src/HOL/Tools/Sledgehammer/sledgehammer_hol_clause.ML
author blanchet
Thu Apr 15 13:49:46 2010 +0200 (2010-04-15)
changeset 36167 c1a35be8e476
parent 35963 943e2582dc87
child 36168 0a6ed065683d
permissions -rw-r--r--
make Sledgehammer's output more debugging friendly
     1 (*  Title:      HOL/Sledgehammer/sledgehammer_hol_clause.ML
     2     Author:     Jia Meng, NICTA
     3 
     4 FOL clauses translated from HOL formulae.
     5 *)
     6 
     7 signature SLEDGEHAMMER_HOL_CLAUSE =
     8 sig
     9   type kind = Sledgehammer_FOL_Clause.kind
    10   type fol_type = Sledgehammer_FOL_Clause.fol_type
    11   type classrel_clause = Sledgehammer_FOL_Clause.classrel_clause
    12   type arity_clause = Sledgehammer_FOL_Clause.arity_clause
    13   type axiom_name = string
    14   type polarity = bool
    15   type hol_clause_id = int
    16 
    17   datatype combterm =
    18     CombConst of string * fol_type * fol_type list (* Const and Free *) |
    19     CombVar of string * fol_type |
    20     CombApp of combterm * combterm
    21   datatype literal = Literal of polarity * combterm
    22   datatype hol_clause =
    23     HOLClause of {clause_id: hol_clause_id, axiom_name: axiom_name, th: thm,
    24                   kind: kind, literals: literal list, ctypes_sorts: typ list}
    25 
    26   val type_of_combterm : combterm -> fol_type
    27   val strip_combterm_comb : combterm -> combterm * combterm list
    28   val literals_of_term : theory -> term -> literal list * typ list
    29   exception TRIVIAL
    30   val make_conjecture_clauses : bool -> theory -> thm list -> hol_clause list
    31   val make_axiom_clauses : bool -> theory ->
    32        (thm * (axiom_name * hol_clause_id)) list -> (axiom_name * hol_clause) list
    33   val get_helper_clauses : bool -> theory -> bool ->
    34        hol_clause list * (thm * (axiom_name * hol_clause_id)) list * string list ->
    35        hol_clause list
    36   val write_tptp_file : bool -> Path.T ->
    37     hol_clause list * hol_clause list * hol_clause list * hol_clause list *
    38     classrel_clause list * arity_clause list ->
    39     int * int
    40   val write_dfg_file : bool -> Path.T ->
    41     hol_clause list * hol_clause list * hol_clause list * hol_clause list *
    42     classrel_clause list * arity_clause list -> int * int
    43 end
    44 
    45 structure Sledgehammer_HOL_Clause : SLEDGEHAMMER_HOL_CLAUSE =
    46 struct
    47 
    48 open Sledgehammer_Util
    49 open Sledgehammer_FOL_Clause
    50 open Sledgehammer_Fact_Preprocessor
    51 
    52 (* Parameter "full_types" below indicates that full type information is to be
    53 exported *)
    54 
    55 (* If true, each function will be directly applied to as many arguments as
    56    possible, avoiding use of the "apply" operator. Use of hBOOL is also
    57    minimized. *)
    58 val minimize_applies = true;
    59 
    60 fun min_arity_of const_min_arity c = the_default 0 (Symtab.lookup const_min_arity c);
    61 
    62 (*True if the constant ever appears outside of the top-level position in literals.
