(* ID: $Id$ 

    Author: Jia Meng, NICTA

 FOL clauses translated from HOL formulae.  Combinators are used to represent lambda terms.

 *)

 structure ResHolClause =

 struct

 val include_combS = ref false;

 val include_min_comb = ref false;

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

 fun init thy = (include_combS:=false;include_min_comb:=false;const_typargs := Sign.const_typargs thy);

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

 (* convert a Term.term with lambdas into a Term.term with combinators *) 

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

 fun is_free (Bound(a)) n = (a = n)

   | is_free (Abs(x,_,b)) n = (is_free b (n+1))

   | is_free (P $ Q) n = ((is_free P n) orelse (is_free Q n))

   | is_free _ _ = false;

 exception LAM2COMB of term;

 exception BND of term;

 fun decre_bndVar (Bound n) = Bound (n-1)

   | decre_bndVar (P $ Q) = (decre_bndVar P) $ (decre_bndVar Q)

   | decre_bndVar t =

     case t of Const(_,_) => t

 	    | Free(_,_) => t

 	    | Var(_,_) => t

 	    | Abs(_,_,_) => raise BND(t); (*should not occur*)

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

 fun lam2comb (Abs(x,tp,Bound 0)) _ = 

     let val tpI = Type("fun",[tp,tp])

     in 

 	include_min_comb:=true;

 	Const("COMBI",tpI) 

     end

   | lam2comb (Abs(x,tp,Bound n)) Bnds = 

     let val (Bound n') = decre_bndVar (Bound n)

 	val tb = List.nth(Bnds,n')

 	val tK = Type("fun",[tb,Type("fun",[tp,tb])])

     in

 	include_min_comb:=true;

 	Const("COMBK",tK) $ (Bound n')

     end

   | lam2comb (Abs(x,t1,Const(c,t2))) _ = 

     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])

     in 

 	include_min_comb:=true;

 	Const("COMBK",tK) $ Const(c,t2) 

     end

   | lam2comb (Abs(x,t1,Free(v,t2))) _ =

     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])

     in

 	include_min_comb:=true;

 	Const("COMBK",tK) $ Free(v,t2)

     end

   | lam2comb (Abs(x,t1,Var(ind,t2))) _=

     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])

     in

 	include_min_comb:=true;

 	Const("COMBK",tK) $ Var(ind,t2)

     end

   | lam2comb (t as (Abs(x,t1,P$(Bound 0)))) Bnds =

     let val nfreeP = not(is_free P 0)

 	val tr = Term.type_of1(t1::Bnds,P)

     in

 	if nfreeP then (decre_bndVar P)

 	else (

 	      let val tI = Type("fun",[t1,t1])

 		  val P' = lam2comb (Abs(x,t1,P)) Bnds

 		  val tp' = Term.type_of1(Bnds,P')

 		  val tS = Type("fun",[tp',Type("fun",[tI,tr])])

 	      in

 		  include_min_comb:=true;

 		  include_combS:=true;

 		  Const("COMBS",tS) $ P' $ Const("COMBI",tI)

 	      end)

     end

   | lam2comb (t as (Abs(x,t1,P$Q))) Bnds =

     let val (nfreeP,nfreeQ) = (not(is_free P 0),not(is_free Q 0))

 	val tpq = Term.type_of1(t1::Bnds, P$Q) 

     in

 	if(nfreeP andalso nfreeQ) then (

 	    let val tK = Type("fun",[tpq,Type("fun",[t1,tpq])])

 		val PQ' = decre_bndVar(P $ Q)

 	    in 

 		include_min_comb:=true;

 		Const("COMBK",tK) $ PQ'

 	    end)

 	else (

 	      if nfreeP then (

 			       let val Q' = lam2comb (Abs(x,t1,Q)) Bnds

 				   val P' = decre_bndVar P

 				   val tp = Term.type_of1(Bnds,P')

 				   val tq' = Term.type_of1(Bnds, Q')

 				   val tB = Type("fun",[tp,Type("fun",[tq',Type("fun",[t1,tpq])])])

 			       in

 				   include_min_comb:=true;

