src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Wed May 04 11:49:46 2011 +0200 (2011-05-04)
changeset 42675 223153bb68a1
parent 42674 af86324707f2
child 42677 25496cd3c199
permissions -rw-r--r--
added type annotation for SML/NJ
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@42613
    20
    Many_Typed |
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@42613
    99
  Many_Typed |
blanchet@42613
   100
  Preds of polymorphism * type_level |
blanchet@42613
   101
  Tags of polymorphism * type_level
blanchet@42613
   102
blanchet@42613
   103
fun type_sys_from_string s =
blanchet@42613
   104
  (case try (unprefix "mangled_") s of
blanchet@42613
   105
     SOME s => (Mangled_Monomorphic, s)
blanchet@42613
   106
   | NONE =>
blanchet@42613
   107
     case try (unprefix "mono_") s of
blanchet@42613
   108
       SOME s => (Monomorphic, s)
blanchet@42613
   109
     | NONE => (Polymorphic, s))
blanchet@42613
   110
  ||> (fn s =>
blanchet@42613
   111
          case try (unsuffix " ?") s of
blanchet@42613
   112
            SOME s => (Nonmonotonic_Types, s)
blanchet@42613
   113
          | NONE =>
blanchet@42613
   114
            case try (unsuffix " !") s of
blanchet@42613
   115
              SOME s => (Finite_Types, s)
blanchet@42613
   116
            | NONE => (All_Types, s))
blanchet@42613
   117
  |> (fn (polymorphism, (level, core)) =>
blanchet@42613
   118
         case (core, (polymorphism, level)) of
blanchet@42613
   119
           ("many_typed", (Polymorphic (* naja *), All_Types)) =>
blanchet@42613
   120
           Many_Typed
blanchet@42613
   121
         | ("preds", extra) => Preds extra
blanchet@42613
   122
         | ("tags", extra) => Tags extra
blanchet@42613
   123
         | ("const_args", (_, All_Types (* naja *))) =>
blanchet@42613
   124
           Preds (polymorphism, Const_Arg_Types)
blanchet@42613
   125
         | ("erased", (Polymorphic, All_Types (* naja *))) =>
blanchet@42613
   126
           Preds (polymorphism, No_Types)
blanchet@42613
   127
         | _ => error ("Unknown type system: " ^ quote s ^ "."))
blanchet@42613
   128
blanchet@42613
   129
fun polymorphism_of_type_sys Many_Typed = Mangled_Monomorphic
blanchet@42613
   130
  | polymorphism_of_type_sys (Preds (poly, _)) = poly
blanchet@42613
   131
  | polymorphism_of_type_sys (Tags (poly, _)) = poly
blanchet@42613
   132
blanchet@42613
   133
fun level_of_type_sys Many_Typed = All_Types
blanchet@42613
   134
  | level_of_type_sys (Preds (_, level)) = level
blanchet@42613
   135
  | level_of_type_sys (Tags (_, level)) = level
blanchet@42613
   136
blanchet@42670
   137
fun is_type_level_virtually_sound s =
blanchet@42670
   138
  s = All_Types orelse s = Nonmonotonic_Types
blanchet@42613
   139
val is_type_sys_virtually_sound =
blanchet@42613
   140
  is_type_level_virtually_sound o level_of_type_sys
blanchet@42613
   141
blanchet@42613
   142
fun is_type_level_fairly_sound level =
blanchet@42613
   143
  is_type_level_virtually_sound level orelse level = Finite_Types
blanchet@42613
   144
val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
blanchet@42613
   145
blanchet@42573
   146
fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi)
blanchet@42573
   147
  | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis)
blanchet@42573
   148
  | formula_map f (AAtom tm) = AAtom (f tm)
blanchet@42573
   149
blanchet@42573
   150
fun formula_fold f (AQuant (_, _, phi)) = formula_fold f phi
blanchet@42573
   151
  | formula_fold f (AConn (_, phis)) = fold (formula_fold f) phis
blanchet@42573
   152
  | formula_fold f (AAtom tm) = f tm
blanchet@42573
   153
blanchet@40114
   154
type translated_formula =
blanchet@38752
   155
  {name: string,
blanchet@42640
   156
   locality: locality,
blanchet@42525
   157
   kind: formula_kind,
blanchet@42562
   158
   combformula: (name, typ, combterm) formula,
blanchet@42562
   159
   atomic_types: typ list}
blanchet@38282
   160
blanchet@42640
   161
fun update_combformula f ({name, locality, kind, combformula, atomic_types}
blanchet@42640
   162
                          : translated_formula) =
blanchet@42640
   163
  {name = name, locality = locality, kind = kind, combformula = f combformula,
blanchet@42562
   164
   atomic_types = atomic_types} : translated_formula
blanchet@42542
   165
blanchet@42558
   166
fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
blanchet@42558
   167
blanchet@42572
   168
val boring_consts = [explicit_app_base, @{const_name Metis.fequal}]
blanchet@42572
   169
blanchet@42572
   170
fun should_omit_type_args type_sys s =
blanchet@42589
   171
  s <> type_pred_base andalso s <> type_tag_name andalso
blanchet@42589
   172
  (s = @{const_name HOL.eq} orelse level_of_type_sys type_sys = No_Types orelse
blanchet@42589
   173
   (case type_sys of
blanchet@42589
   174
      Tags (_, All_Types) => true
blanchet@42589
   175
    | _ => polymorphism_of_type_sys type_sys <> Mangled_Monomorphic andalso
blanchet@42589
   176
           member (op =) boring_consts s))
blanchet@42589
   177
  
blanchet@42589
   178
datatype type_arg_policy = No_Type_Args | Explicit_Type_Args | Mangled_Type_Args
blanchet@41136
   179
blanchet@42589
   180
fun general_type_arg_policy type_sys =
blanchet@42589
   181
  if level_of_type_sys type_sys = No_Types then
blanchet@42589
   182
    No_Type_Args
blanchet@42589
   183
  else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
blanchet@42589
   184
    Mangled_Type_Args
blanchet@42589
   185
  else
blanchet@42589
   186
    Explicit_Type_Args
blanchet@42563
   187
blanchet@42524
   188
fun type_arg_policy type_sys s =
blanchet@42572
   189
  if should_omit_type_args type_sys s then No_Type_Args
blanchet@42563
   190
  else general_type_arg_policy type_sys
blanchet@42227
   191
blanchet@41136
   192
fun num_atp_type_args thy type_sys s =
blanchet@42557
   193
  if type_arg_policy type_sys s = Explicit_Type_Args then num_type_args thy s
blanchet@42557
   194
  else 0
blanchet@41136
   195
blanchet@42353
   196
fun atp_type_literals_for_types type_sys kind Ts =
blanchet@42589
   197
  if level_of_type_sys type_sys = No_Types then
blanchet@42353
   198
    []
blanchet@42353
   199
  else
blanchet@42353
   200
    Ts |> type_literals_for_types
blanchet@42353
   201
       |> filter (fn TyLitVar _ => kind <> Conjecture
blanchet@42353
   202
                   | TyLitFree _ => kind = Conjecture)
blanchet@41137
   203
blanchet@38282
   204
fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
blanchet@42534
   205
fun mk_aconns c phis =
blanchet@42534
   206
  let val (phis', phi') = split_last phis in
blanchet@42534
   207
    fold_rev (mk_aconn c) phis' phi'
blanchet@42534
   208
  end
blanchet@38282
   209
fun mk_ahorn [] phi = phi
blanchet@42534
   210
  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
blanchet@42522
   211
fun mk_aquant _ [] phi = phi
blanchet@42522
   212
  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
blanchet@42522
   213
    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
blanchet@42522
   214
  | mk_aquant q xs phi = AQuant (q, xs, phi)
blanchet@38282
   215
blanchet@42522
   216
fun close_universally atom_vars phi =
