src/HOL/Tools/res_hol_clause.ML
 author paulson Tue Oct 10 15:30:48 2006 +0200 (2006-10-10) changeset 20953 1ea394dc2a0f parent 20865 2cfa020109c1 child 20997 4b500d78cb4f permissions -rw-r--r--
Combinators require the theory name; added settings for SPASS
```     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 (* theorems for combinators and function extensionality *)
```
```    13 val ext = thm "HOL.ext";
```
```    14 val comb_I = thm "Reconstruction.COMBI_def";
```
```    15 val comb_K = thm "Reconstruction.COMBK_def";
```
```    16 val comb_B = thm "Reconstruction.COMBB_def";
```
```    17 val comb_C = thm "Reconstruction.COMBC_def";
```
```    18 val comb_S = thm "Reconstruction.COMBS_def";
```
```    19 val comb_B' = thm "Reconstruction.COMBB'_def";
```
```    20 val comb_C' = thm "Reconstruction.COMBC'_def";
```
```    21 val comb_S' = thm "Reconstruction.COMBS'_def";
```
```    22 val fequal_imp_equal = thm "Reconstruction.fequal_imp_equal";
```
```    23 val equal_imp_fequal = thm "Reconstruction.equal_imp_fequal";
```
```    24
```
```    25
```
```    26 (* a flag to set if we use extra combinators B',C',S' *)
```
```    27 val use_combB'C'S' = ref true;
```
```    28
```
```    29 val combI_count = ref 0;
```
```    30 val combK_count = ref 0;
```
```    31 val combB_count = ref 0;
```
```    32 val combC_count = ref 0;
```
```    33 val combS_count = ref 0;
```
```    34
```
```    35 val combB'_count = ref 0;
```
```    36 val combC'_count = ref 0;
```
```    37 val combS'_count = ref 0;
```
```    38
```
```    39
```
```    40 fun increI count_comb =  if count_comb then combI_count := !combI_count + 1 else ();
```
```    41 fun increK count_comb =  if count_comb then combK_count := !combK_count + 1 else ();
```
```    42 fun increB count_comb =  if count_comb then combB_count := !combB_count + 1 else ();
```
```    43 fun increC count_comb =  if count_comb then combC_count := !combC_count + 1 else ();
```
```    44 fun increS count_comb =  if count_comb then combS_count := !combS_count + 1 else ();
```
```    45 fun increB' count_comb =  if count_comb then combB'_count := !combB'_count + 1 else ();
```
```    46 fun increC' count_comb =  if count_comb then combC'_count := !combC'_count + 1 else ();
```
```    47 fun increS' count_comb =  if count_comb then combS'_count := !combS'_count + 1 else ();
```
```    48
```
```    49
```
```    50 exception DECRE_COMB of string;
```
```    51 fun decreB count_comb n =
```
```    52   if count_comb then
```
```    53     if !combB_count >= n then combB_count := !combB_count - n else raise DECRE_COMB "COMBB"
```
```    54   else ();
```
```    55
```
```    56 fun decreC count_comb n =
```
```    57   if count_comb then
```
```    58     if !combC_count >= n then combC_count := !combC_count - n else raise DECRE_COMB "COMBC"
```
```    59   else ();
```
```    60
```
```    61 fun decreS count_comb n =
```
```    62   if count_comb then
```
```    63     if !combS_count >= n then combS_count := !combS_count - n else raise DECRE_COMB "COMBS"
```
```    64   else ();
```
```    65
```
```    66 val const_typargs = ref (Library.K [] : (string*typ -> typ list));
```
```    67
```
```    68 fun init thy = (combI_count:=0; combK_count:=0;combB_count:=0;combC_count:=0;combS_count:=0;combB'_count:=0;combC'_count:=0;combS'_count:=0;
```
```    69                 const_typargs := Sign.const_typargs thy);
```
```    70
```
```    71 (**********************************************************************)
```
```    72 (* convert a Term.term with lambdas into a Term.term with combinators *)
```
```    73 (**********************************************************************)
```
```    74
```
```    75 fun is_free (Bound(a)) n = (a = n)
```
```    76   | is_free (Abs(x,_,b)) n = (is_free b (n+1))
```
```    77   | is_free (P \$ Q) n = ((is_free P n) orelse (is_free Q n))
```
```    78   | is_free _ _ = false;
```
```    79
```
```    80
```
```    81 exception BND of term;
```
```    82
```
```    83 fun decre_bndVar (Bound n) = Bound (n-1)
```
```    84   | decre_bndVar (P \$ Q) = (decre_bndVar P) \$ (decre_bndVar Q)
```
```    85   | decre_bndVar t =
```
```    86     case t of Const(_,_) => t
```
```    87 	    | Free(_,_) => t
```
```    88 	    | Var(_,_) => t
```
```    89 	    | Abs(_,_,_) => raise BND(t); (*should not occur*)
```
```    90
```
```    91
```
```    92 (*******************************************)
```
```    93 fun mk_compact_comb (tm as (Const("Reconstruction.COMBB",_)\$p) \$ (Const("Reconstruction.COMBB",_)\$q\$r)) Bnds count_comb =
```
```    94     let val tp_p = Term.type_of1(Bnds,p)
```
```    95 	val tp_q = Term.type_of1(Bnds,q)
```
```    96 	val tp_r = Term.type_of1(Bnds,r)
```
```    97 	val typ = Term.type_of1(Bnds,tm)
```
```    98 	val typ_B' = [tp_p,tp_q,tp_r] ---> typ
```
```    99 	val _ = increB' count_comb
```
```   100 	val _ = decreB count_comb 2
```
```   101     in