 				   Const("COMBB",tB) $ P' $ Q' 

 			       end)

 	      else (

 		    if nfreeQ then (

 				    let val P' = lam2comb (Abs(x,t1,P)) Bnds

 					val Q' = decre_bndVar Q

 					val tq = Term.type_of1(Bnds,Q')

 					val tp' = Term.type_of1(Bnds, P')

 					val tC = Type("fun",[tp',Type("fun",[tq,Type("fun",[t1,tpq])])])

 				    in

 					include_min_comb:=true;

 					Const("COMBC",tC) $ P' $ Q'

 				    end)

 		    else(

 			 let val P' = lam2comb (Abs(x,t1,P)) Bnds

 			     val Q' = lam2comb (Abs(x,t1,Q)) Bnds

 			     val tp' = Term.type_of1(Bnds,P')

 			     val tq' = Term.type_of1(Bnds,Q')

 			     val tS = Type("fun",[tp',Type("fun",[tq',Type("fun",[t1,tpq])])])

 			 in

 			     include_min_comb:=true;

 			     include_combS:=true;

 			     Const("COMBS",tS) $ P' $ Q'

 			 end)))

     end

   | lam2comb (t as (Abs(x,t1,_))) _ = raise LAM2COMB (t);

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

 fun to_comb (Abs(x,tp,b)) Bnds =

     let val b' = to_comb b (tp::Bnds)

     in lam2comb (Abs(x,tp,b')) Bnds end

   | to_comb (P $ Q) Bnds = ((to_comb P Bnds) $ (to_comb Q Bnds))

   | to_comb t _ = t;

 fun comb_of t = to_comb t [];

 (* print a term containing combinators, used for debugging *)

 exception TERM_COMB of term;

 fun string_of_term (Const(c,t)) = c

   | string_of_term (Free(v,t)) = v

   | string_of_term (Var((x,n),t)) =

     let val xn = x ^ "_" ^ (string_of_int n)

     in xn end

   | string_of_term (P $ Q) =

     let val P' = string_of_term P

 	val Q' = string_of_term Q

     in

 	"(" ^ P' ^ " " ^ Q' ^ ")" end

   | string_of_term t =  raise TERM_COMB (t);

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

 (* data types for typed combinator expressions        *)

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

 type axiom_name = string;

 datatype kind = Axiom | Conjecture;

 fun name_of_kind Axiom = "axiom"

   | name_of_kind Conjecture = "conjecture";

 type polarity = bool;

 type indexname = Term.indexname;

 type clause_id = int;

 type csort = Term.sort;

 type ctyp = ResClause.fol_type;

 val string_of_ctyp = ResClause.string_of_fol_type;

 type ctyp_var = ResClause.typ_var;

 type ctype_literal = ResClause.type_literal;

 datatype combterm = CombConst of string * ctyp * ctyp list

 		  | CombFree of string * ctyp

 		  | CombVar of string * ctyp

 		  | CombApp of combterm * combterm * ctyp

 		  | Bool of combterm

 		  | Equal of combterm * combterm;

 datatype literal = Literal of polarity * combterm;

 datatype clause = 

 	 Clause of {clause_id: clause_id,

 		    axiom_name: axiom_name,

 		    kind: kind,

 		    literals: literal list,

 		    ctypes_sorts: (ctyp_var * csort) list, 

                     ctvar_type_literals: ctype_literal list, 

                     ctfree_type_literals: ctype_literal list};

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

 fun get_axiomName (Clause cls) = #axiom_name cls;

 fun get_clause_id (Clause cls) = #clause_id cls;

