mengj@17998: (* ID: $Id$ 
mengj@17998:    Author: Jia Meng, NICTA
mengj@17998: 
mengj@17998: FOL clauses translated from HOL formulae.  Combinators are used to represent lambda terms.
mengj@17998: 
mengj@17998: *)
mengj@17998: 
mengj@17998: structure ResHolClause =
mengj@17998: 
mengj@17998: struct
mengj@17998: 
mengj@17998: 
mengj@18276: val include_combS = ref false;
mengj@18276: val include_min_comb = ref false;
mengj@17998: 
mengj@18356: val const_typargs = ref (Library.K [] : (string*typ -> typ list));
mengj@18356: 
mengj@18356: fun init thy = (include_combS:=false;include_min_comb:=false;const_typargs := Sign.const_typargs thy);
mengj@17998: 
mengj@19198: 
mengj@19198: 
mengj@17998: (**********************************************************************)
mengj@17998: (* convert a Term.term with lambdas into a Term.term with combinators *) 
mengj@17998: (**********************************************************************)
mengj@17998: 
mengj@17998: fun is_free (Bound(a)) n = (a = n)
mengj@17998:   | is_free (Abs(x,_,b)) n = (is_free b (n+1))
mengj@17998:   | is_free (P $ Q) n = ((is_free P n) orelse (is_free Q n))
mengj@17998:   | is_free _ _ = false;
mengj@17998: 
mengj@17998: 
mengj@17998: exception LAM2COMB of term;
mengj@17998: 
mengj@17998: exception BND of term;
mengj@17998: 
mengj@17998: fun decre_bndVar (Bound n) = Bound (n-1)
mengj@17998:   | decre_bndVar (P $ Q) = (decre_bndVar P) $ (decre_bndVar Q)
mengj@17998:   | decre_bndVar t =
mengj@17998:     case t of Const(_,_) => t
mengj@17998: 	    | Free(_,_) => t
mengj@17998: 	    | Var(_,_) => t
mengj@17998: 	    | Abs(_,_,_) => raise BND(t); (*should not occur*)
mengj@17998: 
mengj@17998: 
mengj@17998: (*******************************************)
mengj@17998: fun lam2comb (Abs(x,tp,Bound 0)) _ = 
mengj@17998:     let val tpI = Type("fun",[tp,tp])
mengj@17998:     in 
mengj@18276: 	include_min_comb:=true;
mengj@17998: 	Const("COMBI",tpI) 
mengj@17998:     end
mengj@18356:   | lam2comb (Abs(x,tp,Bound n)) Bnds = 
mengj@18356:     let val (Bound n') = decre_bndVar (Bound n)
mengj@18356: 	val tb = List.nth(Bnds,n')
mengj@18356: 	val tK = Type("fun",[tb,Type("fun",[tp,tb])])
mengj@18356:     in
mengj@18356: 	include_min_comb:=true;
mengj@18356: 	Const("COMBK",tK) $ (Bound n')
mengj@18356:     end
mengj@17998:   | lam2comb (Abs(x,t1,Const(c,t2))) _ = 
mengj@17998:     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
mengj@17998:     in 
mengj@18276: 	include_min_comb:=true;
mengj@17998: 	Const("COMBK",tK) $ Const(c,t2) 
mengj@17998:     end
mengj@17998:   | lam2comb (Abs(x,t1,Free(v,t2))) _ =
mengj@17998:     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
mengj@17998:     in
mengj@18276: 	include_min_comb:=true;
mengj@17998: 	Const("COMBK",tK) $ Free(v,t2)
mengj@17998:     end
mengj@17998:   | lam2comb (Abs(x,t1,Var(ind,t2))) _=
mengj@17998:     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
mengj@17998:     in
mengj@18276: 	include_min_comb:=true;
mengj@17998: 	Const("COMBK",tK) $ Var(ind,t2)
mengj@17998:     end
mengj@17998:   | lam2comb (t as (Abs(x,t1,P$(Bound 0)))) Bnds =
mengj@17998:     let val nfreeP = not(is_free P 0)
mengj@17998: 	val tr = Term.type_of1(t1::Bnds,P)
mengj@17998:     in
mengj@17998: 	if nfreeP then (decre_bndVar P)
mengj@17998: 	else (
mengj@17998: 	      let val tI = Type("fun",[t1,t1])
mengj@17998: 		  val P' = lam2comb (Abs(x,t1,P)) Bnds
mengj@17998: 		  val tp' = Term.type_of1(Bnds,P')
mengj@17998: 		  val tS = Type("fun",[tp',Type("fun",[tI,tr])])
mengj@17998: 	      in
mengj@18276: 		  include_min_comb:=true;
mengj@18276: 		  include_combS:=true;
mengj@17998: 		  Const("COMBS",tS) $ P' $ Const("COMBI",tI)
mengj@17998: 	      end)
mengj@17998:     end
mengj@17998: 	    
mengj@17998:   | lam2comb (t as (Abs(x,t1,P$Q))) Bnds =
mengj@17998:     let val (nfreeP,nfreeQ) = (not(is_free P 0),not(is_free Q 0))
mengj@17998: 	val tpq = Term.type_of1(t1::Bnds, P$Q) 
mengj@17998:     in
mengj@17998: 	if(nfreeP andalso nfreeQ) then (
mengj@17998: 	    let val tK = Type("fun",[tpq,Type("fun",[t1,tpq])])
mengj@17998: 		val PQ' = decre_bndVar(P $ Q)
mengj@17998: 	    in 
mengj@18276: 		include_min_comb:=true;
mengj@17998: 		Const("COMBK",tK) $ PQ'
mengj@17998: 	    end)
mengj@17998: 	else (
mengj@17998: 	      if nfreeP then (
mengj@17998: 			       let val Q' = lam2comb (Abs(x,t1,Q)) Bnds