blanchet@41145
   217
  let
blanchet@41145
   218
    fun formula_vars bounds (AQuant (_, xs, phi)) =
blanchet@42526
   219
        formula_vars (map fst xs @ bounds) phi
blanchet@41145
   220
      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
blanchet@42522
   221
      | formula_vars bounds (AAtom tm) =
blanchet@42526
   222
        union (op =) (atom_vars tm []
blanchet@42526
   223
                      |> filter_out (member (op =) bounds o fst))
blanchet@42522
   224
  in mk_aquant AForall (formula_vars [] phi []) phi end
blanchet@42522
   225
blanchet@42531
   226
fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
blanchet@42522
   227
  | combterm_vars (CombConst _) = I
blanchet@42574
   228
  | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
blanchet@42674
   229
fun close_combformula_universally phi = close_universally combterm_vars phi
blanchet@42522
   230
blanchet@42522
   231
fun term_vars (ATerm (name as (s, _), tms)) =
blanchet@42531
   232
  is_atp_variable s ? insert (op =) (name, NONE)
blanchet@42526
   233
  #> fold term_vars tms
blanchet@42674
   234
fun close_formula_universally phi = close_universally term_vars phi
blanchet@41145
   235
blanchet@42562
   236
fun fo_term_from_typ (Type (s, Ts)) =
blanchet@42562
   237
    ATerm (`make_fixed_type_const s, map fo_term_from_typ Ts)
blanchet@42562
   238
  | fo_term_from_typ (TFree (s, _)) =
blanchet@42562
   239
    ATerm (`make_fixed_type_var s, [])
blanchet@42562
   240
  | fo_term_from_typ (TVar ((x as (s, _)), _)) =
blanchet@42562
   241
    ATerm ((make_schematic_type_var x, s), [])
blanchet@42562
   242
blanchet@42562
   243
(* This shouldn't clash with anything else. *)
blanchet@42542
   244
val mangled_type_sep = "\000"
blanchet@42542
   245
blanchet@42562
   246
fun generic_mangled_type_name f (ATerm (name, [])) = f name
blanchet@42562
   247
  | generic_mangled_type_name f (ATerm (name, tys)) =
blanchet@42562
   248
    f name ^ "(" ^ commas (map (generic_mangled_type_name f) tys) ^ ")"
blanchet@42562
   249
val mangled_type_name =
blanchet@42562
   250
  fo_term_from_typ
blanchet@42562
   251
  #> (fn ty => (make_tff_type (generic_mangled_type_name fst ty),
blanchet@42562
   252
                generic_mangled_type_name snd ty))
blanchet@42542
   253
blanchet@42574
   254
fun generic_mangled_type_suffix f g Ts =
blanchet@42542
   255
  fold_rev (curry (op ^) o g o prefix mangled_type_sep
blanchet@42574
   256
            o generic_mangled_type_name f) Ts ""
blanchet@42562
   257
fun mangled_const_name T_args (s, s') =
blanchet@42562
   258
  let val ty_args = map fo_term_from_typ T_args in
blanchet@42562
   259
    (s ^ generic_mangled_type_suffix fst ascii_of ty_args,
blanchet@42562
   260
     s' ^ generic_mangled_type_suffix snd I ty_args)
blanchet@42562
   261
  end
blanchet@42542
   262
blanchet@42542
   263
val parse_mangled_ident =
blanchet@42542
   264
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42542
   265
blanchet@42542
   266
fun parse_mangled_type x =
blanchet@42542
   267
  (parse_mangled_ident
blanchet@42542
   268
   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
blanchet@42542
   269
                    [] >> ATerm) x
blanchet@42542
   270
and parse_mangled_types x =
blanchet@42542
   271
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42542
   272
blanchet@42542
   273
fun unmangled_type s =
blanchet@42542
   274
  s |> suffix ")" |> raw_explode
blanchet@42542
   275
    |> Scan.finite Symbol.stopper
blanchet@42542
   276
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   277
                                                quote s)) parse_mangled_type))
blanchet@42542
   278
    |> fst
blanchet@42542
   279
blanchet@42561
   280
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   281
fun unmangled_const s =
blanchet@42542
   282
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   283
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   284
  end
blanchet@42542
   285
blanchet@42674
   286
fun introduce_proxies tm =
blanchet@42568
   287
  let
blanchet@42568
   288
    fun aux top_level (CombApp (tm1, tm2)) =
blanchet@42568
   289
        CombApp (aux top_level tm1, aux false tm2)
blanchet@42574
   290
      | aux top_level (CombConst (name as (s, s'), T, T_args)) =
blanchet@42570
   291
        (case proxify_const s of
blanchet@42568
   292
           SOME proxy_base =>
blanchet@42568
   293
           if top_level then
blanchet@42568
   294
             (case s of
blanchet@42568
   295
                "c_False" => (tptp_false, s')
blanchet@42568
   296
              | "c_True" => (tptp_true, s')
blanchet@42568
   297
              | _ => name, [])
blanchet@42569
   298
           else
blanchet@42574
   299
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   300
          | NONE => (name, T_args))
blanchet@42574
   301
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42568
   302
      | aux _ tm = tm
blanchet@42674
   303
  in aux true tm end
blanchet@42568
   304
blanchet@42562
   305
fun combformula_from_prop thy eq_as_iff =
blanchet@38282
   306
  let
blanchet@42568
   307
    fun do_term bs t atomic_types =
blanchet@41140
   308
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42568
   309
      |>> (introduce_proxies #> AAtom)
blanchet@42568
   310
      ||> union (op =) atomic_types
blanchet@38282
   311
    fun do_quant bs q s T t' =
blanchet@38518
   312
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   313
        do_formula ((s, T) :: bs) t'
blanchet@42562
   314
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   315
      end
blanchet@38282
   316
    and do_conn bs c t1 t2 =
blanchet@38282
   317
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   318
      #>> uncurry (mk_aconn c)
blanchet@38282
   319
    and do_formula bs t =
blanchet@38282
   320
      case t of
blanchet@42531
   321
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   322
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   323
        do_quant bs AForall s T t'
blanchet@38282
   324
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   325
        do_quant bs AExists s T t'
haftmann@38795
   326
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   327
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   328
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   329
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   330
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   331
      | _ => do_term bs t
blanchet@38282
   332
  in do_formula [] end
blanchet@38282
   333
blanchet@38618
   334
val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
blanchet@38282
   335
wenzelm@41491
   336
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   337
fun conceal_bounds Ts t =
blanchet@38282
   338
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   339
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   340
fun reveal_bounds Ts =
blanchet@38282
   341
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   342
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   343
blanchet@38608
   344
(* Removes the lambdas from an equation of the form "t = (%x. u)".
