move Sledgehammer's HOL -> FOL translation to separate file (sledgehammer_translate.ML)
authorblanchet
Mon, 09 Aug 2010 12:05:48 +0200
changeset 38282 319c59682c51
parent 38281 601b7972eef2
child 38283 1dac99cc8dbd
move Sledgehammer's HOL -> FOL translation to separate file (sledgehammer_translate.ML)
src/HOL/IsaMakefile
src/HOL/Mirabelle/Tools/mirabelle_sledgehammer.ML
src/HOL/Sledgehammer.thy
src/HOL/Tools/Nitpick/nitpick_hol.ML
src/HOL/Tools/Sledgehammer/clausifier.ML
src/HOL/Tools/Sledgehammer/sledgehammer.ML
src/HOL/Tools/Sledgehammer/sledgehammer_fact_minimize.ML
src/HOL/Tools/Sledgehammer/sledgehammer_fact_minimizer.ML
src/HOL/Tools/Sledgehammer/sledgehammer_isar.ML
src/HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
src/HOL/Tools/Sledgehammer/sledgehammer_translate.ML
--- a/src/HOL/IsaMakefile	Mon Aug 09 11:05:45 2010 +0200
+++ b/src/HOL/IsaMakefile	Mon Aug 09 12:05:48 2010 +0200
@@ -321,9 +321,10 @@
   Tools/Sledgehammer/metis_tactics.ML \
   Tools/Sledgehammer/sledgehammer.ML \
   Tools/Sledgehammer/sledgehammer_fact_filter.ML \
-  Tools/Sledgehammer/sledgehammer_fact_minimizer.ML \
+  Tools/Sledgehammer/sledgehammer_fact_minimize.ML \
   Tools/Sledgehammer/sledgehammer_isar.ML \
   Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML \
+  Tools/Sledgehammer/sledgehammer_translate.ML \
   Tools/Sledgehammer/sledgehammer_util.ML \
   Tools/SMT/cvc3_solver.ML \
   Tools/SMT/smtlib_interface.ML \
--- a/src/HOL/Mirabelle/Tools/mirabelle_sledgehammer.ML	Mon Aug 09 11:05:45 2010 +0200
+++ b/src/HOL/Mirabelle/Tools/mirabelle_sledgehammer.ML	Mon Aug 09 12:05:48 2010 +0200
@@ -391,7 +391,7 @@
     val params = Sledgehammer_Isar.default_params thy
       [("atps", prover_name), ("minimize_timeout", Int.toString timeout ^ " s")]
     val minimize =
-      Sledgehammer_Fact_Minimizer.minimize_theorems params 1 (subgoal_count st)
+      Sledgehammer_Fact_Minimize.minimize_theorems params 1 (subgoal_count st)
     val _ = log separator
   in
     case minimize st (these (!named_thms)) of
--- a/src/HOL/Sledgehammer.thy	Mon Aug 09 11:05:45 2010 +0200
+++ b/src/HOL/Sledgehammer.thy	Mon Aug 09 12:05:48 2010 +0200
@@ -20,9 +20,10 @@
   ("Tools/Sledgehammer/metis_tactics.ML")
   ("Tools/Sledgehammer/sledgehammer_util.ML")
   ("Tools/Sledgehammer/sledgehammer_fact_filter.ML")
+  ("Tools/Sledgehammer/sledgehammer_translate.ML")
   ("Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML")
   ("Tools/Sledgehammer/sledgehammer.ML")
-  ("Tools/Sledgehammer/sledgehammer_fact_minimizer.ML")
+  ("Tools/Sledgehammer/sledgehammer_fact_minimize.ML")
   ("Tools/Sledgehammer/sledgehammer_isar.ML")
 begin
 
@@ -100,10 +101,11 @@
 
 use "Tools/Sledgehammer/sledgehammer_util.ML"
 use "Tools/Sledgehammer/sledgehammer_fact_filter.ML"
+use "Tools/Sledgehammer/sledgehammer_translate.ML"
 use "Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML"
 use "Tools/Sledgehammer/sledgehammer.ML"
 setup Sledgehammer.setup
-use "Tools/Sledgehammer/sledgehammer_fact_minimizer.ML"
+use "Tools/Sledgehammer/sledgehammer_fact_minimize.ML"
 use "Tools/Sledgehammer/sledgehammer_isar.ML"
 setup Metis_Tactics.setup
 
--- a/src/HOL/Tools/Nitpick/nitpick_hol.ML	Mon Aug 09 11:05:45 2010 +0200
+++ b/src/HOL/Tools/Nitpick/nitpick_hol.ML	Mon Aug 09 12:05:48 2010 +0200
@@ -149,6 +149,8 @@
     string -> (string * string) list -> theory -> theory
   val unregister_frac_type : string -> Proof.context -> Proof.context
   val unregister_frac_type_global : string -> theory -> theory
+  val register_codatatype_generic :
+    typ -> string -> styp list -> Context.generic -> Context.generic
   val register_codatatype :
     typ -> string -> styp list -> Proof.context -> Proof.context
   val register_codatatype_global :
--- a/src/HOL/Tools/Sledgehammer/clausifier.ML	Mon Aug 09 11:05:45 2010 +0200
+++ b/src/HOL/Tools/Sledgehammer/clausifier.ML	Mon Aug 09 12:05:48 2010 +0200
@@ -100,7 +100,7 @@
 val [g_C,f_C] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_C}));
 val [f_S,g_S] = map (cterm_of @{theory}) (OldTerm.term_vars (prop_of @{thm abs_S}));
 
-(*FIXME: requires more use of cterm constructors*)
+(* FIXME: Requires more use of cterm constructors. *)
 fun abstract ct =
   let
       val thy = theory_of_cterm ct
--- a/src/HOL/Tools/Sledgehammer/sledgehammer.ML	Mon Aug 09 11:05:45 2010 +0200
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer.ML	Mon Aug 09 12:05:48 2010 +0200
@@ -39,7 +39,7 @@
      atp_run_time_in_msecs: int,
      output: string,
      proof: string,
-     internal_thm_names: string Vector.vector,
+     axiom_names: string Vector.vector,
      conjecture_shape: int list list}
   type prover = params -> minimize_command -> problem -> prover_result
 
@@ -64,6 +64,7 @@
 open Metis_Clauses
 open Sledgehammer_Util
 open Sledgehammer_Fact_Filter
+open Sledgehammer_Translate
 open Sledgehammer_Proof_Reconstruct
 
 
@@ -73,9 +74,6 @@
    "Async_Manager". *)
 val das_Tool = "Sledgehammer"
 
-(* Freshness almost guaranteed! *)
-val sledgehammer_weak_prefix = "Sledgehammer:"
-
 fun kill_atps () = Async_Manager.kill_threads das_Tool "ATPs"
 fun running_atps () = Async_Manager.running_threads das_Tool "ATPs"
 val messages = Async_Manager.thread_messages das_Tool "ATP"
@@ -112,7 +110,7 @@
    atp_run_time_in_msecs: int,
    output: string,
    proof: string,
-   internal_thm_names: string Vector.vector,
+   axiom_names: string Vector.vector,
    conjecture_shape: int list list}
 
 type prover = params -> minimize_command -> problem -> prover_result
@@ -158,471 +156,6 @@
                else
                  failure))
 