mengj@17998: 				   val P' = decre_bndVar P
mengj@17998: 				   val tp = Term.type_of1(Bnds,P')
mengj@17998: 				   val tq' = Term.type_of1(Bnds, Q')
mengj@17998: 				   val tB = Type("fun",[tp,Type("fun",[tq',Type("fun",[t1,tpq])])])
mengj@17998: 			       in
mengj@18276: 				   include_min_comb:=true;
mengj@17998: 				   Const("COMBB",tB) $ P' $ Q' 
mengj@17998: 			       end)
mengj@17998: 	      else (
mengj@17998: 		    if nfreeQ then (
mengj@17998: 				    let val P' = lam2comb (Abs(x,t1,P)) Bnds
mengj@17998: 					val Q' = decre_bndVar Q
mengj@17998: 					val tq = Term.type_of1(Bnds,Q')
mengj@17998: 					val tp' = Term.type_of1(Bnds, P')
mengj@17998: 					val tC = Type("fun",[tp',Type("fun",[tq,Type("fun",[t1,tpq])])])
mengj@17998: 				    in
mengj@18276: 					include_min_comb:=true;
mengj@17998: 					Const("COMBC",tC) $ P' $ Q'
mengj@17998: 				    end)
mengj@17998: 		    else(
mengj@17998: 			 let val P' = lam2comb (Abs(x,t1,P)) Bnds
mengj@17998: 			     val Q' = lam2comb (Abs(x,t1,Q)) Bnds
mengj@17998: 			     val tp' = Term.type_of1(Bnds,P')
mengj@17998: 			     val tq' = Term.type_of1(Bnds,Q')
mengj@17998: 			     val tS = Type("fun",[tp',Type("fun",[tq',Type("fun",[t1,tpq])])])
mengj@17998: 			 in
mengj@18276: 			     include_min_comb:=true;
mengj@18276: 			     include_combS:=true;
mengj@17998: 			     Const("COMBS",tS) $ P' $ Q'
mengj@17998: 			 end)))
mengj@17998:     end
mengj@17998:   | lam2comb (t as (Abs(x,t1,_))) _ = raise LAM2COMB (t);
mengj@17998: 
mengj@17998: 	     
mengj@17998: 
mengj@17998: (*********************)
mengj@17998: 
mengj@17998: fun to_comb (Abs(x,tp,b)) Bnds =
mengj@17998:     let val b' = to_comb b (tp::Bnds)
mengj@17998:     in lam2comb (Abs(x,tp,b')) Bnds end
mengj@17998:   | to_comb (P $ Q) Bnds = ((to_comb P Bnds) $ (to_comb Q Bnds))
mengj@17998:   | to_comb t _ = t;
mengj@17998:  
mengj@17998:     
mengj@17998: fun comb_of t = to_comb t [];
mengj@17998: 
mengj@17998: 
mengj@17998: (* print a term containing combinators, used for debugging *)
mengj@17998: exception TERM_COMB of term;
mengj@17998: 
mengj@17998: fun string_of_term (Const(c,t)) = c
mengj@17998:   | string_of_term (Free(v,t)) = v
mengj@17998:   | string_of_term (Var((x,n),t)) =
mengj@17998:     let val xn = x ^ "_" ^ (string_of_int n)
mengj@17998:     in xn end
mengj@17998:   | string_of_term (P $ Q) =
mengj@17998:     let val P' = string_of_term P
mengj@17998: 	val Q' = string_of_term Q
mengj@17998:     in
mengj@17998: 	"(" ^ P' ^ " " ^ Q' ^ ")" end
mengj@17998:   | string_of_term t =  raise TERM_COMB (t);
mengj@17998: 
mengj@17998: 
mengj@17998: 
mengj@17998: (******************************************************)
mengj@17998: (* data types for typed combinator expressions        *)
mengj@17998: (******************************************************)
mengj@17998: 
mengj@17998: type axiom_name = string;
mengj@17998: datatype kind = Axiom | Conjecture;
mengj@17998: fun name_of_kind Axiom = "axiom"
mengj@17998:   | name_of_kind Conjecture = "conjecture";
mengj@17998: 
mengj@17998: type polarity = bool;
mengj@17998: type indexname = Term.indexname;
mengj@17998: type clause_id = int;
mengj@17998: type csort = Term.sort;
mengj@18440: type ctyp = ResClause.fol_type;
mengj@18440: 
mengj@18440: val string_of_ctyp = ResClause.string_of_fol_type;
mengj@17998: 
mengj@17998: type ctyp_var = ResClause.typ_var;
mengj@17998: 
mengj@17998: type ctype_literal = ResClause.type_literal;
mengj@17998: 
mengj@17998: 
mengj@18356: datatype combterm = CombConst of string * ctyp * ctyp list
mengj@17998: 		  | CombFree of string * ctyp
mengj@17998: 		  | CombVar of string * ctyp
mengj@17998: 		  | CombApp of combterm * combterm * ctyp
mengj@17998: 		  | Bool of combterm
mengj@17998: 		  | Equal of combterm * combterm;
mengj@17998: datatype literal = Literal of polarity * combterm;
mengj@17998: 
mengj@17998: 
mengj@17998: 
mengj@17998: datatype clause = 
mengj@17998: 	 Clause of {clause_id: clause_id,
mengj@17998: 		    axiom_name: axiom_name,
mengj@17998: 		    kind: kind,
mengj@17998: 		    literals: literal list,
mengj@17998: 		    ctypes_sorts: (ctyp_var * csort) list, 
mengj@17998:                     ctvar_type_literals: ctype_literal list, 
mengj@17998:                     ctfree_type_literals: ctype_literal list};
mengj@17998: 
mengj@17998: 
mengj@17998: 