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

 exception TERM_ORD of string

 fun term_ord (CombVar(_,_),CombVar(_,_)) = EQUAL

   | term_ord (CombVar(_,_),_) = LESS

   | term_ord (CombFree(_,_),CombVar(_,_)) = GREATER

   | term_ord (CombFree(f1,tp1),CombFree(f2,tp2)) = 

     let val ord1 = string_ord(f1,f2)

     in

 	case ord1 of EQUAL => ResClause.types_ord ([tp1],[tp2])

 		   | _ => ord1

     end

   | term_ord (CombFree(_,_),_) = LESS

   | term_ord (CombConst(_,_,_),CombVar(_,_)) = GREATER

   | term_ord (CombConst(_,_,_),CombFree(_,_)) = GREATER

   | term_ord (CombConst(c1,tp1,_),CombConst(c2,tp2,_)) = 

     let val ord1 = string_ord (c1,c2)

     in

 	case ord1 of EQUAL => ResClause.types_ord ([tp1],[tp2])

 		   | _ => ord1

     end

   | term_ord (CombConst(_,_,_),_) = LESS

   | term_ord (CombApp(_,_,_),Bool(_)) = raise TERM_ORD("bool")

   | term_ord (CombApp(_,_,_),Equal(_,_)) = LESS

   | term_ord (CombApp(f1,arg1,tp1),CombApp(f2,arg2,tp2)) =

     let val ord1 = term_ord (f1,f2)

 	val ord2 = case ord1 of EQUAL => term_ord (arg1,arg2)

 			      | _ => ord1

     in

 	case ord2 of EQUAL => ResClause.types_ord ([tp1],[tp2])

 		   | _ => ord2

     end

   | term_ord (CombApp(_,_,_),_) = GREATER

   | term_ord (Bool(_),_) = raise TERM_ORD("bool")

   | term_ord (Equal(t1,t2),Equal(t3,t4)) = ResClause.list_ord term_ord ([t1,t2],[t3,t4])

   | term_ord (Equal(_,_),_) = GREATER;

 fun predicate_ord (Equal(_,_),Bool(_)) = LESS

   | predicate_ord (Equal(t1,t2),Equal(t3,t4)) = 

     ResClause.list_ord term_ord ([t1,t2],[t3,t4])

   | predicate_ord (Bool(_),Equal(_,_)) = GREATER

   | predicate_ord (Bool(t1),Bool(t2)) = term_ord (t1,t2)

 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;

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

 (* convert a clause with type Term.term to a clause with type clause *)

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

 fun isFalse (Literal(pol,Bool(CombConst(c,_,_)))) =

     (pol andalso c = "c_False") orelse

     (not pol andalso c = "c_True")

   | isFalse _ = false;

 fun isTrue (Literal (pol,Bool(CombConst(c,_,_)))) =

       (pol andalso c = "c_True") orelse

       (not pol andalso c = "c_False")

   | isTrue _ = false;

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

 fun make_clause(clause_id,axiom_name,kind,literals,ctypes_sorts,ctvar_type_literals,ctfree_type_literals) =

     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, ctypes_sorts = ctypes_sorts, 

 		ctvar_type_literals = ctvar_type_literals,

 		ctfree_type_literals = ctfree_type_literals};

 fun type_of (Type (a, Ts)) =

     let val (folTypes,ts) = types_of Ts

 	val t = ResClause.make_fixed_type_const a

     in

 	(ResClause.mk_fol_type("Comp",t,folTypes),ts)

     end

   | type_of (tp as (TFree(a,s))) =

     let val t = ResClause.make_fixed_type_var a

     in

 	(ResClause.mk_fol_type("Fixed",t,[]),[ResClause.mk_typ_var_sort tp])

     end

   | type_of (tp as (TVar(v,s))) =

     let val t = ResClause.make_schematic_type_var v

     in

 	(ResClause.mk_fol_type("Var",t,[]),[ResClause.mk_typ_var_sort tp])

     end

 and types_of Ts =

     let val foltyps_ts = map type_of Ts

 	val (folTyps,ts) = ListPair.unzip foltyps_ts

     in

 	(folTyps,ResClause.union_all ts)

     end;