    63   If false, the constant always receives all of its arguments and is used as a predicate.*)
    64 fun needs_hBOOL const_needs_hBOOL c =
    65   not minimize_applies orelse
    66     the_default false (Symtab.lookup const_needs_hBOOL c);
    67 
    68 
    69 (******************************************************)
    70 (* data types for typed combinator expressions        *)
    71 (******************************************************)
    72 
    73 type axiom_name = string;
    74 type polarity = bool;
    75 type hol_clause_id = int;
    76 
    77 datatype combterm =
    78   CombConst of string * fol_type * fol_type list (* Const and Free *) |
    79   CombVar of string * fol_type |
    80   CombApp of combterm * combterm
    81 
    82 datatype literal = Literal of polarity * combterm;
    83 
    84 datatype hol_clause =
    85   HOLClause of {clause_id: hol_clause_id, axiom_name: axiom_name, th: thm,
    86                 kind: kind, literals: literal list, ctypes_sorts: typ list};
    87 
    88 
    89 (*********************************************************************)
    90 (* convert a clause with type Term.term to a clause with type clause *)
    91 (*********************************************************************)
    92 
    93 fun isFalse (Literal(pol, CombConst(c,_,_))) =
    94       (pol andalso c = "c_False") orelse (not pol andalso c = "c_True")
    95   | isFalse _ = false;
    96 
    97 fun isTrue (Literal (pol, CombConst(c,_,_))) =
    98       (pol andalso c = "c_True") orelse
    99       (not pol andalso c = "c_False")
   100   | isTrue _ = false;
   101 
   102 fun isTaut (HOLClause {literals,...}) = exists isTrue literals;
   103 
   104 fun type_of dfg (Type (a, Ts)) =
   105       let val (folTypes,ts) = types_of dfg Ts
   106       in  (Comp(make_fixed_type_const dfg a, folTypes), ts)  end
   107   | type_of _ (tp as TFree (a, _)) = (AtomF (make_fixed_type_var a), [tp])
   108   | type_of _ (tp as TVar (v, _)) = (AtomV (make_schematic_type_var v), [tp])
   109 and types_of dfg Ts =
   110       let val (folTyps,ts) = ListPair.unzip (map (type_of dfg) Ts)
   111       in  (folTyps, union_all ts)  end;
   112 
   113 (* same as above, but no gathering of sort information *)
   114 fun simp_type_of dfg (Type (a, Ts)) =
   115       Comp(make_fixed_type_const dfg a, map (simp_type_of dfg) Ts)
   116   | simp_type_of _ (TFree (a, _)) = AtomF (make_fixed_type_var a)
   117   | simp_type_of _ (TVar (v, _)) = AtomV (make_schematic_type_var v);
   118 
   119 
   120 fun const_type_of dfg thy (c,t) =
   121       let val (tp,ts) = type_of dfg t
   122       in  (tp, ts, map (simp_type_of dfg) (Sign.const_typargs thy (c,t))) end;
   123 
   124 (* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
   125 fun combterm_of dfg thy (Const(c,t)) =
   126       let val (tp,ts,tvar_list) = const_type_of dfg thy (c,t)
   127           val c' = CombConst(make_fixed_const dfg c, tp, tvar_list)
   128       in  (c',ts)  end
   129   | combterm_of dfg _ (Free(v,t)) =
   130       let val (tp,ts) = type_of dfg t
   131           val v' = CombConst(make_fixed_var v, tp, [])
   132       in  (v',ts)  end
   133   | combterm_of dfg _ (Var(v,t)) =
   134       let val (tp,ts) = type_of dfg t
   135           val v' = CombVar(make_schematic_var v,tp)
   136       in  (v',ts)  end
   137   | combterm_of dfg thy (P $ Q) =
   138       let val (P',tsP) = combterm_of dfg thy P
   139           val (Q',tsQ) = combterm_of dfg thy Q
   140       in  (CombApp(P',Q'), union (op =) tsP tsQ)  end
   141   | combterm_of _ _ (t as Abs _) = raise CLAUSE ("HOL CLAUSE", t);
   142 
   143 fun predicate_of dfg thy ((@{const Not} $ P), polarity) = predicate_of dfg thy (P, not polarity)
