src/HOL/Tools/res_hol_clause.ML
 author haftmann Fri Dec 16 09:00:11 2005 +0100 (2005-12-16) changeset 18418 bf448d999b7e parent 18356 443717b3a9ad child 18440 72ee07f4b56b permissions -rw-r--r--
re-arranged tuples (theory * 'a) to ('a * theory) in Pure
```     1 (* ID: \$Id\$
```
```     2    Author: Jia Meng, NICTA
```
```     3
```
```     4 FOL clauses translated from HOL formulae.  Combinators are used to represent lambda terms.
```
```     5
```
```     6 *)
```
```     7
```
```     8 structure ResHolClause =
```
```     9
```
```    10 struct
```
```    11
```
```    12
```
```    13 val include_combS = ref false;
```
```    14 val include_min_comb = ref false;
```
```    15
```
```    16 val const_typargs = ref (Library.K [] : (string*typ -> typ list));
```
```    17
```
```    18 fun init thy = (include_combS:=false;include_min_comb:=false;const_typargs := Sign.const_typargs thy);
```
```    19
```
```    20 (**********************************************************************)
```
```    21 (* convert a Term.term with lambdas into a Term.term with combinators *)
```
```    22 (**********************************************************************)
```
```    23
```
```    24 fun is_free (Bound(a)) n = (a = n)
```
```    25   | is_free (Abs(x,_,b)) n = (is_free b (n+1))
```
```    26   | is_free (P \$ Q) n = ((is_free P n) orelse (is_free Q n))
```
```    27   | is_free _ _ = false;
```
```    28
```
```    29
```
```    30 exception LAM2COMB of term;
```
```    31
```
```    32 exception BND of term;
```
```    33
```
```    34 fun decre_bndVar (Bound n) = Bound (n-1)
```
```    35   | decre_bndVar (P \$ Q) = (decre_bndVar P) \$ (decre_bndVar Q)
```
```    36   | decre_bndVar t =
```
```    37     case t of Const(_,_) => t
```
```    38 	    | Free(_,_) => t
```
```    39 	    | Var(_,_) => t
```
```    40 	    | Abs(_,_,_) => raise BND(t); (*should not occur*)
```
```    41
```
```    42
```
```    43 (*******************************************)
```
```    44 fun lam2comb (Abs(x,tp,Bound 0)) _ =
```
```    45     let val tpI = Type("fun",[tp,tp])
```
```    46     in
```
```    47 	include_min_comb:=true;
```
```    48 	Const("COMBI",tpI)
```
```    49     end
```
```    50   | lam2comb (Abs(x,tp,Bound n)) Bnds =
```
```    51     let val (Bound n') = decre_bndVar (Bound n)
```
```    52 	val tb = List.nth(Bnds,n')
```
```    53 	val tK = Type("fun",[tb,Type("fun",[tp,tb])])
```
```    54     in
```
```    55 	include_min_comb:=true;
```
```    56 	Const("COMBK",tK) \$ (Bound n')
```
```    57     end
```
```    58   | lam2comb (Abs(x,t1,Const(c,t2))) _ =
```
```    59     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
```
```    60     in
```
```    61 	include_min_comb:=true;
```
```    62 	Const("COMBK",tK) \$ Const(c,t2)
```
```    63     end
```
```    64   | lam2comb (Abs(x,t1,Free(v,t2))) _ =
```
```    65     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
```
```    66     in
```
```    67 	include_min_comb:=true;
```
```    68 	Const("COMBK",tK) \$ Free(v,t2)
```
```    69     end
```
```    70   | lam2comb (Abs(x,t1,Var(ind,t2))) _=
```
```    71     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
```
```    72     in
```
```    73 	include_min_comb:=true;
```
```    74 	Const("COMBK",tK) \$ Var(ind,t2)
```
```    75     end
```
```    76   | lam2comb (t as (Abs(x,t1,P\$(Bound 0)))) Bnds =
```
```    77     let val nfreeP = not(is_free P 0)
```
```    78 	val tr = Term.type_of1(t1::Bnds,P)
```
```    79     in
