(*  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 : thm -> string * int -> clause option

   val make_conjecture_clauses : thm 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 -> ((thm * (string * int)) 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"),

 	  	   ("Orderings.less_eq", "lessequals"),

 		   ("Orderings.less", "less"),

 		   ("op &", "and"),

 		   ("op |", "or"),

 		   ("HOL.plus", "plus"),

 		   ("HOL.minus", "minus"),

 		   ("HOL.times", "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,

 		    th: thm,

 		    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, th, 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, 

              th = th, 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) = 

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

 	 	      | xy_ord => xy_ord);

 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)) = 

       (case string_ord(con1,con2) of EQUAL => types_ord (args1,args2)

 		      | con_ord => con_ord)

 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);

 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

   | lits_eq _ vtvars = (false,vtvars);

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

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

   #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 thm =

     let val t = prop_of thm

 	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", thm, 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 thm (ax_name,cls_id) =

     let val term = prop_of thm

 	val (lits,types_sorts) = literals_of_term term

     in 

 	if not (Meson.is_fol_term term) then

 	   (Output.debug ("Omitting " ^ ax_name ^ ": Axiom is not FOL"); 

 	    NONE)

 	else 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, thm, Axiom, sort_lits lits, types_sorts))

     end

     handle CLAUSE _ => NONE;

 fun make_axiom_clauses [] = []

   | make_axiom_clauses ((thm,(name,id))::thms) =

     case make_axiom_clause thm (name,id) of SOME cls => if isTaut cls then make_axiom_clauses thms else cls :: make_axiom_clauses thms

 						    | NONE => make_axiom_clauses thms;

 (**** 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) =  (*ignore*)

       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 ((tcons,ars) :: tc_arlists) =

       (*Reversal ensures that older entries always get the same axiom name*)

       arity_clause 0 (tcons, rev ars)  @  

       multi_arity_clause tc_arlists 

 fun arity_clause_thy thy =

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

   in multi_arity_clause (rev (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 _ = Output.debug ("Preparing to write the DFG file " ^ filename)

     val conjectures = make_conjecture_clauses 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

     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) 

     val out = TextIO.openOut filename

   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; 

 fun clause2tptp (cls as Clause {clause_id, axiom_name, kind, ...}) =

     let val (lits,tfree_lits) = tptp_type_lits cls 

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

 	val knd = name_of_kind kind

 	val cls_str = gen_tptp_cls(clause_id, axiom_name, knd, bracket_pack lits) 

     in

 	(cls_str,tfree_lits) 

     end;

 fun tptp_tfree_clause tfree_lit =

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

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

       tptp_sign b (c ^ "(" ^ t ^ paren_pack args ^ ")")

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

       tptp_sign b (c ^ "(" ^ str ^ ")")

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

   let val arcls_id = string_of_arClauseID arcls

       val knd = name_of_kind kind

       val lits = map tptp_of_arLit (conclLit :: premLits)

   in

     "input_clause(" ^ arcls_id ^ "," ^ knd ^ "," ^ bracket_pack lits ^ ").\n"

   end;

 fun tptp_classrelLits sub sup = 

     let val tvar = "(T)"

     in 

 	"[--" ^ sub ^ tvar ^ ",++" ^ sup ^ tvar ^ "]"

     end;

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

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

 (* write out a subgoal as tptp clauses to the file "xxxx_N"*)

 fun tptp_write_file thms filename (axclauses,classrel_clauses,arity_clauses) =

   let

     val _ = Output.debug ("Preparing to write the TPTP file " ^ filename)

     val clss = make_conjecture_clauses thms

     val axclauses' = make_axiom_clauses axclauses

     val (tptp_clss,tfree_litss) = ListPair.unzip (map clause2tptp clss)

     val tfree_clss = map tptp_tfree_clause (foldl (op union_string) [] tfree_litss)

     val out = TextIO.openOut filename

   in

     List.app (curry TextIO.output out o #1 o clause2tptp) axclauses';

     writeln_strs out tfree_clss;

     writeln_strs out tptp_clss;

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

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

     TextIO.closeOut out

   end;

 end;