blanchet@39890
   345
   (Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
blanchet@38608
   346
fun extensionalize_term t =
blanchet@38608
   347
  let
blanchet@38608
   348
    fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
blanchet@38608
   349
      | aux j (t as Const (s, Type (_, [Type (_, [_, T']),
blanchet@38608
   350
                                        Type (_, [_, res_T])]))
blanchet@38608
   351
                    $ t2 $ Abs (var_s, var_T, t')) =
haftmann@38864
   352
        if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
blanchet@38608
   353
          let val var_t = Var ((var_s, j), var_T) in
blanchet@38608
   354
            Const (s, T' --> T' --> res_T)
blanchet@38608
   355
              $ betapply (t2, var_t) $ subst_bound (var_t, t')
blanchet@38608
   356
            |> aux (j + 1)
blanchet@38608
   357
          end
blanchet@38608
   358
        else
blanchet@38608
   359
          t
blanchet@38608
   360
      | aux _ t = t
blanchet@38608
   361
  in aux (maxidx_of_term t + 1) t end
blanchet@38608
   362
blanchet@38282
   363
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   364
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   365
    if Meson.is_fol_term thy t then
blanchet@38491
   366
      t
blanchet@38491
   367
    else
blanchet@38491
   368
      let
blanchet@38491
   369
        fun aux Ts t =
blanchet@38491
   370
          case t of
blanchet@38491
   371
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   372
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   373
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   374
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   375
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   376
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   377
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   378
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   379
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   380
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   381
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   382
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   383
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   384
              $ t1 $ t2 =>
blanchet@38491
   385
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   386
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   387
                   t
blanchet@38491
   388
                 else
blanchet@38491
   389
                   t |> conceal_bounds Ts
blanchet@38491
   390
                     |> Envir.eta_contract
blanchet@38491
   391
                     |> cterm_of thy
blanchet@39890
   392
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   393
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   394
                     |> reveal_bounds Ts
blanchet@39370
   395
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   396
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   397
      handle THM _ =>
blanchet@38491
   398
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   399
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   400
             else HOLogic.true_const
blanchet@38491
   401
  end
blanchet@38282
   402
blanchet@38282
   403
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   404
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   405
fun freeze_term t =
blanchet@38282
   406
  let
blanchet@38282
   407
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   408
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   409
      | aux (Var ((s, i), T)) =
blanchet@38282
   410
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   411
      | aux t = t
blanchet@38282
   412
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   413
blanchet@40204
   414
(* making fact and conjecture formulas *)
blanchet@42640
   415
fun make_formula ctxt eq_as_iff presimp name loc kind t =
blanchet@38282
   416
  let
wenzelm@42361
   417
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   418
    val t = t |> Envir.beta_eta_contract
blanchet@38652
   419
              |> transform_elim_term
blanchet@41211
   420
              |> Object_Logic.atomize_term thy
blanchet@42563
   421
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@38652
   422
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@38282
   423
              |> extensionalize_term
blanchet@38282
   424
              |> presimp ? presimplify_term thy
blanchet@38282
   425
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   426
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   427
              |> kind <> Axiom ? freeze_term
blanchet@42562
   428
    val (combformula, atomic_types) =
blanchet@42562
   429
      combformula_from_prop thy eq_as_iff t []
blanchet@38282
   430
  in
blanchet@42640
   431
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   432
     atomic_types = atomic_types}
blanchet@38282
   433
  end
blanchet@38282
   434
blanchet@42640
   435
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, loc), t) =
blanchet@42640
   436
  case (keep_trivial, make_formula ctxt eq_as_iff presimp name loc Axiom t) of
blanchet@41990
   437
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   438
    NONE
blanchet@41990
   439
  | (_, formula) => SOME formula
blanchet@42561
   440
blanchet@42544
   441
fun make_conjecture ctxt ts =
blanchet@38613
   442
  let val last = length ts - 1 in
blanchet@42640
   443
    map2 (fn j => make_formula ctxt true true (string_of_int j) Chained
blanchet@38613
   444
                               (if j = last then Conjecture else Hypothesis))
blanchet@38613
   445
         (0 upto last) ts
blanchet@38613
   446
  end
blanchet@38282
   447
blanchet@42573
   448
(** "hBOOL" and "hAPP" **)
blanchet@41313
   449
blanchet@42574
   450
type sym_info =
blanchet@42563
   451
  {pred_sym : bool, min_ary : int, max_ary : int, typ : typ option}
blanchet@42563
   452
blanchet@42574
   453
fun add_combterm_syms_to_table explicit_apply =
blanchet@42558
   454
  let
blanchet@42558
   455
    fun aux top_level tm =
blanchet@42558
   456
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
   457
        (case head of
blanchet@42563
   458
           CombConst ((s, _), T, _) =>
blanchet@42558
   459
           if String.isPrefix bound_var_prefix s then
blanchet@42558
   460
             I
blanchet@42558
   461
           else
blanchet@42563
