src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Thu May 05 12:40:48 2011 +0200 (2011-05-05)
changeset 42698 ffd1ae4ff5c6
parent 42697 9bc5dc48f1a5
child 42700 f4d17cc370f9
permissions -rw-r--r--
help SOS by ensuring that typing information is marked as part of the conjecture + be more precise w.r.t. typedefs in monotonicity check
blanchet@40114
     1
(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
blanchet@38282
     2
    Author:     Fabian Immler, TU Muenchen
blanchet@38282
     3
    Author:     Makarius
blanchet@38282
     4
    Author:     Jasmin Blanchette, TU Muenchen
blanchet@38282
     5
blanchet@39494
     6
Translation of HOL to FOL for Sledgehammer.
blanchet@38282
     7
*)
blanchet@38282
     8
blanchet@40068
     9
signature SLEDGEHAMMER_ATP_TRANSLATE =
blanchet@38282
    10
sig
blanchet@42227
    11
  type 'a fo_term = 'a ATP_Problem.fo_term
blanchet@38282
    12
  type 'a problem = 'a ATP_Problem.problem
blanchet@42640
    13
  type locality = Sledgehammer_Filter.locality
blanchet@42613
    14
blanchet@42613
    15
  datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
blanchet@42613
    16
  datatype type_level =
blanchet@42613
    17
    All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
blanchet@42613
    18
blanchet@42613
    19
  datatype type_system =
blanchet@42684
    20
    Simple of type_level |
blanchet@42613
    21
    Preds of polymorphism * type_level |
blanchet@42613
    22
    Tags of polymorphism * type_level
blanchet@42613
    23
blanchet@40114
    24
  type translated_formula
blanchet@38282
    25
blanchet@42646
    26
  val readable_names : bool Config.T
blanchet@40204
    27
  val fact_prefix : string
blanchet@38282
    28
  val conjecture_prefix : string
blanchet@42568
    29
  val predicator_base : string
blanchet@42544
    30
  val explicit_app_base : string
blanchet@42549
    31
  val type_pred_base : string
blanchet@42562
    32
  val tff_type_prefix : string
blanchet@42613
    33
  val type_sys_from_string : string -> type_system
blanchet@42613
    34
  val polymorphism_of_type_sys : type_system -> polymorphism
blanchet@42613
    35
  val level_of_type_sys : type_system -> type_level
blanchet@42613
    36
  val is_type_sys_virtually_sound : type_system -> bool
blanchet@42613
    37
  val is_type_sys_fairly_sound : type_system -> bool
blanchet@41136
    38
  val num_atp_type_args : theory -> type_system -> string -> int
blanchet@42542
    39
  val unmangled_const : string -> string * string fo_term list
blanchet@41088
    40
  val translate_atp_fact :
blanchet@42640
    41
    Proof.context -> bool -> (string * locality) * thm
blanchet@42640
    42
    -> translated_formula option * ((string * locality) * thm)
blanchet@40059
    43
  val prepare_atp_problem :
blanchet@42568
    44
    Proof.context -> type_system -> bool -> term list -> term
blanchet@41091
    45
    -> (translated_formula option * ((string * 'a) * thm)) list
blanchet@42541
    46
    -> string problem * string Symtab.table * int * int
blanchet@42541
    47
       * (string * 'a) list vector
blanchet@41313
    48
  val atp_problem_weights : string problem -> (string * real) list
blanchet@38282
    49
end;
blanchet@38282
    50
blanchet@41140
    51
structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
blanchet@38282
    52
struct
blanchet@38282
    53
blanchet@38282
    54
open ATP_Problem
blanchet@39494
    55
open Metis_Translate
blanchet@38282
    56
open Sledgehammer_Util
blanchet@42640
    57
open Sledgehammer_Filter
blanchet@42640
    58
blanchet@42640
    59
(* experimental *)
blanchet@42640
    60
val generate_useful_info = false
blanchet@38282
    61
blanchet@42568
    62
(* Readable names are often much shorter, especially if types are mangled in
blanchet@42589
    63
   names. Also, the logic for generating legal SNARK sort names is only
blanchet@42589
    64
   implemented for readable names. Finally, readable names are, well, more
blanchet@42589
    65
   readable. For these reason, they are enabled by default. *)
blanchet@42646
    66
val readable_names =
blanchet@42646
    67
  Attrib.setup_config_bool @{binding sledgehammer_atp_readable_names} (K true)
blanchet@42568
    68
blanchet@42543
    69
val type_decl_prefix = "type_"
blanchet@42543
    70
val sym_decl_prefix = "sym_"
blanchet@40204
    71
val fact_prefix = "fact_"
blanchet@38282
    72
val conjecture_prefix = "conj_"
blanchet@38282
    73
val helper_prefix = "help_"
blanchet@42543
    74
val class_rel_clause_prefix = "crel_";
blanchet@38282
    75
val arity_clause_prefix = "arity_"
blanchet@39975
    76
val tfree_prefix = "tfree_"
blanchet@38282
    77
blanchet@42568
    78
val predicator_base = "hBOOL"
blanchet@42544
    79
val explicit_app_base = "hAPP"
blanchet@42542
    80
val type_pred_base = "is"
blanchet@42562
    81
val tff_type_prefix = "ty_"
blanchet@42531
    82
blanchet@42562
    83
fun make_tff_type s = tff_type_prefix ^ ascii_of s
blanchet@42531
    84
blanchet@42568
    85
(* official TPTP syntax *)
blanchet@42568
    86
val tptp_tff_type_of_types = "$tType"
blanchet@42568
    87
val tptp_tff_bool_type = "$o"
blanchet@42568
    88
val tptp_false = "$false"
blanchet@42568
    89
val tptp_true = "$true"
blanchet@42534
    90
blanchet@38282
    91
(* Freshness almost guaranteed! *)
blanchet@38282
    92
val sledgehammer_weak_prefix = "Sledgehammer:"
blanchet@38282
    93
blanchet@42613
    94
datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
blanchet@42613
    95
datatype type_level =
blanchet@42613
    96
  All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
blanchet@42613
    97
blanchet@42613
    98
datatype type_system =
blanchet@42684
    99
  Simple of type_level |
blanchet@42613
   100
  Preds of polymorphism * type_level |
blanchet@42613
   101
  Tags of polymorphism * type_level
blanchet@42613
   102
blanchet@42689
   103
fun try_unsuffixes ss s =
blanchet@42689
   104
  fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
blanchet@42689
   105
blanchet@42613
   106
fun type_sys_from_string s =
blanchet@42613
   107
  (case try (unprefix "mangled_") s of
blanchet@42613
   108
     SOME s => (Mangled_Monomorphic, s)
blanchet@42613
   109
   | NONE =>
blanchet@42613
   110
     case try (unprefix "mono_") s of
blanchet@42613
   111
       SOME s => (Monomorphic, s)
blanchet@42613
   112
     | NONE => (Polymorphic, s))
blanchet@42613
   113
  ||> (fn s =>
blanchet@42689
   114
          (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
blanchet@42689
   115
          case try_unsuffixes ["?", "_query"] s of
blanchet@42613
   116
            SOME s => (Nonmonotonic_Types, s)
blanchet@42613
   117
          | NONE =>
blanchet@42689
   118
            case try_unsuffixes ["!", "_bang"] s of
blanchet@42613
   119
              SOME s => (Finite_Types, s)
blanchet@42613
   120
            | NONE => (All_Types, s))
blanchet@42613
   121
  |> (fn (polymorphism, (level, core)) =>
blanchet@42613
   122
         case (core, (polymorphism, level)) of
blanchet@42684
   123
           ("simple", (Polymorphic (* naja *), level)) => Simple level
blanchet@42613
   124
         | ("preds", extra) => Preds extra
blanchet@42613
   125
         | ("tags", extra) => Tags extra
blanchet@42682
   126
         | ("args", (_, All_Types (* naja *))) =>
blanchet@42613
   127
           Preds (polymorphism, Const_Arg_Types)
blanchet@42613
   128
         | ("erased", (Polymorphic, All_Types (* naja *))) =>
blanchet@42613
   129
           Preds (polymorphism, No_Types)
blanchet@42613
   130
         | _ => error ("Unknown type system: " ^ quote s ^ "."))