-
-(* Clause preparation *)
-
-datatype fol_formula =
-  FOLFormula of {name: string,
-                 kind: kind,
-                 combformula: (name, combterm) formula,
-                 ctypes_sorts: typ list}
-
-fun mk_anot phi = AConn (ANot, [phi])
-fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
-fun mk_ahorn [] phi = phi
-  | mk_ahorn (phi :: phis) psi =
-    AConn (AImplies, [fold (mk_aconn AAnd) phis phi, psi])
-
-fun combformula_for_prop thy =
-  let
-    val do_term = combterm_from_term thy
-    fun do_quant bs q s T t' =
-      do_formula ((s, T) :: bs) t'
-      #>> (fn phi => AQuant (q, [`make_bound_var s], phi))
-    and do_conn bs c t1 t2 =
-      do_formula bs t1 ##>> do_formula bs t2
-      #>> (fn (phi1, phi2) => AConn (c, [phi1, phi2]))
-    and do_formula bs t =
-      case t of
-        @{const Not} $ t1 =>
-        do_formula bs t1 #>> (fn phi => AConn (ANot, [phi]))
-      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
-        do_quant bs AForall s T t'
-      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
-        do_quant bs AExists s T t'
-      | @{const "op &"} $ t1 $ t2 => do_conn bs AAnd t1 t2
-      | @{const "op |"} $ t1 $ t2 => do_conn bs AOr t1 t2
-      | @{const "op -->"} $ t1 $ t2 => do_conn bs AImplies t1 t2
-      | Const (@{const_name "op ="}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
-        do_conn bs AIff t1 t2
-      | _ => (fn ts => do_term bs (Envir.eta_contract t)
-                       |>> AAtom ||> union (op =) ts)
-  in do_formula [] end
-
-(* Converts an elim-rule into an equivalent theorem that does not have the
-   predicate variable. Leaves other theorems unchanged. We simply instantiate
-   the conclusion variable to False. (Cf. "transform_elim_term" in
-   "ATP_Systems".) *)
-fun transform_elim_term t =
-  case Logic.strip_imp_concl t of
-    @{const Trueprop} $ Var (z, @{typ bool}) =>
-    subst_Vars [(z, @{const False})] t
-  | Var (z, @{typ prop}) => subst_Vars [(z, @{prop False})] t
-  | _ => t
-
-fun presimplify_term thy =
-  Skip_Proof.make_thm thy
-  #> Meson.presimplify
-  #> prop_of
-
-fun concealed_bound_name j = sledgehammer_weak_prefix ^ Int.toString j
-fun conceal_bounds Ts t =
-  subst_bounds (map (Free o apfst concealed_bound_name)
-                    (0 upto length Ts - 1 ~~ Ts), t)
-fun reveal_bounds Ts =
-  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
-                    (0 upto length Ts - 1 ~~ Ts))
-
-fun introduce_combinators_in_term ctxt kind t =
-  let
-    val thy = ProofContext.theory_of ctxt
-    fun aux Ts t =
-      case t of
-        @{const Not} $ t1 => @{const Not} $ aux Ts t1
-      | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
-        t0 $ Abs (s, T, aux (T :: Ts) t')
-      | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
-        t0 $ Abs (s, T, aux (T :: Ts) t')
-      | (t0 as @{const "op &"}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
-      | (t0 as @{const "op |"}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
-      | (t0 as @{const "op -->"}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
-      | (t0 as Const (@{const_name "op ="}, Type (_, [@{typ bool}, _])))
-          $ t1 $ t2 =>
-        t0 $ aux Ts t1 $ aux Ts t2
-      | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
-               t
-             else
-               let
-                 val t = t |> conceal_bounds Ts
-                           |> Envir.eta_contract
-                 val ([t], ctxt') = Variable.import_terms true [t] ctxt
-               in
-                 t |> cterm_of thy
-                   |> Clausifier.introduce_combinators_in_cterm
-                   |> singleton (Variable.export ctxt' ctxt)
-                   |> prop_of |> Logic.dest_equals |> snd
-                   |> reveal_bounds Ts
-               end
-  in t |> not (Meson.is_fol_term thy t) ? aux [] end
-  handle THM _ =>
-         (* A type variable of sort "{}" will make abstraction fail. *)
-         case kind of
-           Axiom => HOLogic.true_const
-         | Conjecture => HOLogic.false_const
-
-(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
-   same in Sledgehammer to prevent the discovery of unreplable proofs. *)
-fun freeze_term t =
-  let
-    fun aux (t $ u) = aux t $ aux u
-      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
-      | aux (Var ((s, i), T)) =
-        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
-      | aux t = t
-  in t |> exists_subterm is_Var t ? aux end
-
-(* making axiom and conjecture formulas *)
-fun make_formula ctxt presimp (name, kind, t) =
-  let
-    val thy = ProofContext.theory_of ctxt
-    val t = t |> transform_elim_term
-              |> Object_Logic.atomize_term thy
-    val t = t |> fastype_of t = HOLogic.boolT ? HOLogic.mk_Trueprop
-              |> extensionalize_term
-              |> presimp ? presimplify_term thy
-              |> perhaps (try (HOLogic.dest_Trueprop))
-              |> introduce_combinators_in_term ctxt kind
-              |> kind = Conjecture ? freeze_term
-    val (combformula, ctypes_sorts) = combformula_for_prop thy t []
-  in
-    FOLFormula {name = name, combformula = combformula, kind = kind,
-                ctypes_sorts = ctypes_sorts}
-  end
-
-fun make_axiom ctxt presimp (name, th) =
-  (name, make_formula ctxt presimp (name, Axiom, prop_of th))
-fun make_conjectures ctxt ts =
-  map2 (fn j => fn t => make_formula ctxt true (Int.toString j, Conjecture, t))
-       (0 upto length ts - 1) ts
-
-(** Helper facts **)
-
-fun count_combterm (CombConst ((s, _), _, _)) =
-    Symtab.map_entry s (Integer.add 1)
-  | count_combterm (CombVar _) = I
-  | count_combterm (CombApp (t1, t2)) = fold count_combterm [t1, t2]
-fun count_combformula (AQuant (_, _, phi)) = count_combformula phi
-  | count_combformula (AConn (_, phis)) = fold count_combformula phis
-  | count_combformula (AAtom tm) = count_combterm tm
-fun count_fol_formula (FOLFormula {combformula, ...}) =
-  count_combformula combformula
-
-val optional_helpers =
-  [(["c_COMBI", "c_COMBK"], @{thms COMBI_def COMBK_def}),
-   (["c_COMBB", "c_COMBC"], @{thms COMBB_def COMBC_def}),
-   (["c_COMBS"], @{thms COMBS_def})]
-val optional_typed_helpers =
-  [(["c_True", "c_False"], @{thms True_or_False}),
-   (["c_If"], @{thms if_True if_False True_or_False})]
-val mandatory_helpers = @{thms fequal_imp_equal equal_imp_fequal}
-
-val init_counters =
-  Symtab.make (maps (maps (map (rpair 0) o fst))
-                    [optional_helpers, optional_typed_helpers])
-
-fun get_helper_facts ctxt is_FO full_types conjectures axioms =
-  let
-    val ct = fold (fold count_fol_formula) [conjectures, axioms] init_counters
-    fun is_needed c = the (Symtab.lookup ct c) > 0
-  in
-    (optional_helpers
-     |> full_types ? append optional_typed_helpers
-     |> maps (fn (ss, ths) =>
-                 if exists is_needed ss then map (`Thm.get_name_hint) ths
-                 else [])) @
-    (if is_FO then [] else map (`Thm.get_name_hint) mandatory_helpers)
-    |> map (snd o make_axiom ctxt false)
-  end
-
-fun meta_not t = @{const "==>"} $ t $ @{prop False}
-
-fun prepare_formulas ctxt full_types hyp_ts concl_t axioms =
-  let
-    val thy = ProofContext.theory_of ctxt
-    (* Remove existing axioms from the conjecture, as this can dramatically
-       boost an ATP's performance (for some reason). *)
-    val axiom_ts = map (prop_of o snd) axioms
-    val hyp_ts =
-      if null hyp_ts then
-        []
-      else
-        let
-          val axiom_table = fold (Termtab.update o rpair ()) axiom_ts
-                                 Termtab.empty
-        in hyp_ts |> filter_out (Termtab.defined axiom_table) end
-    val goal_t = Logic.list_implies (hyp_ts, concl_t)
-    val is_FO = Meson.is_fol_term thy goal_t
-    val subs = tfree_classes_of_terms [goal_t]
-    val supers = tvar_classes_of_terms axiom_ts
-    val tycons = type_consts_of_terms thy (goal_t :: axiom_ts)
-    (* TFrees in the conjecture; TVars in the axioms *)
-    val conjectures = map meta_not hyp_ts @ [concl_t] |> make_conjectures ctxt
-    val (axiom_names, axioms) =
-      ListPair.unzip (map (make_axiom ctxt true) axioms)
-    val helper_facts = get_helper_facts ctxt is_FO full_types conjectures axioms
-    val (supers', arity_clauses) = make_arity_clauses thy tycons supers
-    val class_rel_clauses = make_class_rel_clauses thy subs supers'
-  in
-    (Vector.fromList axiom_names,
-     (conjectures, axioms, helper_facts, class_rel_clauses, arity_clauses))
-  end
-
-fun wrap_type ty t = ATerm ((type_wrapper_name, type_wrapper_name), [ty, t])
-
-fun fo_term_for_combtyp (CombTVar name) = ATerm (name, [])
-  | fo_term_for_combtyp (CombTFree name) = ATerm (name, [])
-  | fo_term_for_combtyp (CombType (name, tys)) =
-    ATerm (name, map fo_term_for_combtyp tys)
-
-fun fo_literal_for_type_literal (TyLitVar (class, name)) =
-    (true, ATerm (class, [ATerm (name, [])]))
-  | fo_literal_for_type_literal (TyLitFree (class, name)) =
-    (true, ATerm (class, [ATerm (name, [])]))
-
-fun formula_for_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
-
-fun fo_term_for_combterm full_types =
-  let
-    fun aux top_level u =
-      let
-        val (head, args) = strip_combterm_comb u
-        val (x, ty_args) =
-          case head of
-            CombConst (name as (s, s'), _, ty_args) =>
-            if s = "equal" then
-              (if top_level andalso length args = 2 then name
-               else ("c_fequal", @{const_name fequal}), [])
-            else if top_level then
-              case s of
-                "c_False" => (("$false", s'), [])
-              | "c_True" => (("$true", s'), [])
-              | _ => (name, if full_types then [] else ty_args)
-            else
-              (name, if full_types then [] else ty_args)
-          | CombVar (name, _) => (name, [])
-          | CombApp _ => raise Fail "impossible \"CombApp\""