```
```   102 	Const("Reconstruction.COMBB'",typ_B') \$ p \$ q \$ r
```
```   103     end
```
```   104   | mk_compact_comb (tm as (Const("Reconstruction.COMBC",_) \$ (Const("Reconstruction.COMBB",_)\$p\$q) \$ r)) Bnds count_comb =
```
```   105     let val tp_p = Term.type_of1(Bnds,p)
```
```   106 	val tp_q = Term.type_of1(Bnds,q)
```
```   107 	val tp_r = Term.type_of1(Bnds,r)
```
```   108 	val typ = Term.type_of1(Bnds,tm)
```
```   109 	val typ_C' = [tp_p,tp_q,tp_r] ---> typ
```
```   110 	val _ = increC' count_comb
```
```   111 	val _ = decreC count_comb 1
```
```   112 	val _ = decreB count_comb 1
```
```   113     in
```
```   114 	Const("Reconstruction.COMBC'",typ_C') \$ p \$ q \$ r
```
```   115     end
```
```   116   | mk_compact_comb (tm as (Const("Reconstruction.COMBS",_) \$ (Const("Reconstruction.COMBB",_)\$p\$q) \$ r)) Bnds count_comb =
```
```   117     let val tp_p = Term.type_of1(Bnds,p)
```
```   118 	val tp_q = Term.type_of1(Bnds,q)
```
```   119 	val tp_r = Term.type_of1(Bnds,r)
```
```   120 	val typ = Term.type_of1(Bnds,tm)
```
```   121 	val typ_S' = [tp_p,tp_q,tp_r] ---> typ
```
```   122 	val _ = increS' count_comb
```
```   123 	val _ = decreS count_comb 1
```
```   124 	val _ = decreB count_comb 1
```
```   125     in
```
```   126 	Const("Reconstruction.COMBS'",typ_S') \$ p \$ q \$ r
```
```   127     end
```
```   128   | mk_compact_comb tm _ _ = tm;
```
```   129
```
```   130 fun compact_comb t Bnds count_comb = if !use_combB'C'S' then mk_compact_comb t Bnds count_comb else t;
```
```   131
```
```   132 fun lam2comb (Abs(x,tp,Bound 0)) _ count_comb =
```
```   133     let val tpI = Type("fun",[tp,tp])
```
```   134 	val _ = increI count_comb
```
```   135     in
```
```   136 	Const("Reconstruction.COMBI",tpI)
```
```   137     end
```
```   138   | lam2comb (Abs(x,tp,Bound n)) Bnds count_comb =
```
```   139     let val (Bound n') = decre_bndVar (Bound n)
```
```   140 	val tb = List.nth(Bnds,n')
```
```   141 	val tK = Type("fun",[tb,Type("fun",[tp,tb])])
```
```   142 	val _ = increK count_comb
```
```   143     in
```
```   144 	Const("Reconstruction.COMBK",tK) \$ (Bound n')
```
```   145     end
```
```   146   | lam2comb (Abs(x,t1,Const(c,t2))) _ count_comb =
```
```   147     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
```
```   148 	val _ = increK count_comb
```
```   149     in
```
```   150 	Const("Reconstruction.COMBK",tK) \$ Const(c,t2)
```
```   151     end
```
```   152   | lam2comb (Abs(x,t1,Free(v,t2))) _ count_comb =
```
```   153     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
```
```   154 	val _ = increK count_comb
```
```   155     in
```
```   156 	Const("Reconstruction.COMBK",tK) \$ Free(v,t2)
```
```   157     end
```
```   158   | lam2comb (Abs(x,t1,Var(ind,t2))) _ count_comb =
```
```   159     let val tK = Type("fun",[t2,Type("fun",[t1,t2])])
```
```   160 	val _ = increK count_comb
```
```   161     in
```
```   162 	Const("Reconstruction.COMBK",tK) \$ Var(ind,t2)
```
```   163     end
```
```   164   | lam2comb (t as (Abs(x,t1,P\$(Bound 0)))) Bnds count_comb =
```
```   165     let val nfreeP = not(is_free P 0)
```
```   166 	val tr = Term.type_of1(t1::Bnds,P)
```
```   167     in
```
```   168 	if nfreeP then (decre_bndVar P)
```
```   169 	else (
```
```   170 	      let val tI = Type("fun",[t1,t1])
```
```   171 		  val P' = lam2comb (Abs(x,t1,P)) Bnds count_comb
```
```   172 		  val tp' = Term.type_of1(Bnds,P')
```
```   173 		  val tS = Type("fun",[tp',Type("fun",[tI,tr])])
```
```   174 		  val _ = increI count_comb
```
```   175 		  val _ = increS count_comb
```
```   176 	      in
```
```   177 		  compact_comb (Const("Reconstruction.COMBS",tS) \$ P' \$ Const("Reconstruction.COMBI",tI)) Bnds count_comb
```
```   178 	      end)
```
```   179     end
```
```   180
```
```   181   | lam2comb (t as (Abs(x,t1,P\$Q))) Bnds count_comb =
```
```   182     let val (nfreeP,nfreeQ) = (not(is_free P 0),not(is_free Q 0))
```
```   183 	val tpq = Term.type_of1(t1::Bnds, P\$Q)
```
```   184     in
```
```   185 	if(nfreeP andalso nfreeQ) then (
```
```   186 	    let val tK = Type("fun",[tpq,Type("fun",[t1,tpq])])
```
```   187 		val PQ' = decre_bndVar(P \$ Q)
```
```   188 		val _ = increK count_comb
```
```   189 	    in
```
```   190 		Const("Reconstruction.COMBK",tK) \$ PQ'
```
```   191 	    end)
```
```   192 	else (
```
```   193 	      if nfreeP then (
```
```   194 			       let val Q' = lam2comb (Abs(x,t1,Q)) Bnds count_comb
```
```   195 				   val P' = decre_bndVar P
```
```   196 				   val tp = Term.type_of1(Bnds,P')
```
```   197 				   val tq' = Term.type_of1(Bnds, Q')
```
```   198 				   val tB = Type("fun",[tp,Type("fun",[tq',Type("fun",[t1,tpq])])])
```
```   199 				   val _ = increB count_comb
```
```   200 			       in
```
```   201 				   compact_comb (Const("Reconstruction.COMBB",tB) \$ P' \$ Q') Bnds count_comb
```
```   202 			       end)
```