blanchet@42613
   131
blanchet@42684
   132
fun polymorphism_of_type_sys (Simple _) = Mangled_Monomorphic
blanchet@42613
   133
  | polymorphism_of_type_sys (Preds (poly, _)) = poly
blanchet@42613
   134
  | polymorphism_of_type_sys (Tags (poly, _)) = poly
blanchet@42613
   135
blanchet@42684
   136
fun level_of_type_sys (Simple level) = level
blanchet@42613
   137
  | level_of_type_sys (Preds (_, level)) = level
blanchet@42613
   138
  | level_of_type_sys (Tags (_, level)) = level
blanchet@42613
   139
blanchet@42687
   140
fun is_type_level_virtually_sound level =
blanchet@42687
   141
  level = All_Types orelse level = Nonmonotonic_Types
blanchet@42613
   142
val is_type_sys_virtually_sound =
blanchet@42613
   143
  is_type_level_virtually_sound o level_of_type_sys
blanchet@42613
   144
blanchet@42613
   145
fun is_type_level_fairly_sound level =
blanchet@42613
   146
  is_type_level_virtually_sound level orelse level = Finite_Types
blanchet@42613
   147
val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
blanchet@42613
   148
blanchet@42687
   149
fun is_type_level_partial level =
blanchet@42687
   150
  level = Nonmonotonic_Types orelse level = Finite_Types
blanchet@42687
   151
blanchet@42573
   152
fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
blanchet@42573
   153
  | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
blanchet@42573
   154
  | formula_map f (AAtom tm) = AAtom (f tm)
blanchet@42573
   155
blanchet@42680
   156
fun formula_fold pos f =
blanchet@42677
   157
  let
blanchet@42677
   158
    fun aux pos (AQuant (_, _, phi)) = aux pos phi
blanchet@42680
   159
      | aux pos (AConn (ANot, [phi])) = aux (Option.map not pos) phi
blanchet@42677
   160
      | aux pos (AConn (AImplies, [phi1, phi2])) =
blanchet@42680
   161
        aux (Option.map not pos) phi1 #> aux pos phi2
blanchet@42680
   162
      | aux pos (AConn (AAnd, phis)) = fold (aux pos) phis
blanchet@42680
   163
      | aux pos (AConn (AOr, phis)) = fold (aux pos) phis
blanchet@42680
   164
      | aux _ (AConn (_, phis)) = fold (aux NONE) phis
blanchet@42677
   165
      | aux pos (AAtom tm) = f pos tm
blanchet@42680
   166
  in aux (SOME pos) end
blanchet@42573
   167
blanchet@40114
   168
type translated_formula =
blanchet@38752
   169
  {name: string,
blanchet@42640
   170
   locality: locality,
blanchet@42525
   171
   kind: formula_kind,
blanchet@42562
   172
   combformula: (name, typ, combterm) formula,
blanchet@42562
   173
   atomic_types: typ list}
blanchet@38282
   174
blanchet@42640
   175
fun update_combformula f ({name, locality, kind, combformula, atomic_types}
blanchet@42640
   176
                          : translated_formula) =
blanchet@42640
   177
  {name = name, locality = locality, kind = kind, combformula = f combformula,
blanchet@42562
   178
   atomic_types = atomic_types} : translated_formula
blanchet@42542
   179
blanchet@42558
   180
fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
blanchet@42558
   181
blanchet@42572
   182
val boring_consts = [explicit_app_base, @{const_name Metis.fequal}]
blanchet@42572
   183
blanchet@42572
   184
fun should_omit_type_args type_sys s =
blanchet@42589
   185
  s <> type_pred_base andalso s <> type_tag_name andalso
blanchet@42589
   186
  (s = @{const_name HOL.eq} orelse level_of_type_sys type_sys = No_Types orelse
blanchet@42589
   187
   (case type_sys of
blanchet@42589
   188
      Tags (_, All_Types) => true
blanchet@42589
   189
    | _ => polymorphism_of_type_sys type_sys <> Mangled_Monomorphic andalso
blanchet@42589
   190
           member (op =) boring_consts s))
blanchet@42677
   191
blanchet@42589
   192
datatype type_arg_policy = No_Type_Args | Explicit_Type_Args | Mangled_Type_Args
blanchet@41136
   193
blanchet@42589
   194
fun general_type_arg_policy type_sys =
blanchet@42589
   195
  if level_of_type_sys type_sys = No_Types then
blanchet@42589
   196
    No_Type_Args
blanchet@42589
   197
  else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
blanchet@42589
   198
    Mangled_Type_Args
blanchet@42589
   199
  else
blanchet@42589
   200
    Explicit_Type_Args
blanchet@42563
   201
blanchet@42524
   202
fun type_arg_policy type_sys s =
blanchet@42572
   203
  if should_omit_type_args type_sys s then No_Type_Args
blanchet@42563
   204
  else general_type_arg_policy type_sys
blanchet@42227
   205
blanchet@41136
   206
fun num_atp_type_args thy type_sys s =
blanchet@42557
   207
  if type_arg_policy type_sys s = Explicit_Type_Args then num_type_args thy s
blanchet@42557
   208
  else 0
blanchet@41136
   209
blanchet@42353
   210
fun atp_type_literals_for_types type_sys kind Ts =
blanchet@42589
   211
  if level_of_type_sys type_sys = No_Types then
blanchet@42353
   212
    []
blanchet@42353
   213
  else
blanchet@42353
   214
    Ts |> type_literals_for_types
blanchet@42353
   215
       |> filter (fn TyLitVar _ => kind <> Conjecture
blanchet@42353
   216
                   | TyLitFree _ => kind = Conjecture)
blanchet@41137
   217
blanchet@38282
   218
fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
blanchet@42534
   219
fun mk_aconns c phis =
blanchet@42534
   220
  let val (phis', phi') = split_last phis in
blanchet@42534
   221
    fold_rev (mk_aconn c) phis' phi'
blanchet@42534
   222
  end
blanchet@38282
   223
fun mk_ahorn [] phi = phi
blanchet@42534
   224
  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
blanchet@42522
   225
fun mk_aquant _ [] phi = phi
blanchet@42522
   226
  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
blanchet@42522
   227
    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
blanchet@42522
   228
  | mk_aquant q xs phi = AQuant (q, xs, phi)
blanchet@38282
   229
blanchet@42522
   230
fun close_universally atom_vars phi =
blanchet@41145
   231
  let
blanchet@41145
   232
    fun formula_vars bounds (AQuant (_, xs, phi)) =
blanchet@42526
   233
        formula_vars (map fst xs @ bounds) phi
blanchet@41145
   234
      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
blanchet@42522
   235
      | formula_vars bounds (AAtom tm) =
blanchet@42526
   236
        union (op =) (atom_vars tm []
blanchet@42526
   237
                      |> filter_out (member (op =) bounds o fst))
blanchet@42522
   238
  in mk_aquant AForall (formula_vars [] phi []) phi end
blanchet@42522
   239
blanchet@42531
   240
fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
blanchet@42522
   241
  | combterm_vars (CombConst _) = I