   144   | predicate_of dfg thy (t,polarity) = (combterm_of dfg thy (Envir.eta_contract t), polarity);
   145 
   146 fun literals_of_term1 dfg thy args (@{const Trueprop} $ P) = literals_of_term1 dfg thy args P
   147   | literals_of_term1 dfg thy args (@{const "op |"} $ P $ Q) =
   148       literals_of_term1 dfg thy (literals_of_term1 dfg thy args P) Q
   149   | literals_of_term1 dfg thy (lits,ts) P =
   150       let val ((pred,ts'),pol) = predicate_of dfg thy (P,true)
   151       in
   152           (Literal(pol,pred)::lits, union (op =) ts ts')
   153       end;
   154 
   155 fun literals_of_term_dfg dfg thy P = literals_of_term1 dfg thy ([],[]) P;
   156 val literals_of_term = literals_of_term_dfg false;
   157 
   158 (* Trivial problem, which resolution cannot handle (empty clause) *)
   159 exception TRIVIAL;
   160 
   161 (* making axiom and conjecture clauses *)
   162 fun make_clause dfg thy (clause_id, axiom_name, kind, th) =
   163     let val (lits,ctypes_sorts) = literals_of_term_dfg dfg thy (prop_of th)
   164     in
   165         if forall isFalse lits then
   166             raise TRIVIAL
   167         else
   168             HOLClause {clause_id = clause_id, axiom_name = axiom_name, th = th,
   169                        kind = kind, literals = lits, ctypes_sorts = ctypes_sorts}
   170     end;
   171 
   172 
   173 fun add_axiom_clause dfg thy ((th,(name,id)), pairs) =
   174   let val cls = make_clause dfg thy (id, name, Axiom, th)
   175   in
   176       if isTaut cls then pairs else (name,cls)::pairs
   177   end;
   178 
   179 fun make_axiom_clauses dfg thy = List.foldl (add_axiom_clause dfg thy) [];
   180 
   181 fun make_conjecture_clauses_aux _ _ _ [] = []
   182   | make_conjecture_clauses_aux dfg thy n (th::ths) =
   183       make_clause dfg thy (n,"conjecture", Conjecture, th) ::
   184       make_conjecture_clauses_aux dfg thy (n+1) ths;
   185 
   186 fun make_conjecture_clauses dfg thy = make_conjecture_clauses_aux dfg thy 0;
   187 
   188 
   189 (**********************************************************************)
   190 (* convert clause into ATP specific formats:                          *)
   191 (* TPTP used by Vampire and E                                         *)
   192 (* DFG used by SPASS                                                  *)
   193 (**********************************************************************)
   194 
   195 (*Result of a function type; no need to check that the argument type matches.*)
   196 fun result_type (Comp ("tc_fun", [_, tp2])) = tp2
   197   | result_type _ = error "result_type"
   198 
   199 fun type_of_combterm (CombConst (_, tp, _)) = tp
   200   | type_of_combterm (CombVar (_, tp)) = tp
   201   | type_of_combterm (CombApp (t1, _)) = result_type (type_of_combterm t1);
   202 
   203 (*gets the head of a combinator application, along with the list of arguments*)
   204 fun strip_combterm_comb u =
   205     let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
   206         |   stripc  x =  x
   207     in  stripc(u,[])  end;
   208 
   209 val type_wrapper = "ti";
   210 
   211 fun head_needs_hBOOL const_needs_hBOOL (CombConst(c,_,_)) = needs_hBOOL const_needs_hBOOL c
   212   | head_needs_hBOOL _ _ = true;
   213 
   214 fun wrap_type full_types (s, tp) =
   215   if full_types then type_wrapper ^ paren_pack [s, string_of_fol_type tp] else s;
   216 
   217 fun apply ss = "hAPP" ^ paren_pack ss;
   218 
   219 fun rev_apply (v, []) = v
   220   | rev_apply (v, arg::args) = apply [rev_apply (v, args), arg];
   221 
   222 fun string_apply (v, args) = rev_apply (v, rev args);
   223 
   224 (*Apply an operator to the argument strings, using either the "apply" operator or