```
```    80 	if nfreeP then (decre_bndVar P)
```
```    81 	else (
```
```    82 	      let val tI = Type("fun",[t1,t1])
```
```    83 		  val P' = lam2comb (Abs(x,t1,P)) Bnds
```
```    84 		  val tp' = Term.type_of1(Bnds,P')
```
```    85 		  val tS = Type("fun",[tp',Type("fun",[tI,tr])])
```
```    86 	      in
```
```    87 		  include_min_comb:=true;
```
```    88 		  include_combS:=true;
```
```    89 		  Const("COMBS",tS) \$ P' \$ Const("COMBI",tI)
```
```    90 	      end)
```
```    91     end
```
```    92
```
```    93   | lam2comb (t as (Abs(x,t1,P\$Q))) Bnds =
```
```    94     let val (nfreeP,nfreeQ) = (not(is_free P 0),not(is_free Q 0))
```
```    95 	val tpq = Term.type_of1(t1::Bnds, P\$Q)
```
```    96     in
```
```    97 	if(nfreeP andalso nfreeQ) then (
```
```    98 	    let val tK = Type("fun",[tpq,Type("fun",[t1,tpq])])
```
```    99 		val PQ' = decre_bndVar(P \$ Q)
```
```   100 	    in
```
```   101 		include_min_comb:=true;
```
```   102 		Const("COMBK",tK) \$ PQ'
```
```   103 	    end)
```
```   104 	else (
```
```   105 	      if nfreeP then (
```
```   106 			       let val Q' = lam2comb (Abs(x,t1,Q)) Bnds
```
```   107 				   val P' = decre_bndVar P
```
```   108 				   val tp = Term.type_of1(Bnds,P')
```
```   109 				   val tq' = Term.type_of1(Bnds, Q')
```
```   110 				   val tB = Type("fun",[tp,Type("fun",[tq',Type("fun",[t1,tpq])])])
```
```   111 			       in
```
```   112 				   include_min_comb:=true;
```
```   113 				   Const("COMBB",tB) \$ P' \$ Q'
```
```   114 			       end)
```
```   115 	      else (
```
```   116 		    if nfreeQ then (
```
```   117 				    let val P' = lam2comb (Abs(x,t1,P)) Bnds
```
```   118 					val Q' = decre_bndVar Q
```
```   119 					val tq = Term.type_of1(Bnds,Q')
```
```   120 					val tp' = Term.type_of1(Bnds, P')
```
```   121 					val tC = Type("fun",[tp',Type("fun",[tq,Type("fun",[t1,tpq])])])
```
```   122 				    in
```
```   123 					include_min_comb:=true;
```
```   124 					Const("COMBC",tC) \$ P' \$ Q'
```
```   125 				    end)
```
```   126 		    else(
```
```   127 			 let val P' = lam2comb (Abs(x,t1,P)) Bnds
```
```   128 			     val Q' = lam2comb (Abs(x,t1,Q)) Bnds
```
```   129 			     val tp' = Term.type_of1(Bnds,P')
```
```   130 			     val tq' = Term.type_of1(Bnds,Q')
```
```   131 			     val tS = Type("fun",[tp',Type("fun",[tq',Type("fun",[t1,tpq])])])
```
```   132 			 in
```
```   133 			     include_min_comb:=true;
```
```   134 			     include_combS:=true;
```
```   135 			     Const("COMBS",tS) \$ P' \$ Q'
```
```   136 			 end)))
```
```   137     end
```
```   138   | lam2comb (t as (Abs(x,t1,_))) _ = raise LAM2COMB (t);
```
```   139
```
```   140
```
```   141
```
```   142 (*********************)
```
```   143
```
```   144 fun to_comb (Abs(x,tp,b)) Bnds =
```
```   145     let val b' = to_comb b (tp::Bnds)
```
```   146     in lam2comb (Abs(x,tp,b')) Bnds end
```
```   147   | to_comb (P \$ Q) Bnds = ((to_comb P Bnds) \$ (to_comb Q Bnds))
```
```   148   | to_comb t _ = t;
```
```   149
```
```   150
```
```   151 fun comb_of t = to_comb t [];
```
```   152
```
```   153
```
```   154 (* print a term containing combinators, used for debugging *)
```
```   155 exception TERM_COMB of term;
```
```   156
```
```   157 fun string_of_term (Const(c,t)) = c
```
```   158   | string_of_term (Free(v,t)) = v
```
```   159   | string_of_term (Var((x,n),t)) =
```
```   160     let val xn = x ^ "_" ^ (string_of_int n)
```
```   161     in xn end
```