```   203 	      else (
```
```   204 		    if nfreeQ then (
```
```   205 				    let val P' = lam2comb (Abs(x,t1,P)) Bnds count_comb
```
```   206 					val Q' = decre_bndVar Q
```
```   207 					val tq = Term.type_of1(Bnds,Q')
```
```   208 					val tp' = Term.type_of1(Bnds, P')
```
```   209 					val tC = Type("fun",[tp',Type("fun",[tq,Type("fun",[t1,tpq])])])
```
```   210 					val _ = increC count_comb
```
```   211 				    in
```
```   212 					compact_comb (Const("Reconstruction.COMBC",tC) \$ P' \$ Q') Bnds count_comb
```
```   213 				    end)
```
```   214 		    else(
```
```   215 			 let val P' = lam2comb (Abs(x,t1,P)) Bnds count_comb
```
```   216 			     val Q' = lam2comb (Abs(x,t1,Q)) Bnds count_comb
```
```   217 			     val tp' = Term.type_of1(Bnds,P')
```
```   218 			     val tq' = Term.type_of1(Bnds,Q')
```
```   219 			     val tS = Type("fun",[tp',Type("fun",[tq',Type("fun",[t1,tpq])])])
```
```   220 			     val _ = increS count_comb
```
```   221 			 in
```
```   222 			     compact_comb (Const("Reconstruction.COMBS",tS) \$ P' \$ Q') Bnds count_comb
```
```   223 			 end)))
```
```   224     end
```
```   225   | lam2comb (t as (Abs(x,t1,_))) _ _ = raise ResClause.CLAUSE("HOL CLAUSE",t);
```
```   226
```
```   227 (*********************)
```
```   228
```
```   229 fun to_comb (Abs(x,tp,b)) Bnds count_comb =
```
```   230     let val b' = to_comb b (tp::Bnds) count_comb
```
```   231     in lam2comb (Abs(x,tp,b')) Bnds count_comb end
```
```   232   | to_comb (P \$ Q) Bnds count_comb = ((to_comb P Bnds count_comb) \$ (to_comb Q Bnds count_comb))
```
```   233   | to_comb t _ _ = t;
```
```   234
```
```   235
```
```   236 fun comb_of t count_comb = to_comb t [] count_comb;
```
```   237
```
```   238 (* print a term containing combinators, used for debugging *)
```
```   239 exception TERM_COMB of term;
```
```   240
```
```   241 fun string_of_term (Const(c,t)) = c
```
```   242   | string_of_term (Free(v,t)) = v
```
```   243   | string_of_term (Var((x,n),t)) = x ^ "_" ^ (string_of_int n)
```
```   244   | string_of_term (P \$ Q) =
```
```   245       "(" ^ string_of_term P ^ " " ^ string_of_term Q ^ ")"
```
```   246   | string_of_term t =  raise TERM_COMB (t);
```
```   247
```
```   248
```
```   249
```
```   250 (******************************************************)
```
```   251 (* data types for typed combinator expressions        *)
```
```   252 (******************************************************)
```
```   253
```
```   254 datatype type_level = T_FULL | T_PARTIAL | T_CONST | T_NONE;
```
```   255
```
```   256 val typ_level = ref T_CONST;
```
```   257
```
```   258 fun full_types () = (typ_level:=T_FULL);
```
```   259 fun partial_types () = (typ_level:=T_PARTIAL);
```
```   260 fun const_types_only () = (typ_level:=T_CONST);
```
```   261 fun no_types () = (typ_level:=T_NONE);
```
```   262
```
```   263
```
```   264 fun find_typ_level () = !typ_level;
```
```   265
```
```   266
```
```   267 type axiom_name = string;
```
```   268 datatype kind = Axiom | Conjecture;
```
```   269
```
```   270 fun name_of_kind Axiom = "axiom"
```
```   271   | name_of_kind Conjecture = "conjecture";
```
```   272
```
```   273 type polarity = bool;
```
```   274 type indexname = Term.indexname;
```
```   275 type clause_id = int;
```
```   276 type csort = Term.sort;
```
```   277 type ctyp = ResClause.fol_type;
```
```   278
```
```   279 val string_of_ctyp = ResClause.string_of_fol_type;
```
```   280
```
```   281 type ctyp_var = ResClause.typ_var;
```
```   282
```
```   283 type ctype_literal = ResClause.type_literal;
```
```   284
```
```   285
```
```   286 datatype combterm = CombConst of string * ctyp * ctyp list
```
```   287 		  | CombFree of string * ctyp
```
```   288 		  | CombVar of string * ctyp
```
```   289 		  | CombApp of combterm * combterm * ctyp
```
```   290 		  | Bool of combterm;
```
```   291
```
```   292 datatype literal = Literal of polarity * combterm;
```
```   293
```
```   294 datatype clause =
```
```   295 	 Clause of {clause_id: clause_id,
```
```   296 		    axiom_name: axiom_name,
```
```   297 		    th: thm,
```
```   298 		    kind: kind,
```
```   299 		    literals: literal list,
```
```   300 		    ctypes_sorts: (ctyp_var * csort) list,
```
```   301                     ctvar_type_literals: ctype_literal list,
```
```   302                     ctfree_type_literals: ctype_literal list};
```
```   303
```
```   304
```
```   305 fun string_of_kind (Clause cls) = name_of_kind (#kind cls);
```
```   306 fun get_axiomName (Clause cls) = #axiom_name cls;
```
```   307 fun get_clause_id (Clause cls) = #clause_id cls;
```
```   308
```
```   309 fun get_literals (c as Clause(cls)) = #literals cls;
```
```   310
```
```   311
```
```   312 (*********************************************************************)
```
```   313 (* convert a clause with type Term.term to a clause with type clause *)