   225   direct function application.*)
   226 fun string_of_applic full_types cma (CombConst (c, _, tvars), args) =
   227       let val c = if c = "equal" then "c_fequal" else c
   228           val nargs = min_arity_of cma c
   229           val args1 = List.take(args, nargs)
   230             handle Subscript => error ("string_of_applic: " ^ c ^ " has arity " ^
   231                                          Int.toString nargs ^ " but is applied to " ^
   232                                          space_implode ", " args)
   233           val args2 = List.drop(args, nargs)
   234           val targs = if full_types then [] else map string_of_fol_type tvars
   235       in
   236           string_apply (c ^ paren_pack (args1@targs), args2)
   237       end
   238   | string_of_applic _ _ (CombVar (v, _), args) = string_apply (v, args)
   239   | string_of_applic _ _ _ = error "string_of_applic";
   240 
   241 fun wrap_type_if full_types cnh (head, s, tp) =
   242   if head_needs_hBOOL cnh head then wrap_type full_types (s, tp) else s;
   243 
   244 fun string_of_combterm (params as (full_types, cma, cnh)) t =
   245   let val (head, args) = strip_combterm_comb t
   246   in  wrap_type_if full_types cnh (head,
   247           string_of_applic full_types cma
   248                            (head, map (string_of_combterm (params)) args),
   249           type_of_combterm t)
   250   end;
   251 
   252 (*Boolean-valued terms are here converted to literals.*)
   253 fun boolify params t =
   254   "hBOOL" ^ paren_pack [string_of_combterm params t];
   255 
   256 fun string_of_predicate (params as (_,_,cnh)) t =
   257   case t of
   258       (CombApp(CombApp(CombConst("equal",_,_), t1), t2)) =>
   259           (*DFG only: new TPTP prefers infix equality*)
   260           ("equal" ^ paren_pack [string_of_combterm params t1, string_of_combterm params t2])
   261     | _ =>
   262           case #1 (strip_combterm_comb t) of
   263               CombConst(c,_,_) => if needs_hBOOL cnh c then boolify params t else string_of_combterm params t
   264             | _ => boolify params t;
   265 
   266 
   267 (*** tptp format ***)
   268 
   269 fun tptp_of_equality params pol (t1,t2) =
   270   let val eqop = if pol then " = " else " != "
   271   in  string_of_combterm params t1 ^ eqop ^ string_of_combterm params t2  end;
   272 
   273 fun tptp_literal params (Literal(pol, CombApp(CombApp(CombConst("equal", _, _), t1), t2))) =
   274       tptp_of_equality params pol (t1,t2)
   275   | tptp_literal params (Literal(pol,pred)) =
   276       tptp_sign pol (string_of_predicate params pred);
   277 
   278 (*Given a clause, returns its literals paired with a list of literals concerning TFrees;
   279   the latter should only occur in conjecture clauses.*)
   280 fun tptp_type_lits params pos (HOLClause {literals, ctypes_sorts, ...}) =
   281       (map (tptp_literal params) literals, 
   282        map (tptp_of_typeLit pos) (add_typs ctypes_sorts));
   283 
   284 fun clause2tptp params (cls as HOLClause {axiom_name, clause_id, kind, ...}) =
   285   let val (lits,tylits) = tptp_type_lits params (kind = Conjecture) cls
   286   in
   287       (gen_tptp_cls (clause_id, axiom_name, kind, lits, tylits), tylits)
   288   end;
   289 
   290 
   291 (*** dfg format ***)
   292 
   293 fun dfg_literal params (Literal(pol,pred)) = dfg_sign pol (string_of_predicate params pred);
   294 
   295 fun dfg_type_lits params pos (HOLClause {literals, ctypes_sorts, ...}) =
   296       (map (dfg_literal params) literals, 
   297        map (dfg_of_typeLit pos) (add_typs ctypes_sorts));
   298 
   299 fun get_uvars (CombConst _) vars = vars
   300   | get_uvars (CombVar(v,_)) vars = (v::vars)