mengj@17998: fun string_of_kind (Clause cls) = name_of_kind (#kind cls);
mengj@17998: fun get_axiomName (Clause cls) = #axiom_name cls;
mengj@17998: fun get_clause_id (Clause cls) = #clause_id cls;
mengj@17998: 
mengj@18440: fun get_literals (c as Clause(cls)) = #literals cls;
mengj@17998: 
mengj@17998: 
mengj@17998: 
mengj@18440: exception TERM_ORD of string
mengj@18440: 
mengj@18440: fun term_ord (CombVar(_,_),CombVar(_,_)) = EQUAL
mengj@18440:   | term_ord (CombVar(_,_),_) = LESS
mengj@18440:   | term_ord (CombFree(_,_),CombVar(_,_)) = GREATER
mengj@18440:   | term_ord (CombFree(f1,tp1),CombFree(f2,tp2)) = 
mengj@18440:     let val ord1 = string_ord(f1,f2)
mengj@18440:     in
mengj@18440: 	case ord1 of EQUAL => ResClause.types_ord ([tp1],[tp2])
mengj@18440: 		   | _ => ord1
mengj@18440:     end
mengj@18440:   | term_ord (CombFree(_,_),_) = LESS
mengj@18440:   | term_ord (CombConst(_,_,_),CombVar(_,_)) = GREATER
mengj@18440:   | term_ord (CombConst(_,_,_),CombFree(_,_)) = GREATER
mengj@18440:   | term_ord (CombConst(c1,tp1,_),CombConst(c2,tp2,_)) = 
mengj@18440:     let val ord1 = string_ord (c1,c2)
mengj@18440:     in
mengj@18440: 	case ord1 of EQUAL => ResClause.types_ord ([tp1],[tp2])
mengj@18440: 		   | _ => ord1
mengj@18440:     end
mengj@18440:   | term_ord (CombConst(_,_,_),_) = LESS
mengj@18440:   | term_ord (CombApp(_,_,_),Bool(_)) = raise TERM_ORD("bool")
mengj@18440:   | term_ord (CombApp(_,_,_),Equal(_,_)) = LESS
mengj@18440:   | term_ord (CombApp(f1,arg1,tp1),CombApp(f2,arg2,tp2)) =
mengj@18440:     let val ord1 = term_ord (f1,f2)
mengj@18440: 	val ord2 = case ord1 of EQUAL => term_ord (arg1,arg2)
mengj@18440: 			      | _ => ord1
mengj@18440:     in
mengj@18440: 	case ord2 of EQUAL => ResClause.types_ord ([tp1],[tp2])
mengj@18440: 		   | _ => ord2
mengj@18440:     end
mengj@18440:   | term_ord (CombApp(_,_,_),_) = GREATER
mengj@18440:   | term_ord (Bool(_),_) = raise TERM_ORD("bool")
mengj@18440:   | term_ord (Equal(t1,t2),Equal(t3,t4)) = ResClause.list_ord term_ord ([t1,t2],[t3,t4])
mengj@18440:   | term_ord (Equal(_,_),_) = GREATER;
mengj@18440: 
mengj@18440: fun predicate_ord (Equal(_,_),Bool(_)) = LESS
mengj@18440:   | predicate_ord (Equal(t1,t2),Equal(t3,t4)) = 
mengj@18440:     ResClause.list_ord term_ord ([t1,t2],[t3,t4])
mengj@18440:   | predicate_ord (Bool(_),Equal(_,_)) = GREATER
mengj@18440:   | predicate_ord (Bool(t1),Bool(t2)) = term_ord (t1,t2)
mengj@18440: 
mengj@18440: 
mengj@18440: fun literal_ord (Literal(false,_),Literal(true,_)) = LESS
mengj@18440:   | literal_ord (Literal(true,_),Literal(false,_)) = GREATER
mengj@18440:   | literal_ord (Literal(_,pred1),Literal(_,pred2)) = predicate_ord(pred1,pred2);
mengj@18440: 
mengj@18440: fun sort_lits lits = sort literal_ord lits;
mengj@18440: 
mengj@17998: (*********************************************************************)
mengj@17998: (* convert a clause with type Term.term to a clause with type clause *)
mengj@17998: (*********************************************************************)
mengj@17998: 
mengj@18356: fun isFalse (Literal(pol,Bool(CombConst(c,_,_)))) =
mengj@17998:     (pol andalso c = "c_False") orelse
mengj@17998:     (not pol andalso c = "c_True")
mengj@17998:   | isFalse _ = false;
mengj@17998: 
mengj@17998: 
mengj@18356: fun isTrue (Literal (pol,Bool(CombConst(c,_,_)))) =
mengj@17998:       (pol andalso c = "c_True") orelse
mengj@17998:       (not pol andalso c = "c_False")
mengj@17998:   | isTrue _ = false;
mengj@17998:   
mengj@17998: fun isTaut (Clause {literals,...}) = exists isTrue literals;  
mengj@17998: 
mengj@17998: 
mengj@17998: 
mengj@17998: fun make_clause(clause_id,axiom_name,kind,literals,ctypes_sorts,ctvar_type_literals,ctfree_type_literals) =
mengj@17998:     if forall isFalse literals
mengj@17998:     then error "Problem too trivial for resolution (empty clause)"
mengj@17998:     else
mengj@17998: 	Clause {clause_id = clause_id, axiom_name = axiom_name, kind = kind,
mengj@17998: 		literals = literals, ctypes_sorts = ctypes_sorts, 
mengj@17998: 		ctvar_type_literals = ctvar_type_literals,
mengj@17998: 		ctfree_type_literals = ctfree_type_literals};
mengj@17998: 
mengj@18440: fun type_of (Type (a, Ts)) =
mengj@18440:     let val (folTypes,ts) = types_of Ts
mengj@17998: 	val t = ResClause.make_fixed_type_const a
mengj@17998:     in