blanchet@42574
   242
  | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
blanchet@42674
   243
fun close_combformula_universally phi = close_universally combterm_vars phi
blanchet@42522
   244
blanchet@42522
   245
fun term_vars (ATerm (name as (s, _), tms)) =
blanchet@42531
   246
  is_atp_variable s ? insert (op =) (name, NONE)
blanchet@42526
   247
  #> fold term_vars tms
blanchet@42674
   248
fun close_formula_universally phi = close_universally term_vars phi
blanchet@41145
   249
blanchet@42562
   250
fun fo_term_from_typ (Type (s, Ts)) =
blanchet@42562
   251
    ATerm (`make_fixed_type_const s, map fo_term_from_typ Ts)
blanchet@42562
   252
  | fo_term_from_typ (TFree (s, _)) =
blanchet@42562
   253
    ATerm (`make_fixed_type_var s, [])
blanchet@42562
   254
  | fo_term_from_typ (TVar ((x as (s, _)), _)) =
blanchet@42562
   255
    ATerm ((make_schematic_type_var x, s), [])
blanchet@42562
   256
blanchet@42562
   257
(* This shouldn't clash with anything else. *)
blanchet@42542
   258
val mangled_type_sep = "\000"
blanchet@42542
   259
blanchet@42562
   260
fun generic_mangled_type_name f (ATerm (name, [])) = f name
blanchet@42562
   261
  | generic_mangled_type_name f (ATerm (name, tys)) =
blanchet@42562
   262
    f name ^ "(" ^ commas (map (generic_mangled_type_name f) tys) ^ ")"
blanchet@42562
   263
val mangled_type_name =
blanchet@42562
   264
  fo_term_from_typ
blanchet@42562
   265
  #> (fn ty => (make_tff_type (generic_mangled_type_name fst ty),
blanchet@42562
   266
                generic_mangled_type_name snd ty))
blanchet@42542
   267
blanchet@42574
   268
fun generic_mangled_type_suffix f g Ts =
blanchet@42542
   269
  fold_rev (curry (op ^) o g o prefix mangled_type_sep
blanchet@42574
   270
            o generic_mangled_type_name f) Ts ""
blanchet@42562
   271
fun mangled_const_name T_args (s, s') =
blanchet@42562
   272
  let val ty_args = map fo_term_from_typ T_args in
blanchet@42562
   273
    (s ^ generic_mangled_type_suffix fst ascii_of ty_args,
blanchet@42562
   274
     s' ^ generic_mangled_type_suffix snd I ty_args)
blanchet@42562
   275
  end
blanchet@42542
   276
blanchet@42542
   277
val parse_mangled_ident =
blanchet@42542
   278
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42542
   279
blanchet@42542
   280
fun parse_mangled_type x =
blanchet@42542
   281
  (parse_mangled_ident
blanchet@42542
   282
   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
blanchet@42542
   283
                    [] >> ATerm) x
blanchet@42542
   284
and parse_mangled_types x =
blanchet@42542
   285
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42542
   286
blanchet@42542
   287
fun unmangled_type s =
blanchet@42542
   288
  s |> suffix ")" |> raw_explode
blanchet@42542
   289
    |> Scan.finite Symbol.stopper
blanchet@42542
   290
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   291
                                                quote s)) parse_mangled_type))
blanchet@42542
   292
    |> fst
blanchet@42542
   293
blanchet@42561
   294
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   295
fun unmangled_const s =
blanchet@42542
   296
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   297
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   298
  end
blanchet@42542
   299
blanchet@42674
   300
fun introduce_proxies tm =
blanchet@42568
   301
  let
blanchet@42568
   302
    fun aux top_level (CombApp (tm1, tm2)) =
blanchet@42568
   303
        CombApp (aux top_level tm1, aux false tm2)
blanchet@42574
   304
      | aux top_level (CombConst (name as (s, s'), T, T_args)) =
blanchet@42570
   305
        (case proxify_const s of
blanchet@42568
   306
           SOME proxy_base =>
blanchet@42568
   307
           if top_level then
blanchet@42568
   308
             (case s of
blanchet@42568
   309
                "c_False" => (tptp_false, s')
blanchet@42568
   310
              | "c_True" => (tptp_true, s')
blanchet@42568
   311
              | _ => name, [])
blanchet@42569
   312
           else
blanchet@42574
   313
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   314
          | NONE => (name, T_args))
blanchet@42574
   315
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42568
   316
      | aux _ tm = tm
blanchet@42674
   317
  in aux true tm end
blanchet@42568
   318
blanchet@42562
   319
fun combformula_from_prop thy eq_as_iff =
blanchet@38282
   320
  let
blanchet@42568
   321
    fun do_term bs t atomic_types =
blanchet@41140
   322
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42568
   323
      |>> (introduce_proxies #> AAtom)
blanchet@42568
   324
      ||> union (op =) atomic_types
blanchet@38282
   325
    fun do_quant bs q s T t' =
blanchet@38518
   326
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   327
        do_formula ((s, T) :: bs) t'
blanchet@42562
   328
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   329
      end
blanchet@38282
   330
    and do_conn bs c t1 t2 =
blanchet@38282
   331
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   332
      #>> uncurry (mk_aconn c)
blanchet@38282
   333
    and do_formula bs t =
blanchet@38282
   334
      case t of
blanchet@42531
   335
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   336
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   337
        do_quant bs AForall s T t'
blanchet@38282
   338
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   339
        do_quant bs AExists s T t'
haftmann@38795
   340
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   341
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   342
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   343
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   344
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   345
      | _ => do_term bs t
blanchet@38282
   346
  in do_formula [] end
blanchet@38282
   347
blanchet@38618
   348
val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
blanchet@38282
   349
wenzelm@41491
   350
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   351
fun conceal_bounds Ts t =
blanchet@38282
   352
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   353
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   354
fun reveal_bounds Ts =
blanchet@38282
   355
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   356
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   357
blanchet@38608
   358
(* Removes the lambdas from an equation of the form "t = (%x. u)".