   301   | get_uvars (CombApp(P,Q)) vars = get_uvars P (get_uvars Q vars);
   302 
   303 fun get_uvars_l (Literal(_,c)) = get_uvars c [];
   304 
   305 fun dfg_vars (HOLClause {literals,...}) = union_all (map get_uvars_l literals);
   306 
   307 fun clause2dfg params (cls as HOLClause {axiom_name, clause_id, kind,
   308                                          ctypes_sorts, ...}) =
   309   let val (lits,tylits) = dfg_type_lits params (kind = Conjecture) cls
   310       val vars = dfg_vars cls
   311       val tvars = get_tvar_strs ctypes_sorts
   312   in
   313       (gen_dfg_cls (clause_id, axiom_name, kind, lits, tylits, tvars@vars), tylits)
   314   end;
   315 
   316 
   317 (** For DFG format: accumulate function and predicate declarations **)
   318 
   319 fun addtypes tvars tab = List.foldl add_foltype_funcs tab tvars;
   320 
   321 fun add_decls (full_types, cma, cnh) (CombConst (c, _, tvars), (funcs, preds)) =
   322       if c = "equal" then (addtypes tvars funcs, preds)
   323       else
   324         let val arity = min_arity_of cma c
   325             val ntys = if not full_types then length tvars else 0
   326             val addit = Symtab.update(c, arity+ntys)
   327         in
   328             if needs_hBOOL cnh c then (addtypes tvars (addit funcs), preds)
   329             else (addtypes tvars funcs, addit preds)
   330         end
   331   | add_decls _ (CombVar(_,ctp), (funcs,preds)) =
   332       (add_foltype_funcs (ctp,funcs), preds)
   333   | add_decls params (CombApp(P,Q),decls) = add_decls params (P,add_decls params (Q,decls));
   334 
   335 fun add_literal_decls params (Literal (_,c), decls) = add_decls params (c,decls);
   336 
   337 fun add_clause_decls params (HOLClause {literals, ...}, decls) =
   338     List.foldl (add_literal_decls params) decls literals
   339     handle Symtab.DUP a => error ("function " ^ a ^ " has multiple arities")
   340 
   341 fun decls_of_clauses params clauses arity_clauses =
   342   let val init_functab = Symtab.update (type_wrapper,2) (Symtab.update ("hAPP",2) init_functab)
   343       val init_predtab = Symtab.update ("hBOOL",1) Symtab.empty
   344       val (functab,predtab) = (List.foldl (add_clause_decls params) (init_functab, init_predtab) clauses)
   345   in
   346       (Symtab.dest (List.foldl add_arity_clause_funcs functab arity_clauses),
   347        Symtab.dest predtab)
   348   end;
   349 
   350 fun add_clause_preds (HOLClause {ctypes_sorts, ...}, preds) =
   351   List.foldl add_type_sort_preds preds ctypes_sorts
   352   handle Symtab.DUP a => error ("predicate " ^ a ^ " has multiple arities")
   353 
   354 (*Higher-order clauses have only the predicates hBOOL and type classes.*)
   355 fun preds_of_clauses clauses clsrel_clauses arity_clauses =
   356     Symtab.dest
   357         (List.foldl add_classrel_clause_preds
   358                (List.foldl add_arity_clause_preds
   359                       (List.foldl add_clause_preds Symtab.empty clauses)
   360                       arity_clauses)
   361                clsrel_clauses)
   362 
   363 
   364 (**********************************************************************)
   365 (* write clauses to files                                             *)
   366 (**********************************************************************)
   367 
   368 val init_counters =
   369   Symtab.make [("c_COMBI", 0), ("c_COMBK", 0), ("c_COMBB", 0), ("c_COMBC", 0),
   370                ("c_COMBS", 0)];
   371 
   372 fun count_combterm (CombConst (c, _, _), ct) =
   373      (case Symtab.lookup ct c of NONE => ct  (*no counter*)
   374                                | SOME n => Symtab.update (c,n+1) ct)
   375   | count_combterm (CombVar _, ct) = ct