mengj@18440: 	(ResClause.mk_fol_type("Comp",t,folTypes),ts)
mengj@17998:     end
mengj@18440:   | type_of (tp as (TFree(a,s))) =
mengj@18440:     let val t = ResClause.make_fixed_type_var a
mengj@18440:     in
mengj@18440: 	(ResClause.mk_fol_type("Fixed",t,[]),[ResClause.mk_typ_var_sort tp])
mengj@18440:     end
mengj@18440:   | type_of (tp as (TVar(v,s))) =
mengj@18440:     let val t = ResClause.make_schematic_type_var v
mengj@18440:     in
mengj@18440: 	(ResClause.mk_fol_type("Var",t,[]),[ResClause.mk_typ_var_sort tp])
mengj@18440:     end
mengj@18356: 
mengj@18440: and types_of Ts =
mengj@18440:     let val foltyps_ts = map type_of Ts
mengj@18440: 	val (folTyps,ts) = ListPair.unzip foltyps_ts
mengj@18440:     in
mengj@18440: 	(folTyps,ResClause.union_all ts)
mengj@18440:     end;
mengj@17998: 
mengj@17998: (* same as above, but no gathering of sort information *)
mengj@18440: fun simp_type_of (Type (a, Ts)) = 
mengj@18356:     let val typs = map simp_type_of Ts
mengj@17998: 	val t = ResClause.make_fixed_type_const a
mengj@17998:     in
mengj@18440: 	ResClause.mk_fol_type("Comp",t,typs)
mengj@17998:     end
mengj@18440:   | simp_type_of (TFree (a,s)) = ResClause.mk_fol_type("Fixed",ResClause.make_fixed_type_var a,[])
mengj@18440:   | simp_type_of (TVar (v,s)) = ResClause.mk_fol_type("Var",ResClause.make_schematic_type_var v,[]);
mengj@18440: 
mengj@18356: fun comb_typ ("COMBI",t) = 
mengj@18356:     let val t' = domain_type t
mengj@18356:     in
mengj@18356: 	[simp_type_of t']
mengj@18356:     end
mengj@18356:   | comb_typ ("COMBK",t) = 
mengj@18725:     let val a = domain_type t
mengj@18725: 	val b = domain_type (range_type t)
mengj@18356:     in
mengj@18725: 	map simp_type_of [a,b]
mengj@18356:     end
mengj@18356:   | comb_typ ("COMBS",t) = 
mengj@18356:     let val t' = domain_type t
mengj@18725: 	val a = domain_type t'
mengj@18725: 	val b = domain_type (range_type t')
mengj@18725: 	val c = range_type (range_type t')
mengj@18356:     in 
mengj@18356: 	map simp_type_of [a,b,c]
mengj@18356:     end
mengj@18356:   | comb_typ ("COMBB",t) = 
mengj@18725:     let val ab = domain_type t
mengj@18725: 	val ca = domain_type (range_type t)
mengj@18356: 	val a = domain_type ab
mengj@18725: 	val b = range_type ab
mengj@18725: 	val c = domain_type ca
mengj@18356:     in
mengj@18356: 	map simp_type_of [a,b,c]
mengj@18356:     end
mengj@18356:   | comb_typ ("COMBC",t) =
mengj@18356:     let val t1 = domain_type t
mengj@18725: 	val a = domain_type t1
mengj@18725: 	val b = domain_type (range_type t1)
mengj@18725: 	val c = range_type (range_type t1)
mengj@18356:     in
mengj@18356: 	map simp_type_of [a,b,c]
mengj@18356:     end;
mengj@18356: 
mengj@18356: fun const_type_of ("COMBI",t) = 
mengj@18356:     let val (tp,ts) = type_of t
mengj@18356: 	val I_var = comb_typ ("COMBI",t)
mengj@18356:     in
mengj@18356: 	(tp,ts,I_var)
mengj@18356:     end
mengj@18356:   | const_type_of ("COMBK",t) =
mengj@18356:     let val (tp,ts) = type_of t
mengj@18356: 	val K_var = comb_typ ("COMBK",t)
mengj@18356:     in
mengj@18356: 	(tp,ts,K_var)
mengj@18356:     end
mengj@18356:   | const_type_of ("COMBS",t) =
mengj@18356:     let val (tp,ts) = type_of t
mengj@18356: 	val S_var = comb_typ ("COMBS",t)
mengj@18356:     in
mengj@18356: 	(tp,ts,S_var)
mengj@18356:     end
mengj@18356:   | const_type_of ("COMBB",t) =
mengj@18356:     let val (tp,ts) = type_of t
mengj@18356: 	val B_var = comb_typ ("COMBB",t)
mengj@18356:     in
mengj@18356: 	(tp,ts,B_var)
mengj@18356:     end
mengj@18356:   | const_type_of ("COMBC",t) =
mengj@18356:     let val (tp,ts) = type_of t
mengj@18356: 	val C_var = comb_typ ("COMBC",t)
mengj@18356:     in
mengj@18356: 	(tp,ts,C_var)
mengj@18356:     end
mengj@18356:   | const_type_of (c,t) =
mengj@18356:     let val (tp,ts) = type_of t
mengj@18356: 	val tvars = !const_typargs(c,t)
mengj@18356: 	val tvars' = map simp_type_of tvars
mengj@18356:     in
mengj@18356: 	(tp,ts,tvars')
mengj@18356:     end;
mengj@18356: 
mengj@18356: fun is_bool_type (Type("bool",[])) = true
mengj@18356:   | is_bool_type _ = false;
mengj@17998: 
mengj@17998: 
mengj@17998: (* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
mengj@17998: fun combterm_of (Const(c,t)) =
mengj@18356:     let val (tp,ts,tvar_list) = const_type_of (c,t)
mengj@18356: 	val is_bool = is_bool_type t
mengj@18356: 	val c' = CombConst(ResClause.make_fixed_const c,tp,tvar_list)