blanchet@39890
   359
   (Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
blanchet@38608
   360
fun extensionalize_term t =
blanchet@38608
   361
  let
blanchet@38608
   362
    fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
blanchet@38608
   363
      | aux j (t as Const (s, Type (_, [Type (_, [_, T']),
blanchet@38608
   364
                                        Type (_, [_, res_T])]))
blanchet@38608
   365
                    $ t2 $ Abs (var_s, var_T, t')) =
haftmann@38864
   366
        if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
blanchet@38608
   367
          let val var_t = Var ((var_s, j), var_T) in
blanchet@38608
   368
            Const (s, T' --> T' --> res_T)
blanchet@38608
   369
              $ betapply (t2, var_t) $ subst_bound (var_t, t')
blanchet@38608
   370
            |> aux (j + 1)
blanchet@38608
   371
          end
blanchet@38608
   372
        else
blanchet@38608
   373
          t
blanchet@38608
   374
      | aux _ t = t
blanchet@38608
   375
  in aux (maxidx_of_term t + 1) t end
blanchet@38608
   376
blanchet@38282
   377
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   378
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   379
    if Meson.is_fol_term thy t then
blanchet@38491
   380
      t
blanchet@38491
   381
    else
blanchet@38491
   382
      let
blanchet@38491
   383
        fun aux Ts t =
blanchet@38491
   384
          case t of
blanchet@38491
   385
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   386
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   387
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   388
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   389
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   390
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   391
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   392
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   393
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   394
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   395
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   396
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   397
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   398
              $ t1 $ t2 =>
blanchet@38491
   399
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   400
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   401
                   t
blanchet@38491
   402
                 else
blanchet@38491
   403
                   t |> conceal_bounds Ts
blanchet@38491
   404
                     |> Envir.eta_contract
blanchet@38491
   405
                     |> cterm_of thy
blanchet@39890
   406
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   407
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   408
                     |> reveal_bounds Ts
blanchet@39370
   409
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   410
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   411
      handle THM _ =>
blanchet@38491
   412
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   413
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   414
             else HOLogic.true_const
blanchet@38491
   415
  end
blanchet@38282
   416
blanchet@38282
   417
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   418
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   419
fun freeze_term t =
blanchet@38282
   420
  let
blanchet@38282
   421
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   422
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   423
      | aux (Var ((s, i), T)) =
blanchet@38282
   424
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   425
      | aux t = t
blanchet@38282
   426
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   427
blanchet@40204
   428
(* making fact and conjecture formulas *)
blanchet@42640
   429
fun make_formula ctxt eq_as_iff presimp name loc kind t =
blanchet@38282
   430
  let
wenzelm@42361
   431
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   432
    val t = t |> Envir.beta_eta_contract
blanchet@38652
   433
              |> transform_elim_term
blanchet@41211
   434
              |> Object_Logic.atomize_term thy
blanchet@42563
   435
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   436
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@38282
   437
              |> extensionalize_term
blanchet@38282
   438
              |> presimp ? presimplify_term thy
blanchet@38282
   439
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   440
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   441
              |> kind <> Axiom ? freeze_term
blanchet@42562
   442
    val (combformula, atomic_types) =
blanchet@42562
   443
      combformula_from_prop thy eq_as_iff t []
blanchet@38282
   444
  in
blanchet@42640
   445
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   446
     atomic_types = atomic_types}
blanchet@38282
   447
  end
blanchet@38282
   448
blanchet@42640
   449
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, loc), t) =
blanchet@42640
   450
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   451
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   452
    NONE
blanchet@41990
   453
  | (_, formula) => SOME formula
blanchet@42561
   454
blanchet@42544
   455
fun make_conjecture ctxt ts =
blanchet@38613
   456
  let val last = length ts - 1 in
blanchet@42640
   457
    map2 (fn j => make_formula ctxt true true (string_of_int j) Chained
blanchet@38613
   458
                               (if j = last then Conjecture else Hypothesis))
blanchet@38613
   459
         (0 upto last) ts
blanchet@38613
   460
  end
blanchet@38282
   461
blanchet@42682
   462
(** Finite and infinite type inference **)
blanchet@42682
   463
blanchet@42682
   464
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   465
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   466
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   467
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   468
blanchet@42682
   469
fun datatype_constrs thy (T as Type (s, Ts)) =
blanchet@42682
   470
    (case Datatype.get_info thy s of
blanchet@42682
   471
       SOME {index, descr, ...} =>
blanchet@42682
   472
       let val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the in
blanchet@42682
   473
         map (apsnd (fn Us => map (typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T))
blanchet@42682
   474
             constrs
blanchet@42682
   475
       end
blanchet@42682
   476
     | NONE => [])
blanchet@42682
   477
  | datatype_constrs _ _ = []
blanchet@42682
   478
blanchet@42682
   479
(* Similar to "Nitpick_HOL.bounded_exact_card_of_type".
blanchet@42682
   480
   0 means infinite type, 1 means singleton type (e.g., "unit"), and 2 means
blanchet@42682
   481
   cardinality 2 or more. The specified default cardinality is returned if the
blanchet@42682
   482
   cardinality of the type can't be determined. *)
blanchet@42682
   483
fun tiny_card_of_type ctxt default_card T =
blanchet@42682
   484
  let
blanchet@42682
   485
    val max = 2 (* 1 would be too small for the "fun" case *)
blanchet@42698
   486
    fun aux slack avoid T =
blanchet@42682
   487
      (if member (op =) avoid T then
blanchet@42682
   488
         0
blanchet@42682
   489
       else case T of
blanchet@42682
   490
         Type (@{type_name fun}, [T1, T2]) =>
blanchet@42698
   491
         (case (aux slack avoid T1, aux slack avoid T2) of
blanchet@42698
   492
            (k, 1) => if slack andalso k = 0 then 0 else 1
blanchet@42682
   493
          | (0, _) => 0
blanchet@42682
   494
          | (_, 0) => 0
blanchet@42682
   495
          | (k1, k2) =>
blanchet@42682
   496
            if k1 >= max orelse k2 >= max then max
blanchet@42682
   497
            else Int.min (max, Integer.pow k2 k1))
blanchet@42682
   498
       | @{typ bool} => 2 (* optimization *)
blanchet@42697
   499
       | @{typ nat} => 0 (* optimization *)
blanchet@42697
   500
       | @{typ int} => 0 (* optimization *)
blanchet@42697
   501
       | Type (s, _) =>
blanchet@42682
   502
         let val thy = Proof_Context.theory_of ctxt in
blanchet@42682
   503
           case datatype_constrs thy T of
blanchet@42697
   504
             constrs as _ :: _ =>
blanchet@42682
   505
             let
blanchet@42682
   506
               val constr_cards =
blanchet@42698
   507
                 map (Integer.prod o map (aux slack (T :: avoid)) o binder_types
blanchet@42682
   508
                      o snd) constrs
blanchet@42682
   509
             in
blanchet@42682
   510
               if exists (curry (op =) 0) constr_cards then 0
blanchet@42682
   511
               else Int.min (max, Integer.sum constr_cards)
blanchet@42682
   512
             end
blanchet@42697
   513
           | [] =>
blanchet@42697
   514
             case Typedef.get_info ctxt s of
blanchet@42697
   515
               ({abs_type, rep_type, ...}, _) :: _ =>
blanchet@42697
   516
               (* We cheat here by assuming that typedef types are infinite if