-        val t = ATerm (x, map fo_term_for_combtyp ty_args @
-                          map (aux false) args)
-    in
-      if full_types then wrap_type (fo_term_for_combtyp (combtyp_of u)) t else t
-    end
-  in aux true end
-
-fun formula_for_combformula full_types =
-  let
-    fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
-      | aux (AConn (c, phis)) = AConn (c, map aux phis)
-      | aux (AAtom tm) = AAtom (fo_term_for_combterm full_types tm)
-  in aux end
-
-fun formula_for_axiom full_types (FOLFormula {combformula, ctypes_sorts, ...}) =
-  mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal)
-                (type_literals_for_types ctypes_sorts))
-           (formula_for_combformula full_types combformula)
-
-fun problem_line_for_fact prefix full_types
-                          (formula as FOLFormula {name, kind, ...}) =
-  Fof (prefix ^ ascii_of name, kind, formula_for_axiom full_types formula)
-
-fun problem_line_for_class_rel_clause (ClassRelClause {name, subclass,
-                                                       superclass, ...}) =
-  let val ty_arg = ATerm (("T", "T"), []) in
-    Fof (class_rel_clause_prefix ^ ascii_of name, Axiom,
-         AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
-                           AAtom (ATerm (superclass, [ty_arg]))]))
-  end
-
-fun fo_literal_for_arity_literal (TConsLit (c, t, args)) =
-    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
-  | fo_literal_for_arity_literal (TVarLit (c, sort)) =
-    (false, ATerm (c, [ATerm (sort, [])]))
-
-fun problem_line_for_arity_clause (ArityClause {name, conclLit, premLits,
-                                                ...}) =
-  Fof (arity_clause_prefix ^ ascii_of name, Axiom,
-       mk_ahorn (map (formula_for_fo_literal o apfst not
-                      o fo_literal_for_arity_literal) premLits)
-                (formula_for_fo_literal
-                     (fo_literal_for_arity_literal conclLit)))
-
-fun problem_line_for_conjecture full_types
-                                (FOLFormula {name, kind, combformula, ...}) =
-  Fof (conjecture_prefix ^ name, kind,
-       formula_for_combformula full_types combformula)
-
-fun free_type_literals_for_conjecture (FOLFormula {ctypes_sorts, ...}) =
-  map fo_literal_for_type_literal (type_literals_for_types ctypes_sorts)
-
-fun problem_line_for_free_type lit =
-  Fof (tfrees_name, Conjecture, mk_anot (formula_for_fo_literal lit))
-fun problem_lines_for_free_types conjectures =
-  let
-    val litss = map free_type_literals_for_conjecture conjectures
-    val lits = fold (union (op =)) litss []
-  in map problem_line_for_free_type lits end
-
-(** "hBOOL" and "hAPP" **)
-
-type const_info = {min_arity: int, max_arity: int, sub_level: bool}
-
-fun consider_term top_level (ATerm ((s, _), ts)) =
-  (if is_tptp_variable s then
-     I
-   else
-     let val n = length ts in
-       Symtab.map_default
-           (s, {min_arity = n, max_arity = 0, sub_level = false})
-           (fn {min_arity, max_arity, sub_level} =>
-               {min_arity = Int.min (n, min_arity),
-                max_arity = Int.max (n, max_arity),
-                sub_level = sub_level orelse not top_level})
-     end)
-  #> fold (consider_term (top_level andalso s = type_wrapper_name)) ts
-fun consider_formula (AQuant (_, _, phi)) = consider_formula phi
-  | consider_formula (AConn (_, phis)) = fold consider_formula phis
-  | consider_formula (AAtom tm) = consider_term true tm
-
-fun consider_problem_line (Fof (_, _, phi)) = consider_formula phi
-fun consider_problem problem = fold (fold consider_problem_line o snd) problem
-
-fun const_table_for_problem explicit_apply problem =
-  if explicit_apply then NONE
-  else SOME (Symtab.empty |> consider_problem problem)
-
-val tc_fun = make_fixed_type_const @{type_name fun}
-
-fun min_arity_of thy full_types NONE s =
-    (if s = "equal" orelse s = type_wrapper_name orelse
-        String.isPrefix type_const_prefix s orelse
-        String.isPrefix class_prefix s then
-       16383 (* large number *)
-     else if full_types then
-       0
-     else case strip_prefix_and_undo_ascii const_prefix s of
-       SOME s' => num_type_args thy (invert_const s')
-     | NONE => 0)
-  | min_arity_of _ _ (SOME the_const_tab) s =
-    case Symtab.lookup the_const_tab s of
-      SOME ({min_arity, ...} : const_info) => min_arity
-    | NONE => 0
-
-fun full_type_of (ATerm ((s, _), [ty, _])) =
-    if s = type_wrapper_name then ty else raise Fail "expected type wrapper"
-  | full_type_of _ = raise Fail "expected type wrapper"
-
-fun list_hAPP_rev _ t1 [] = t1
-  | list_hAPP_rev NONE t1 (t2 :: ts2) =
-    ATerm (`I "hAPP", [list_hAPP_rev NONE t1 ts2, t2])
-  | list_hAPP_rev (SOME ty) t1 (t2 :: ts2) =
-    let val ty' = ATerm (`make_fixed_type_const @{type_name fun},
-                         [full_type_of t2, ty]) in
-      ATerm (`I "hAPP", [wrap_type ty' (list_hAPP_rev (SOME ty') t1 ts2), t2])
-    end
-
-fun repair_applications_in_term thy full_types const_tab =
-  let
-    fun aux opt_ty (ATerm (name as (s, _), ts)) =
-      if s = type_wrapper_name then
-        case ts of
-          [t1, t2] => ATerm (name, [aux NONE t1, aux (SOME t1) t2])
-        | _ => raise Fail "malformed type wrapper"
-      else
-        let
-          val ts = map (aux NONE) ts
-          val (ts1, ts2) = chop (min_arity_of thy full_types const_tab s) ts
-        in list_hAPP_rev opt_ty (ATerm (name, ts1)) (rev ts2) end
-  in aux NONE end
-
-fun boolify t = ATerm (`I "hBOOL", [t])
-
-(* True if the constant ever appears outside of the top-level position in
-   literals, or if it appears with different arities (e.g., because of different
-   type instantiations). If false, the constant always receives all of its
-   arguments and is used as a predicate. *)
-fun is_predicate NONE s =
-    s = "equal" orelse String.isPrefix type_const_prefix s orelse
-    String.isPrefix class_prefix s
-  | is_predicate (SOME the_const_tab) s =
-    case Symtab.lookup the_const_tab s of
-      SOME {min_arity, max_arity, sub_level} =>
-      not sub_level andalso min_arity = max_arity
-    | NONE => false
-
-fun repair_predicates_in_term const_tab (t as ATerm ((s, _), ts)) =
-  if s = type_wrapper_name then
-    case ts of
-      [_, t' as ATerm ((s', _), _)] =>
-      if is_predicate const_tab s' then t' else boolify t
-    | _ => raise Fail "malformed type wrapper"
-  else
-    t |> not (is_predicate const_tab s) ? boolify
-
-fun close_universally phi =
-  let
-    fun term_vars bounds (ATerm (name as (s, _), tms)) =
-        (is_tptp_variable s andalso not (member (op =) bounds name))
-          ? insert (op =) name
-        #> fold (term_vars bounds) tms
-    fun formula_vars bounds (AQuant (q, xs, phi)) =
-        formula_vars (xs @ bounds) phi
-      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
-      | formula_vars bounds (AAtom tm) = term_vars bounds tm
-  in
-    case formula_vars [] phi [] of [] => phi | xs => AQuant (AForall, xs, phi)
-  end
-
-fun repair_formula thy explicit_forall full_types const_tab =
-  let
-    fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
-      | aux (AConn (c, phis)) = AConn (c, map aux phis)
-      | aux (AAtom tm) =
-        AAtom (tm |> repair_applications_in_term thy full_types const_tab
-                  |> repair_predicates_in_term const_tab)
-  in aux #> explicit_forall ? close_universally end
-
-fun repair_problem_line thy explicit_forall full_types const_tab
-                        (Fof (ident, kind, phi)) =
-  Fof (ident, kind, repair_formula thy explicit_forall full_types const_tab phi)
-fun repair_problem_with_const_table thy =
-  map o apsnd o map ooo repair_problem_line thy
-
-fun repair_problem thy explicit_forall full_types explicit_apply problem =
-  repair_problem_with_const_table thy explicit_forall full_types
-      (const_table_for_problem explicit_apply problem) problem
-
-fun write_tptp_file thy readable_names explicit_forall full_types explicit_apply
-                    file (conjectures, axioms, helper_facts, class_rel_clauses,
-                          arity_clauses) =
-  let
-    val axiom_lines = map (problem_line_for_fact axiom_prefix full_types) axioms
-    val helper_lines =
-      map (problem_line_for_fact helper_prefix full_types) helper_facts
-    val conjecture_lines =
-      map (problem_line_for_conjecture full_types) conjectures
-    val tfree_lines = problem_lines_for_free_types conjectures
-    val class_rel_lines =
-      map problem_line_for_class_rel_clause class_rel_clauses
-    val arity_lines = map problem_line_for_arity_clause arity_clauses
-    (* Reordering these might or might not confuse the proof reconstruction
-       code or the SPASS Flotter hack. *)
-    val problem =
-      [("Relevant facts", axiom_lines),
-       ("Class relationships", class_rel_lines),
-       ("Arity declarations", arity_lines),
-       ("Helper facts", helper_lines),
-       ("Conjectures", conjecture_lines),
-       ("Type variables", tfree_lines)]
-      |> repair_problem thy explicit_forall full_types explicit_apply
-    val (problem, pool) = nice_tptp_problem readable_names problem
-    val conjecture_offset =
-      length axiom_lines + length class_rel_lines + length arity_lines
-      + length helper_lines
-    val _ = File.write_list file (strings_for_tptp_problem problem)
-  in
-    (case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
-     conjecture_offset)
-  end
-
 fun extract_clause_sequence output =
   let
     val tokens_of = String.tokens (not o Char.isAlphaNum)
@@ -694,8 +227,6 @@
                     max_new_relevant_facts_per_iter
                     (the_default prefers_theory_relevant theory_relevant)
                     relevance_override goal hyp_ts concl_t
-    val (internal_thm_names, formulas) =
-      prepare_formulas ctxt full_types hyp_ts concl_t the_axioms
 