mengj@17998: 	val c'' = if is_bool then Bool(c') else c'
mengj@17998:     in
mengj@17998: 	(c'',ts)
mengj@17998:     end
mengj@17998:   | combterm_of (Free(v,t)) =
mengj@18356:     let val (tp,ts) = type_of t
mengj@18356: 	val is_bool = is_bool_type t
mengj@17998: 	val v' = if ResClause.isMeta v then CombVar(ResClause.make_schematic_var(v,0),tp)
mengj@17998: 		 else CombFree(ResClause.make_fixed_var v,tp)
mengj@17998: 	val v'' = if is_bool then Bool(v') else v'
mengj@17998:     in
mengj@17998: 	(v'',ts)
mengj@17998:     end
mengj@17998:   | combterm_of (Var(v,t)) =
mengj@18356:     let val (tp,ts) = type_of t
mengj@18356: 	val is_bool = is_bool_type t
mengj@17998: 	val v' = CombVar(ResClause.make_schematic_var v,tp)
mengj@17998: 	val v'' = if is_bool then Bool(v') else v'
mengj@17998:     in
mengj@17998: 	(v'',ts)
mengj@17998:     end
mengj@17998:   | combterm_of (Const("op =",T) $ P $ Q) = (*FIXME: allow equal between bools?*)
mengj@17998:     let val (P',tsP) = combterm_of P        
mengj@17998: 	val (Q',tsQ) = combterm_of Q
mengj@17998:     in
mengj@17998: 	(Equal(P',Q'),tsP union tsQ)
mengj@17998:     end
mengj@17998:   | combterm_of (t as (P $ Q)) =
mengj@17998:     let val (P',tsP) = combterm_of P
mengj@17998: 	val (Q',tsQ) = combterm_of Q
mengj@17998: 	val tp = Term.type_of t
mengj@18356: 	val tp' = simp_type_of tp
mengj@18356: 	val is_bool = is_bool_type tp
mengj@17998: 	val t' = CombApp(P',Q',tp')
mengj@17998: 	val t'' = if is_bool then Bool(t') else t'
mengj@17998:     in
mengj@17998: 	(t'',tsP union tsQ)
mengj@17998:     end;
mengj@17998: 
mengj@17998: fun predicate_of ((Const("Not",_) $ P), polarity) =
mengj@17998:     predicate_of (P, not polarity)
mengj@17998:   | predicate_of (term,polarity) = (combterm_of term,polarity);
mengj@17998: 
mengj@17998: 
mengj@17998: fun literals_of_term1 args (Const("Trueprop",_) $ P) = literals_of_term1 args P
mengj@17998:   | literals_of_term1 args (Const("op |",_) $ P $ Q) = 
mengj@17998:     let val args' = literals_of_term1 args P
mengj@17998:     in
mengj@17998: 	literals_of_term1 args' Q
mengj@17998:     end
mengj@17998:   | literals_of_term1 (lits,ts) P =
mengj@17998:     let val ((pred,ts'),pol) = predicate_of (P,true)
mengj@17998: 	val lits' = Literal(pol,pred)::lits
mengj@17998:     in
mengj@17998: 	(lits',ts union ts')
mengj@17998:     end;
mengj@17998: 
mengj@17998: 
mengj@17998: fun literals_of_term P = literals_of_term1 ([],[]) P;
mengj@17998: 
mengj@17998: 
mengj@17998: (* making axiom and conjecture clauses *)
mengj@19444: fun make_axiom_clause thm (ax_name,cls_id) =
mengj@19444:     let val term = prop_of thm
mengj@19444: 	val term' = comb_of term
mengj@17998: 	val (lits,ctypes_sorts) = literals_of_term term'
mengj@18440: 	val lits' = sort_lits lits
paulson@18856: 	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux ctypes_sorts
mengj@17998:     in
mengj@17998: 	make_clause(cls_id,ax_name,Axiom,
mengj@18440: 		    lits',ctypes_sorts,ctvar_lits,ctfree_lits)
mengj@17998:     end;
mengj@17998: 
mengj@19444: fun make_axiom_clauses [] = []
mengj@19444:   | make_axiom_clauses ((thm,(name,id))::thms) =
mengj@19444:     let val cls = make_axiom_clause thm (name,id)
mengj@19444: 	val clss = make_axiom_clauses thms
mengj@19198:     in
mengj@19198: 	if isTaut cls then clss else (cls::clss)
mengj@19198:     end;
mengj@17998: 
mengj@19354: 
mengj@19444: fun make_conjecture_clause n thm =
mengj@19444:     let val t = prop_of thm
mengj@19444: 	val t' = comb_of t
mengj@17998: 	val (lits,ctypes_sorts) = literals_of_term t'
paulson@18856: 	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux ctypes_sorts
mengj@17998:     in
mengj@17998: 	make_clause(n,"conjecture",Conjecture,lits,ctypes_sorts,ctvar_lits,ctfree_lits)
mengj@17998:     end;
mengj@17998: 
mengj@17998: 
mengj@17998: 
mengj@17998: fun make_conjecture_clauses_aux _ [] = []
mengj@17998:   | make_conjecture_clauses_aux n (t::ts) =
mengj@17998:     make_conjecture_clause n t :: make_conjecture_clauses_aux (n+1) ts;
mengj@17998: 
mengj@17998: val make_conjecture_clauses = make_conjecture_clauses_aux 0;
mengj@17998: 
mengj@17998: 
mengj@17998: (**********************************************************************)
mengj@17998: (* convert clause into ATP specific formats:                          *)