```
```   314 (*********************************************************************)
```
```   315
```
```   316 fun isFalse (Literal(pol,Bool(CombConst(c,_,_)))) =
```
```   317       (pol andalso c = "c_False") orelse
```
```   318       (not pol andalso c = "c_True")
```
```   319   | isFalse _ = false;
```
```   320
```
```   321
```
```   322 fun isTrue (Literal (pol,Bool(CombConst(c,_,_)))) =
```
```   323       (pol andalso c = "c_True") orelse
```
```   324       (not pol andalso c = "c_False")
```
```   325   | isTrue _ = false;
```
```   326
```
```   327 fun isTaut (Clause {literals,...}) = exists isTrue literals;
```
```   328
```
```   329 fun type_of (Type (a, Ts)) =
```
```   330     let val (folTypes,ts) = types_of Ts
```
```   331 	val t = ResClause.make_fixed_type_const a
```
```   332     in
```
```   333 	(ResClause.mk_fol_type("Comp",t,folTypes),ts)
```
```   334     end
```
```   335   | type_of (tp as (TFree(a,s))) =
```
```   336     let val t = ResClause.make_fixed_type_var a
```
```   337     in
```
```   338 	(ResClause.mk_fol_type("Fixed",t,[]),[ResClause.mk_typ_var_sort tp])
```
```   339     end
```
```   340   | type_of (tp as (TVar(v,s))) =
```
```   341     let val t = ResClause.make_schematic_type_var v
```
```   342     in
```
```   343 	(ResClause.mk_fol_type("Var",t,[]),[ResClause.mk_typ_var_sort tp])
```
```   344     end
```
```   345
```
```   346 and types_of Ts =
```
```   347     let val foltyps_ts = map type_of Ts
```
```   348 	val (folTyps,ts) = ListPair.unzip foltyps_ts
```
```   349     in
```
```   350 	(folTyps,ResClause.union_all ts)
```
```   351     end;
```
```   352
```
```   353 (* same as above, but no gathering of sort information *)
```
```   354 fun simp_type_of (Type (a, Ts)) =
```
```   355     let val typs = map simp_type_of Ts
```
```   356 	val t = ResClause.make_fixed_type_const a
```
```   357     in
```
```   358 	ResClause.mk_fol_type("Comp",t,typs)
```
```   359     end
```
```   360   | simp_type_of (TFree (a,s)) = ResClause.mk_fol_type("Fixed",ResClause.make_fixed_type_var a,[])
```
```   361   | simp_type_of (TVar (v,s)) = ResClause.mk_fol_type("Var",ResClause.make_schematic_type_var v,[]);
```
```   362
```
```   363
```
```   364 fun const_type_of (c,t) =
```
```   365     let val (tp,ts) = type_of t
```
```   366 	val tvars = !const_typargs(c,t)
```
```   367 	val tvars' = map simp_type_of tvars
```
```   368     in
```
```   369 	(tp,ts,tvars')
```
```   370     end;
```
```   371
```
```   372
```
```   373 fun is_bool_type (Type("bool",[])) = true
```
```   374   | is_bool_type _ = false;
```
```   375
```
```   376
```
```   377 (* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
```
```   378 fun combterm_of (Const(c,t)) =
```
```   379     let val (tp,ts,tvar_list) = const_type_of (c,t)
```
```   380 	val is_bool = is_bool_type t
```
```   381 	val c' = CombConst(ResClause.make_fixed_const c,tp,tvar_list)
```
```   382 	val c'' = if is_bool then Bool(c') else c'
```
```   383     in
```
```   384 	(c'',ts)
```
```   385     end
```
```   386   | combterm_of (Free(v,t)) =
```
```   387     let val (tp,ts) = type_of t
```
```   388 	val is_bool = is_bool_type t
```
```   389 	val v' = if ResClause.isMeta v then CombVar(ResClause.make_schematic_var(v,0),tp)
```
```   390 		 else CombFree(ResClause.make_fixed_var v,tp)
```
```   391 	val v'' = if is_bool then Bool(v') else v'
```
```   392     in
```
```   393 	(v'',ts)
```
```   394     end
```
```   395   | combterm_of (Var(v,t)) =
```
```   396     let val (tp,ts) = type_of t
```
```   397 	val is_bool = is_bool_type t
```
```   398 	val v' = CombVar(ResClause.make_schematic_var v,tp)
```
```   399 	val v'' = if is_bool then Bool(v') else v'
```
```   400     in
```
```   401 	(v'',ts)
```
```   402     end
```
```   403   | combterm_of (t as (P \$ Q)) =
```
```   404     let val (P',tsP) = combterm_of P
```
```   405 	val (Q',tsQ) = combterm_of Q
```
```   406 	val tp = Term.type_of t
```
```   407 	val tp' = simp_type_of tp
```
```   408 	val is_bool = is_bool_type tp
```
```   409 	val t' = CombApp(P',Q',tp')
```
```   410 	val t'' = if is_bool then Bool(t') else t'
```
```   411     in
```
```   412 	(t'',tsP union tsQ)
```
```   413     end;
```
```   414
```
```   415 fun predicate_of ((Const("Not",_) \$ P), polarity) =
```
```   416     predicate_of (P, not polarity)
```
```   417   | predicate_of (term,polarity) = (combterm_of term,polarity);
```
```   418
```
```   419
```
```   420 fun literals_of_term1 args (Const("Trueprop",_) \$ P) = literals_of_term1 args P
```
```   421   | literals_of_term1 args (Const("op |",_) \$ P \$ Q) =
```
```   422     let val args' = literals_of_term1 args P
```
```   423     in
```
```   424 	literals_of_term1 args' Q
```
```   425     end
```
```   426   | literals_of_term1 (lits,ts) P =
```
```   427     let val ((pred,ts'),pol) = predicate_of (P,true)
```