     (* path to unique problem file *)
     val the_dest_dir = if overlord then getenv "ISABELLE_HOME_USER"
@@ -760,9 +291,10 @@
                                             known_failures output
               in (output, msecs, proof, outcome) end
             val readable_names = debug andalso overlord
-            val (pool, conjecture_offset) =
-              write_tptp_file thy readable_names explicit_forall full_types
-                              explicit_apply probfile formulas
+            val (problem, pool, conjecture_offset, axiom_names) =
+              prepare_problem ctxt readable_names explicit_forall full_types
+                              explicit_apply hyp_ts concl_t the_axioms
+            val _ = File.write_list probfile (strings_for_tptp_problem problem)
             val conjecture_shape =
               conjecture_offset + 1 upto conjecture_offset + length hyp_ts + 1
               |> map single
@@ -773,7 +305,7 @@
                      |> (fn (output, msecs, proof, outcome) =>
                             (output, msecs0 + msecs, proof, outcome))
                    | result => result)
-          in ((pool, conjecture_shape), result) end
+          in ((pool, conjecture_shape, axiom_names), result) end
         else
           error ("Bad executable: " ^ Path.implode command ^ ".")
 
@@ -787,24 +319,24 @@
       else
         File.write (Path.explode (Path.implode probfile ^ "_proof")) output
 
-    val ((pool, conjecture_shape), (output, msecs, proof, outcome)) =
+    val ((pool, conjecture_shape, axiom_names),
+         (output, msecs, proof, outcome)) =
       with_path cleanup export run_on (prob_pathname subgoal)
-    val (conjecture_shape, internal_thm_names) =
+    val (conjecture_shape, axiom_names) =
       repair_conjecture_shape_and_theorem_names output conjecture_shape
-                                                internal_thm_names
+                                                axiom_names
 
     val (message, used_thm_names) =
       case outcome of
         NONE =>
         proof_text isar_proof
             (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
-            (full_types, minimize_command, proof, internal_thm_names, th,
-             subgoal)
+            (full_types, minimize_command, proof, axiom_names, th, subgoal)
       | SOME failure => (string_for_failure failure ^ "\n", [])
   in
     {outcome = outcome, message = message, pool = pool,
      used_thm_names = used_thm_names, atp_run_time_in_msecs = msecs,
-     output = output, proof = proof, internal_thm_names = internal_thm_names,
+     output = output, proof = proof, axiom_names = axiom_names,
      conjecture_shape = conjecture_shape}
   end
 
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_fact_minimize.ML	Mon Aug 09 12:05:48 2010 +0200
@@ -0,0 +1,174 @@
+(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_fact_minimize.ML
+    Author:     Philipp Meyer, TU Muenchen
+    Author:     Jasmin Blanchette, TU Muenchen
+
+Minimization of theorem list for Metis using automatic theorem provers.
+*)
+
+signature SLEDGEHAMMER_FACT_MINIMIZE =
+sig
+  type params = Sledgehammer.params
+
+  val minimize_theorems :
+    params -> int -> int -> Proof.state -> (string * thm list) list
+    -> (string * thm list) list option * string
+  val run_minimize : params -> int -> Facts.ref list -> Proof.state -> unit
+end;
+
+structure Sledgehammer_Fact_Minimize : SLEDGEHAMMER_FACT_MINIMIZE =
+struct
+
+open ATP_Systems
+open Sledgehammer_Util
+open Sledgehammer_Fact_Filter
+open Sledgehammer_Proof_Reconstruct
+open Sledgehammer
+
+(* wrapper for calling external prover *)
+
+fun string_for_failure Unprovable = "Unprovable."
+  | string_for_failure TimedOut = "Timed out."
+  | string_for_failure _ = "Unknown error."
+
+fun n_theorems name_thms_pairs =
+  let val n = length name_thms_pairs in
+    string_of_int n ^ " theorem" ^ plural_s n ^
+    (if n > 0 then
+       ": " ^ space_implode " "
+                  (name_thms_pairs
+                   |> map (perhaps (try (unprefix chained_prefix)))
+                   |> sort_distinct string_ord)
+     else
+       "")
+  end
+
+fun test_theorems ({debug, verbose, overlord, atps, full_types,
+                    relevance_threshold, relevance_convergence, theory_relevant,
+                    defs_relevant, isar_proof, isar_shrink_factor,
+                    ...} : params)
+                  (prover : prover) explicit_apply timeout subgoal state
+                  name_thms_pairs =
+  let
+    val _ =
+      priority ("Testing " ^ n_theorems (map fst name_thms_pairs) ^ "...")
+    val params =
+      {debug = debug, verbose = verbose, overlord = overlord, atps = atps,
+       full_types = full_types, explicit_apply = explicit_apply,
+       relevance_threshold = relevance_threshold,
+       relevance_convergence = relevance_convergence,
+       theory_relevant = theory_relevant, defs_relevant = defs_relevant,
+       isar_proof = isar_proof, isar_shrink_factor = isar_shrink_factor,
+       timeout = timeout, minimize_timeout = timeout}
+    val axioms = maps (fn (n, ths) => map (pair n) ths) name_thms_pairs
+    val {context = ctxt, facts, goal} = Proof.goal state
+    val problem =
+     {subgoal = subgoal, goal = (ctxt, (facts, goal)),
+      relevance_override = {add = [], del = [], only = false},
+      axioms = SOME axioms}
+    val result as {outcome, used_thm_names, ...} =
+      prover params (K "") problem
+  in
+    priority (case outcome of
+                NONE =>
+                if length used_thm_names = length name_thms_pairs then
+                  "Found proof."
+                else
+                  "Found proof with " ^ n_theorems used_thm_names ^ "."
+              | SOME failure => string_for_failure failure);
+    result
+  end
+
+(* minimalization of thms *)
+
+fun filter_used_facts used =
+  filter (member (op =) used o perhaps (try (unprefix chained_prefix)) o fst)
+
+fun sublinear_minimize _ [] p = p
+  | sublinear_minimize test (x :: xs) (seen, result) =
+    case test (xs @ seen) of
+      result as {outcome = NONE, proof, used_thm_names, ...}
+      : prover_result =>
+      sublinear_minimize test (filter_used_facts used_thm_names xs)
+                         (filter_used_facts used_thm_names seen, result)
+    | _ => sublinear_minimize test xs (x :: seen, result)
+
+(* Give the ATP some slack. The ATP gets further slack because the Sledgehammer
+   preprocessing time is included in the estimate below but isn't part of the
+   timeout. *)
+val fudge_msecs = 250
+
+fun minimize_theorems {atps = [], ...} _ _ _ _ = error "No ATP is set."
+  | minimize_theorems
+        (params as {debug, verbose, overlord, atps as atp :: _, full_types,
+                    relevance_threshold, relevance_convergence, theory_relevant,
+                    defs_relevant, isar_proof, isar_shrink_factor,
+                    minimize_timeout, ...})
+        i n state name_thms_pairs =
+  let
+    val thy = Proof.theory_of state
+    val prover = get_prover_fun thy atp
+    val msecs = Time.toMilliseconds minimize_timeout
+    val _ =
+      priority ("Sledgehammer minimize: ATP " ^ quote atp ^
+                " with a time limit of " ^ string_of_int msecs ^ " ms.")
+    val {context = ctxt, goal, ...} = Proof.goal state
+    val (_, hyp_ts, concl_t) = strip_subgoal goal i
+    val explicit_apply =
+      not (forall (Meson.is_fol_term thy)
+                  (concl_t :: hyp_ts @ maps (map prop_of o snd) name_thms_pairs))
+    fun do_test timeout =
+      test_theorems params prover explicit_apply timeout i state
+    val timer = Timer.startRealTimer ()
+  in
+    (case do_test minimize_timeout name_thms_pairs of
+       result as {outcome = NONE, pool, used_thm_names,
+                  conjecture_shape, ...} =>
+       let
+         val time = Timer.checkRealTimer timer
+         val new_timeout =
+           Int.min (msecs, Time.toMilliseconds time + fudge_msecs)
+           |> Time.fromMilliseconds
+         val (min_thms, {proof, axiom_names, ...}) =
+           sublinear_minimize (do_test new_timeout)
+               (filter_used_facts used_thm_names name_thms_pairs) ([], result)
+         val n = length min_thms
+         val _ = priority (cat_lines
+           ["Minimized: " ^ string_of_int n ^ " theorem" ^ plural_s n] ^
+            (case filter (String.isPrefix chained_prefix o fst) min_thms of
+               [] => ""
+             | chained => " (including " ^ Int.toString (length chained) ^
+                          " chained)") ^ ".")
+       in
+         (SOME min_thms,
+          proof_text isar_proof
+              (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
+              (full_types, K "", proof, axiom_names, goal, i) |> fst)
+       end
+     | {outcome = SOME TimedOut, ...} =>
+       (NONE, "Timeout: You can increase the time limit using the \"timeout\" \
+              \option (e.g., \"timeout = " ^
+              string_of_int (10 + msecs div 1000) ^ " s\").")
+     | {outcome = SOME UnknownError, ...} =>
+       (* Failure sometimes mean timeout, unfortunately. *)
+       (NONE, "Failure: No proof was found with the current time limit. You \
+              \can increase the time limit using the \"timeout\" \
+              \option (e.g., \"timeout = " ^
+              string_of_int (10 + msecs div 1000) ^ " s\").")
+     | {message, ...} => (NONE, "ATP error: " ^ message))
+    handle ERROR msg => (NONE, "Error: " ^ msg)
+  end
+
+fun run_minimize params i refs state =
+  let
+    val ctxt = Proof.context_of state
+    val chained_ths = #facts (Proof.goal state)
+    val name_thms_pairs = map (name_thms_pair_from_ref ctxt chained_ths) refs
+  in
+    case subgoal_count state of
+      0 => priority "No subgoal!"
+    | n =>
+      (kill_atps ();
+       priority (#2 (minimize_theorems params i n state name_thms_pairs)))
+  end
+
+end;
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_fact_minimizer.ML	Mon Aug 09 11:05:45 2010 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,174 +0,0 @@
-(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_fact_minimizer.ML
-    Author:     Philipp Meyer, TU Muenchen
-    Author:     Jasmin Blanchette, TU Muenchen
-
-Minimization of theorem list for Metis using automatic theorem provers.
-*)
-
-signature SLEDGEHAMMER_FACT_MINIMIZER =
-sig
-  type params = Sledgehammer.params
-
-  val minimize_theorems :
-    params -> int -> int -> Proof.state -> (string * thm list) list
-    -> (string * thm list) list option * string
-  val run_minimizer : params -> int -> Facts.ref list -> Proof.state -> unit
-end;
-
-structure Sledgehammer_Fact_Minimizer : SLEDGEHAMMER_FACT_MINIMIZER =
-struct
-
-open ATP_Systems
-open Sledgehammer_Util
-open Sledgehammer_Fact_Filter
-open Sledgehammer_Proof_Reconstruct
-open Sledgehammer
-
-(* wrapper for calling external prover *)
-
-fun string_for_failure Unprovable = "Unprovable."
-  | string_for_failure TimedOut = "Timed out."
-  | string_for_failure _ = "Unknown error."
-
-fun n_theorems name_thms_pairs =
-  let val n = length name_thms_pairs in
-    string_of_int n ^ " theorem" ^ plural_s n ^
-    (if n > 0 then
-       ": " ^ space_implode " "
-                  (name_thms_pairs
-                   |> map (perhaps (try (unprefix chained_prefix)))
-                   |> sort_distinct string_ord)
-     else
-       "")
-  end
-
-fun test_theorems ({debug, verbose, overlord, atps, full_types,
-                    relevance_threshold, relevance_convergence, theory_relevant,
-                    defs_relevant, isar_proof, isar_shrink_factor,
-                    ...} : params)
-                  (prover : prover) explicit_apply timeout subgoal state
-                  name_thms_pairs =
-  let
-    val _ =
-      priority ("Testing " ^ n_theorems (map fst name_thms_pairs) ^ "...")
-    val params =
-      {debug = debug, verbose = verbose, overlord = overlord, atps = atps,
-       full_types = full_types, explicit_apply = explicit_apply,
-       relevance_threshold = relevance_threshold,
-       relevance_convergence = relevance_convergence,
-       theory_relevant = theory_relevant, defs_relevant = defs_relevant,
-       isar_proof = isar_proof, isar_shrink_factor = isar_shrink_factor,
-       timeout = timeout, minimize_timeout = timeout}
-    val axioms = maps (fn (n, ths) => map (pair n) ths) name_thms_pairs
-    val {context = ctxt, facts, goal} = Proof.goal state
-    val problem =
-     {subgoal = subgoal, goal = (ctxt, (facts, goal)),
-      relevance_override = {add = [], del = [], only = false},
-      axioms = SOME axioms}
-    val result as {outcome, used_thm_names, ...} =
-      prover params (K "") problem
-  in
-    priority (case outcome of
-                NONE =>
-                if length used_thm_names = length name_thms_pairs then
-                  "Found proof."
-                else
-                  "Found proof with " ^ n_theorems used_thm_names ^ "."
-              | SOME failure => string_for_failure failure);
-    result
-  end
-
-(* minimalization of thms *)
-
-fun filter_used_facts used =
-  filter (member (op =) used o perhaps (try (unprefix chained_prefix)) o fst)
-
-fun sublinear_minimize _ [] p = p
-  | sublinear_minimize test (x :: xs) (seen, result) =
-    case test (xs @ seen) of
-      result as {outcome = NONE, proof, used_thm_names, ...}
-      : prover_result =>
-      sublinear_minimize test (filter_used_facts used_thm_names xs)
-                         (filter_used_facts used_thm_names seen, result)
-    | _ => sublinear_minimize test xs (x :: seen, result)
-
-(* Give the ATP some slack. The ATP gets further slack because the Sledgehammer
-   preprocessing time is included in the estimate below but isn't part of the
-   timeout. *)
-val fudge_msecs = 250
-
-fun minimize_theorems {atps = [], ...} _ _ _ _ = error "No ATP is set."
-  | minimize_theorems
-        (params as {debug, verbose, overlord, atps as atp :: _, full_types,
-                    relevance_threshold, relevance_convergence, theory_relevant,
-                    defs_relevant, isar_proof, isar_shrink_factor,
-                    minimize_timeout, ...})
-        i n state name_thms_pairs =
-  let
-    val thy = Proof.theory_of state
-    val prover = get_prover_fun thy atp
-    val msecs = Time.toMilliseconds minimize_timeout
-    val _ =
-      priority ("Sledgehammer minimizer: ATP " ^ quote atp ^
-                " with a time limit of " ^ string_of_int msecs ^ " ms.")
-    val {context = ctxt, goal, ...} = Proof.goal state
-    val (_, hyp_ts, concl_t) = strip_subgoal goal i
-    val explicit_apply =
-      not (forall (Meson.is_fol_term thy)
-                  (concl_t :: hyp_ts @ maps (map prop_of o snd) name_thms_pairs))
-    fun do_test timeout =
-      test_theorems params prover explicit_apply timeout i state
-    val timer = Timer.startRealTimer ()
-  in
-    (case do_test minimize_timeout name_thms_pairs of
-       result as {outcome = NONE, pool, used_thm_names,
-                  conjecture_shape, ...} =>
-       let
-         val time = Timer.checkRealTimer timer
-         val new_timeout =
-           Int.min (msecs, Time.toMilliseconds time + fudge_msecs)
-           |> Time.fromMilliseconds
-         val (min_thms, {proof, internal_thm_names, ...}) =
-           sublinear_minimize (do_test new_timeout)
-               (filter_used_facts used_thm_names name_thms_pairs) ([], result)
-         val n = length min_thms
-         val _ = priority (cat_lines
-           ["Minimized: " ^ string_of_int n ^ " theorem" ^ plural_s n] ^
-            (case filter (String.isPrefix chained_prefix o fst) min_thms of
-               [] => ""
-             | chained => " (including " ^ Int.toString (length chained) ^
-                          " chained)") ^ ".")
-       in
-         (SOME min_thms,
-          proof_text isar_proof
-              (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
-              (full_types, K "", proof, internal_thm_names, goal, i) |> fst)
-       end
-     | {outcome = SOME TimedOut, ...} =>
-       (NONE, "Timeout: You can increase the time limit using the \"timeout\" \
-              \option (e.g., \"timeout = " ^
-              string_of_int (10 + msecs div 1000) ^ " s\").")
-     | {outcome = SOME UnknownError, ...} =>
-       (* Failure sometimes mean timeout, unfortunately. *)
-       (NONE, "Failure: No proof was found with the current time limit. You \
-              \can increase the time limit using the \"timeout\" \
-              \option (e.g., \"timeout = " ^
-              string_of_int (10 + msecs div 1000) ^ " s\").")
-     | {message, ...} => (NONE, "ATP error: " ^ message))
-    handle ERROR msg => (NONE, "Error: " ^ msg)
-  end
-
-fun run_minimizer params i refs state =
-  let
-    val ctxt = Proof.context_of state
-    val chained_ths = #facts (Proof.goal state)
-    val name_thms_pairs = map (name_thms_pair_from_ref ctxt chained_ths) refs
-  in
-    case subgoal_count state of
-      0 => priority "No subgoal!"
-    | n =>
-      (kill_atps ();
-       priority (#2 (minimize_theorems params i n state name_thms_pairs)))
-  end
-
-end;
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_isar.ML	Mon Aug 09 11:05:45 2010 +0200
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_isar.ML	Mon Aug 09 12:05:48 2010 +0200
@@ -20,7 +20,7 @@
 open ATP_Systems
 open Sledgehammer_Util
 open Sledgehammer
-open Sledgehammer_Fact_Minimizer
+open Sledgehammer_Fact_Minimize
 
