelClauses_of_aux n sub [] = []

  | classrelClauses_of_aux n sub ("HOL.type"::sups) = (*Should be ignored*)

      classrelClauses_of_aux n sub sups

  | classrelClauses_of_aux n sub (sup::sups) =

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

fun classrelClauses_of (sub,sups) = classrelClauses_of_aux 0 sub sups;

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;

(** Isabelle arities **)

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

  | arity_clause n (tcons, ("HOL.type",_)::ars) =  (*Should be ignored*)

      arity_clause n (tcons,ars)

  | 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;

(**** 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_predicate_preds (Predicate(pname,tys,tms), preds) = 

  if pname = "equal" then preds (*equality is built-in and requires no declaration*)

  else Symtab.update (pname, length tys + length tms) preds

fun add_literal_preds (Literal(_,pred,_), preds) = add_predicate_preds (pred,preds)

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_clause_preds (Clause {literals, types_sorts, ...}, preds) =

  foldl add_literal_preds (foldl add_type_sort_preds preds types_sorts) literals

  handle Symtab.DUP a => raise ERROR ("predicate " ^ a ^ " has multiple arities")

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

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

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

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

  in  Symtab.update (tclass,1) preds  end;

fun preds_of_clauses clauses clsrel_clauses arity_clauses = 

  Symtab.dest

    (foldl add_classrelClause_preds 

      (foldl add_arityClause_preds

        (foldl add_clause_preds Symtab.empty clauses)

        arity_clauses)

      clsrel_clauses)

(*** 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;

fun add_folterm_funcs (UVar _, funcs) = funcs

  | add_folterm_funcs (Fun(a,tys,[]), funcs) = Symtab.update (a,0) funcs

      (*A constant is a special case: it has no type argument even if overloaded*)

  | add_folterm_funcs (Fun(a,tys,tms), funcs) = 

      foldl add_foltype_funcs 

	    (foldl add_folterm_funcs (Symtab.update (a, length tys + length tms) funcs) 

	           tms) 

	    tys

fun add_predicate_funcs (Predicate(_,tys,tms), funcs) = 

    foldl add_foltype_funcs (foldl add_folterm_funcs funcs tms) tys;

fun add_literal_funcs (Literal(_,pred,_), funcs) = add_predicate_funcs (pred,funcs)

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

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

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

fun add_clause_funcs (Clause {literals, ...}, funcs) =

  foldl add_literal_funcs funcs literals

  handle Symtab.DUP a => raise ERROR ("function " ^ a ^ " has multiple arities")

fun funcs_of_clauses clauses arity_clauses = 

  Symtab.dest (foldl add_arityClause_funcs 

                     (foldl add_clause_funcs Symtab.empty clauses)

                     arity_clauses)

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

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;

(* 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;

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);

(*Write a list of strings to a file*)

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_literal (Literal(pol,pred,tag)) = dfg_sign pol (string_of_predicate pred)

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 dfg_clause_aux (Clause{literals, types_sorts, ...}) = 

  let val lits = map dfg_literal literals

      val (tvar_lits,tfree_lits) = add_typs_aux types_sorts

      val tvar_lits_strs = 

	  if !keep_types then map dfg_of_typeLit tvar_lits else []

      val tfree_lits =

          if !keep_types then map dfg_of_typeLit tfree_lits else []

  in

      (tvar_lits_strs @ lits, tfree_lits)

  end; 

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

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

  in  folterms  end

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

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

fun dfg_vars (Clause {literals,...}) =

  union_all (map get_uvars (List.concat (map dfg_folterms literals)))

fun clause2dfg (cls as Clause{axiom_name,clause_id,kind,types_sorts,...}) =

    let val (lits,tfree_lits) = dfg_clause_aux cls 

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

        val vars = dfg_vars cls

        val tvars = get_tvar_strs types_sorts

	val knd = name_of_kind kind

	val lits_str = commas lits

	val cls_str = gen_dfg_cls(clause_id, axiom_name, knd, lits_str, tvars@vars) 

    in (cls_str, tfree_lits) end;

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

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

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

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

      dfg_sign pol (c ^ "(" ^ t ^ paren_pack args ^ ")")

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

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

fun dfg_classrelLits sub sup = 

    let val tvar = "(T)"

    in 

	"not(" ^ sub ^ tvar ^ "), " ^ sup ^ tvar

    end;

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

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

  axiom_name ^ ").\n\n";

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

  let val arcls_id = string_of_arClauseID arcls

      val knd = name_of_kind kind

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

      val lits = map dfg_of_arLit (conclLit :: premLits)

  in

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

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

      arcls_id ^ ").\n\n"

  end;

(* write out a subgoal in DFG format to the file "xxxx_N"*)

fun dfg_write_file ths filename (axclauses,classrel_clauses,arity_clauses) = 

  let 

    val conjectures = make_conjecture_clauses (map prop_of ths)

    val (dfg_clss, tfree_litss) = ListPair.unzip (map clause2dfg conjectures)

    val clss = conjectures @ axclauses

    val funcs = funcs_of_clauses clss arity_clauses

    and preds = preds_of_clauses clss classrel_clauses arity_clauses

    val out = TextIO.openOut filename

    and probname = Path.pack (Path.base (Path.unpack filename))

    val (axstrs, _) = ListPair.unzip (map clause2dfg axclauses)

    val tfree_clss = map dfg_tfree_clause (union_all tfree_litss) 

  in

    TextIO.output (out, string_of_start probname); 

    TextIO.output (out, string_of_descrip probname); 

    TextIO.output (out, string_of_symbols (string_of_funcs funcs) (string_of_preds preds)); 

    TextIO.output (out, "list_of_clauses(axioms,cnf).\n");

    writeln_strs out axstrs;

    List.app (curry TextIO.output out o dfg_classrelClause) classrel_clauses;

    List.app (curry TextIO.output out o dfg_arity_clause) arity_clauses;

    TextIO.output (out, "end_of_list.\n\nlist_of_clauses(conjectures,cnf).\n");

    writeln_strs out tfree_clss;

    writeln_strs out dfg_clss;

    TextIO.output (out, "end_of_list.\n\nend_problem.\n");

    TextIO.closeOut out

  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_literal (Literal(pol,pred,tag)) =  (*FIXME REMOVE TAGGING*)

    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 (s,ty)) = "--" ^ s ^ "(" ^ ty ^ ")"

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

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

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

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

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 ^ "]).\n";

fun tptp_type_lits (Clause {literals, types_sorts, ...}) = 

    let val lits = map tptp_literal literals

	val (tvar_lits,tfree_lits) = add_typs_aux types_sorts

        val tvar_lits_strs =

            if !keep_types then map tptp_of_typeLit tvar_lits else []

	val tfree_lits =

	    if !keep_types then map tptp_of_typeLit tfree_lits else []

    in

	(tvar_lits_strs @ lits, tfree_lits)

    end;