mengj@17998: (* TPTP used by Vampire and E                                         *)
mengj@17998: (**********************************************************************)
mengj@17998: 
mengj@17998: val type_wrapper = "typeinfo";
mengj@17998: 
mengj@18356: datatype type_level = T_FULL | T_PARTIAL | T_CONST | T_NONE;
mengj@17998: 
mengj@19130: val typ_level = ref T_FULL;
mengj@18356: 
mengj@18356: fun full_types () = (typ_level:=T_FULL);
mengj@18356: fun partial_types () = (typ_level:=T_PARTIAL);
mengj@18356: fun const_types_only () = (typ_level:=T_CONST);
mengj@18356: fun no_types () = (typ_level:=T_NONE);
mengj@18356: 
mengj@18356: 
mengj@18356: fun find_typ_level () = !typ_level;
mengj@18356: 
mengj@18356: fun wrap_type (c,t) = 
mengj@18356:     case !typ_level of T_FULL => type_wrapper ^ (ResClause.paren_pack [c,t])
mengj@18356: 		     | _ => c;
mengj@18356:     
mengj@17998: 
mengj@17998: val bool_tp = ResClause.make_fixed_type_const "bool";
mengj@17998: 
mengj@17998: val app_str = "hAPP";
mengj@17998: 
mengj@17998: val bool_str = "hBOOL";
mengj@17998: 
mengj@18356: exception STRING_OF_COMBTERM of int;
mengj@17998: 
mengj@17998: (* convert literals of clauses into strings *)
mengj@18440: fun string_of_combterm1_aux _ (CombConst(c,tp,_)) = 
mengj@18440:     let val tp' = string_of_ctyp tp
mengj@18440:     in
mengj@18440: 	(wrap_type (c,tp'),tp')
mengj@18440:     end
mengj@18440:   | string_of_combterm1_aux _ (CombFree(v,tp)) = 
mengj@18440:     let val tp' = string_of_ctyp tp
mengj@18440:     in
mengj@18440: 	(wrap_type (v,tp'),tp')
mengj@18440:     end
mengj@18440:   | string_of_combterm1_aux _ (CombVar(v,tp)) = 
mengj@18440:     let val tp' = string_of_ctyp tp
mengj@18440:     in
mengj@18440: 	(wrap_type (v,tp'),tp')
mengj@18440:     end
mengj@18356:   | string_of_combterm1_aux is_pred (CombApp(t1,t2,tp)) =
mengj@18356:     let val (s1,tp1) = string_of_combterm1_aux is_pred t1
mengj@18356: 	val (s2,tp2) = string_of_combterm1_aux is_pred t2
mengj@18440: 	val tp' = ResClause.string_of_fol_type tp
mengj@18440: 	val r =	case !typ_level of T_FULL => type_wrapper ^  (ResClause.paren_pack [(app_str ^ (ResClause.paren_pack [s1,s2])),tp'])
mengj@18356: 				 | T_PARTIAL => app_str ^ (ResClause.paren_pack [s1,s2,tp1])
mengj@18356: 				 | T_NONE => app_str ^ (ResClause.paren_pack [s1,s2])
mengj@18356: 				 | T_CONST => raise STRING_OF_COMBTERM (1) (*should not happen, if happened may be a bug*)
mengj@18440:     in	(r,tp')
mengj@18356: 
mengj@17998:     end
mengj@18356:   | string_of_combterm1_aux is_pred (Bool(t)) = 
mengj@18356:     let val (t',_) = string_of_combterm1_aux false t
mengj@18356: 	val r = if is_pred then bool_str ^ (ResClause.paren_pack [t'])
mengj@18356: 		else t'
mengj@18356:     in
mengj@18356: 	(r,bool_tp)
mengj@18356:     end
mengj@18356:   | string_of_combterm1_aux _ (Equal(t1,t2)) =
mengj@18356:     let val (s1,_) = string_of_combterm1_aux false t1
mengj@18356: 	val (s2,_) = string_of_combterm1_aux false t2
mengj@18356:     in
mengj@18356: 	("equal" ^ (ResClause.paren_pack [s1,s2]),bool_tp) 
mengj@18356:     end;
mengj@18356: 
mengj@18356: fun string_of_combterm1 is_pred term = fst (string_of_combterm1_aux is_pred term);
mengj@18356: 
mengj@18440: fun string_of_combterm2 _ (CombConst(c,tp,tvars)) = 
mengj@18440:     let val tvars' = map string_of_ctyp tvars
mengj@18440:     in
mengj@18440: 	c ^ (ResClause.paren_pack tvars')
mengj@18440:     end
mengj@18356:   | string_of_combterm2 _ (CombFree(v,tp)) = v
mengj@18356:   | string_of_combterm2 _ (CombVar(v,tp)) = v
mengj@18356:   | string_of_combterm2 is_pred (CombApp(t1,t2,tp)) =
mengj@18356:     let val s1 = string_of_combterm2 is_pred t1
mengj@18356: 	val s2 = string_of_combterm2 is_pred t2
mengj@18356:     in
mengj@18356: 	app_str ^ (ResClause.paren_pack [s1,s2])
mengj@18356:     end
mengj@18356:   | string_of_combterm2 is_pred (Bool(t)) = 
mengj@18356:     let val t' = string_of_combterm2 false t
mengj@17998:     in
mengj@18200: 	if is_pred then bool_str ^ (ResClause.paren_pack [t'])
mengj@18200: 	else t'
mengj@17998:     end
mengj@18356:   | string_of_combterm2 _ (Equal(t1,t2)) =
mengj@18356:     let val s1 = string_of_combterm2 false t1
mengj@18356: 	val s2 = string_of_combterm2 false t2
mengj@17998:     in
mengj@18356: 	("equal" ^ (ResClause.paren_pack [s1,s2])) 
mengj@17998:     end;
mengj@17998: 
mengj@18356: 
mengj@18356: 