   462
             let val ary = length args in
blanchet@42558
   463
               Symtab.map_default
blanchet@42558
   464
                   (s, {pred_sym = true,
blanchet@42563
   465
                        min_ary = if explicit_apply then 0 else ary,
blanchet@42563
   466
                        max_ary = 0, typ = SOME T})
blanchet@42563
   467
                   (fn {pred_sym, min_ary, max_ary, typ} =>
blanchet@42558
   468
                       {pred_sym = pred_sym andalso top_level,
blanchet@42563
   469
                        min_ary = Int.min (ary, min_ary),
blanchet@42563
   470
                        max_ary = Int.max (ary, max_ary),
blanchet@42563
   471
                        typ = if typ = SOME T then typ else NONE})
blanchet@42558
   472
            end
blanchet@42558
   473
         | _ => I)
blanchet@42558
   474
        #> fold (aux false) args
blanchet@42558
   475
      end
blanchet@42558
   476
  in aux true end
blanchet@42674
   477
fun add_fact_syms_to_table explicit_apply =
blanchet@42674
   478
  fact_lift (formula_fold (add_combterm_syms_to_table explicit_apply))
blanchet@38282
   479
blanchet@42675
   480
val default_sym_table_entries : (string * sym_info) list =
blanchet@42563
   481
  [("equal", {pred_sym = true, min_ary = 2, max_ary = 2, typ = NONE}),
blanchet@42568
   482
   (make_fixed_const predicator_base,
blanchet@42563
   483
    {pred_sym = true, min_ary = 1, max_ary = 1, typ = NONE})] @
blanchet@42568
   484
  ([tptp_false, tptp_true]
blanchet@42563
   485
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, typ = NONE}))
blanchet@41140
   486
blanchet@42544
   487
fun sym_table_for_facts explicit_apply facts =
blanchet@42568
   488
  Symtab.empty |> fold Symtab.default default_sym_table_entries
blanchet@42574
   489
               |> fold (add_fact_syms_to_table explicit_apply) facts
blanchet@38282
   490
blanchet@42558
   491
fun min_arity_of sym_tab s =
blanchet@42558
   492
  case Symtab.lookup sym_tab s of
blanchet@42574
   493
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
   494
  | NONE =>
blanchet@42558
   495
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
   496
      SOME s =>
blanchet@42570
   497
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42568
   498
        if s = predicator_base then 1
blanchet@42547
   499
        else if s = explicit_app_base then 2
blanchet@42547
   500
        else if s = type_pred_base then 1
blanchet@42557
   501
        else 0
blanchet@42547
   502
      end
blanchet@42544
   503
    | NONE => 0
blanchet@38282
   504
blanchet@38282
   505
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   506
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   507
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   508
   arguments and is used as a predicate. *)
blanchet@42558
   509
fun is_pred_sym sym_tab s =
blanchet@42558
   510
  case Symtab.lookup sym_tab s of
blanchet@42574
   511
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
   512
    pred_sym andalso min_ary = max_ary
blanchet@42558
   513
  | NONE => false
blanchet@38282
   514
blanchet@42568
   515
val predicator_combconst =
blanchet@42568
   516
  CombConst (`make_fixed_const predicator_base, @{typ "bool => bool"}, [])
blanchet@42568
   517
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
   518
blanchet@42568
   519
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
   520
  case strip_combterm_comb tm of
blanchet@42542
   521
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
   522
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
   523
  | _ => predicator tm
blanchet@42542
   524
blanchet@42544
   525
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
   526
blanchet@42544
   527
fun explicit_app arg head =
blanchet@42544
   528
  let
blanchet@42562
   529
    val head_T = combtyp_of head
blanchet@42562
   530
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
   531
    val explicit_app =
blanchet@42562
   532
      CombConst (`make_fixed_const explicit_app_base, head_T --> head_T,
blanchet@42562
   533
                 [arg_T, res_T])
blanchet@42544
   534
  in list_app explicit_app [head, arg] end
blanchet@42544
   535
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
   536
blanchet@42565
   537
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
   538
  let
blanchet@42544
   539
    fun aux tm =
blanchet@42544
   540
      case strip_combterm_comb tm of
blanchet@42544
   541
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
   542
        args |> map aux
blanchet@42557
   543
             |> chop (min_arity_of sym_tab s)
blanchet@42544
   544
             |>> list_app head
blanchet@42544
   545
             |-> list_explicit_app
blanchet@42544
   546
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
   547
  in aux end
blanchet@38282
   548
blanchet@42573
   549
fun impose_type_arg_policy_in_combterm type_sys =
blanchet@42573
   550
  let
blanchet@42573
   551
    fun aux (CombApp tmp) = CombApp (pairself aux tmp)
blanchet@42574
   552
      | aux (CombConst (name as (s, _), T, T_args)) =
blanchet@42573
   553
        (case strip_prefix_and_unascii const_prefix s of
blanchet@42574
   554
           NONE => (name, T_args)
blanchet@42573
   555
         | SOME s'' =>
blanchet@42573
   556
           let val s'' = invert_const s'' in
blanchet@42573
   557
             case type_arg_policy type_sys s'' of
blanchet@42573
   558
               No_Type_Args => (name, [])
blanchet@42574
   559
             | Explicit_Type_Args => (name, T_args)
blanchet@42589
   560
             | Mangled_Type_Args => (mangled_const_name T_args name, [])
blanchet@42573
   561
           end)
blanchet@42574
   562
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42573
   563
      | aux tm = tm
blanchet@42573
   564
  in aux end
blanchet@42573
   565
blanchet@42573
   566
fun repair_combterm type_sys sym_tab =
blanchet@42565
   567
  introduce_explicit_apps_in_combterm sym_tab
blanchet@42568
   568
  #> introduce_predicators_in_combterm sym_tab
blanchet@42573
   569
  #> impose_type_arg_policy_in_combterm type_sys
blanchet@42674
   570
fun repair_fact type_sys sym_tab =
blanchet@42674
   571
  update_combformula (formula_map (repair_combterm type_sys sym_tab))
blanchet@42573
   572
blanchet@42573
   573
(** Helper facts **)
blanchet@42573
   574
blanchet@42573
   575
fun ti_ti_helper_fact () =
blanchet@42573