   376   | count_combterm (CombApp(t1,t2), ct) = count_combterm(t1, count_combterm(t2, ct));
   377 
   378 fun count_literal (Literal(_,t), ct) = count_combterm(t,ct);
   379 
   380 fun count_clause (HOLClause {literals, ...}, ct) =
   381   List.foldl count_literal ct literals;
   382 
   383 fun count_user_clause user_lemmas (HOLClause {axiom_name, literals, ...}, ct) =
   384   if axiom_name mem_string user_lemmas then List.foldl count_literal ct literals
   385   else ct;
   386 
   387 fun cnf_helper_thms thy = cnf_rules_pairs thy o map pairname
   388 
   389 fun get_helper_clauses dfg thy isFO (conjectures, axcls, user_lemmas) =
   390   if isFO then
   391     []
   392   else
   393     let
   394         val axclauses = map #2 (make_axiom_clauses dfg thy axcls)
   395         val ct0 = List.foldl count_clause init_counters conjectures
   396         val ct = List.foldl (count_user_clause user_lemmas) ct0 axclauses
   397         fun needed c = the (Symtab.lookup ct c) > 0
   398         val IK = if needed "c_COMBI" orelse needed "c_COMBK"
   399                  then cnf_helper_thms thy [@{thm COMBI_def}, @{thm COMBK_def}]
   400                  else []
   401         val BC = if needed "c_COMBB" orelse needed "c_COMBC"
   402                  then cnf_helper_thms thy [@{thm COMBB_def}, @{thm COMBC_def}]
   403                  else []
   404         val S = if needed "c_COMBS" then cnf_helper_thms thy [@{thm COMBS_def}]
   405                 else []
   406         val other = cnf_helper_thms thy [@{thm fequal_imp_equal},
   407                                          @{thm equal_imp_fequal}]
   408     in
   409         map #2 (make_axiom_clauses dfg thy (other @ IK @ BC @ S))
   410     end;
   411 
   412 (*Find the minimal arity of each function mentioned in the term. Also, note which uses
   413   are not at top level, to see if hBOOL is needed.*)
   414 fun count_constants_term toplev t (const_min_arity, const_needs_hBOOL) =
   415   let val (head, args) = strip_combterm_comb t
   416       val n = length args
   417       val (const_min_arity, const_needs_hBOOL) = fold (count_constants_term false) args (const_min_arity, const_needs_hBOOL)
   418   in
   419       case head of
   420           CombConst (a,_,_) => (*predicate or function version of "equal"?*)
   421             let val a = if a="equal" andalso not toplev then "c_fequal" else a
   422             val const_min_arity = Symtab.map_default (a, n) (Integer.min n) const_min_arity
   423             in
   424               if toplev then (const_min_arity, const_needs_hBOOL)
   425               else (const_min_arity, Symtab.update (a,true) (const_needs_hBOOL))
   426             end
   427         | _ => (const_min_arity, const_needs_hBOOL)
   428   end;
   429 
   430 (*A literal is a top-level term*)
   431 fun count_constants_lit (Literal (_,t)) (const_min_arity, const_needs_hBOOL) =
   432   count_constants_term true t (const_min_arity, const_needs_hBOOL);
   433 
   434 fun count_constants_clause (HOLClause {literals, ...})
   435                            (const_min_arity, const_needs_hBOOL) =
   436   fold count_constants_lit literals (const_min_arity, const_needs_hBOOL);
   437 
   438 fun display_arity const_needs_hBOOL (c,n) =
   439   trace_msg (fn () => "Constant: " ^ c ^
   440                 " arity:\t" ^ Int.toString n ^
   441                 (if needs_hBOOL const_needs_hBOOL c then " needs hBOOL" else ""));
   442 
   443 fun count_constants (conjectures, _, extra_clauses, helper_clauses, _, _) =
   444   if minimize_applies then
   445      let val (const_min_arity, const_needs_hBOOL) =
   446           fold count_constants_clause conjectures (Symtab.empty, Symtab.empty)