```   162   | string_of_term (P \$ Q) =
```
```   163     let val P' = string_of_term P
```
```   164 	val Q' = string_of_term Q
```
```   165     in
```
```   166 	"(" ^ P' ^ " " ^ Q' ^ ")" end
```
```   167   | string_of_term t =  raise TERM_COMB (t);
```
```   168
```
```   169
```
```   170
```
```   171 (******************************************************)
```
```   172 (* data types for typed combinator expressions        *)
```
```   173 (******************************************************)
```
```   174
```
```   175 type axiom_name = string;
```
```   176 datatype kind = Axiom | Conjecture;
```
```   177 fun name_of_kind Axiom = "axiom"
```
```   178   | name_of_kind Conjecture = "conjecture";
```
```   179
```
```   180 type polarity = bool;
```
```   181 type indexname = Term.indexname;
```
```   182 type clause_id = int;
```
```   183 type csort = Term.sort;
```
```   184 type ctyp = string;
```
```   185
```
```   186 type ctyp_var = ResClause.typ_var;
```
```   187
```
```   188 type ctype_literal = ResClause.type_literal;
```
```   189
```
```   190
```
```   191 datatype combterm = CombConst of string * ctyp * ctyp list
```
```   192 		  | CombFree of string * ctyp
```
```   193 		  | CombVar of string * ctyp
```
```   194 		  | CombApp of combterm * combterm * ctyp
```
```   195 		  | Bool of combterm
```
```   196 		  | Equal of combterm * combterm;
```
```   197 datatype literal = Literal of polarity * combterm;
```
```   198
```
```   199
```
```   200
```
```   201 datatype clause =
```
```   202 	 Clause of {clause_id: clause_id,
```
```   203 		    axiom_name: axiom_name,
```
```   204 		    kind: kind,
```
```   205 		    literals: literal list,
```
```   206 		    ctypes_sorts: (ctyp_var * csort) list,
```
```   207                     ctvar_type_literals: ctype_literal list,
```
```   208                     ctfree_type_literals: ctype_literal list};
```
```   209
```
```   210
```
```   211
```
```   212 fun string_of_kind (Clause cls) = name_of_kind (#kind cls);
```
```   213 fun get_axiomName (Clause cls) = #axiom_name cls;
```
```   214 fun get_clause_id (Clause cls) = #clause_id cls;
```
```   215
```
```   216
```
```   217
```
```   218
```
```   219 (*********************************************************************)
```
```   220 (* convert a clause with type Term.term to a clause with type clause *)
```
```   221 (*********************************************************************)
```
```   222
```
```   223 fun isFalse (Literal(pol,Bool(CombConst(c,_,_)))) =
```
```   224     (pol andalso c = "c_False") orelse
```
```   225     (not pol andalso c = "c_True")
```
```   226   | isFalse _ = false;
```
```   227
```
```   228
```
```   229 fun isTrue (Literal (pol,Bool(CombConst(c,_,_)))) =
```
```   230       (pol andalso c = "c_True") orelse
```
```   231       (not pol andalso c = "c_False")
```
```   232   | isTrue _ = false;
```
```   233
```
```   234 fun isTaut (Clause {literals,...}) = exists isTrue literals;
```
```   235
```
```   236
```
```   237
```
```   238 fun make_clause(clause_id,axiom_name,kind,literals,ctypes_sorts,ctvar_type_literals,ctfree_type_literals) =
```
```   239     if forall isFalse literals
```
```   240     then error "Problem too trivial for resolution (empty clause)"
```
```   241     else
```
```   242 	Clause {clause_id = clause_id, axiom_name = axiom_name, kind = kind,
```
```   243 		literals = literals, ctypes_sorts = ctypes_sorts,
```
```   244 		ctvar_type_literals = ctvar_type_literals,
