(* 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