   576
  let
blanchet@42573
   577
    fun var s = ATerm (`I s, [])
blanchet@42589
   578
    fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
blanchet@42573
   579
  in
blanchet@42612
   580
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@42573
   581
             AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42573
   582
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   583
  end
blanchet@42573
   584
blanchet@42574
   585
fun helper_facts_for_sym ctxt type_sys (s, {typ, ...} : sym_info) =
blanchet@42573
   586
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
   587
    SOME mangled_s =>
blanchet@42573
   588
    let
blanchet@42573
   589
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
   590
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42579
   591
      fun dub_and_inst c needs_some_types (th, j) =
blanchet@42579
   592
        ((c ^ "_" ^ string_of_int j ^ (if needs_some_types then "T" else ""),
blanchet@42640
   593
          Chained),
blanchet@42573
   594
         let val t = th |> prop_of in
blanchet@42589
   595
           t |> (general_type_arg_policy type_sys = Mangled_Type_Args andalso
blanchet@42573
   596
                 not (null (Term.hidden_polymorphism t)))
blanchet@42573
   597
                ? (case typ of
blanchet@42573
   598
                     SOME T => specialize_type thy (invert_const unmangled_s, T)
blanchet@42573
   599
                   | NONE => I)
blanchet@42573
   600
         end)
blanchet@42573
   601
      fun make_facts eq_as_iff =
blanchet@42573
   602
        map_filter (make_fact ctxt false eq_as_iff false)
blanchet@42589
   603
      val has_some_types = is_type_sys_fairly_sound type_sys
blanchet@42573
   604
    in
blanchet@42573
   605
      metis_helpers
blanchet@42579
   606
      |> maps (fn (metis_s, (needs_some_types, ths)) =>
blanchet@42573
   607
                  if metis_s <> unmangled_s orelse
blanchet@42589
   608
                     (needs_some_types andalso not has_some_types) then
blanchet@42573
   609
                    []
blanchet@42573
   610
                  else
blanchet@42573
   611
                    ths ~~ (1 upto length ths)
blanchet@42579
   612
                    |> map (dub_and_inst mangled_s needs_some_types)
blanchet@42579
   613
                    |> make_facts (not needs_some_types))
blanchet@42573
   614
    end
blanchet@42573
   615
  | NONE => []
blanchet@42573
   616
fun helper_facts_for_sym_table ctxt type_sys sym_tab =
blanchet@42573
   617
  Symtab.fold_rev (append o helper_facts_for_sym ctxt type_sys) sym_tab []
blanchet@42573
   618
blanchet@42573
   619
fun translate_atp_fact ctxt keep_trivial =
blanchet@42573
   620
  `(make_fact ctxt keep_trivial true true o apsnd prop_of)
blanchet@42573
   621
blanchet@42573
   622
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
blanchet@42573
   623
  let
blanchet@42573
   624
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
   625
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
   626
    val (facts, fact_names) =
blanchet@42573
   627
      rich_facts
blanchet@42573
   628
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
   629
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
   630
      |> ListPair.unzip
blanchet@42573
   631
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
   632
       boost an ATP's performance (for some reason). *)
blanchet@42573
   633
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
   634
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
   635
    val all_ts = goal_t :: fact_ts
blanchet@42573
   636
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
   637
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
   638
    val tycons = type_consts_of_terms thy all_ts
blanchet@42573
   639
    val conjs = make_conjecture ctxt (hyp_ts @ [concl_t])
blanchet@42573
   640
    val (supers', arity_clauses) =
blanchet@42589
   641
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
   642
      else make_arity_clauses thy tycons supers
blanchet@42573
   643
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
   644
  in
blanchet@42573
   645
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
   646
  end
blanchet@42573
   647
blanchet@42573
   648
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
   649
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   650
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
   651
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
   652
blanchet@42573
   653
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
   654
blanchet@42573
   655
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42573
   656
   considered dangerous because their "exhaust" properties can easily lead to
blanchet@42573
   657
   unsound ATP proofs. The checks below are an (unsound) approximation of
blanchet@42573
   658
   finiteness. *)
blanchet@42573
   659
blanchet@42589
   660
fun is_dtyp_finite _ (Datatype_Aux.DtTFree _) = true
blanchet@42589
   661
  | is_dtyp_finite ctxt (Datatype_Aux.DtType (s, Us)) =
blanchet@42589
   662
    is_type_constr_finite ctxt s andalso forall (is_dtyp_finite ctxt) Us
blanchet@42589
   663
  | is_dtyp_finite _ (Datatype_Aux.DtRec _) = false
blanchet@42589
   664
and is_type_finite ctxt (Type (s, Ts)) =
blanchet@42589
   665
    is_type_constr_finite ctxt s andalso forall (is_type_finite ctxt) Ts
blanchet@42589
   666
  | is_type_finite _ _ = false
blanchet@42589
   667
and is_type_constr_finite ctxt s =
blanchet@42573
   668
  let val thy = Proof_Context.theory_of ctxt in
blanchet@42573
   669
    case Datatype_Data.get_info thy s of
blanchet@42573
   670
      SOME {descr, ...} =>
blanchet@42573
   671
      forall (fn (_, (_, _, constrs)) =>
blanchet@42589
   672
                 forall (forall (is_dtyp_finite ctxt) o snd) constrs) descr
blanchet@42573
   673
    | NONE =>
blanchet@42573
   674
      case Typedef.get_info ctxt s of
blanchet@42589
   675
        ({rep_type, ...}, _) :: _ => is_type_finite ctxt rep_type
blanchet@42573
   676
      | [] => true
blanchet@42573
   677
  end
blanchet@42573
   678
blanchet@42589
   679
fun should_encode_type _ All_Types _ = true
blanchet@42589
   680
  | should_encode_type ctxt Finite_Types T = is_type_finite ctxt T
blanchet@42589
   681
  | should_encode_type _ Nonmonotonic_Types _ =
blanchet@42589
   682
    error "Monotonicity inference not implemented yet."