blanchet@42697
   517
                  their underlying type is infinite. This is unsound in general
blanchet@42697
   518
                  but it's hard to think of a realistic example where this would
blanchet@42698
   519
                  not be the case. We are also slack with representation types:
blanchet@42698
   520
                  If it has the form "sigma => tau", we consider it enough to
blanchet@42698
   521
                  check "sigma" for infiniteness. (Look for "slack" in this
blanchet@42698
   522
                  function.) *)
blanchet@42697
   523
               (case varify_and_instantiate_type ctxt
blanchet@42697
   524
                         (Logic.varifyT_global abs_type) T
blanchet@42697
   525
                         (Logic.varifyT_global rep_type)
blanchet@42698
   526
                     |> aux true avoid of
blanchet@42697
   527
                  0 => 0
blanchet@42697
   528
                | 1 => 1
blanchet@42697
   529
                | _ => default_card)
blanchet@42697
   530
             | [] => default_card
blanchet@42682
   531
         end
blanchet@42698
   532
       | TFree _ =>
blanchet@42698
   533
         (* Very slightly unsound: Type variables are assumed not to be
blanchet@42698
   534
            constrained to have cardinality 1. (In practice, the user would most
blanchet@42698
   535
            likely have used "unit" directly in that case.) *)
blanchet@42698
   536
         if default_card = 1 then 2 else default_card
blanchet@42682
   537
       | _ => default_card)
blanchet@42698
   538
  in Int.min (max, aux false [] T) end
blanchet@42682
   539
blanchet@42682
   540
fun is_type_surely_finite ctxt T = tiny_card_of_type ctxt 0 T <> 0
blanchet@42682
   541
fun is_type_surely_infinite ctxt T = tiny_card_of_type ctxt 1 T = 0
blanchet@42682
   542
blanchet@42682
   543
fun should_encode_type _ _ All_Types _ = true
blanchet@42682
   544
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   545
  | should_encode_type _ nonmono_Ts Nonmonotonic_Types T =
blanchet@42682
   546
    exists (curry Type.raw_instance T) nonmono_Ts
blanchet@42682
   547
  | should_encode_type _ _ _ _ = false
blanchet@42682
   548
blanchet@42682
   549
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level)) T =
blanchet@42682
   550
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   551
  | should_predicate_on_type _ _ _ _ = false
blanchet@42682
   552
blanchet@42682
   553
fun should_tag_with_type ctxt nonmono_Ts (Tags (_, level)) T =
blanchet@42682
   554
    should_encode_type ctxt nonmono_Ts level T
blanchet@42682
   555
  | should_tag_with_type _ _ _ _ = false
blanchet@42682
   556
blanchet@42682
   557
val homo_infinite_T = @{typ ind} (* any infinite type *)
blanchet@42682
   558
blanchet@42682
   559
fun homogenized_type ctxt nonmono_Ts level T =
blanchet@42682
   560
  if should_encode_type ctxt nonmono_Ts level T then T else homo_infinite_T
blanchet@42682
   561
blanchet@42573
   562
(** "hBOOL" and "hAPP" **)
blanchet@41313
   563
blanchet@42574
   564
type sym_info =
blanchet@42563
   565
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   566
blanchet@42574
   567
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   568
  let
blanchet@42558
   569
    fun aux top_level tm =
blanchet@42558
   570
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   571
        (case head of
blanchet@42563
   572
           CombConst ((s, _), T, _) =>
blanchet@42558
   573
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   574
             I
blanchet@42558
   575
           else
blanchet@42563
   576
             let val ary = length args in
blanchet@42558
   577
               Symtab.map_default
blanchet@42558
   578
                   (s, {pred_sym = true,
blanchet@42563
   579
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   580
                        max_ary = 0, typ = SOME T})
blanchet@42563
   581
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   582
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   583
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   584
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   585
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   586
            end
blanchet@42558
   587
         | _ => I)
blanchet@42558
   588
        #> fold (aux false) args
blanchet@42558
   589
      end
blanchet@42558
   590
  in aux true end
blanchet@42674
   591
fun add_fact_syms_to_table explicit_apply =
blanchet@42680
   592
  fact_lift (formula_fold true (K (add_combterm_syms_to_table explicit_apply)))
blanchet@38282
   593
blanchet@42675
   594
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   595
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42568
   596
   (make_fixed_const predicator_base,
blanchet@42563
   597
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   598
  ([tptp_false, tptp_true]
blanchet@42563
   599
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   600
blanchet@42544
   601
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   602
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   603
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   604
blanchet@42558
   605
fun min_arity_of sym_tab s =
blanchet@42558
   606
  case Symtab.lookup sym_tab s of
blanchet@42574
   607
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   608
  | NONE =>
blanchet@42558
   609
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   610
      SOME s =>
blanchet@42570
   611
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42568
   612
        if s = predicator_base then 1
blanchet@42547
   613
        else if s = explicit_app_base then 2
blanchet@42547
   614
        else if s = type_pred_base then 1
blanchet@42557
   615
        else 0
blanchet@42547
   616
      end
blanchet@42544
   617
    | NONE => 0
blanchet@38282
   618
blanchet@38282
   619
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   620
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   621
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   622
   arguments and is used as a predicate. *)
blanchet@42558
   623
fun is_pred_sym sym_tab s =
blanchet@42558
   624
  case Symtab.lookup sym_tab s of
blanchet@42574
   625
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   626
    pred_sym andalso min_ary = max_ary
blanchet@42558
   627
  | NONE => false
blanchet@38282
   628
blanchet@42568
   629
val predicator_combconst =
blanchet@42568
   630
  CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
blanchet@42568
   631
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   632
blanchet@42568
   633
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   634
  case strip_combterm_comb tm of
blanchet@42542
   635
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   636
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   637
  | _ => predicator tm
blanchet@42542
   638
blanchet@42544
   639
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   640
blanchet@42544
   641
fun explicit_app arg head =
blanchet@42544
   642
  let
blanchet@42562
   643
    val head_T = combtyp_of head
blanchet@42693
   644
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   645
    val explicit_app =
blanchet@42562
   646
      CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
blanchet@42693
   647
                 [arg_T, res_T])
blanchet@42544
   648
  in list_app explicit_app [head, arg] end
blanchet@42544
   649
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   650
blanchet@42565
   651
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   652
  let
blanchet@42544
   653
    fun aux tm =
blanchet@42544
   654
      case strip_combterm_comb tm of
blanchet@42544
   655
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   656
        args |> map aux
blanchet@42557
   657
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   658
             |>> list_app head
blanchet@42544
   659
             |-> list_explicit_app
blanchet@42544
   660
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   661
  in aux end
blanchet@38282
   662
blanchet@42690
   663
fun impose_type_arg_policy_in_combterm type_sys =
blanchet@42573
   664
  let
blanchet@42573
   665
    fun aux (CombApp tmp) = CombApp (pairself aux tmp)
blanchet@42574
   666
      | aux (CombConst (name as (s, _), T, T_args)) =
blanchet@42690
   667
        (case strip_prefix_and_unascii const_prefix s of
blanchet@42690
   668
           NONE => (name, T_args)
blanchet@42690
   669
         | SOME s'' =>
blanchet@42690
   670
           let val s'' = invert_const s'' in
blanchet@42690
   671
             case type_arg_policy type_sys s'' of
blanchet@42690
   672
               No_Type_Args => (name, [])
blanchet@42690
   673
             | Explicit_Type_Args => (name, T_args)
blanchet@42690
   674
             | Mangled_Type_Args => (mangled_const_name T_args name, [])
blanchet@42690
   675
           end)
blanchet@42690
   676
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42573
   677
      | aux tm = tm
blanchet@42573