```   428 	val lits' = Literal(pol,pred)::lits
```
```   429     in
```
```   430 	(lits',ts union ts')
```
```   431     end;
```
```   432
```
```   433
```
```   434 fun literals_of_term P = literals_of_term1 ([],[]) P;
```
```   435
```
```   436 fun occurs a (CombVar(b,_)) = a = b
```
```   437   | occurs a (CombApp(t1,t2,_)) = (occurs a t1) orelse (occurs a t2)
```
```   438   | occurs _ _ = false
```
```   439
```
```   440 fun too_general_terms (CombVar(v,_), t) = not (occurs v t)
```
```   441   | too_general_terms _ = false;
```
```   442
```
```   443 fun too_general_lit (Literal(true,(Bool(CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))))) =
```
```   444       too_general_terms (t1,t2) orelse too_general_terms (t2,t1)
```
```   445   | too_general_lit _ = false;
```
```   446
```
```   447 (* forbid a clause that contains hBOOL(V) *)
```
```   448 fun too_general [] = false
```
```   449   | too_general (lit::lits) =
```
```   450     case lit of Literal(_,Bool(CombVar(_,_))) => true
```
```   451 	      | _ => too_general lits;
```
```   452
```
```   453 (* making axiom and conjecture clauses *)
```
```   454 exception MAKE_CLAUSE
```
```   455 fun make_clause(clause_id,axiom_name,kind,thm,is_user) =
```
```   456     let val term = prop_of thm
```
```   457 	val term' = comb_of term is_user
```
```   458 	val (lits,ctypes_sorts) = literals_of_term term'
```
```   459 	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux ctypes_sorts
```
```   460     in
```
```   461 	if forall isFalse lits
```
```   462 	then error "Problem too trivial for resolution (empty clause)"
```
```   463 	else if too_general lits
```
```   464 	then (Output.debug ("Omitting " ^ axiom_name ^ ": clause contains universal predicates");
```
```   465 	     raise MAKE_CLAUSE)
```
```   466 	else
```
```   467 	    if (!typ_level <> T_FULL) andalso kind=Axiom andalso forall too_general_lit lits
```
```   468 	    then (Output.debug ("Omitting " ^ axiom_name ^ ": equalities are too general");
```
```   469 	          raise MAKE_CLAUSE)
```
```   470 	else
```
```   471 	    Clause {clause_id = clause_id, axiom_name = axiom_name, th = thm, kind = kind,
```
```   472 		    literals = lits, ctypes_sorts = ctypes_sorts,
```
```   473 		    ctvar_type_literals = ctvar_lits,
```
```   474 		    ctfree_type_literals = ctfree_lits}
```
```   475     end;
```
```   476
```
```   477
```
```   478 fun make_axiom_clause thm (ax_name,cls_id,is_user) =
```
```   479       make_clause(cls_id,ax_name,Axiom,thm,is_user);
```
```   480
```
```   481 fun make_axiom_clauses [] user_lemmas = []
```
```   482   | make_axiom_clauses ((thm,(name,id))::thms) user_lemmas =
```
```   483     let val is_user = name mem user_lemmas
```
```   484 	val cls = SOME (make_axiom_clause thm (name,id,is_user))
```
```   485 	          handle MAKE_CLAUSE => NONE
```
```   486 	val clss = make_axiom_clauses thms user_lemmas
```
```   487     in
```
```   488 	case cls of NONE => clss
```
```   489 		  | SOME(cls') => if isTaut cls' then clss
```
```   490 		                  else (name,cls')::clss
```
```   491     end;
```
```   492
```
```   493
```
```   494 fun make_conjecture_clauses_aux _ [] = []
```
```   495   | make_conjecture_clauses_aux n (th::ths) =
```
```   496       make_clause(n,"conjecture",Conjecture,th,true) ::
```
```   497       make_conjecture_clauses_aux (n+1) ths;
```
```   498
```
```   499 val make_conjecture_clauses = make_conjecture_clauses_aux 0;
```
```   500
```
```   501
```
```   502 (**********************************************************************)
```
```   503 (* convert clause into ATP specific formats:                          *)
```
```   504 (* TPTP used by Vampire and E                                         *)
```
```   505 (* DFG used by SPASS                                                  *)
```
```   506 (**********************************************************************)
```
```   507
```
```   508 val type_wrapper = "typeinfo";
```
```   509
```
```   510 fun wrap_type (c,t) =
```
```   511     case !typ_level of T_FULL => type_wrapper ^ (ResClause.paren_pack [c,t])
```
```   512 		     | _ => c;
```
```   513
```
```   514
```
```   515 val bool_tp = ResClause.make_fixed_type_const "bool";
```
```   516
```
```   517 val app_str = "hAPP";
```
```   518
```
```   519 val bool_str = "hBOOL";
```
```   520
```
```   521 exception STRING_OF_COMBTERM of int;
```
```   522
```
```   523 (* convert literals of clauses into strings *)
```
```   524 fun string_of_combterm1_aux _ (CombConst(c,tp,_)) =
```
```   525     let val tp' = string_of_ctyp tp
```
```   526 	val c' = if c = "equal" then "c_fequal" else c
```
```   527     in
```
```   528 	(wrap_type (c',tp'),tp')
```
```   529     end
```
```   530   | string_of_combterm1_aux _ (CombFree(v,tp)) =
```
```   531     let val tp' = string_of_ctyp tp
```
```   532     in
```
```   533 	(wrap_type (v,tp'),tp')
```