blanchet@42589
   683
  | should_encode_type _ _ _ = false
blanchet@42589
   684
blanchet@42589
   685
fun should_predicate_on_type ctxt (Preds (_, level)) T =
blanchet@42589
   686
    should_encode_type ctxt level T
blanchet@42589
   687
  | should_predicate_on_type _ _ _ = false
blanchet@42579
   688
blanchet@42579
   689
fun should_tag_with_type ctxt (Tags (_, level)) T =
blanchet@42579
   690
    should_encode_type ctxt level T
blanchet@42573
   691
  | should_tag_with_type _ _ _ = false
blanchet@42573
   692
blanchet@42573
   693
fun type_pred_combatom type_sys T tm =
blanchet@42573
   694
  CombApp (CombConst (`make_fixed_const type_pred_base, T --> @{typ bool}, [T]),
blanchet@42573
   695
           tm)
blanchet@42573
   696
  |> impose_type_arg_policy_in_combterm type_sys
blanchet@42573
   697
  |> AAtom
blanchet@42573
   698
blanchet@42573
   699
fun formula_from_combformula ctxt type_sys =
blanchet@42573
   700
  let
blanchet@42589
   701
    fun tag_with_type type_sys T tm =
blanchet@42589
   702
      CombConst (`make_fixed_const type_tag_name, T --> T, [T])
blanchet@42589
   703
      |> impose_type_arg_policy_in_combterm type_sys
blanchet@42589
   704
      |> do_term true
blanchet@42589
   705
      |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42589
   706
    and do_term top_level u =
blanchet@42573
   707
      let
blanchet@42573
   708
        val (head, args) = strip_combterm_comb u
blanchet@42574
   709
        val (x, T_args) =
blanchet@42573
   710
          case head of
blanchet@42574
   711
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42573
   712
          | CombVar (name, _) => (name, [])
blanchet@42573
   713
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42574
   714
        val t = ATerm (x, map fo_term_from_typ T_args @
blanchet@42573
   715
                          map (do_term false) args)
blanchet@42574
   716
        val T = combtyp_of u
blanchet@42573
   717
      in
blanchet@42574
   718
        t |> (if not top_level andalso should_tag_with_type ctxt type_sys T then
blanchet@42589
   719
                tag_with_type type_sys T
blanchet@42573
   720
              else
blanchet@42573
   721
                I)
blanchet@42573
   722
      end
blanchet@42573
   723
    val do_bound_type =
blanchet@42573
   724
      if type_sys = Many_Typed then SOME o mangled_type_name else K NONE
blanchet@42573
   725
    fun do_out_of_bound_type (s, T) =
blanchet@42579
   726
      if should_predicate_on_type ctxt type_sys T then
blanchet@42573
   727
        type_pred_combatom type_sys T (CombVar (s, T))
blanchet@42573
   728
        |> do_formula |> SOME
blanchet@42573
   729
      else
blanchet@42573
   730
        NONE
blanchet@42573
   731
    and do_formula (AQuant (q, xs, phi)) =
blanchet@42573
   732
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42574
   733
                                      | SOME T => do_bound_type T)),
blanchet@42573
   734
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42573
   735
                    (map_filter
blanchet@42573
   736
                         (fn (_, NONE) => NONE
blanchet@42574
   737
                           | (s, SOME T) => do_out_of_bound_type (s, T)) xs)
blanchet@42573
   738
                    (do_formula phi))
blanchet@42573
   739
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42573
   740
      | do_formula (AAtom tm) = AAtom (do_term true tm)
blanchet@42573
   741
  in do_formula end
blanchet@42573
   742
blanchet@42573
   743
fun formula_for_fact ctxt type_sys
blanchet@42573
   744
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42573
   745
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@42573
   746
                (atp_type_literals_for_types type_sys Axiom atomic_types))
blanchet@42573
   747
           (formula_from_combformula ctxt type_sys
blanchet@42573
   748
                (close_combformula_universally combformula))
blanchet@42573
   749
  |> close_formula_universally
blanchet@42573
   750
blanchet@42640
   751
fun useful_isabelle_info s = SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
blanchet@42640
   752
blanchet@42573
   753
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
   754
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
   755
   the remote provers might care. *)
blanchet@42573
   756
fun formula_line_for_fact ctxt prefix type_sys
blanchet@42640
   757
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42647
   758
  Formula (prefix ^
blanchet@42647
   759
           (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42647
   760
            else string_of_int j ^ "_") ^
blanchet@42647
   761
           ascii_of name,
blanchet@42647
   762
           kind, formula_for_fact ctxt type_sys formula, NONE,
blanchet@42640
   763
           if generate_useful_info then
blanchet@42640
   764
             case locality of
blanchet@42640
   765
               Intro => useful_isabelle_info "intro"
blanchet@42640
   766
             | Elim => useful_isabelle_info "elim"
blanchet@42640
   767
             | Simp => useful_isabelle_info "simp"
blanchet@42640
   768
             | _ => NONE
blanchet@42640
   769
           else
blanchet@42640
   770
             NONE)
blanchet@42573
   771
blanchet@42573
   772
fun formula_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@42573
   773
                                                       superclass, ...}) =
blanchet@42573
   774
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
   775
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   776
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
   777
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42573
   778
             |> close_formula_universally, NONE, NONE)
blanchet@42573
   779
  end
blanchet@42573
   780
blanchet@42573
   781
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
   782
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
   783
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
   784
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
   785
blanchet@42573
   786
fun formula_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@42573
   787
                                                ...}) =
blanchet@42577
   788
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
   789
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42573
   790
                          o fo_literal_from_arity_literal) premLits)
blanchet@42573
   791
                    (formula_from_fo_literal
blanchet@42573
   792
                         (fo_literal_from_arity_literal conclLit))
blanchet@42573
   793
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   794
blanchet@42573
   795
fun formula_line_for_conjecture ctxt type_sys
blanchet@42573
   796
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42577
   797
  Formula (conjecture_prefix ^ name, kind,
blanchet@42573
   798
           formula_from_combformula ctxt type_sys
blanchet@42573
   799
                                    (close_combformula_universally combformula)