 (** Sledgehammer commands **)
 
@@ -226,9 +226,9 @@
                          (minimize_command override_params i) state
       end
     else if subcommand = minimizeN then
-      run_minimizer (get_params thy (map (apfst minimizize_raw_param_name)
-                                override_params))
-                    (the_default 1 opt_i) (#add relevance_override) state
+      run_minimize (get_params thy (map (apfst minimizize_raw_param_name)
+                               override_params))
+                   (the_default 1 opt_i) (#add relevance_override) state
     else if subcommand = messagesN then
       messages opt_i
     else if subcommand = available_atpsN then
--- a/src/HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML	Mon Aug 09 11:05:45 2010 +0200
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML	Mon Aug 09 12:05:48 2010 +0200
@@ -10,12 +10,6 @@
 sig
   type minimize_command = string list -> string
 
-  val axiom_prefix : string
-  val conjecture_prefix : string
-  val helper_prefix : string
-  val class_rel_clause_prefix : string
-  val arity_clause_prefix : string
-  val tfrees_name : string
   val metis_line: bool -> int -> int -> string list -> string
   val metis_proof_text:
     bool * minimize_command * string * string vector * thm * int
@@ -37,16 +31,10 @@
 open Metis_Clauses
 open Sledgehammer_Util
 open Sledgehammer_Fact_Filter
+open Sledgehammer_Translate
 
 type minimize_command = string list -> string
 
-val axiom_prefix = "ax_"
-val conjecture_prefix = "conj_"
-val helper_prefix = "help_"
-val class_rel_clause_prefix = "clrel_";
-val arity_clause_prefix = "arity_"
-val tfrees_name = "tfrees"
-
 (* Simple simplifications to ensure that sort annotations don't leave a trail of
    spurious "True"s. *)
 fun s_not @{const False} = @{const True}
@@ -71,9 +59,9 @@
 fun mk_aconn c (phi1, phi2) = AConn (c, [phi1, phi2])
 
 fun index_in_shape x = find_index (exists (curry (op =) x))
-fun is_axiom_number thm_names num =
-  num > 0 andalso num <= Vector.length thm_names andalso
-  Vector.sub (thm_names, num - 1) <> ""
+fun is_axiom_number axiom_names num =
+  num > 0 andalso num <= Vector.length axiom_names andalso
+  Vector.sub (axiom_names, num - 1) <> ""
 fun is_conjecture_number conjecture_shape num =
   index_in_shape num conjecture_shape >= 0
 