 (* same as above, but no gathering of sort information *)

 fun simp_type_of (Type (a, Ts)) = 

     let val typs = map simp_type_of Ts

 	val t = ResClause.make_fixed_type_const a

     in

 	ResClause.mk_fol_type("Comp",t,typs)

     end

   | simp_type_of (TFree (a,s)) = ResClause.mk_fol_type("Fixed",ResClause.make_fixed_type_var a,[])

   | simp_type_of (TVar (v,s)) = ResClause.mk_fol_type("Var",ResClause.make_schematic_type_var v,[]);

 fun comb_typ ("COMBI",t) = 

     let val t' = domain_type t

     in

 	[simp_type_of t']

     end

   | comb_typ ("COMBK",t) = 

     let val a = domain_type t

 	val b = domain_type (range_type t)

     in

 	map simp_type_of [a,b]

     end

   | comb_typ ("COMBS",t) = 

     let val t' = domain_type t

 	val a = domain_type t'

 	val b = domain_type (range_type t')

 	val c = range_type (range_type t')

     in 

 	map simp_type_of [a,b,c]

     end

   | comb_typ ("COMBB",t) = 

     let val ab = domain_type t

 	val ca = domain_type (range_type t)

 	val a = domain_type ab

 	val b = range_type ab

 	val c = domain_type ca

     in

 	map simp_type_of [a,b,c]

     end

   | comb_typ ("COMBC",t) =

     let val t1 = domain_type t

 	val a = domain_type t1

 	val b = domain_type (range_type t1)

 	val c = range_type (range_type t1)

     in

 	map simp_type_of [a,b,c]

     end;

 fun const_type_of ("COMBI",t) = 

     let val (tp,ts) = type_of t

 	val I_var = comb_typ ("COMBI",t)

     in

 	(tp,ts,I_var)

     end

   | const_type_of ("COMBK",t) =

     let val (tp,ts) = type_of t

 	val K_var = comb_typ ("COMBK",t)

     in

 	(tp,ts,K_var)

     end

   | const_type_of ("COMBS",t) =

     let val (tp,ts) = type_of t

 	val S_var = comb_typ ("COMBS",t)

     in

 	(tp,ts,S_var)

     end

   | const_type_of ("COMBB",t) =

     let val (tp,ts) = type_of t

 	val B_var = comb_typ ("COMBB",t)

     in

 	(tp,ts,B_var)

     end

   | const_type_of ("COMBC",t) =

     let val (tp,ts) = type_of t

 	val C_var = comb_typ ("COMBC",t)

     in

 	(tp,ts,C_var)

     end

   | const_type_of (c,t) =

     let val (tp,ts) = type_of t

 	val tvars = !const_typargs(c,t)

 	val tvars' = map simp_type_of tvars

     in

 	(tp,ts,tvars')

     end;

 fun is_bool_type (Type("bool",[])) = true

   | is_bool_type _ = false;

 (* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)

 fun combterm_of (Const(c,t)) =

     let val (tp,ts,tvar_list) = const_type_of (c,t)

 	val is_bool = is_bool_type t

 	val c' = CombConst(ResClause.make_fixed_const c,tp,tvar_list)

 	val c'' = if is_bool then Bool(c') else c'

     in

 	(c'',ts)

     end

   | combterm_of (Free(v,t)) =

     let val (tp,ts) = type_of t

 	val is_bool = is_bool_type t

 	val v' = if ResClause.isMeta v then CombVar(ResClause.make_schematic_var(v,0),tp)

 		 else CombFree(ResClause.make_fixed_var v,tp)

 	val v'' = if is_bool then Bool(v') else v'

     in

 	(v'',ts)

     end

   | combterm_of (Var(v,t)) =

     let val (tp,ts) = type_of t

 	val is_bool = is_bool_type t

 	val v' = CombVar(ResClause.make_schematic_var v,tp)

 	val v'' = if is_bool then Bool(v') else v'

     in

 	(v'',ts)

     end

   | combterm_of (Const("op =",T) $ P $ Q) = (*FIXME: allow equal between bools?*)

     let val (P',tsP) = combterm_of P        

 	val (Q',tsQ) = combterm_of Q

     in

 	(Equal(P',Q'),tsP union tsQ)

     end

   | combterm_of (t as (P $ Q)) =

     let val (P',tsP) = combterm_of P

 	val (Q',tsQ) = combterm_of Q

 	val tp = Term.type_of t

 	val tp' = simp_type_of tp

 	val is_bool = is_bool_type tp

 	val t' = CombApp(P',Q',tp')

 	val t'' = if is_bool then Bool(t') else t'

     in

 	(t'',tsP union tsQ)

     end;