blanchet@42573
   800
           |> close_formula_universally, NONE, NONE)
blanchet@42573
   801
blanchet@42573
   802
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@42573
   803
  atomic_types |> atp_type_literals_for_types type_sys Conjecture
blanchet@42573
   804
               |> map fo_literal_from_type_literal
blanchet@42573
   805
blanchet@42573
   806
fun formula_line_for_free_type j lit =
blanchet@42577
   807
  Formula (tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
   808
           formula_from_fo_literal lit, NONE, NONE)
blanchet@42573
   809
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
   810
  let
blanchet@42573
   811
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
   812
    val lits = fold (union (op =)) litss []
blanchet@42573
   813
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
   814
blanchet@42573
   815
(** Symbol declarations **)
blanchet@42544
   816
blanchet@42574
   817
fun should_declare_sym type_sys pred_sym s =
blanchet@42542
   818
  not (String.isPrefix bound_var_prefix s) andalso s <> "equal" andalso
blanchet@42645
   819
  not (String.isPrefix "$" s) andalso
blanchet@42574
   820
  (type_sys = Many_Typed orelse not pred_sym)
blanchet@38282
   821
blanchet@42574
   822
fun add_combterm_syms_to_decl_table type_sys repaired_sym_tab =
blanchet@42574
   823
  let
blanchet@42576
   824
    fun declare_sym (decl as (_, _, T, _, _)) decls =
blanchet@42579
   825
      case type_sys of
blanchet@42589
   826
        Preds (Polymorphic, All_Types) =>
blanchet@42579
   827
        if exists (curry Type.raw_instance T o #3) decls then
blanchet@42579
   828
          decls
blanchet@42579
   829
        else
blanchet@42579
   830
          decl :: filter_out ((fn T' => Type.raw_instance (T', T)) o #3) decls
blanchet@42579
   831
      | _ => insert (op =) decl decls
blanchet@42576
   832
    fun do_term tm =
blanchet@42574
   833
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
   834
        (case head of
blanchet@42574
   835
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
   836
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
   837
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
   838
               Symtab.map_default (s, [])
blanchet@42576
   839
                   (declare_sym (s', T_args, T, pred_sym, length args))
blanchet@42574
   840
             else
blanchet@42574
   841
               I
blanchet@42574
   842
           end
blanchet@42574
   843
         | _ => I)
blanchet@42576
   844
        #> fold do_term args
blanchet@42574
   845
      end
blanchet@42576
   846
  in do_term end
blanchet@42574
   847
fun add_fact_syms_to_decl_table type_sys repaired_sym_tab =
blanchet@42574
   848
  fact_lift (formula_fold
blanchet@42574
   849
      (add_combterm_syms_to_decl_table type_sys repaired_sym_tab))
blanchet@42574
   850
fun sym_decl_table_for_facts type_sys repaired_sym_tab facts =
blanchet@42589
   851
  Symtab.empty |> is_type_sys_fairly_sound type_sys
blanchet@42574
   852
                  ? fold (add_fact_syms_to_decl_table type_sys repaired_sym_tab)
blanchet@42574
   853
                         facts
blanchet@42533
   854
blanchet@42574
   855
fun n_ary_strip_type 0 T = ([], T)
blanchet@42574
   856
  | n_ary_strip_type n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42574
   857
    n_ary_strip_type (n - 1) ran_T |>> cons dom_T
blanchet@42574
   858
  | n_ary_strip_type _ _ = raise Fail "unexpected non-function"
blanchet@42533
   859
blanchet@42579
   860
fun result_type_of_decl (_, _, T, _, ary) = n_ary_strip_type ary T |> snd
blanchet@42579
   861
blanchet@42579
   862
fun decl_line_for_sym_decl s (s', _, T, pred_sym, ary) =
blanchet@42579
   863
  let val (arg_Ts, res_T) = n_ary_strip_type ary T in
blanchet@42612
   864
    Decl (sym_decl_prefix ^ s, (s, s'), map mangled_type_name arg_Ts,
blanchet@42579
   865
          if pred_sym then `I tptp_tff_bool_type else mangled_type_name res_T)
blanchet@42579
   866
  end
blanchet@42579
   867
blanchet@42592
   868
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
   869
blanchet@42579
   870
fun formula_line_for_sym_decl ctxt type_sys n s j (s', T_args, T, _, ary) =
blanchet@42579
   871
  let
blanchet@42579
   872
    val (arg_Ts, res_T) = n_ary_strip_type ary T
blanchet@42579
   873
    val bound_names =
blanchet@42579
   874
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42579
   875
    val bound_tms =
blanchet@42579
   876
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
   877
    val bound_Ts =
blanchet@42592
   878
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
   879
                             else NONE)
blanchet@42579
   880
  in
blanchet@42612
   881
    Formula (sym_decl_prefix ^ s ^
blanchet@42612
   882
             (if n > 1 then "_" ^ string_of_int j else ""), Axiom,
blanchet@42579
   883
             CombConst ((s, s'), T, T_args)
blanchet@42579
   884
             |> fold (curry (CombApp o swap)) bound_tms
blanchet@42579
   885
             |> type_pred_combatom type_sys res_T
blanchet@42579
   886
             |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42586
   887
             |> formula_from_combformula ctxt type_sys
blanchet@42586
   888
             |> close_formula_universally,
blanchet@42579
   889
             NONE, NONE)
blanchet@42579
   890
  end
blanchet@42579
   891
blanchet@42579
   892
fun problem_lines_for_sym_decls ctxt type_sys (s, decls) =
blanchet@42574
   893
  if type_sys = Many_Typed then
blanchet@42579
   894
    map (decl_line_for_sym_decl s) decls
blanchet@42574
   895
  else
blanchet@42574
   896
    let
blanchet@42579
   897
      val decls =
blanchet@42579
   898
        case decls of
blanchet@42579
   899
          decl :: (decls' as _ :: _) =>
blanchet@42592
   900
          let val T = result_type_of_decl decl in
blanchet@42592
   901
            if forall ((fn T' => Type.raw_instance (T', T))
blanchet@42592
   902
                       o result_type_of_decl) decls' then
blanchet@42592
   903
              [decl]
blanchet@42592
   904
            else
blanchet@42592
   905
              decls
blanchet@42592
   906
          end
blanchet@42579
   907
        | _ => decls
blanchet@42579
   908
      val n = length decls
blanchet@42579
   909
      val decls =
blanchet@42579
   910
        decls |> filter (should_predicate_on_type ctxt type_sys
blanchet@42579
   911
                         o result_type_of_decl)
blanchet@42574
   912
    in
blanchet@42579
   913
      map2 (formula_line_for_sym_decl ctxt type_sys n s)
blanchet@42579
   914
           (0 upto length decls - 1) decls
blanchet@42574
   915
    end
blanchet@42579
   916
blanchet@42574
   917
fun problem_lines_for_sym_decl_table ctxt type_sys sym_decl_tab =
blanchet@42574
   918
  Symtab.fold_rev (append o problem_lines_for_sym_decls ctxt type_sys)
blanchet@42574
   919
                  sym_decl_tab []
blanchet@42543
   920
blanchet@42543
   921