   678
  in aux end
blanchet@42573
   679
blanchet@42690
   680
fun repair_combterm type_sys sym_tab =
blanchet@42565
   681
  introduce_explicit_apps_in_combterm sym_tab
blanchet@42568
   682
  #> introduce_predicators_in_combterm sym_tab
blanchet@42690
   683
  #> impose_type_arg_policy_in_combterm type_sys
blanchet@42690
   684
fun repair_fact type_sys sym_tab =
blanchet@42690
   685
  update_combformula (formula_map (repair_combterm type_sys sym_tab))
blanchet@42573
   686
blanchet@42573
   687
(** Helper facts **)
blanchet@42573
   688
blanchet@42573
   689
fun ti_ti_helper_fact () =
blanchet@42573
   690
  let
blanchet@42573
   691
    fun var s = ATerm (`I s, [])
blanchet@42589
   692
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   693
  in
blanchet@42612
   694
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   695
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42573
   696
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   697
  end
blanchet@42573
   698
blanchet@42574
   699
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   700
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   701
    SOME mangled_s =>
blanchet@42573
   702
    let
blanchet@42573
   703
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   704
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42579
   705
      fun dub_and_inst c needs_some_types (th, j) =
blanchet@42579
   706
        ((c ^ "_" ^ string_of_int j ^ (if needs_some_types then "T" else ""),
blanchet@42640
   707
          Chained),
blanchet@42573
   708
         let val t = th |> prop_of in
blanchet@42589
   709
           t |> (general_type_arg_policy type_sys = Mangled_Type_Args andalso
blanchet@42573
   710
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   711
                ? (case typ of
blanchet@42573
   712
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   713
                   | NONE => I)
blanchet@42573
   714
         end)
blanchet@42573
   715
      fun make_facts eq_as_iff =
blanchet@42573
   716
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42589
   717
      val has_some_types = is_type_sys_fairly_sound type_sys
blanchet@42573
   718
    in
blanchet@42573
   719
      metis_helpers
blanchet@42579
   720
      |> maps (fn (metis_s, (needs_some_types, ths)) =>
blanchet@42573
   721
                  if metis_s <> unmangled_s orelse
blanchet@42589
   722
                     (needs_some_types andalso not has_some_types) then
blanchet@42573
   723
                    []
blanchet@42573
   724
                  else
blanchet@42573
   725
                    ths ~~ (1 upto length ths)
blanchet@42579
   726
                    |> map (dub_and_inst mangled_s needs_some_types)
blanchet@42579
   727
                    |> make_facts (not needs_some_types))
blanchet@42573
   728
    end
blanchet@42573
   729
  | NONE => []
blanchet@42573
   730
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
blanchet@42573
   731
  Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
blanchet@42573
   732
blanchet@42573
   733
fun translate_atp_fact ctxt keep_trivial =
blanchet@42573
   734
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@42573
   735
blanchet@42573
   736
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
blanchet@42573
   737
  let
blanchet@42573
   738
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   739
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   740
    val (facts, fact_names) =
blanchet@42573
   741
      rich_facts
blanchet@42573
   742
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   743
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   744
      |> ListPair.unzip
blanchet@42573
   745
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   746
       boost an ATP's performance (for some reason). *)
blanchet@42573
   747
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   748
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   749
    val all_ts = goal_t :: fact_ts
blanchet@42573
   750
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   751
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   752
    val tycons = type_consts_of_terms thy all_ts
blanchet@42573
   753
    val conjs = make_conjecture ctxt (hyp_ts @ [concl_t])
blanchet@42573
   754
    val (supers', arity_clauses) =
blanchet@42589
   755
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   756
      else make_arity_clauses thy tycons supers
blanchet@42573
   757
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   758
  in
blanchet@42573
   759
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   760
  end
blanchet@42573
   761
blanchet@42573
   762
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   763
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   764
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   765
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   766
blanchet@42573
   767
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   768
blanchet@42690
   769
fun type_pred_combatom type_sys T tm =
blanchet@42573
   770
  CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T]),
blanchet@42573
   771
           tm)
blanchet@42690
   772
  |> impose_type_arg_policy_in_combterm type_sys
blanchet@42573
   773
  |> AAtom
blanchet@42573
   774
blanchet@42680
   775
fun formula_from_combformula ctxt nonmono_Ts type_sys =
blanchet@42573
   776
  let
blanchet@42589
   777
    fun tag_with_type type_sys T tm =
blanchet@42589
   778
      CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42690
   779
      |> impose_type_arg_policy_in_combterm type_sys
blanchet@42589
   780
      |> do_term true
blanchet@42589
   781
      |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42589
   782
    and do_term top_level u =
blanchet@42573
   783
      let
blanchet@42573
   784
        val (head, args) = strip_combterm_comb u
blanchet@42574
   785
        val (x, T_args) =
blanchet@42573
   786
          case head of
blanchet@42574
   787
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42573
   788
          | CombVar (name, _) => (name, [])
blanchet@42573
   789
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42574
   790
        val t = ATerm (x, map fo_term_from_typ T_args @
blanchet@42573
   791
                          map (do_term false) args)
blanchet@42574
   792
        val T = combtyp_of u
blanchet@42573
   793
      in
blanchet@42680
   794
        t |> (if not top_level andalso
blanchet@42680
   795
                should_tag_with_type ctxt nonmono_Ts type_sys T then
blanchet@42589
   796
                tag_with_type type_sys T
blanchet@42573
   797
              else
blanchet@42573
   798
                I)
blanchet@42573
   799
      end
blanchet@42573
   800
    val do_bound_type =
blanchet@42682
   801
      case type_sys of
blanchet@42684
   802
        Simple level =>
blanchet@42682
   803
        SOME o mangled_type_name o homogenized_type ctxt nonmono_Ts level
blanchet@42682
   804
      | _ => K NONE
blanchet@42573
   805
    fun do_out_of_bound_type (s, T) =
blanchet@42680
   806
      if should_predicate_on_type ctxt nonmono_Ts type_sys T then
blanchet@42690
   807
        type_pred_combatom type_sys T (CombVar (s, T))
blanchet@42573
   808
        |> do_formula |> SOME
blanchet@42573
   809
      else
blanchet@42573
   810
        NONE
blanchet@42573
   811
    and do_formula (AQuant (q, xs, phi)) =
blanchet@42573
   812
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42574
   813
                                      | SOME T => do_bound_type T)),
blanchet@42573
   814
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42573
   815
                    (map_filter
blanchet@42573
   816
                         (fn (_, NONE) => NONE
blanchet@42574
   817
                           | (s, SOME T) => do_out_of_bound_type (s, T)) xs)
blanchet@42573
   818
                    (do_formula phi))
blanchet@42573
   819
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42573
   820
      | do_formula (AAtom tm) = AAtom (do_term true tm)
blanchet@42573
   821
  in do_formula end
blanchet@42573
   822
blanchet@42680
   823
fun formula_for_fact ctxt nonmono_Ts type_sys
blanchet@42573
   824
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42573
   825
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42573
   826
                (atp_type_literals_for_types type_sys Axiom atomic_types))
blanchet@42680
   827
           (formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42573
   828
                (close_combformula_universally combformula))
blanchet@42573
   829
  |> close_formula_universally
blanchet@42573
   830
blanchet@42640
   831
fun useful_isabelle_info s = SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
blanchet@42640
   832
blanchet@42573
   833
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   834
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   835
   the remote provers might care. *)
blanchet@42680
   836
fun formula_line_for_fact ctxt prefix nonmono_Ts type_sys