```   534     end
```
```   535   | string_of_combterm1_aux _ (CombVar(v,tp)) =
```
```   536     let val tp' = string_of_ctyp tp
```
```   537     in
```
```   538 	(wrap_type (v,tp'),tp')
```
```   539     end
```
```   540   | string_of_combterm1_aux is_pred (CombApp(t1,t2,tp)) =
```
```   541     let val (s1,tp1) = string_of_combterm1_aux is_pred t1
```
```   542 	val (s2,tp2) = string_of_combterm1_aux is_pred t2
```
```   543 	val tp' = ResClause.string_of_fol_type tp
```
```   544 	val r =	case !typ_level of T_FULL => type_wrapper ^  (ResClause.paren_pack [(app_str ^ (ResClause.paren_pack [s1,s2])),tp'])
```
```   545 				 | T_PARTIAL => app_str ^ (ResClause.paren_pack [s1,s2,tp1])
```
```   546 				 | T_NONE => app_str ^ (ResClause.paren_pack [s1,s2])
```
```   547 				 | T_CONST => raise STRING_OF_COMBTERM (1) (*should not happen, if happened may be a bug*)
```
```   548     in	(r,tp')
```
```   549
```
```   550     end
```
```   551   | string_of_combterm1_aux is_pred (Bool(CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))) =
```
```   552     if is_pred then
```
```   553 	let val (s1,_) = string_of_combterm1_aux false t1
```
```   554 	    val (s2,_) = string_of_combterm1_aux false t2
```
```   555 	in
```
```   556 	    ("equal" ^ (ResClause.paren_pack [s1,s2]),bool_tp)
```
```   557 	end
```
```   558     else
```
```   559 	let val (t,_) = string_of_combterm1_aux false (CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))
```
```   560 	in
```
```   561 	    (t,bool_tp)
```
```   562 	end
```
```   563   | string_of_combterm1_aux is_pred (Bool(t)) =
```
```   564     let val (t',_) = string_of_combterm1_aux false t
```
```   565 	val r = if is_pred then bool_str ^ (ResClause.paren_pack [t'])
```
```   566 		else t'
```
```   567     in
```
```   568 	(r,bool_tp)
```
```   569     end;
```
```   570
```
```   571 fun string_of_combterm1 is_pred term = fst (string_of_combterm1_aux is_pred term);
```
```   572
```
```   573 fun string_of_combterm2 _ (CombConst(c,tp,tvars)) =
```
```   574     let val tvars' = map string_of_ctyp tvars
```
```   575 	val c' = if c = "equal" then "c_fequal" else c
```
```   576     in
```
```   577 	c' ^ (ResClause.paren_pack tvars')
```
```   578     end
```
```   579   | string_of_combterm2 _ (CombFree(v,tp)) = v
```
```   580   | string_of_combterm2 _ (CombVar(v,tp)) = v
```
```   581   | string_of_combterm2 is_pred (CombApp(t1,t2,tp)) =
```
```   582     let val s1 = string_of_combterm2 is_pred t1
```
```   583 	val s2 = string_of_combterm2 is_pred t2
```
```   584     in
```
```   585 	app_str ^ (ResClause.paren_pack [s1,s2])
```
```   586     end
```
```   587   | string_of_combterm2 is_pred (Bool(CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))) =
```
```   588     if is_pred then
```
```   589 	let val s1 = string_of_combterm2 false t1
```
```   590 	    val s2 = string_of_combterm2 false t2
```
```   591 	in
```
```   592 	    ("equal" ^ (ResClause.paren_pack [s1,s2]))
```
```   593 	end
```
```   594     else
```
```   595 	string_of_combterm2 false (CombApp(CombApp(CombConst("equal",tp,tps),t1,tp1),t2,tp2))
```
```   596
```
```   597   | string_of_combterm2 is_pred (Bool(t)) =
```
```   598     let val t' = string_of_combterm2 false t
```
```   599     in
```
```   600 	if is_pred then bool_str ^ (ResClause.paren_pack [t'])
```
```   601 	else t'
```
```   602     end;
```
```   603
```
```   604
```
```   605
```
```   606 fun string_of_combterm is_pred term =
```
```   607     case !typ_level of T_CONST => string_of_combterm2 is_pred term
```
```   608 		     | _ => string_of_combterm1 is_pred term;
```
```   609
```
```   610
```
```   611 fun string_of_clausename (cls_id,ax_name) =
```
```   612     ResClause.clause_prefix ^ ResClause.ascii_of ax_name ^ "_" ^ Int.toString cls_id;
```
```   613
```
```   614 fun string_of_type_clsname (cls_id,ax_name,idx) =
```
```   615     string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);
```
```   616
```
```   617
```
```   618 (* tptp format *)
```
```   619
```
```   620 fun tptp_literal (Literal(pol,pred)) =
```
```   621     let val pred_string = string_of_combterm true pred
```
```   622 	val pol_str = if pol then "++" else "--"
```
```   623     in
```
```   624 	pol_str ^ pred_string
```
```   625     end;
```
```   626
```
```   627
```
```   628 fun tptp_type_lits (Clause cls) =
```
```   629     let val lits = map tptp_literal (#literals cls)
```
```   630 	val ctvar_lits_strs =
```
```   631 	    case !typ_level of T_NONE => []
```
```   632 	      | _ => map ResClause.tptp_of_typeLit (#ctvar_type_literals cls)
```
```   633 	val ctfree_lits =
```
```   634 	    case !typ_level of T_NONE => []
```
```   635 	      | _ => map ResClause.tptp_of_typeLit (#ctfree_type_literals cls)
```
```   636     in
```
```   637 	(ctvar_lits_strs @ lits, ctfree_lits)
```
```   638     end;
```
```   639
```
```   640
```