```
```   245 		ctfree_type_literals = ctfree_type_literals};
```
```   246
```
```   247 (* convert a Term.type to a string; gather sort information of type variables *)
```
```   248 fun type_of (Type (a, [])) = (ResClause.make_fixed_type_const a,[])
```
```   249   | type_of (Type (a, Ts)) =
```
```   250     let val typ_ts = map type_of Ts
```
```   251 	val (typs,tsorts) = ListPair.unzip typ_ts
```
```   252 	val ts = ResClause.union_all tsorts
```
```   253 	val t = ResClause.make_fixed_type_const a
```
```   254     in
```
```   255 	(t ^ (ResClause.paren_pack typs),ts)
```
```   256     end
```
```   257   | type_of (tp as (TFree (a,s))) = (ResClause.make_fixed_type_var a,[ResClause.mk_typ_var_sort tp])
```
```   258   | type_of (tp as (TVar (v,s))) = (ResClause.make_schematic_type_var v,[ResClause.mk_typ_var_sort tp]);
```
```   259
```
```   260
```
```   261
```
```   262 (* same as above, but no gathering of sort information *)
```
```   263 fun simp_type_of (Type (a, [])) = ResClause.make_fixed_type_const a
```
```   264   | simp_type_of (Type (a, Ts)) =
```
```   265     let val typs = map simp_type_of Ts
```
```   266 	val t = ResClause.make_fixed_type_const a
```
```   267     in
```
```   268 	t ^ ResClause.paren_pack typs
```
```   269     end
```
```   270   | simp_type_of (TFree (a,s)) = ResClause.make_fixed_type_var a
```
```   271   | simp_type_of (TVar (v,s)) = ResClause.make_schematic_type_var v;
```
```   272
```
```   273
```
```   274 fun comb_typ ("COMBI",t) =
```
```   275     let val t' = domain_type t
```
```   276     in
```
```   277 	[simp_type_of t']
```
```   278     end
```
```   279   | comb_typ ("COMBK",t) =
```
```   280     let val (ab,_) = strip_type t
```
```   281     in
```
```   282 	map simp_type_of ab
```
```   283     end
```
```   284   | comb_typ ("COMBS",t) =
```
```   285     let val t' = domain_type t
```
```   286 	val ([a,b],c) = strip_type t'
```
```   287     in
```
```   288 	map simp_type_of [a,b,c]
```
```   289     end
```
```   290   | comb_typ ("COMBB",t) =
```
```   291     let val ([ab,ca,c],b) = strip_type t
```
```   292 	val a = domain_type ab
```
```   293     in
```
```   294 	map simp_type_of [a,b,c]
```
```   295     end
```
```   296   | comb_typ ("COMBC",t) =
```
```   297     let val t1 = domain_type t
```
```   298 	val ([a,b],c) = strip_type t1
```
```   299     in
```
```   300 	map simp_type_of [a,b,c]
```
```   301     end;
```
```   302
```
```   303 fun const_type_of ("COMBI",t) =
```
```   304     let val (tp,ts) = type_of t
```
```   305 	val I_var = comb_typ ("COMBI",t)
```
```   306     in
```
```   307 	(tp,ts,I_var)
```
```   308     end
```
```   309   | const_type_of ("COMBK",t) =
```
```   310     let val (tp,ts) = type_of t
```
```   311 	val K_var = comb_typ ("COMBK",t)
```
```   312     in
```
```   313 	(tp,ts,K_var)
```
```   314     end
```
```   315   | const_type_of ("COMBS",t) =
```
```   316     let val (tp,ts) = type_of t
```
```   317 	val S_var = comb_typ ("COMBS",t)
```
```   318     in
```
```   319 	(tp,ts,S_var)
```
```   320     end
```
```   321   | const_type_of ("COMBB",t) =
```
```   322     let val (tp,ts) = type_of t
```
```   323 	val B_var = comb_typ ("COMBB",t)
```
```   324     in
```
```   325 	(tp,ts,B_var)
```
```   326     end
```
```   327   | const_type_of ("COMBC",t) =
```
```   328     let val (tp,ts) = type_of t
```
```   329 	val C_var = comb_typ ("COMBC",t)
```
```   330     in
```
```   331 	(tp,ts,C_var)