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

     predicate_of (P, not polarity)

   | predicate_of (term,polarity) = (combterm_of term,polarity);

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

   | literals_of_term1 args (Const("op |",_) $ P $ Q) = 

     let val args' = literals_of_term1 args P

     in

 	literals_of_term1 args' Q

     end

   | literals_of_term1 (lits,ts) P =

     let val ((pred,ts'),pol) = predicate_of (P,true)

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

     in

 	(lits',ts union ts')

     end;

 fun literals_of_term P = literals_of_term1 ([],[]) P;

 (* making axiom and conjecture clauses *)

 fun make_axiom_clause thm (ax_name,cls_id) =

     let val term = prop_of thm

 	val term' = comb_of term

 	val (lits,ctypes_sorts) = literals_of_term term'

 	val lits' = sort_lits lits

 	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux ctypes_sorts

     in

 	make_clause(cls_id,ax_name,Axiom,

 		    lits',ctypes_sorts,ctvar_lits,ctfree_lits)

     end;

 fun make_axiom_clauses [] = []

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

     let val cls = make_axiom_clause thm (name,id)

 	val clss = make_axiom_clauses thms

     in

 	if isTaut cls then clss else (cls::clss)

     end;

 fun make_conjecture_clause n thm =

     let val t = prop_of thm

 	val t' = comb_of t

 	val (lits,ctypes_sorts) = literals_of_term t'

 	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux ctypes_sorts

     in

 	make_clause(n,"conjecture",Conjecture,lits,ctypes_sorts,ctvar_lits,ctfree_lits)

     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;

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

 (* convert clause into ATP specific formats:                          *)

 (* TPTP used by Vampire and E                                         *)

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

 val type_wrapper = "typeinfo";

 datatype type_level = T_FULL | T_PARTIAL | T_CONST | T_NONE;

 val typ_level = ref T_FULL;

 fun full_types () = (typ_level:=T_FULL);

 fun partial_types () = (typ_level:=T_PARTIAL);

 fun const_types_only () = (typ_level:=T_CONST);

 fun no_types () = (typ_level:=T_NONE);

 fun find_typ_level () = !typ_level;

 fun wrap_type (c,t) = 

     case !typ_level of T_FULL => type_wrapper ^ (ResClause.paren_pack [c,t])

 		     | _ => c;

 val bool_tp = ResClause.make_fixed_type_const "bool";

 val app_str = "hAPP";

 val bool_str = "hBOOL";

 exception STRING_OF_COMBTERM of int;

 (* convert literals of clauses into strings *)

 fun string_of_combterm1_aux _ (CombConst(c,tp,_)) = 

     let val tp' = string_of_ctyp tp

     in

 	(wrap_type (c,tp'),tp')

     end

   | string_of_combterm1_aux _ (CombFree(v,tp)) = 

     let val tp' = string_of_ctyp tp

     in

 	(wrap_type (v,tp'),tp')

     end

   | string_of_combterm1_aux _ (CombVar(v,tp)) = 

     let val tp' = string_of_ctyp tp

     in

 	(wrap_type (v,tp'),tp')

     end

   | string_of_combterm1_aux is_pred (CombApp(t1,t2,tp)) =

     let val (s1,tp1) = string_of_combterm1_aux is_pred t1

 	val (s2,tp2) = string_of_combterm1_aux is_pred t2

 	val tp' = ResClause.string_of_fol_type tp

 	val r =	case !typ_level of T_FULL => type_wrapper ^  (ResClause.paren_pack [(app_str ^ (ResClause.paren_pack [s1,s2])),tp'])

 				 | T_PARTIAL => app_str ^ (ResClause.paren_pack [s1,s2,tp1])

 				 | T_NONE => app_str ^ (ResClause.paren_pack [s1,s2])

 				 | T_CONST => raise STRING_OF_COMBTERM (1) (*should not happen, if happened may be a bug*)

     in	(r,tp')

     end

   | string_of_combterm1_aux is_pred (Bool(t)) = 

     let val (t',_) = string_of_combterm1_aux false t

 	val r = if is_pred then bool_str ^ (ResClause.paren_pack [t'])