fun add_tff_types_in_formula (AQuant (_, xs, phi)) =
blanchet@42543
   922
    union (op =) (map_filter snd xs) #> add_tff_types_in_formula phi
blanchet@42543
   923
  | add_tff_types_in_formula (AConn (_, phis)) =
blanchet@42543
   924
    fold add_tff_types_in_formula phis
blanchet@42543
   925
  | add_tff_types_in_formula (AAtom _) = I
blanchet@42539
   926
blanchet@42562
   927
fun add_tff_types_in_problem_line (Decl (_, _, arg_Ts, res_T)) =
blanchet@42562
   928
    union (op =) (res_T :: arg_Ts)
blanchet@42577
   929
  | add_tff_types_in_problem_line (Formula (_, _, phi, _, _)) =
blanchet@42543
   930
    add_tff_types_in_formula phi
blanchet@42543
   931
blanchet@42543
   932
fun tff_types_in_problem problem =
blanchet@42543
   933
  fold (fold add_tff_types_in_problem_line o snd) problem []
blanchet@42543
   934
blanchet@42545
   935
fun decl_line_for_tff_type (s, s') =
blanchet@42568
   936
  Decl (type_decl_prefix ^ ascii_of s, (s, s'), [], `I tptp_tff_type_of_types)
blanchet@42543
   937
blanchet@42543
   938
val type_declsN = "Types"
blanchet@42544
   939
val sym_declsN = "Symbol types"
blanchet@41157
   940
val factsN = "Relevant facts"
blanchet@41157
   941
val class_relsN = "Class relationships"
blanchet@42543
   942
val aritiesN = "Arities"
blanchet@41157
   943
val helpersN = "Helper facts"
blanchet@41157
   944
val conjsN = "Conjectures"
blanchet@41313
   945
val free_typesN = "Type variables"
blanchet@41157
   946
blanchet@41157
   947
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
   948
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
   949
    if heading = needle then j
blanchet@41157
   950
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
   951
blanchet@42568
   952
fun prepare_atp_problem ctxt type_sys explicit_apply hyp_ts concl_t facts =
blanchet@38282
   953
  let
blanchet@41313
   954
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@41134
   955
      translate_formulas ctxt type_sys hyp_ts concl_t facts
blanchet@42563
   956
    val sym_tab = conjs @ facts |> sym_table_for_facts explicit_apply
blanchet@42565
   957
    val (conjs, facts) =
blanchet@42573
   958
      (conjs, facts) |> pairself (map (repair_fact type_sys sym_tab))
blanchet@42573
   959
    val repaired_sym_tab = conjs @ facts |> sym_table_for_facts false
blanchet@42561
   960
    val sym_decl_lines =
blanchet@42574
   961
      conjs @ facts
blanchet@42574
   962
      |> sym_decl_table_for_facts type_sys repaired_sym_tab
blanchet@42574
   963
      |> problem_lines_for_sym_decl_table ctxt type_sys
blanchet@42573
   964
    val helpers =
blanchet@42573
   965
      helper_facts_for_sym_table ctxt type_sys repaired_sym_tab
blanchet@42573
   966
      |> map (repair_fact type_sys sym_tab)
blanchet@42522
   967
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
   968
       Flotter hack. *)
blanchet@38282
   969
    val problem =
blanchet@42561
   970
      [(sym_declsN, sym_decl_lines),
blanchet@42545
   971
       (factsN, map (formula_line_for_fact ctxt fact_prefix type_sys)
blanchet@42180
   972
                    (0 upto length facts - 1 ~~ facts)),
blanchet@42545
   973
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
   974
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42561
   975
       (helpersN, map (formula_line_for_fact ctxt helper_prefix type_sys)
blanchet@42563
   976
                      (0 upto length helpers - 1 ~~ helpers)
blanchet@42579
   977
                  |> (case type_sys of
blanchet@42589
   978
                        Tags (Polymorphic, level) =>
blanchet@42589
   979
                        member (op =) [Finite_Types, Nonmonotonic_Types] level
blanchet@42589
   980
                        ? cons (ti_ti_helper_fact ())
blanchet@42579
   981
                      | _ => I)),
blanchet@42545
   982
       (conjsN, map (formula_line_for_conjecture ctxt type_sys) conjs),
blanchet@42545
   983
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
   984
    val problem =
blanchet@42561
   985
      problem
blanchet@42561
   986
      |> (if type_sys = Many_Typed then
blanchet@42561
   987
            cons (type_declsN,
blanchet@42561
   988
                  map decl_line_for_tff_type (tff_types_in_problem problem))
blanchet@42561
   989
          else
blanchet@42561
   990
            I)
blanchet@42646
   991
    val (problem, pool) =
blanchet@42646
   992
      problem |> nice_atp_problem (Config.get ctxt readable_names)
blanchet@38282
   993
  in
blanchet@38282
   994
    (problem,
blanchet@38282
   995
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
   996
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
   997
     offset_of_heading_in_problem factsN problem 0,
blanchet@41157
   998
     fact_names |> Vector.fromList)
blanchet@38282
   999
  end
blanchet@38282
  1000
blanchet@41313
  1001
(* FUDGE *)
blanchet@41313
  1002
val conj_weight = 0.0
blanchet@41770
  1003
val hyp_weight = 0.1
blanchet@41770
  1004
val fact_min_weight = 0.2
blanchet@41313
  1005
val fact_max_weight = 1.0
blanchet@42608
  1006
val type_info_default_weight = 0.8
blanchet@41313
  1007
blanchet@41313
  1008
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@41313
  1009
  (not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
blanchet@41313
  1010
  #> fold (add_term_weights weight) tms
blanchet@42577
  1011
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42542
  1012
    formula_fold (add_term_weights weight) phi
blanchet@42528
  1013
  | add_problem_line_weights _ _ = I
blanchet@41313
  1014
blanchet@41313
  1015
fun add_conjectures_weights [] = I
blanchet@41313
  1016
  | add_conjectures_weights conjs =
blanchet@41313
  1017
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1018
      add_problem_line_weights conj_weight conj
blanchet@41313
  1019
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1020
    end
blanchet@41313
  1021
blanchet@41313
  1022
fun add_facts_weights facts =
blanchet@41313
  1023
  let
blanchet@41313
  1024
    val num_facts = length facts
blanchet@41313
  1025
    fun weight_of j =
blanchet@41313
  1026
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1027
                        / Real.fromInt num_facts
blanchet@41313
  1028
  in
blanchet@41313
  1029
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1030
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1031
  end
blanchet@41313
  1032
blanchet@41313
  1033
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1034
fun atp_problem_weights problem =
blanchet@42608
  1035
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1036
    Symtab.empty
blanchet@42608
  1037
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1038
    |> add_facts_weights (get factsN)
blanchet@42608
  1039
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42608
  1040
            [sym_declsN, class_relsN, aritiesN]
blanchet@42608
  1041
    |> Symtab.dest
blanchet@42608
  1042
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1043
  end
blanchet@41313
  1044
blanchet@38282
  1045
end;