```
```   332     end
```
```   333   | const_type_of (c,t) =
```
```   334     let val (tp,ts) = type_of t
```
```   335 	val tvars = !const_typargs(c,t)
```
```   336 	val tvars' = map simp_type_of tvars
```
```   337     in
```
```   338 	(tp,ts,tvars')
```
```   339     end;
```
```   340
```
```   341 fun is_bool_type (Type("bool",[])) = true
```
```   342   | is_bool_type _ = false;
```
```   343
```
```   344
```
```   345 (* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
```
```   346 fun combterm_of (Const(c,t)) =
```
```   347     let val (tp,ts,tvar_list) = const_type_of (c,t)
```
```   348 	val is_bool = is_bool_type t
```
```   349 	val c' = CombConst(ResClause.make_fixed_const c,tp,tvar_list)
```
```   350 	val c'' = if is_bool then Bool(c') else c'
```
```   351     in
```
```   352 	(c'',ts)
```
```   353     end
```
```   354   | combterm_of (Free(v,t)) =
```
```   355     let val (tp,ts) = type_of t
```
```   356 	val is_bool = is_bool_type t
```
```   357 	val v' = if ResClause.isMeta v then CombVar(ResClause.make_schematic_var(v,0),tp)
```
```   358 		 else CombFree(ResClause.make_fixed_var v,tp)
```
```   359 	val v'' = if is_bool then Bool(v') else v'
```
```   360     in
```
```   361 	(v'',ts)
```
```   362     end
```
```   363   | combterm_of (Var(v,t)) =
```
```   364     let val (tp,ts) = type_of t
```
```   365 	val is_bool = is_bool_type t
```
```   366 	val v' = CombVar(ResClause.make_schematic_var v,tp)
```
```   367 	val v'' = if is_bool then Bool(v') else v'
```
```   368     in
```
```   369 	(v'',ts)
```
```   370     end
```
```   371   | combterm_of (Const("op =",T) \$ P \$ Q) = (*FIXME: allow equal between bools?*)
```
```   372     let val (P',tsP) = combterm_of P
```
```   373 	val (Q',tsQ) = combterm_of Q
```
```   374     in
```
```   375 	(Equal(P',Q'),tsP union tsQ)
```
```   376     end
```
```   377   | combterm_of (t as (P \$ Q)) =
```
```   378     let val (P',tsP) = combterm_of P
```
```   379 	val (Q',tsQ) = combterm_of Q
```
```   380 	val tp = Term.type_of t
```
```   381 	val tp' = simp_type_of tp
```
```   382 	val is_bool = is_bool_type tp
```
```   383 	val t' = CombApp(P',Q',tp')
```
```   384 	val t'' = if is_bool then Bool(t') else t'
```
```   385     in
```
```   386 	(t'',tsP union tsQ)
```
```   387     end;
```
```   388
```
```   389 fun predicate_of ((Const("Not",_) \$ P), polarity) =
```
```   390     predicate_of (P, not polarity)
```
```   391   | predicate_of (term,polarity) = (combterm_of term,polarity);
```
```   392
```
```   393
```
```   394 fun literals_of_term1 args (Const("Trueprop",_) \$ P) = literals_of_term1 args P
```
```   395   | literals_of_term1 args (Const("op |",_) \$ P \$ Q) =
```
```   396     let val args' = literals_of_term1 args P
```
```   397     in
```
```   398 	literals_of_term1 args' Q
```
```   399     end
```
```   400   | literals_of_term1 (lits,ts) P =
```
```   401     let val ((pred,ts'),pol) = predicate_of (P,true)
```
```   402 	val lits' = Literal(pol,pred)::lits
```
```   403     in
```
```   404 	(lits',ts union ts')
```
```   405     end;
```
```   406
```
```   407
```
```   408 fun literals_of_term P = literals_of_term1 ([],[]) P;
```
```   409
```
```   410
```
```   411 (* making axiom and conjecture clauses *)
```
```   412 fun make_axiom_clause term (ax_name,cls_id) =
```
```   413     let val term' = comb_of term
```
```   414 	val (lits,ctypes_sorts) = literals_of_term term'
```
```   415 	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux2 ctypes_sorts