 		else t'

     in

 	(r,bool_tp)

     end

   | string_of_combterm1_aux _ (Equal(t1,t2)) =

     let val (s1,_) = string_of_combterm1_aux false t1

 	val (s2,_) = string_of_combterm1_aux false t2

     in

 	("equal" ^ (ResClause.paren_pack [s1,s2]),bool_tp) 

     end;

 fun string_of_combterm1 is_pred term = fst (string_of_combterm1_aux is_pred term);

 fun string_of_combterm2 _ (CombConst(c,tp,tvars)) = 

     let val tvars' = map string_of_ctyp tvars

     in

 	c ^ (ResClause.paren_pack tvars')

     end

   | string_of_combterm2 _ (CombFree(v,tp)) = v

   | string_of_combterm2 _ (CombVar(v,tp)) = v

   | string_of_combterm2 is_pred (CombApp(t1,t2,tp)) =

     let val s1 = string_of_combterm2 is_pred t1

 	val s2 = string_of_combterm2 is_pred t2

     in

 	app_str ^ (ResClause.paren_pack [s1,s2])

     end

   | string_of_combterm2 is_pred (Bool(t)) = 

     let val t' = string_of_combterm2 false t

     in

 	if is_pred then bool_str ^ (ResClause.paren_pack [t'])

 	else t'

     end

   | string_of_combterm2 _ (Equal(t1,t2)) =

     let val s1 = string_of_combterm2 false t1

 	val s2 = string_of_combterm2 false t2

     in

 	("equal" ^ (ResClause.paren_pack [s1,s2])) 

     end;

 fun string_of_combterm is_pred term = 

     case !typ_level of T_CONST => string_of_combterm2 is_pred term

 		     | _ => string_of_combterm1 is_pred term;

 fun string_of_clausename (cls_id,ax_name) = 

     ResClause.clause_prefix ^ ResClause.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 tptp_literal (Literal(pol,pred)) =

     let val pred_string = string_of_combterm true pred

 	val pol_str = if pol then "++" else "--"

     in

 	pol_str ^ pred_string

     end;

 fun tptp_type_lits (Clause cls) = 

     let val lits = map tptp_literal (#literals cls)

 	val ctvar_lits_strs =

 	    case !typ_level of T_NONE => []

 			     | _ => (map ResClause.tptp_of_typeLit (#ctvar_type_literals cls)) 

 	val ctfree_lits = 

 	    case !typ_level of T_NONE => []

 			     | _ => (map ResClause.tptp_of_typeLit (#ctfree_type_literals cls)) 

     in

 	(ctvar_lits_strs @ lits, ctfree_lits)

     end; 

 fun clause2tptp cls =

     let val (lits,ctfree_lits) = tptp_type_lits cls

 	val cls_id = get_clause_id cls

 	val ax_name = get_axiomName cls

 	val knd = string_of_kind cls

 	val lits_str = ResClause.bracket_pack lits

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

     in

 	(cls_str,ctfree_lits)

     end;

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

 (* clause equalities and hashing functions                            *)

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

 fun combterm_eq (CombConst(c1,tp1,tps1),CombConst(c2,tp2,tps2)) vtvars =

     let val (eq1,vtvars1) = if c1 = c2 then ResClause.types_eq (tps1,tps2) vtvars

 			    else (false,vtvars)

     in

 	(eq1,vtvars1)

     end

   | combterm_eq (CombConst(_,_,_),_) vtvars = (false,vtvars)

   | combterm_eq (CombFree(a1,tp1),CombFree(a2,tp2)) vtvars = 

     if a1 = a2 then ResClause.types_eq ([tp1],[tp2]) vtvars

     else (false,vtvars)

   | combterm_eq (CombFree(_,_),_) vtvars = (false,vtvars)

   | combterm_eq (CombVar(v1,tp1),CombVar(v2,tp2)) (vars,tvars) = 

     (case ResClause.check_var_pairs(v1,v2) vars of 0 => ResClause.types_eq ([tp1],[tp2]) ((v1,v2)::vars,tvars)

 						 | 1 => ResClause.types_eq ([tp1],[tp2]) (vars,tvars)