@@ -491,10 +479,10 @@
 (* Discard axioms; consolidate adjacent lines that prove the same formula, since
    they differ only in type information.*)
 fun add_line _ _ (line as Definition _) lines = line :: lines
-  | add_line conjecture_shape thm_names (Inference (num, t, [])) lines =
+  | add_line conjecture_shape axiom_names (Inference (num, t, [])) lines =
     (* No dependencies: axiom, conjecture, or (for Vampire) internal axioms or
        definitions. *)
-    if is_axiom_number thm_names num then
+    if is_axiom_number axiom_names num then
       (* Axioms are not proof lines. *)
       if is_only_type_information t then
         map (replace_deps_in_line (num, [])) lines
@@ -540,10 +528,10 @@
 
 fun add_desired_line _ _ _ _ (line as Definition (num, _, _)) (j, lines) =
     (j, line :: map (replace_deps_in_line (num, [])) lines)
-  | add_desired_line isar_shrink_factor conjecture_shape thm_names frees
+  | add_desired_line isar_shrink_factor conjecture_shape axiom_names frees
                      (Inference (num, t, deps)) (j, lines) =
     (j + 1,
-     if is_axiom_number thm_names num orelse
+     if is_axiom_number axiom_names num orelse
         is_conjecture_number conjecture_shape num orelse
         (not (is_only_type_information t) andalso
          null (Term.add_tvars t []) andalso
@@ -562,16 +550,18 @@
    (108) is extracted. For SPASS, lines have the form "108[0:Inp] ...", where
    the first number (108) is extracted. For Vampire, we look for
    "108. ... [input]". *)
-fun used_facts_in_atp_proof thm_names atp_proof =
+fun used_facts_in_atp_proof axiom_names atp_proof =
   let
     fun axiom_name num =
       let val j = Int.fromString num |> the_default ~1 in
-        if is_axiom_number thm_names j then SOME (Vector.sub (thm_names, j - 1))
-        else NONE
+        if is_axiom_number axiom_names j then
+          SOME (Vector.sub (axiom_names, j - 1))
+        else
+          NONE
       end
     val tokens_of =
       String.tokens (fn c => not (Char.isAlphaNum c) andalso c <> #"_")
-    val thm_name_list = Vector.foldr (op ::) [] thm_names
+    val thm_name_list = Vector.foldr (op ::) [] axiom_names
     fun do_line ("fof" :: num :: "axiom" :: (rest as _ :: _)) =
         (case strip_prefix_and_undo_ascii axiom_prefix (List.last rest) of
            SOME name =>
@@ -617,16 +607,16 @@
 
 val unprefix_chained = perhaps (try (unprefix chained_prefix))
 
-fun used_facts thm_names =
-  used_facts_in_atp_proof thm_names
+fun used_facts axiom_names =
+  used_facts_in_atp_proof axiom_names
   #> List.partition (String.isPrefix chained_prefix)
   #>> map (unprefix chained_prefix)
   #> pairself (sort_distinct string_ord)
 
-fun metis_proof_text (full_types, minimize_command, atp_proof, thm_names, goal,
-                      i) =
+fun metis_proof_text (full_types, minimize_command, atp_proof, axiom_names,
+                      goal, i) =
   let
-    val (chained_lemmas, other_lemmas) = used_facts thm_names atp_proof
+    val (chained_lemmas, other_lemmas) = used_facts axiom_names atp_proof
     val lemmas = other_lemmas @ chained_lemmas
     val n = Logic.count_prems (prop_of goal)
   in
@@ -656,9 +646,9 @@
 fun smart_case_split [] facts = ByMetis facts
   | smart_case_split proofs facts = CaseSplit (proofs, facts)
 
-fun add_fact_from_dep thm_names num =
-  if is_axiom_number thm_names num then
-    apsnd (insert (op =) (Vector.sub (thm_names, num - 1)))
+fun add_fact_from_dep axiom_names num =
+  if is_axiom_number axiom_names num then
+    apsnd (insert (op =) (Vector.sub (axiom_names, num - 1)))
   else
     apfst (insert (op =) (raw_prefix, num))
 
@@ -667,27 +657,27 @@
 
 fun step_for_line _ _ (Definition (_, t1, t2)) = Let (t1, t2)
   | step_for_line _ _ (Inference (num, t, [])) = Assume ((raw_prefix, num), t)
-  | step_for_line thm_names j (Inference (num, t, deps)) =
+  | step_for_line axiom_names j (Inference (num, t, deps)) =
     Have (if j = 1 then [Show] else [], (raw_prefix, num),
           forall_vars t,
-          ByMetis (fold (add_fact_from_dep thm_names) deps ([], [])))
+          ByMetis (fold (add_fact_from_dep axiom_names) deps ([], [])))
 
 fun proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
-                         atp_proof conjecture_shape thm_names params frees =
+                         atp_proof conjecture_shape axiom_names params frees =
   let
     val lines =
       atp_proof ^ "$" (* the $ sign acts as a sentinel (FIXME: needed?) *)
       |> parse_proof pool
       |> sort (int_ord o pairself raw_step_number)
       |> decode_lines ctxt full_types tfrees
-      |> rpair [] |-> fold_rev (add_line conjecture_shape thm_names)
+      |> rpair [] |-> fold_rev (add_line conjecture_shape axiom_names)
       |> rpair [] |-> fold_rev add_nontrivial_line
       |> rpair (0, []) |-> fold_rev (add_desired_line isar_shrink_factor
-                                               conjecture_shape thm_names frees)
+                                             conjecture_shape axiom_names frees)
       |> snd
   in
     (if null params then [] else [Fix params]) @
-    map2 (step_for_line thm_names) (length lines downto 1) lines
+    map2 (step_for_line axiom_names) (length lines downto 1) lines
   end
 
 (* When redirecting proofs, we keep information about the labels seen so far in
@@ -995,8 +985,8 @@
   in do_proof end
 