```
```   416     in
```
```   417 	make_clause(cls_id,ax_name,Axiom,
```
```   418 		    lits,ctypes_sorts,ctvar_lits,ctfree_lits)
```
```   419     end;
```
```   420
```
```   421
```
```   422 fun make_conjecture_clause n t =
```
```   423     let val t' = comb_of t
```
```   424 	val (lits,ctypes_sorts) = literals_of_term t'
```
```   425 	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux2 ctypes_sorts
```
```   426     in
```
```   427 	make_clause(n,"conjecture",Conjecture,lits,ctypes_sorts,ctvar_lits,ctfree_lits)
```
```   428     end;
```
```   429
```
```   430
```
```   431
```
```   432 fun make_conjecture_clauses_aux _ [] = []
```
```   433   | make_conjecture_clauses_aux n (t::ts) =
```
```   434     make_conjecture_clause n t :: make_conjecture_clauses_aux (n+1) ts;
```
```   435
```
```   436 val make_conjecture_clauses = make_conjecture_clauses_aux 0;
```
```   437
```
```   438
```
```   439 (**********************************************************************)
```
```   440 (* convert clause into ATP specific formats:                          *)
```
```   441 (* TPTP used by Vampire and E                                         *)
```
```   442 (**********************************************************************)
```
```   443
```
```   444 val type_wrapper = "typeinfo";
```
```   445
```
```   446 datatype type_level = T_FULL | T_PARTIAL | T_CONST | T_NONE;
```
```   447
```
```   448 val typ_level = ref T_PARTIAL;
```
```   449
```
```   450 fun full_types () = (typ_level:=T_FULL);
```
```   451 fun partial_types () = (typ_level:=T_PARTIAL);
```
```   452 fun const_types_only () = (typ_level:=T_CONST);
```
```   453 fun no_types () = (typ_level:=T_NONE);
```
```   454
```
```   455
```
```   456 fun find_typ_level () = !typ_level;
```
```   457
```
```   458 fun wrap_type (c,t) =
```
```   459     case !typ_level of T_FULL => type_wrapper ^ (ResClause.paren_pack [c,t])
```
```   460 		     | _ => c;
```
```   461
```
```   462
```
```   463 val bool_tp = ResClause.make_fixed_type_const "bool";
```
```   464
```
```   465 val app_str = "hAPP";
```
```   466
```
```   467 val bool_str = "hBOOL";
```
```   468
```
```   469 exception STRING_OF_COMBTERM of int;
```
```   470
```
```   471 (* convert literals of clauses into strings *)
```
```   472 fun string_of_combterm1_aux _ (CombConst(c,tp,_)) = (wrap_type (c,tp),tp)
```
```   473   | string_of_combterm1_aux _ (CombFree(v,tp)) = (wrap_type (v,tp),tp)
```
```   474   | string_of_combterm1_aux _ (CombVar(v,tp)) = (wrap_type (v,tp),tp)
```
```   475   | string_of_combterm1_aux is_pred (CombApp(t1,t2,tp)) =
```
```   476     let val (s1,tp1) = string_of_combterm1_aux is_pred t1
```
```   477 	val (s2,tp2) = string_of_combterm1_aux is_pred t2
```
```   478 	val r =	case !typ_level of T_FULL => type_wrapper ^  (ResClause.paren_pack [(app_str ^ (ResClause.paren_pack [s1,s2])),tp])
```
```   479 				 | T_PARTIAL => app_str ^ (ResClause.paren_pack [s1,s2,tp1])
```
```   480 				 | T_NONE => app_str ^ (ResClause.paren_pack [s1,s2])
```
```   481 				 | T_CONST => raise STRING_OF_COMBTERM (1) (*should not happen, if happened may be a bug*)
```
```   482     in
```
```   483 	(r,tp)
```
```   484
```
```   485     end
```
```   486   | string_of_combterm1_aux is_pred (Bool(t)) =
```
```   487     let val (t',_) = string_of_combterm1_aux false t
```
```   488 	val r = if is_pred then bool_str ^ (ResClause.paren_pack [t'])
```
```   489 		else t'