```   641 fun clause2tptp cls =
```
```   642     let val (lits,ctfree_lits) = tptp_type_lits cls
```
```   643 	val cls_id = get_clause_id cls
```
```   644 	val ax_name = get_axiomName cls
```
```   645 	val knd = string_of_kind cls
```
```   646 	val lits_str = ResClause.bracket_pack lits
```
```   647 	val cls_str = ResClause.gen_tptp_cls(cls_id,ax_name,knd,lits_str)
```
```   648     in
```
```   649 	(cls_str,ctfree_lits)
```
```   650     end;
```
```   651
```
```   652
```
```   653 (* dfg format *)
```
```   654 fun dfg_literal (Literal(pol,pred)) = ResClause.dfg_sign pol (string_of_combterm true pred);
```
```   655
```
```   656 fun dfg_clause_aux (Clause{literals, ctypes_sorts, ...}) =
```
```   657   let val lits = map dfg_literal literals
```
```   658       val (tvar_lits,tfree_lits) = ResClause.add_typs_aux ctypes_sorts
```
```   659       val tvar_lits_strs =
```
```   660 	  case !typ_level of T_NONE => []
```
```   661 	      | _ => map ResClause.dfg_of_typeLit tvar_lits
```
```   662       val tfree_lits =
```
```   663           case !typ_level of T_NONE => []
```
```   664 	      | _ => map ResClause.dfg_of_typeLit tfree_lits
```
```   665   in
```
```   666       (tvar_lits_strs @ lits, tfree_lits)
```
```   667   end;
```
```   668
```
```   669 fun get_uvars (CombConst(_,_,_)) vars = vars
```
```   670   | get_uvars (CombFree(_,_)) vars = vars
```
```   671   | get_uvars (CombVar(v,tp)) vars = (v::vars)
```
```   672   | get_uvars (CombApp(P,Q,tp)) vars = get_uvars P (get_uvars Q vars)
```
```   673   | get_uvars (Bool(c)) vars = get_uvars c vars;
```
```   674
```
```   675
```
```   676 fun get_uvars_l (Literal(_,c)) = get_uvars c [];
```
```   677
```
```   678 fun dfg_vars (Clause {literals,...}) = ResClause.union_all (map get_uvars_l literals);
```
```   679
```
```   680 fun clause2dfg (cls as Clause{axiom_name,clause_id,kind,ctypes_sorts,...}) =
```
```   681     let val (lits,tfree_lits) = dfg_clause_aux cls
```
```   682         val vars = dfg_vars cls
```
```   683         val tvars = ResClause.get_tvar_strs ctypes_sorts
```
```   684 	val knd = name_of_kind kind
```
```   685 	val lits_str = commas lits
```
```   686 	val cls_str = ResClause.gen_dfg_cls(clause_id, axiom_name, knd, lits_str, tvars@vars)
```
```   687     in (cls_str, tfree_lits) end;
```
```   688
```
```   689
```
```   690 fun init_funcs_tab funcs =
```
```   691     let val tp = !typ_level
```
```   692 	val funcs1 = case tp of T_PARTIAL => Symtab.update ("hAPP",3) funcs
```
```   693 				      | _ => Symtab.update ("hAPP",2) funcs
```
```   694 	val funcs2 = case tp of T_FULL => Symtab.update ("typeinfo",2) funcs1
```
```   695 				      | _ => funcs1
```
```   696     in
```
```   697 	funcs2
```
```   698     end;
```
```   699
```
```   700
```
```   701 fun add_funcs (CombConst(c,_,tvars),funcs) =
```
```   702     if c = "equal" then foldl ResClause.add_foltype_funcs funcs tvars
```
```   703     else
```
```   704 	(case !typ_level of T_CONST => foldl ResClause.add_foltype_funcs (Symtab.update(c,length tvars) funcs) tvars
```
```   705 			  | _ => foldl ResClause.add_foltype_funcs (Symtab.update(c,0) funcs) tvars)
```
```   706   | add_funcs (CombFree(v,ctp),funcs) = ResClause.add_foltype_funcs (ctp,Symtab.update (v,0) funcs)
```
```   707   | add_funcs (CombVar(_,ctp),funcs) = ResClause.add_foltype_funcs (ctp,funcs)
```
```   708   | add_funcs (CombApp(P,Q,_),funcs) = add_funcs(P,add_funcs (Q,funcs))
```
```   709   | add_funcs (Bool(t),funcs) = add_funcs (t,funcs);
```
```   710
```
```   711
```
```   712 fun add_literal_funcs (Literal(_,c), funcs) = add_funcs (c,funcs);
```
```   713
```
```   714 fun add_clause_funcs (Clause {literals, ...}, funcs) =
```
```   715     foldl add_literal_funcs funcs literals
```
```   716     handle Symtab.DUP a => raise ERROR ("function " ^ a ^ " has multiple arities")
```
```   717
```
```   718 fun funcs_of_clauses clauses arity_clauses =
```
```   719     Symtab.dest (foldl ResClause.add_arityClause_funcs
```
```   720                        (foldl add_clause_funcs (init_funcs_tab Symtab.empty) clauses)
```
```   721                        arity_clauses)
```
```   722
```
```   723 fun preds_of clsrel_clauses arity_clauses =
```
```   724     Symtab.dest
```
```   725 	(foldl ResClause.add_classrelClause_preds
```
```   726 	       (foldl ResClause.add_arityClause_preds
```
```   727 		      (Symtab.update ("hBOOL",1) Symtab.empty)
```
```   728 		      arity_clauses)
```
```   729 	       clsrel_clauses)
```
```   730
```
```   731
```
```   732 (**********************************************************************)
```
```   733 (* write clauses to files                                             *)
```
```   734 (**********************************************************************)
```
```   735
```
```   736 local
```
```   737
```
```   738 val cnf_helper_thms = ResAxioms.cnf_rules_pairs o (map ResAxioms.pairname)