 fun isar_proof_text (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
-                    (other_params as (full_types, _, atp_proof, thm_names, goal,
-                                      i)) =
+                    (other_params as (full_types, _, atp_proof, axiom_names,
+                                      goal, i)) =
   let
     val (params, hyp_ts, concl_t) = strip_subgoal goal i
     val frees = fold Term.add_frees (concl_t :: hyp_ts) []
@@ -1005,7 +995,7 @@
     val (one_line_proof, lemma_names) = metis_proof_text other_params
     fun isar_proof_for () =
       case proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
-                                atp_proof conjecture_shape thm_names params
+                                atp_proof conjecture_shape axiom_names params
                                 frees
            |> redirect_proof conjecture_shape hyp_ts concl_t
            |> kill_duplicate_assumptions_in_proof
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_translate.ML	Mon Aug 09 12:05:48 2010 +0200
@@ -0,0 +1,505 @@
+(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_translate.ML
+    Author:     Fabian Immler, TU Muenchen
+    Author:     Makarius
+    Author:     Jasmin Blanchette, TU Muenchen
+
+Translation of HOL to FOL.
+*)
+
+signature SLEDGEHAMMER_TRANSLATE =
+sig
+  type 'a problem = 'a ATP_Problem.problem
+
+  val axiom_prefix : string
+  val conjecture_prefix : string
+  val helper_prefix : string
+  val class_rel_clause_prefix : string
+  val arity_clause_prefix : string
+  val tfrees_name : string
+  val prepare_problem :
+    Proof.context -> bool -> bool -> bool -> bool -> term list -> term
+    -> (string * thm) list
+    -> string problem * string Symtab.table * int * string Vector.vector
+end;
+
+structure Sledgehammer_Translate : SLEDGEHAMMER_TRANSLATE =
+struct
+
+open ATP_Problem
+open Metis_Clauses
+open Sledgehammer_Util
+
+val axiom_prefix = "ax_"
+val conjecture_prefix = "conj_"
+val helper_prefix = "help_"
+val class_rel_clause_prefix = "clrel_";
+val arity_clause_prefix = "arity_"
+val tfrees_name = "tfrees"
+
+(* Freshness almost guaranteed! *)
+val sledgehammer_weak_prefix = "Sledgehammer:"
+
+datatype fol_formula =
+  FOLFormula of {name: string,
+                 kind: kind,
+                 combformula: (name, combterm) formula,
+                 ctypes_sorts: typ list}
+
+fun mk_anot phi = AConn (ANot, [phi])
+fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
+fun mk_ahorn [] phi = phi
+  | mk_ahorn (phi :: phis) psi =
+    AConn (AImplies, [fold (mk_aconn AAnd) phis phi, psi])
+
+fun combformula_for_prop thy =
+  let
+    val do_term = combterm_from_term thy
+    fun do_quant bs q s T t' =
+      do_formula ((s, T) :: bs) t'
+      #>> (fn phi => AQuant (q, [`make_bound_var s], phi))
+    and do_conn bs c t1 t2 =
+      do_formula bs t1 ##>> do_formula bs t2
+      #>> (fn (phi1, phi2) => AConn (c, [phi1, phi2]))
+    and do_formula bs t =
+      case t of
+        @{const Not} $ t1 =>
+        do_formula bs t1 #>> (fn phi => AConn (ANot, [phi]))
+      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
+        do_quant bs AForall s T t'
+      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
+        do_quant bs AExists s T t'
+      | @{const "op &"} $ t1 $ t2 => do_conn bs AAnd t1 t2
+      | @{const "op |"} $ t1 $ t2 => do_conn bs AOr t1 t2
+      | @{const "op -->"} $ t1 $ t2 => do_conn bs AImplies t1 t2
+      | Const (@{const_name "op ="}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
+        do_conn bs AIff t1 t2
+      | _ => (fn ts => do_term bs (Envir.eta_contract t)
+                       |>> AAtom ||> union (op =) ts)
+  in do_formula [] end
+
+(* Converts an elim-rule into an equivalent theorem that does not have the
+   predicate variable. Leaves other theorems unchanged. We simply instantiate
+   the conclusion variable to False. (Cf. "transform_elim_term" in
+   "ATP_Systems".) *)
+fun transform_elim_term t =
+  case Logic.strip_imp_concl t of
+    @{const Trueprop} $ Var (z, @{typ bool}) =>
+    subst_Vars [(z, @{const False})] t
+  | Var (z, @{typ prop}) => subst_Vars [(z, @{prop False})] t
+  | _ => t
+
+fun presimplify_term thy =
+  Skip_Proof.make_thm thy
+  #> Meson.presimplify
+  #> prop_of
+
+fun concealed_bound_name j = sledgehammer_weak_prefix ^ Int.toString j
+fun conceal_bounds Ts t =
+  subst_bounds (map (Free o apfst concealed_bound_name)
+                    (0 upto length Ts - 1 ~~ Ts), t)
+fun reveal_bounds Ts =
+  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
+                    (0 upto length Ts - 1 ~~ Ts))
+
+fun introduce_combinators_in_term ctxt kind t =
+  let
+    val thy = ProofContext.theory_of ctxt
+    fun aux Ts t =
+      case t of
+        @{const Not} $ t1 => @{const Not} $ aux Ts t1
+      | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
+        t0 $ Abs (s, T, aux (T :: Ts) t')
+      | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
+        t0 $ Abs (s, T, aux (T :: Ts) t')
+      | (t0 as @{const "op &"}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
+      | (t0 as @{const "op |"}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
+      | (t0 as @{const "op -->"}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
+      | (t0 as Const (@{const_name "op ="}, Type (_, [@{typ bool}, _])))
+          $ t1 $ t2 =>
+        t0 $ aux Ts t1 $ aux Ts t2
+      | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
+               t
+             else
+               let
+                 val t = t |> conceal_bounds Ts
+                           |> Envir.eta_contract
+                 val ([t], ctxt') = Variable.import_terms true [t] ctxt
+               in
+                 t |> cterm_of thy
+                   |> Clausifier.introduce_combinators_in_cterm
+                   |> singleton (Variable.export ctxt' ctxt)
+                   |> prop_of |> Logic.dest_equals |> snd
+                   |> reveal_bounds Ts
+               end
+  in t |> not (Meson.is_fol_term thy t) ? aux [] end
+  handle THM _ =>
+         (* A type variable of sort "{}" will make abstraction fail. *)
+         case kind of
+           Axiom => HOLogic.true_const
+         | Conjecture => HOLogic.false_const
+
+(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
+   same in Sledgehammer to prevent the discovery of unreplable proofs. *)
+fun freeze_term t =
+  let
+    fun aux (t $ u) = aux t $ aux u
+      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
+      | aux (Var ((s, i), T)) =
+        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
+      | aux t = t
+  in t |> exists_subterm is_Var t ? aux end
+
+(* making axiom and conjecture formulas *)
+fun make_formula ctxt presimp (name, kind, t) =
+  let
+    val thy = ProofContext.theory_of ctxt
+    val t = t |> transform_elim_term
+              |> Object_Logic.atomize_term thy
+    val t = t |> fastype_of t = HOLogic.boolT ? HOLogic.mk_Trueprop
+              |> extensionalize_term
+              |> presimp ? presimplify_term thy
+              |> perhaps (try (HOLogic.dest_Trueprop))
+              |> introduce_combinators_in_term ctxt kind
+              |> kind = Conjecture ? freeze_term
+    val (combformula, ctypes_sorts) = combformula_for_prop thy t []
+  in
+    FOLFormula {name = name, combformula = combformula, kind = kind,
+                ctypes_sorts = ctypes_sorts}
+  end
+
+fun make_axiom ctxt presimp (name, th) =
+  (name, make_formula ctxt presimp (name, Axiom, prop_of th))
+fun make_conjectures ctxt ts =
+  map2 (fn j => fn t => make_formula ctxt true (Int.toString j, Conjecture, t))
+       (0 upto length ts - 1) ts
+
+(** Helper facts **)
+
+fun count_combterm (CombConst ((s, _), _, _)) =
+    Symtab.map_entry s (Integer.add 1)
+  | count_combterm (CombVar _) = I
+  | count_combterm (CombApp (t1, t2)) = fold count_combterm [t1, t2]
+fun count_combformula (AQuant (_, _, phi)) = count_combformula phi
+  | count_combformula (AConn (_, phis)) = fold count_combformula phis
+  | count_combformula (AAtom tm) = count_combterm tm
+fun count_fol_formula (FOLFormula {combformula, ...}) =
+  count_combformula combformula
+
+val optional_helpers =
+  [(["c_COMBI", "c_COMBK"], @{thms COMBI_def COMBK_def}),
+   (["c_COMBB", "c_COMBC"], @{thms COMBB_def COMBC_def}),
+   (["c_COMBS"], @{thms COMBS_def})]
+val optional_typed_helpers =
+  [(["c_True", "c_False"], @{thms True_or_False}),
+   (["c_If"], @{thms if_True if_False True_or_False})]
+val mandatory_helpers = @{thms fequal_imp_equal equal_imp_fequal}
+
+val init_counters =
+  Symtab.make (maps (maps (map (rpair 0) o fst))
+                    [optional_helpers, optional_typed_helpers])
+
+fun get_helper_facts ctxt is_FO full_types conjectures axioms =
+  let
+    val ct = fold (fold count_fol_formula) [conjectures, axioms] init_counters
+    fun is_needed c = the (Symtab.lookup ct c) > 0
+  in
+    (optional_helpers
+     |> full_types ? append optional_typed_helpers
+     |> maps (fn (ss, ths) =>
+                 if exists is_needed ss then map (`Thm.get_name_hint) ths
+                 else [])) @
+    (if is_FO then [] else map (`Thm.get_name_hint) mandatory_helpers)
+    |> map (snd o make_axiom ctxt false)
+  end
+
+fun meta_not t = @{const "==>"} $ t $ @{prop False}
+
+fun prepare_formulas ctxt full_types hyp_ts concl_t axioms =
+  let
+    val thy = ProofContext.theory_of ctxt
+    val axiom_ts = map (prop_of o snd) axioms
+    val hyp_ts =
+      if null hyp_ts then
+        []
+      else
+        (* Remove existing axioms from the conjecture, as this can dramatically
+           boost an ATP's performance (for some reason). *)
+        let
+          val axiom_table = fold (Termtab.update o rpair ()) axiom_ts
+                                 Termtab.empty
+        in hyp_ts |> filter_out (Termtab.defined axiom_table) end
+    val goal_t = Logic.list_implies (hyp_ts, concl_t)
+    val is_FO = Meson.is_fol_term thy goal_t
+    val subs = tfree_classes_of_terms [goal_t]
+    val supers = tvar_classes_of_terms axiom_ts
+    val tycons = type_consts_of_terms thy (goal_t :: axiom_ts)
+    (* TFrees in the conjecture; TVars in the axioms *)
+    val conjectures = map meta_not hyp_ts @ [concl_t] |> make_conjectures ctxt
+    val (axiom_names, axioms) =
+      ListPair.unzip (map (make_axiom ctxt true) axioms)
+    val helper_facts = get_helper_facts ctxt is_FO full_types conjectures axioms
+    val (supers', arity_clauses) = make_arity_clauses thy tycons supers
+    val class_rel_clauses = make_class_rel_clauses thy subs supers'
+  in
+    (Vector.fromList axiom_names,
+     (conjectures, axioms, helper_facts, class_rel_clauses, arity_clauses))
+  end
+
+fun wrap_type ty t = ATerm ((type_wrapper_name, type_wrapper_name), [ty, t])
+