mengj@18356: fun string_of_combterm is_pred term = 
mengj@18356:     case !typ_level of T_CONST => string_of_combterm2 is_pred term
mengj@18356: 		     | _ => string_of_combterm1 is_pred term;
mengj@18356: 
mengj@18356: 
mengj@17998: fun string_of_clausename (cls_id,ax_name) = 
mengj@17998:     ResClause.clause_prefix ^ ResClause.ascii_of ax_name ^ "_" ^ Int.toString cls_id;
mengj@17998: 
mengj@17998: fun string_of_type_clsname (cls_id,ax_name,idx) = 
mengj@17998:     string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);
mengj@17998: 
mengj@17998: 
mengj@17998: fun tptp_literal (Literal(pol,pred)) =
mengj@18200:     let val pred_string = string_of_combterm true pred
mengj@17998: 	val pol_str = if pol then "++" else "--"
mengj@17998:     in
mengj@17998: 	pol_str ^ pred_string
mengj@17998:     end;
mengj@17998: 
mengj@17998:  
mengj@17998: fun tptp_type_lits (Clause cls) = 
mengj@17998:     let val lits = map tptp_literal (#literals cls)
mengj@17998: 	val ctvar_lits_strs =
mengj@18356: 	    case !typ_level of T_NONE => []
mengj@18356: 			     | _ => (map ResClause.tptp_of_typeLit (#ctvar_type_literals cls)) 
mengj@17998: 	val ctfree_lits = 
mengj@18356: 	    case !typ_level of T_NONE => []
mengj@18356: 			     | _ => (map ResClause.tptp_of_typeLit (#ctfree_type_literals cls)) 
mengj@17998:     in
mengj@17998: 	(ctvar_lits_strs @ lits, ctfree_lits)
mengj@17998:     end; 
mengj@18356:     
mengj@18356:     
mengj@17998: fun clause2tptp cls =
mengj@17998:     let val (lits,ctfree_lits) = tptp_type_lits cls
mengj@17998: 	val cls_id = get_clause_id cls
mengj@17998: 	val ax_name = get_axiomName cls
mengj@17998: 	val knd = string_of_kind cls
mengj@17998: 	val lits_str = ResClause.bracket_pack lits
mengj@17998: 	val cls_str = ResClause.gen_tptp_cls(cls_id,ax_name,knd,lits_str)
mengj@17998:     in
mengj@17998: 	(cls_str,ctfree_lits)
mengj@17998:     end;
mengj@17998: 
mengj@17998: 
mengj@18440: 
mengj@18440: (**********************************************************************)
mengj@18440: (* clause equalities and hashing functions                            *)
mengj@18440: (**********************************************************************)
mengj@18440: 
mengj@18440: 
mengj@18440: fun combterm_eq (CombConst(c1,tp1,tps1),CombConst(c2,tp2,tps2)) vtvars =
mengj@18440:     let val (eq1,vtvars1) = if c1 = c2 then ResClause.types_eq (tps1,tps2) vtvars
mengj@18440: 			    else (false,vtvars)
mengj@18440:     in
mengj@18440: 	(eq1,vtvars1)
mengj@18440:     end
mengj@18440:   | combterm_eq (CombConst(_,_,_),_) vtvars = (false,vtvars)
mengj@18440:   | combterm_eq (CombFree(a1,tp1),CombFree(a2,tp2)) vtvars = 
mengj@18440:     if a1 = a2 then ResClause.types_eq ([tp1],[tp2]) vtvars
mengj@18440:     else (false,vtvars)
mengj@18440:   | combterm_eq (CombFree(_,_),_) vtvars = (false,vtvars)
mengj@18440:   | combterm_eq (CombVar(v1,tp1),CombVar(v2,tp2)) (vars,tvars) = 
mengj@18440:     (case ResClause.check_var_pairs(v1,v2) vars of 0 => ResClause.types_eq ([tp1],[tp2]) ((v1,v2)::vars,tvars)
mengj@18440: 						 | 1 => ResClause.types_eq ([tp1],[tp2]) (vars,tvars)
mengj@18440: 						 | 2 => (false,(vars,tvars)))
mengj@18440:   | combterm_eq (CombVar(_,_),_) vtvars = (false,vtvars)
mengj@18440:   | combterm_eq (CombApp(f1,arg1,tp1),CombApp(f2,arg2,tp2)) vtvars =
mengj@18440:     let val (eq1,vtvars1) = combterm_eq (f1,f2) vtvars
mengj@18440: 	val (eq2,vtvars2) = if eq1 then combterm_eq (arg1,arg2) vtvars1
mengj@18440: 			    else (eq1,vtvars1)
mengj@18440:     in
mengj@18440: 	if eq2 then ResClause.types_eq ([tp1],[tp2]) vtvars2
mengj@18440: 	else (eq2,vtvars2)
mengj@18440:     end
mengj@18440:   | combterm_eq (CombApp(_,_,_),_) vtvars = (false,vtvars)
mengj@18440:   | combterm_eq (Bool(t1),Bool(t2)) vtvars = combterm_eq (t1,t2) vtvars
mengj@18440:   | combterm_eq (Bool(_),_) vtvars = (false,vtvars)
mengj@18440:   | combterm_eq (Equal(t1,t2),Equal(t3,t4)) vtvars =
mengj@18440:     let val (eq1,vtvars1) = combterm_eq (t1,t3) vtvars
mengj@18440:     in
mengj@18440: 	if eq1 then combterm_eq (t2,t4) vtvars1
mengj@18440: 	else (eq1,vtvars1)
mengj@18440:     end
mengj@18440:   | combterm_eq (Equal(t1,t2),_) vtvars = (false,vtvars);
mengj@18440: 
mengj@18440: fun lit_eq (Literal(pol1,pred1),Literal(pol2,pred2)) vtvars =
mengj@18440:     if (pol1 = pol2) then combterm_eq (pred1,pred2) vtvars