```
```   739
```
```   740 in
```
```   741
```
```   742 fun get_helper_clauses () =
```
```   743     let val IK = if !combI_count > 0 orelse !combK_count > 0 then (Output.debug "Include combinator I K"; cnf_helper_thms [comb_I,comb_K]) else []
```
```   744 	val BC = if !combB_count > 0 orelse !combC_count > 0 then (Output.debug "Include combinator B C"; cnf_helper_thms [comb_B,comb_C]) else []
```
```   745 	val S = if !combS_count > 0 then (Output.debug "Include combinator S"; cnf_helper_thms [comb_S]) else []
```
```   746 	val B'C' = if !combB'_count > 0 orelse !combC'_count > 0 then (Output.debug "Include combinator B' C'"; cnf_helper_thms [comb_B', comb_C']) else []
```
```   747 	val S' = if !combS'_count > 0 then (Output.debug "Include combinator S'"; cnf_helper_thms [comb_S']) else []
```
```   748 	val other = cnf_helper_thms [ext,fequal_imp_equal,equal_imp_fequal]
```
```   749     in
```
```   750 	make_axiom_clauses (other @ IK @ BC @ S @ B'C' @ S') []
```
```   751     end
```
```   752
```
```   753 end
```
```   754
```
```   755 (* tptp format *)
```
```   756
```
```   757 (* write TPTP format to a single file *)
```
```   758 (* when "get_helper_clauses" is called, "include_combS" and "include_min_comb" should have correct values already *)
```
```   759 fun tptp_write_file thms filename (axclauses,classrel_clauses,arity_clauses) user_lemmas=
```
```   760     let val clss = make_conjecture_clauses thms
```
```   761         val (clnames,axclauses') = ListPair.unzip (make_axiom_clauses axclauses user_lemmas)
```
```   762 	val (tptp_clss,tfree_litss) = ListPair.unzip (map clause2tptp clss)
```
```   763 	val tfree_clss = map ResClause.tptp_tfree_clause (foldl (op union_string) [] tfree_litss)
```
```   764 	val out = TextIO.openOut filename
```
```   765 	val helper_clauses = (#2 o ListPair.unzip o get_helper_clauses) ()
```
```   766     in
```
```   767 	List.app (curry TextIO.output out o #1 o clause2tptp) axclauses';
```
```   768 	ResClause.writeln_strs out tfree_clss;
```
```   769 	ResClause.writeln_strs out tptp_clss;
```
```   770 	List.app (curry TextIO.output out o ResClause.tptp_classrelClause) classrel_clauses;
```
```   771 	List.app (curry TextIO.output out o ResClause.tptp_arity_clause) arity_clauses;
```
```   772 	List.app (curry TextIO.output out o #1 o clause2tptp) helper_clauses;
```
```   773 	TextIO.closeOut out;
```
```   774 	clnames
```
```   775     end;
```
```   776
```
```   777
```
```   778
```
```   779 (* dfg format *)
```
```   780
```
```   781 fun dfg_write_file  thms filename (axclauses,classrel_clauses,arity_clauses) user_lemmas =
```
```   782     let val _ = Output.debug ("Preparing to write the DFG file " ^ filename)
```
```   783 	val conjectures = make_conjecture_clauses thms
```
```   784         val (clnames,axclauses') = ListPair.unzip (make_axiom_clauses axclauses user_lemmas)
```
```   785 	val (dfg_clss,tfree_litss) = ListPair.unzip (map clause2dfg conjectures)
```
```   786 	and probname = Path.pack (Path.base (Path.unpack filename))
```
```   787 	val (axstrs,_) =  ListPair.unzip (map clause2dfg axclauses')
```
```   788 	val tfree_clss = map ResClause.dfg_tfree_clause (ResClause.union_all tfree_litss)
```
```   789 	val out = TextIO.openOut filename
```
```   790 	val helper_clauses = (#2 o ListPair.unzip o get_helper_clauses) ()
```
```   791 	val helper_clauses_strs = (#1 o ListPair.unzip o (map clause2dfg)) helper_clauses
```
```   792 	val funcs = funcs_of_clauses (helper_clauses @ conjectures @ axclauses') arity_clauses
```
```   793 	and preds = preds_of classrel_clauses arity_clauses
```
```   794     in
```
```   795 	TextIO.output (out, ResClause.string_of_start probname);
```
```   796 	TextIO.output (out, ResClause.string_of_descrip probname);
```
```   797 	TextIO.output (out, ResClause.string_of_symbols (ResClause.string_of_funcs funcs) (ResClause.string_of_preds preds));
```
```   798 	TextIO.output (out, "list_of_clauses(axioms,cnf).\n");
```
```   799 	ResClause.writeln_strs out axstrs;
```
```   800 	List.app (curry TextIO.output out o ResClause.dfg_classrelClause) classrel_clauses;
```
```   801 	List.app (curry TextIO.output out o ResClause.dfg_arity_clause) arity_clauses;
```
```   802 	ResClause.writeln_strs out helper_clauses_strs;
```
```   803 	TextIO.output (out, "end_of_list.\n\nlist_of_clauses(conjectures,cnf).\n");
```
```   804 	ResClause.writeln_strs out tfree_clss;
```
```   805 	ResClause.writeln_strs out dfg_clss;
```
```   806 	TextIO.output (out, "end_of_list.\n\n");
```
```   807 	(*VarWeight=3 helps the HO problems, probably by counteracting the presence of hAPP*)
```
```   808 	TextIO.output (out, "list_of_settings(SPASS).\n{*\nset_flag(VarWeight,3).\n*}\nend_of_list.\n\n");
```
```   809 	TextIO.output (out, "end_problem.\n");
```
```   810 	TextIO.closeOut out;
```
```   811 	clnames
```
```   812     end;
```
```   813
```
`   814 end`