```
```   490     in
```
```   491 	(r,bool_tp)
```
```   492     end
```
```   493   | string_of_combterm1_aux _ (Equal(t1,t2)) =
```
```   494     let val (s1,_) = string_of_combterm1_aux false t1
```
```   495 	val (s2,_) = string_of_combterm1_aux false t2
```
```   496     in
```
```   497 	("equal" ^ (ResClause.paren_pack [s1,s2]),bool_tp)
```
```   498     end;
```
```   499
```
```   500 fun string_of_combterm1 is_pred term = fst (string_of_combterm1_aux is_pred term);
```
```   501
```
```   502 fun string_of_combterm2 _ (CombConst(c,tp,tvars)) = c ^ (ResClause.paren_pack tvars)
```
```   503   | string_of_combterm2 _ (CombFree(v,tp)) = v
```
```   504   | string_of_combterm2 _ (CombVar(v,tp)) = v
```
```   505   | string_of_combterm2 is_pred (CombApp(t1,t2,tp)) =
```
```   506     let val s1 = string_of_combterm2 is_pred t1
```
```   507 	val s2 = string_of_combterm2 is_pred t2
```
```   508     in
```
```   509 	app_str ^ (ResClause.paren_pack [s1,s2])
```
```   510     end
```
```   511   | string_of_combterm2 is_pred (Bool(t)) =
```
```   512     let val t' = string_of_combterm2 false t
```
```   513     in
```
```   514 	if is_pred then bool_str ^ (ResClause.paren_pack [t'])
```
```   515 	else t'
```
```   516     end
```
```   517   | string_of_combterm2 _ (Equal(t1,t2)) =
```
```   518     let val s1 = string_of_combterm2 false t1
```
```   519 	val s2 = string_of_combterm2 false t2
```
```   520     in
```
```   521 	("equal" ^ (ResClause.paren_pack [s1,s2]))
```
```   522     end;
```
```   523
```
```   524
```
```   525
```
```   526 fun string_of_combterm is_pred term =
```
```   527     case !typ_level of T_CONST => string_of_combterm2 is_pred term
```
```   528 		     | _ => string_of_combterm1 is_pred term;
```
```   529
```
```   530
```
```   531 fun string_of_clausename (cls_id,ax_name) =
```
```   532     ResClause.clause_prefix ^ ResClause.ascii_of ax_name ^ "_" ^ Int.toString cls_id;
```
```   533
```
```   534 fun string_of_type_clsname (cls_id,ax_name,idx) =
```
```   535     string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);
```
```   536
```
```   537
```
```   538 fun tptp_literal (Literal(pol,pred)) =
```
```   539     let val pred_string = string_of_combterm true pred
```
```   540 	val pol_str = if pol then "++" else "--"
```
```   541     in
```
```   542 	pol_str ^ pred_string
```
```   543     end;
```
```   544
```
```   545
```
```   546 fun tptp_type_lits (Clause cls) =
```
```   547     let val lits = map tptp_literal (#literals cls)
```
```   548 	val ctvar_lits_strs =
```
```   549 	    case !typ_level of T_NONE => []
```
```   550 			     | _ => (map ResClause.tptp_of_typeLit (#ctvar_type_literals cls))
```
```   551 	val ctfree_lits =
```
```   552 	    case !typ_level of T_NONE => []
```
```   553 			     | _ => (map ResClause.tptp_of_typeLit (#ctfree_type_literals cls))
```
```   554     in
```
```   555 	(ctvar_lits_strs @ lits, ctfree_lits)
```
```   556     end;
```
```   557
```
```   558
```
```   559 fun clause2tptp cls =
```
```   560     let val (lits,ctfree_lits) = tptp_type_lits cls
```
```   561 	val cls_id = get_clause_id cls
```
```   562 	val ax_name = get_axiomName cls
```
```   563 	val knd = string_of_kind cls
```
```   564 	val lits_str = ResClause.bracket_pack lits
```
```   565 	val cls_str = ResClause.gen_tptp_cls(cls_id,ax_name,knd,lits_str)
```
```   566     in
```
```   567 	(cls_str,ctfree_lits)
```
```   568     end;
```
```   569
```
```   570
```
`   571 end`