mengj@18440:     else (false,vtvars);
mengj@18440: 
mengj@18440: fun lits_eq ([],[]) vtvars = (true,vtvars)
mengj@18440:   | lits_eq (l1::ls1,l2::ls2) vtvars = 
mengj@18440:     let val (eq1,vtvars1) = lit_eq (l1,l2) vtvars
mengj@18440:     in
mengj@18440: 	if eq1 then lits_eq (ls1,ls2) vtvars1
mengj@18440: 	else (false,vtvars1)
mengj@18440:     end;
mengj@18440: 
mengj@18440: fun clause_eq (cls1,cls2) =
mengj@18440:     let val lits1 = get_literals cls1
mengj@18440: 	val lits2 = get_literals cls2
mengj@18440:     in
mengj@18440: 	length lits1 = length lits2 andalso #1 (lits_eq (lits1,lits2) ([],[]))
mengj@18440:     end;
mengj@18440: 
mengj@18440: val xor_words = List.foldl Word.xorb 0w0;
mengj@18440: 
mengj@18440: fun hash_combterm (CombVar(_,_),w) = w
paulson@18449:   | hash_combterm (CombFree(f,_),w) = Polyhash.hashw_string(f,w)
paulson@18449:   | hash_combterm (CombConst(c,tp,tps),w) = Polyhash.hashw_string(c,w)
paulson@18449:   | hash_combterm (CombApp(f,arg,tp),w) = hash_combterm (arg, hash_combterm (f,w))
mengj@18440:   | hash_combterm (Bool(t),w) = hash_combterm (t,w)
mengj@18440:   | hash_combterm (Equal(t1,t2),w) = 
paulson@18449:     List.foldl hash_combterm (Polyhash.hashw_string ("equal",w)) [t1,t2]
mengj@18440: 
mengj@18440: fun hash_literal (Literal(true,pred)) = hash_combterm(pred,0w0)
mengj@18440:   | hash_literal (Literal(false,pred)) = Word.notb(hash_combterm(pred,0w0));
mengj@18440: 
mengj@18440: fun hash_clause clause = xor_words (map hash_literal (get_literals clause));
mengj@18440: 
mengj@19198: (**********************************************************************)
mengj@19198: (* write clauses to files                                             *)
mengj@19198: (**********************************************************************)
mengj@19198: 
mengj@19198: fun read_in [] = []
mengj@19198:   | read_in (f1::fs) =
mengj@19198:     let val lines = read_in fs
mengj@19198: 	val input = TextIO.openIn f1
mengj@19198: 	fun reading () =
mengj@19198: 	    let val nextline = TextIO.inputLine input
mengj@19198: 	    in
mengj@19198: 		if nextline = "" then (TextIO.closeIn input; [])
mengj@19198: 		else nextline::(reading ())
mengj@19198: 	    end
mengj@19198:     in
mengj@19198: 	((reading ()) @ lines)
mengj@19198:     end;
mengj@19198: 
mengj@19198:  
mengj@19198: fun get_helper_clauses (full,partial,const,untyped) =
mengj@19198:     let val (helper1,noS,inclS) = case !typ_level of T_FULL => (warning "Fully-typed HOL"; full)
mengj@19198: 						   | T_PARTIAL => (warning "Partially-typed HOL"; partial)
mengj@19198: 						   | T_CONST => (warning "Const-only-typed HOL"; const)
mengj@19198: 						   | T_NONE => (warning "Untyped HOL"; untyped)
mengj@19198: 	val needed_helpers = if !include_combS then (warning "Include combinator S"; [helper1,inclS]) else
mengj@19198: 			     if !include_min_comb then (warning "Include min combinators"; [helper1,noS])
mengj@19198: 			     else (warning "No combinator is used"; [helper1])
mengj@19198:     in
mengj@19198: 	read_in needed_helpers
mengj@19198:     end;
mengj@19198: 
mengj@19198: 
mengj@19198: (* write TPTP format to a single file *)
mengj@19198: (* when "get_helper_clauses" is called, "include_combS" and "include_min_comb" should have correct values already *)
mengj@19444: fun tptp_write_file thms filename (axclauses,classrel_clauses,arity_clauses) helpers =
mengj@19444:     let val clss = make_conjecture_clauses thms
mengj@19444: 	val axclauses' = make_axiom_clauses axclauses
mengj@19198: 	val (tptp_clss,tfree_litss) = ListPair.unzip (map clause2tptp clss)
mengj@19198: 	val tfree_clss = map ResClause.tptp_tfree_clause (foldl (op union_string) [] tfree_litss)
mengj@19198: 	val out = TextIO.openOut filename
mengj@19198: 	val helper_clauses = get_helper_clauses helpers
mengj@19198:     in
mengj@19198: 	List.app (curry TextIO.output out o #1 o clause2tptp) axclauses';
mengj@19198: 	ResClause.writeln_strs out tfree_clss;
mengj@19198: 	ResClause.writeln_strs out tptp_clss;
mengj@19198: 	List.app (curry TextIO.output out o ResClause.tptp_classrelClause) classrel_clauses;
mengj@19198: 	List.app (curry TextIO.output out o ResClause.tptp_arity_clause) arity_clauses;
mengj@19198: 	List.app (curry TextIO.output out) helper_clauses;
mengj@19198: 	TextIO.closeOut out
mengj@19198:     end;
mengj@19198: 
mengj@17998: end