   447        |> fold count_constants_clause extra_clauses
   448        |> fold count_constants_clause helper_clauses
   449      val _ = List.app (display_arity const_needs_hBOOL) (Symtab.dest (const_min_arity))
   450      in (const_min_arity, const_needs_hBOOL) end
   451   else (Symtab.empty, Symtab.empty);
   452 
   453 (* TPTP format *)
   454 
   455 fun write_tptp_file full_types file clauses =
   456   let
   457     fun section _ [] = []
   458       | section name ss = "\n% " ^ name ^ plural_s (length ss) ^ "\n" :: ss
   459     val (conjectures, axclauses, _, helper_clauses,
   460       classrel_clauses, arity_clauses) = clauses
   461     val (cma, cnh) = count_constants clauses
   462     val params = (full_types, cma, cnh)
   463     val (tptp_clss,tfree_litss) = ListPair.unzip (map (clause2tptp params) conjectures)
   464     val tfree_clss = map tptp_tfree_clause (List.foldl (uncurry (union (op =))) [] tfree_litss)
   465     val timestamp = Date.fmt "%Y-%m-%d %H:%M:%S" (Date.fromTimeLocal (Time.now ()))
   466     val _ =
   467       File.write_list file (
   468         "% This file was generated by Isabelle (most likely Sledgehammer)\n" ^
   469         "% " ^ timestamp ^ "\n" ::
   470         section "Relevant fact" (map (#1 o (clause2tptp params)) axclauses) @
   471         section "Type variable" tfree_clss @
   472         section "Class relationship"
   473                 (map tptp_classrel_clause classrel_clauses) @
   474         section "Arity declaration" (map tptp_arity_clause arity_clauses) @
   475         section "Helper fact" (map (#1 o (clause2tptp params)) helper_clauses) @
   476         section "Conjecture" tptp_clss)
   477     in (length axclauses + 1, length tfree_clss + length tptp_clss)
   478   end;
   479 
   480 
   481 (* DFG format *)
   482 
   483 fun write_dfg_file full_types file clauses =
   484   let
   485     val (conjectures, axclauses, _, helper_clauses,
   486       classrel_clauses, arity_clauses) = clauses
   487     val (cma, cnh) = count_constants clauses
   488     val params = (full_types, cma, cnh)
   489     val (dfg_clss, tfree_litss) = ListPair.unzip (map (clause2dfg params) conjectures)
   490     and probname = Path.implode (Path.base file)
   491     val axstrs = map (#1 o (clause2dfg params)) axclauses
   492     val tfree_clss = map dfg_tfree_clause (union_all tfree_litss)
   493     val helper_clauses_strs = map (#1 o (clause2dfg params)) helper_clauses
   494     val (funcs,cl_preds) = decls_of_clauses params (helper_clauses @ conjectures @ axclauses) arity_clauses
   495     and ty_preds = preds_of_clauses axclauses classrel_clauses arity_clauses
   496     val _ =
   497       File.write_list file (
   498         string_of_start probname ::
   499         string_of_descrip probname ::
   500         string_of_symbols (string_of_funcs funcs)
   501           (string_of_preds (cl_preds @ ty_preds)) ::
   502         "list_of_clauses(axioms, cnf).\n" ::
   503         axstrs @
   504         map dfg_classrel_clause classrel_clauses @
   505         map dfg_arity_clause arity_clauses @
   506         helper_clauses_strs @
   507         ["end_of_list.\n\nlist_of_clauses(conjectures, cnf).\n"] @
   508         tfree_clss @
   509         dfg_clss @
   510         ["end_of_list.\n\n",
   511         (*VarWeight=3 helps the HO problems, probably by counteracting the presence of hAPP*)
   512          "list_of_settings(SPASS).\n{*\nset_flag(VarWeight, 3).\n*}\nend_of_list.\n\n",
   513          "end_problem.\n"])
   514 
   515     in (length axclauses + length classrel_clauses + length arity_clauses +
   516       length helper_clauses + 1, length tfree_clss + length dfg_clss)
   517   end;
   518 
   519 end;