blanchet@42640
   837
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
   838
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
   839
                     else string_of_int j ^ "_") ^
blanchet@42647
   840
           ascii_of name,
blanchet@42680
   841
           kind, formula_for_fact ctxt nonmono_Ts type_sys formula, NONE,
blanchet@42640
   842
           if generate_useful_info then
blanchet@42640
   843
             case locality of
blanchet@42640
   844
               Intro => useful_isabelle_info "intro"
blanchet@42640
   845
             | Elim => useful_isabelle_info "elim"
blanchet@42640
   846
             | Simp => useful_isabelle_info "simp"
blanchet@42640
   847
             | _ => NONE
blanchet@42640
   848
           else
blanchet@42640
   849
             NONE)
blanchet@42573
   850
blanchet@42573
   851
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@42573
   852
                                                       superclass, ...}) =
blanchet@42573
   853
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   854
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   855
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   856
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42573
   857
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   858
  end
blanchet@42573
   859
blanchet@42573
   860
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   861
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   862
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   863
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   864
blanchet@42573
   865
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@42573
   866
                                                ...}) =
blanchet@42577
   867
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   868
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42573
   869
                          o fo_literal_from_arity_literal) premLits)
blanchet@42573
   870
                    (formula_from_fo_literal
blanchet@42573
   871
                         (fo_literal_from_arity_literal conclLit))
blanchet@42573
   872
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   873
blanchet@42680
   874
fun formula_line_for_conjecture ctxt nonmono_Ts type_sys
blanchet@42573
   875
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   876
  Formula (conjecture_prefix ^ name, kind,
blanchet@42680
   877
           formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42573
   878
                                    (close_combformula_universally combformula)
blanchet@42573
   879
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   880
blanchet@42573
   881
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@42573
   882
  atomic_types |> atp_type_literals_for_types type_sys Conjecture
blanchet@42573
   883
               |> map fo_literal_from_type_literal
blanchet@42573
   884
blanchet@42573
   885
fun formula_line_for_free_type j lit =
blanchet@42577
   886
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   887
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42573
   888
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
   889
  let
blanchet@42573
   890
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
   891
    val lits = fold (union (op =)) litss []
blanchet@42573
   892
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   893
blanchet@42573
   894
(** Symbol declarations **)
blanchet@42544
   895
blanchet@42677
   896
fun insert_type get_T x xs =
blanchet@42677
   897
  let val T = get_T x in
blanchet@42677
   898
    if exists (curry Type.raw_instance T o get_T) xs then xs
blanchet@42677
   899
    else x :: filter_out ((fn T' => Type.raw_instance (T', T)) o get_T) xs
blanchet@42677
   900
  end
blanchet@42677
   901
blanchet@42574
   902
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
   903
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42645
   904
  not (String.isPrefix "$" s) andalso
blanchet@42684
   905
  ((case type_sys of Simple _ => true | _ => false) orelse not pred_sym)
blanchet@38282
   906
blanchet@42698
   907
fun sym_decl_table_for_facts type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
   908
  let
blanchet@42698
   909
    fun add_combterm in_conj tm =
blanchet@42574
   910
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
   911
        (case head of
blanchet@42574
   912
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
   913
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
   914
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
   915
               Symtab.map_default (s, [])
blanchet@42698
   916
                   (insert_type #3 (s', T_args, T, pred_sym, length args,
blanchet@42698
   917
                                    in_conj))
blanchet@42574
   918
             else
blanchet@42574
   919
               I
blanchet@42574
   920
           end
blanchet@42574
   921
         | _ => I)
blanchet@42698
   922
        #> fold (add_combterm in_conj) args
blanchet@42574
   923
      end
blanchet@42698
   924
    fun add_fact in_conj =
blanchet@42698
   925
      fact_lift (formula_fold true (K (add_combterm in_conj)))
blanchet@42698
   926
  in
blanchet@42698
   927
    Symtab.empty
blanchet@42698
   928
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
   929
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
   930
  end
blanchet@42533
   931
blanchet@42677
   932
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42677
   933
    String.isPrefix bound_var_prefix s
blanchet@42677
   934
  | is_var_or_bound_var (CombVar _) = true
blanchet@42677
   935
  | is_var_or_bound_var _ = false
blanchet@42677
   936
blanchet@42685
   937
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
   938
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42680
   939
fun add_combterm_nonmonotonic_types _ (SOME false) _ = I
blanchet@42680
   940
  | add_combterm_nonmonotonic_types ctxt _
blanchet@42680
   941
        (CombApp (CombApp (CombConst (("equal", _), Type (_, [T, _]), _), tm1),
blanchet@42680
   942
                  tm2)) =
blanchet@42680
   943
    (exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42680
   944
     not (is_type_surely_infinite ctxt T)) ? insert_type I T
blanchet@42680
   945
  | add_combterm_nonmonotonic_types _ _ _ = I
blanchet@42680
   946
fun add_fact_nonmonotonic_types ctxt ({kind, combformula, ...}
blanchet@42680
   947
                                      : translated_formula) =
blanchet@42680
   948
  formula_fold (kind <> Conjecture) (add_combterm_nonmonotonic_types ctxt)
blanchet@42680
   949
               combformula
blanchet@42680
   950
fun add_nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42680
   951
  level_of_type_sys type_sys = Nonmonotonic_Types
blanchet@42682
   952
  ? (insert_type I @{typ bool} (* in case helper "True_or_False" is included *)
blanchet@42682
   953
     #> fold (add_fact_nonmonotonic_types ctxt) facts)
blanchet@42677
   954
blanchet@42574
   955
fun n_ary_strip_type 0 T = ([], T)
blanchet@42574
   956
  | n_ary_strip_type n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42574
   957
    n_ary_strip_type (n - 1) ran_T |>> cons dom_T
blanchet@42574
   958
  | n_ary_strip_type _ _ = raise Fail "unexpected non-function"
blanchet@42533
   959
blanchet@42698
   960
fun result_type_of_decl (_, _, T, _, ary, _) = n_ary_strip_type ary T |> snd
blanchet@42579
   961
blanchet@42698
   962
fun decl_line_for_sym s (s', _, T, pred_sym, ary, _) =
blanchet@42579
   963
  let val (arg_Ts, res_T) = n_ary_strip_type ary T in
blanchet@42612
   964
    Decl (sym_decl_prefix ^ s, (s, s'), map mangled_type_name arg_Ts,
blanchet@42579
   965
          if pred_sym then `I tptp_tff_bool_type else mangled_type_name res_T)
blanchet@42579
   966
  end
blanchet@42579
   967
blanchet@42592
   968
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
   969
blanchet@42680
   970
fun formula_line_for_sym_decl ctxt nonmono_Ts type_sys n s j
blanchet@42698
   971
                              (s', T_args, T, _, ary, in_conj) =
blanchet@42579
   972
  let
blanchet@42579
   973
    val (arg_Ts, res_T) = n_ary_strip_type ary T
blanchet@42579
   974
    val bound_names =
blanchet@42579
   975
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42579
   976
    val bound_tms =
blanchet@42579
   977
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
   978
    val bound_Ts =
blanchet@42592
   979
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
   980
                             else NONE)
blanchet@42579
   981
  in
blanchet@42612
   982
    Formula (sym_decl_prefix ^ s ^
blanchet@42698
   983
             (if n > 1 then "_" ^ string_of_int j else ""),
blanchet@42698
   984
             if in_conj then Hypothesis else Axiom,
blanchet@42579
   985
             CombConst ((s, s'), T, T_args)
blanchet@42579
   986
             |> fold (curry (CombApp o swap)) bound_tms
blanchet@42690
   987
             |> type_pred_combatom type_sys res_T
blanchet@42579