+fun fo_term_for_combtyp (CombTVar name) = ATerm (name, [])
+  | fo_term_for_combtyp (CombTFree name) = ATerm (name, [])
+  | fo_term_for_combtyp (CombType (name, tys)) =
+    ATerm (name, map fo_term_for_combtyp tys)
+
+fun fo_literal_for_type_literal (TyLitVar (class, name)) =
+    (true, ATerm (class, [ATerm (name, [])]))
+  | fo_literal_for_type_literal (TyLitFree (class, name)) =
+    (true, ATerm (class, [ATerm (name, [])]))
+
+fun formula_for_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
+
+fun fo_term_for_combterm full_types =
+  let
+    fun aux top_level u =
+      let
+        val (head, args) = strip_combterm_comb u
+        val (x, ty_args) =
+          case head of
+            CombConst (name as (s, s'), _, ty_args) =>
+            if s = "equal" then
+              (if top_level andalso length args = 2 then name
+               else ("c_fequal", @{const_name fequal}), [])
+            else if top_level then
+              case s of
+                "c_False" => (("$false", s'), [])
+              | "c_True" => (("$true", s'), [])
+              | _ => (name, if full_types then [] else ty_args)
+            else
+              (name, if full_types then [] else ty_args)
+          | CombVar (name, _) => (name, [])
+          | CombApp _ => raise Fail "impossible \"CombApp\""
+        val t = ATerm (x, map fo_term_for_combtyp ty_args @
+                          map (aux false) args)
+    in
+      if full_types then wrap_type (fo_term_for_combtyp (combtyp_of u)) t else t
+    end
+  in aux true end
+
+fun formula_for_combformula full_types =
+  let
+    fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
+      | aux (AConn (c, phis)) = AConn (c, map aux phis)
+      | aux (AAtom tm) = AAtom (fo_term_for_combterm full_types tm)
+  in aux end
+
+fun formula_for_axiom full_types (FOLFormula {combformula, ctypes_sorts, ...}) =
+  mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal)
+                (type_literals_for_types ctypes_sorts))
+           (formula_for_combformula full_types combformula)
+
+fun problem_line_for_fact prefix full_types
+                          (formula as FOLFormula {name, kind, ...}) =
+  Fof (prefix ^ ascii_of name, kind, formula_for_axiom full_types formula)
+
+fun problem_line_for_class_rel_clause (ClassRelClause {name, subclass,
+                                                       superclass, ...}) =
+  let val ty_arg = ATerm (("T", "T"), []) in
+    Fof (class_rel_clause_prefix ^ ascii_of name, Axiom,
+         AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
+                           AAtom (ATerm (superclass, [ty_arg]))]))
+  end
+
+fun fo_literal_for_arity_literal (TConsLit (c, t, args)) =
+    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
+  | fo_literal_for_arity_literal (TVarLit (c, sort)) =
+    (false, ATerm (c, [ATerm (sort, [])]))
+
+fun problem_line_for_arity_clause (ArityClause {name, conclLit, premLits,
+                                                ...}) =
+  Fof (arity_clause_prefix ^ ascii_of name, Axiom,
+       mk_ahorn (map (formula_for_fo_literal o apfst not
+                      o fo_literal_for_arity_literal) premLits)
+                (formula_for_fo_literal
+                     (fo_literal_for_arity_literal conclLit)))
+
+fun problem_line_for_conjecture full_types
+                                (FOLFormula {name, kind, combformula, ...}) =
+  Fof (conjecture_prefix ^ name, kind,
+       formula_for_combformula full_types combformula)
+
+fun free_type_literals_for_conjecture (FOLFormula {ctypes_sorts, ...}) =
+  map fo_literal_for_type_literal (type_literals_for_types ctypes_sorts)
+
+fun problem_line_for_free_type lit =
+  Fof (tfrees_name, Conjecture, mk_anot (formula_for_fo_literal lit))
+fun problem_lines_for_free_types conjectures =
+  let
+    val litss = map free_type_literals_for_conjecture conjectures
+    val lits = fold (union (op =)) litss []
+  in map problem_line_for_free_type lits end
+
+(** "hBOOL" and "hAPP" **)
+
+type const_info = {min_arity: int, max_arity: int, sub_level: bool}
+
+fun consider_term top_level (ATerm ((s, _), ts)) =
+  (if is_tptp_variable s then
+     I
+   else
+     let val n = length ts in
+       Symtab.map_default
+           (s, {min_arity = n, max_arity = 0, sub_level = false})
+           (fn {min_arity, max_arity, sub_level} =>
+               {min_arity = Int.min (n, min_arity),
+                max_arity = Int.max (n, max_arity),
+                sub_level = sub_level orelse not top_level})
+     end)
+  #> fold (consider_term (top_level andalso s = type_wrapper_name)) ts
+fun consider_formula (AQuant (_, _, phi)) = consider_formula phi
+  | consider_formula (AConn (_, phis)) = fold consider_formula phis
+  | consider_formula (AAtom tm) = consider_term true tm
+
+fun consider_problem_line (Fof (_, _, phi)) = consider_formula phi
+fun consider_problem problem = fold (fold consider_problem_line o snd) problem
+
+fun const_table_for_problem explicit_apply problem =
+  if explicit_apply then NONE
+  else SOME (Symtab.empty |> consider_problem problem)
+
+fun min_arity_of thy full_types NONE s =
+    (if s = "equal" orelse s = type_wrapper_name orelse
+        String.isPrefix type_const_prefix s orelse
+        String.isPrefix class_prefix s then
+       16383 (* large number *)
+     else if full_types then
+       0
+     else case strip_prefix_and_undo_ascii const_prefix s of
+       SOME s' => num_type_args thy (invert_const s')
+     | NONE => 0)
+  | min_arity_of _ _ (SOME the_const_tab) s =
+    case Symtab.lookup the_const_tab s of
+      SOME ({min_arity, ...} : const_info) => min_arity
+    | NONE => 0
+
+fun full_type_of (ATerm ((s, _), [ty, _])) =
+    if s = type_wrapper_name then ty else raise Fail "expected type wrapper"
+  | full_type_of _ = raise Fail "expected type wrapper"
+
+fun list_hAPP_rev _ t1 [] = t1
+  | list_hAPP_rev NONE t1 (t2 :: ts2) =
+    ATerm (`I "hAPP", [list_hAPP_rev NONE t1 ts2, t2])
+  | list_hAPP_rev (SOME ty) t1 (t2 :: ts2) =
+    let val ty' = ATerm (`make_fixed_type_const @{type_name fun},
+                         [full_type_of t2, ty]) in
+      ATerm (`I "hAPP", [wrap_type ty' (list_hAPP_rev (SOME ty') t1 ts2), t2])
+    end
+
+fun repair_applications_in_term thy full_types const_tab =
+  let
+    fun aux opt_ty (ATerm (name as (s, _), ts)) =
+      if s = type_wrapper_name then
+        case ts of
+          [t1, t2] => ATerm (name, [aux NONE t1, aux (SOME t1) t2])
+        | _ => raise Fail "malformed type wrapper"
+      else
+        let
+          val ts = map (aux NONE) ts
+          val (ts1, ts2) = chop (min_arity_of thy full_types const_tab s) ts
+        in list_hAPP_rev opt_ty (ATerm (name, ts1)) (rev ts2) end
+  in aux NONE end
+
+fun boolify t = ATerm (`I "hBOOL", [t])
+
+(* True if the constant ever appears outside of the top-level position in
+   literals, or if it appears with different arities (e.g., because of different
+   type instantiations). If false, the constant always receives all of its
+   arguments and is used as a predicate. *)
+fun is_predicate NONE s =
+    s = "equal" orelse String.isPrefix type_const_prefix s orelse
+    String.isPrefix class_prefix s
+  | is_predicate (SOME the_const_tab) s =
+    case Symtab.lookup the_const_tab s of
+      SOME {min_arity, max_arity, sub_level} =>
+      not sub_level andalso min_arity = max_arity
+    | NONE => false
+
+fun repair_predicates_in_term const_tab (t as ATerm ((s, _), ts)) =
+  if s = type_wrapper_name then
+    case ts of
+      [_, t' as ATerm ((s', _), _)] =>
+      if is_predicate const_tab s' then t' else boolify t
+    | _ => raise Fail "malformed type wrapper"
+  else
+    t |> not (is_predicate const_tab s) ? boolify
+
+fun close_universally phi =
+  let
+    fun term_vars bounds (ATerm (name as (s, _), tms)) =
+        (is_tptp_variable s andalso not (member (op =) bounds name))
+          ? insert (op =) name
+        #> fold (term_vars bounds) tms
+    fun formula_vars bounds (AQuant (q, xs, phi)) =
+        formula_vars (xs @ bounds) phi
+      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
+      | formula_vars bounds (AAtom tm) = term_vars bounds tm
+  in
+    case formula_vars [] phi [] of [] => phi | xs => AQuant (AForall, xs, phi)
+  end
+
+fun repair_formula thy explicit_forall full_types const_tab =
+  let
+    fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
+      | aux (AConn (c, phis)) = AConn (c, map aux phis)
+      | aux (AAtom tm) =
+        AAtom (tm |> repair_applications_in_term thy full_types const_tab
+                  |> repair_predicates_in_term const_tab)
+  in aux #> explicit_forall ? close_universally end
+
+fun repair_problem_line thy explicit_forall full_types const_tab
+                        (Fof (ident, kind, phi)) =
+  Fof (ident, kind, repair_formula thy explicit_forall full_types const_tab phi)
+fun repair_problem_with_const_table thy =
+  map o apsnd o map ooo repair_problem_line thy
+
+fun repair_problem thy explicit_forall full_types explicit_apply problem =
+  repair_problem_with_const_table thy explicit_forall full_types
+      (const_table_for_problem explicit_apply problem) problem
+
+fun prepare_problem ctxt readable_names explicit_forall full_types
+                    explicit_apply hyp_ts concl_t axiom_ts =
+  let
+    val thy = ProofContext.theory_of ctxt
+    val (axiom_names, (conjectures, axioms, helper_facts, class_rel_clauses,
+                       arity_clauses)) =
+      prepare_formulas ctxt full_types hyp_ts concl_t axiom_ts
+    val axiom_lines = map (problem_line_for_fact axiom_prefix full_types) axioms
+    val helper_lines =
+      map (problem_line_for_fact helper_prefix full_types) helper_facts
+    val conjecture_lines =
+      map (problem_line_for_conjecture full_types) conjectures
+    val tfree_lines = problem_lines_for_free_types conjectures
+    val class_rel_lines =
+      map problem_line_for_class_rel_clause class_rel_clauses
+    val arity_lines = map problem_line_for_arity_clause arity_clauses
+    (* Reordering these might or might not confuse the proof reconstruction
+       code or the SPASS Flotter hack. *)
+    val problem =
+      [("Relevant facts", axiom_lines),
+       ("Class relationships", class_rel_lines),
+       ("Arity declarations", arity_lines),
+       ("Helper facts", helper_lines),
+       ("Conjectures", conjecture_lines),
+       ("Type variables", tfree_lines)]
+      |> repair_problem thy explicit_forall full_types explicit_apply
+    val (problem, pool) = nice_tptp_problem readable_names problem
+    val conjecture_offset =
+      length axiom_lines + length class_rel_lines + length arity_lines
+      + length helper_lines
+  in
+    (problem,
+     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
+     conjecture_offset, axiom_names)
+  end
+
+end;