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

   | combterm_eq (CombVar(_,_),_) vtvars = (false,vtvars)

   | combterm_eq (CombApp(f1,arg1,tp1),CombApp(f2,arg2,tp2)) vtvars =

     let val (eq1,vtvars1) = combterm_eq (f1,f2) vtvars

 	val (eq2,vtvars2) = if eq1 then combterm_eq (arg1,arg2) vtvars1

 			    else (eq1,vtvars1)

     in

 	if eq2 then ResClause.types_eq ([tp1],[tp2]) vtvars2

 	else (eq2,vtvars2)

     end

   | combterm_eq (CombApp(_,_,_),_) vtvars = (false,vtvars)

   | combterm_eq (Bool(t1),Bool(t2)) vtvars = combterm_eq (t1,t2) vtvars

   | combterm_eq (Bool(_),_) vtvars = (false,vtvars)

   | combterm_eq (Equal(t1,t2),Equal(t3,t4)) vtvars =

     let val (eq1,vtvars1) = combterm_eq (t1,t3) vtvars

     in

 	if eq1 then combterm_eq (t2,t4) vtvars1

 	else (eq1,vtvars1)

     end

   | combterm_eq (Equal(t1,t2),_) vtvars = (false,vtvars);

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

     if (pol1 = pol2) then combterm_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;

 fun clause_eq (cls1,cls2) =

     let val lits1 = get_literals cls1

 	val lits2 = get_literals cls2

     in

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

     end;

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

 fun hash_combterm (CombVar(_,_),w) = w

   | hash_combterm (CombFree(f,_),w) = Polyhash.hashw_string(f,w)

   | hash_combterm (CombConst(c,tp,tps),w) = Polyhash.hashw_string(c,w)

   | hash_combterm (CombApp(f,arg,tp),w) = hash_combterm (arg, hash_combterm (f,w))

   | hash_combterm (Bool(t),w) = hash_combterm (t,w)

   | hash_combterm (Equal(t1,t2),w) = 

     List.foldl hash_combterm (Polyhash.hashw_string ("equal",w)) [t1,t2]

 fun hash_literal (Literal(true,pred)) = hash_combterm(pred,0w0)

   | hash_literal (Literal(false,pred)) = Word.notb(hash_combterm(pred,0w0));

 fun hash_clause clause = xor_words (map hash_literal (get_literals clause));

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

 (* write clauses to files                                             *)

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

 fun read_in [] = []

   | read_in (f1::fs) =

     let val lines = read_in fs

 	val input = TextIO.openIn f1

 	fun reading () =

 	    let val nextline = TextIO.inputLine input

 	    in

 		if nextline = "" then (TextIO.closeIn input; [])

 		else nextline::(reading ())

 	    end

     in

 	((reading ()) @ lines)

     end;

 fun get_helper_clauses (full,partial,const,untyped) =

     let val (helper1,noS,inclS) = case !typ_level of T_FULL => (warning "Fully-typed HOL"; full)

 						   | T_PARTIAL => (warning "Partially-typed HOL"; partial)

 						   | T_CONST => (warning "Const-only-typed HOL"; const)

 						   | T_NONE => (warning "Untyped HOL"; untyped)

 	val needed_helpers = if !include_combS then (warning "Include combinator S"; [helper1,inclS]) else

 			     if !include_min_comb then (warning "Include min combinators"; [helper1,noS])

 			     else (warning "No combinator is used"; [helper1])

     in

 	read_in needed_helpers

     end;

 (* write TPTP format to a single file *)

 (* when "get_helper_clauses" is called, "include_combS" and "include_min_comb" should have correct values already *)

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

     let 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 ResClause.tptp_tfree_clause (foldl (op union_string) [] tfree_litss)

 	val out = TextIO.openOut filename

 	val helper_clauses = get_helper_clauses helpers

     in

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

 	ResClause.writeln_strs out tfree_clss;

 	ResClause.writeln_strs out tptp_clss;

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

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

 	List.app (curry TextIO.output out) helper_clauses;

 	TextIO.closeOut out

     end;

 end