   988
             |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42680
   989
             |> formula_from_combformula ctxt nonmono_Ts type_sys
blanchet@42586
   990
             |> close_formula_universally,
blanchet@42579
   991
             NONE, NONE)
blanchet@42579
   992
  end
blanchet@42579
   993
blanchet@42680
   994
fun problem_lines_for_sym_decls ctxt nonmono_Ts type_sys (s, decls) =
blanchet@42682
   995
  case type_sys of
blanchet@42684
   996
    Simple _ => map (decl_line_for_sym s) decls
blanchet@42682
   997
  | _ =>
blanchet@42574
   998
    let
blanchet@42579
   999
      val decls =
blanchet@42579
  1000
        case decls of
blanchet@42579
  1001
          decl :: (decls' as _ :: _) =>
blanchet@42592
  1002
          let val T = result_type_of_decl decl in
blanchet@42592
  1003
            if forall ((fn T' => Type.raw_instance (T', T))
blanchet@42592
  1004
                       o result_type_of_decl) decls' then
blanchet@42592
  1005
              [decl]
blanchet@42592
  1006
            else
blanchet@42592
  1007
              decls
blanchet@42592
  1008
          end
blanchet@42579
  1009
        | _ => decls
blanchet@42579
  1010
      val n = length decls
blanchet@42579
  1011
      val decls =
blanchet@42680
  1012
        decls |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42579
  1013
                         o result_type_of_decl)
blanchet@42574
  1014
    in
blanchet@42680
  1015
      map2 (formula_line_for_sym_decl ctxt nonmono_Ts type_sys n s)
blanchet@42579
  1016
           (0 upto length decls - 1) decls
blanchet@42574
  1017
    end
blanchet@42579
  1018
blanchet@42680
  1019
fun problem_lines_for_sym_decl_table ctxt nonmono_Ts type_sys sym_decl_tab =
blanchet@42680
  1020
  Symtab.fold_rev (append o problem_lines_for_sym_decls ctxt nonmono_Ts
blanchet@42680
  1021
                                                        type_sys)
blanchet@42574
  1022
                  sym_decl_tab []
blanchet@42543
  1023
blanchet@42543
  1024
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
  1025
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
  1026
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
  1027
    fold add_tff_types_in_formula phis
blanchet@42543
  1028
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
  1029
blanchet@42562
  1030
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
blanchet@42562
  1031
    union (op =) (res_T :: arg_Ts)
blanchet@42577
  1032
  | add_tff_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42543
  1033
    add_tff_types_in_formula phi
blanchet@42543
  1034
blanchet@42543
  1035
fun tff_types_in_problem problem =
blanchet@42543
  1036
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
  1037
blanchet@42545
  1038
fun decl_line_for_tff_type (s, s') =
blanchet@42568
  1039
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
blanchet@42543
  1040
blanchet@42543
  1041
val type_declsN = "Types"
blanchet@42544
  1042
val sym_declsN = "Symbol types"
blanchet@41157
  1043
val factsN = "Relevant facts"
blanchet@41157
  1044
val class_relsN = "Class relationships"
blanchet@42543
  1045
val aritiesN = "Arities"
blanchet@41157
  1046
val helpersN = "Helper facts"
blanchet@41157
  1047
val conjsN = "Conjectures"
blanchet@41313
  1048
val free_typesN = "Type variables"
blanchet@41157
  1049
blanchet@41157
  1050
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
  1051
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
  1052
    if heading = needle then j
blanchet@41157
  1053
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
  1054
blanchet@42568
  1055
fun prepare_atp_problem ctxt type_sys explicit_apply hyp_ts concl_t facts =
blanchet@38282
  1056
  let
blanchet@41313
  1057
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@41134
  1058
      translate_formulas ctxt type_sys hyp_ts concl_t facts
blanchet@42563
  1059
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42682
  1060
    val nonmono_Ts =
blanchet@42682
  1061
      [] |> fold (add_nonmonotonic_types_for_facts ctxt type_sys) [facts, conjs]
blanchet@42690
  1062
    val repair = repair_fact type_sys sym_tab
blanchet@42682
  1063
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@42680
  1064
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42573
  1065
    val helpers =
blanchet@42682
  1066
      repaired_sym_tab |> helper_facts_for_sym_table ctxt type_sys |> map repair
blanchet@42680
  1067
    val sym_decl_lines =
blanchet@42698
  1068
      (conjs, facts) (* FIXME: what if "True_or_False" is among helpers? *)
blanchet@42680
  1069
      |> sym_decl_table_for_facts type_sys repaired_sym_tab
blanchet@42680
  1070
      |> problem_lines_for_sym_decl_table ctxt nonmono_Ts type_sys
blanchet@42522
  1071
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
  1072
       Flotter hack. *)
blanchet@38282
  1073
    val problem =
blanchet@42561
  1074
      [(sym_declsN, sym_decl_lines),
blanchet@42680
  1075
       (factsN, map (formula_line_for_fact ctxt fact_prefix nonmono_Ts type_sys)
blanchet@42180
  1076
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1077
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1078
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42680
  1079
       (helpersN, map (formula_line_for_fact ctxt helper_prefix nonmono_Ts
blanchet@42680
  1080
                                             type_sys)
blanchet@42563
  1081
                      (0 upto length helpers - 1 ~~ helpers)
blanchet@42579
  1082
                  |> (case type_sys of
blanchet@42589
  1083
                        Tags (Polymorphic, level) =>
blanchet@42687
  1084
                        is_type_level_partial level
blanchet@42589
  1085
                        ? cons (ti_ti_helper_fact ())
blanchet@42579
  1086
                      | _ => I)),
blanchet@42680
  1087
       (conjsN, map (formula_line_for_conjecture ctxt nonmono_Ts type_sys)
blanchet@42680
  1088
                    conjs),
blanchet@42545
  1089
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
  1090
    val problem =
blanchet@42561
  1091
      problem
blanchet@42682
  1092
      |> (case type_sys of
blanchet@42684
  1093
            Simple _ =>
blanchet@42561
  1094
            cons (type_declsN,
blanchet@42561
  1095
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42682
  1096
          | _ => I)
blanchet@42646
  1097
    val (problem, pool) =
blanchet@42646
  1098
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@38282
  1099
  in
blanchet@38282
  1100
    (problem,
blanchet@38282
  1101
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1102
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1103
     offset_of_heading_in_problem factsN problem 0,
blanchet@41157
  1104
     fact_names |> Vector.fromList)
blanchet@38282
  1105
  end
blanchet@38282
  1106
blanchet@41313
  1107
(* FUDGE *)
blanchet@41313
  1108
val conj_weight = 0.0
blanchet@41770
  1109
val hyp_weight = 0.1
blanchet@41770
  1110
val fact_min_weight = 0.2
blanchet@41313
  1111
val fact_max_weight = 1.0
blanchet@42608
  1112
val type_info_default_weight = 0.8
blanchet@41313
  1113
blanchet@41313
  1114
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@41313
  1115
  (not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
blanchet@41313
  1116
  #> fold (add_term_weights weight) tms
blanchet@42577
  1117
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42680
  1118
    formula_fold true (K (add_term_weights weight)) phi
blanchet@42528
  1119
  | add_problem_line_weights _ _ = I
blanchet@41313
  1120
blanchet@41313
  1121
fun add_conjectures_weights [] = I
blanchet@41313
  1122
  | add_conjectures_weights conjs =
blanchet@41313
  1123
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1124
      add_problem_line_weights conj_weight conj
blanchet@41313
  1125
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1126
    end
blanchet@41313
  1127
blanchet@41313
  1128
fun add_facts_weights facts =
blanchet@41313
  1129
  let
blanchet@41313
  1130
    val num_facts = length facts
blanchet@41313
  1131
    fun weight_of j =
blanchet@41313
  1132
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1133
                        / Real.fromInt num_facts
blanchet@41313
  1134
  in
blanchet@41313
  1135
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1136
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1137
  end
blanchet@41313
  1138
blanchet@41313
  1139
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1140
fun atp_problem_weights problem =
blanchet@42608
  1141
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1142
    Symtab.empty
blanchet@42608
  1143
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1144
    |> add_facts_weights (get factsN)
blanchet@42608
  1145
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1146
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1147
    |> Symtab.dest
blanchet@42608
  1148
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1149
  end
blanchet@41313
  1150
blanchet@38282
  1151
end;