src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
author blanchet
Sun May 01 18:37:24 2011 +0200 (2011-05-01)
changeset 42538 9e3e45636459
parent 42534 46e690db16b8
child 42539 f6ba908b8b27
permissions -rw-r--r--
generate pure TFF problems -- ToFoF doesn't like mixtures of FOF and TFF, even when the two logics coincide (e.g. for ground formulas)
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@40114
    13
  type translated_formula
blanchet@38282
    14
blanchet@41134
    15
  datatype type_system =
blanchet@42523
    16
    Many_Typed |
blanchet@41134
    17
    Tags of bool |
blanchet@42523
    18
    Args of bool |
blanchet@42523
    19
    Mangled of bool |
blanchet@41134
    20
    No_Types
blanchet@41134
    21
blanchet@40204
    22
  val fact_prefix : string
blanchet@38282
    23
  val conjecture_prefix : string
blanchet@42449
    24
  val is_type_system_sound : type_system -> bool
blanchet@42449
    25
  val type_system_types_dangerous_types : type_system -> bool
blanchet@41136
    26
  val num_atp_type_args : theory -> type_system -> string -> int
blanchet@41088
    27
  val translate_atp_fact :
blanchet@41990
    28
    Proof.context -> bool -> (string * 'a) * thm
blanchet@41091
    29
    -> translated_formula option * ((string * 'a) * thm)
blanchet@42227
    30
  val unmangled_const : string -> string * string fo_term list
blanchet@40059
    31
  val prepare_atp_problem :
blanchet@42521
    32
    Proof.context -> bool -> type_system -> bool -> term list -> term
blanchet@41091
    33
    -> (translated_formula option * ((string * 'a) * thm)) list
blanchet@38818
    34
    -> string problem * string Symtab.table * int * (string * 'a) list vector
blanchet@41313
    35
  val atp_problem_weights : string problem -> (string * real) list
blanchet@38282
    36
end;
blanchet@38282
    37
blanchet@41140
    38
structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
blanchet@38282
    39
struct
blanchet@38282
    40
blanchet@38282
    41
open ATP_Problem
blanchet@39494
    42
open Metis_Translate
blanchet@38282
    43
open Sledgehammer_Util
blanchet@38282
    44
blanchet@40204
    45
val fact_prefix = "fact_"
blanchet@38282
    46
val conjecture_prefix = "conj_"
blanchet@38282
    47
val helper_prefix = "help_"
blanchet@42533
    48
val type_decl_prefix = "type_"
blanchet@38282
    49
val class_rel_clause_prefix = "clrel_";
blanchet@38282
    50
val arity_clause_prefix = "arity_"
blanchet@39975
    51
val tfree_prefix = "tfree_"
blanchet@38282
    52
blanchet@42531
    53
val is_base = "is"
blanchet@42531
    54
val type_prefix = "ty_"
blanchet@42531
    55
blanchet@42531
    56
fun make_type ty = type_prefix ^ ascii_of ty
blanchet@42531
    57
blanchet@42534
    58
(* official TPTP TFF syntax *)
blanchet@42534
    59
val tff_bool_type = "$o"
blanchet@42534
    60
blanchet@38282
    61
(* Freshness almost guaranteed! *)
blanchet@38282
    62
val sledgehammer_weak_prefix = "Sledgehammer:"
blanchet@38282
    63
blanchet@40114
    64
type translated_formula =
blanchet@38752
    65
  {name: string,
blanchet@42525
    66
   kind: formula_kind,
blanchet@42531
    67
   combformula: (name, combtyp, combterm) formula,
blanchet@38752
    68
   ctypes_sorts: typ list}
blanchet@38282
    69
blanchet@41134
    70
datatype type_system =
blanchet@42523
    71
  Many_Typed |
blanchet@41134
    72
  Tags of bool |
blanchet@42523
    73
  Args of bool |
blanchet@42523
    74
  Mangled of bool |
blanchet@41134
    75
  No_Types
blanchet@41134
    76
blanchet@42523
    77
fun is_type_system_sound Many_Typed = true
blanchet@42523
    78
  | is_type_system_sound (Tags full_types) = full_types
blanchet@42523
    79
  | is_type_system_sound (Args full_types) = full_types
blanchet@42523
    80
  | is_type_system_sound (Mangled full_types) = full_types
blanchet@42523
    81
  | is_type_system_sound No_Types = false
blanchet@42449
    82
blanchet@42449
    83
fun type_system_types_dangerous_types (Tags _) = true
blanchet@42523
    84
  | type_system_types_dangerous_types type_sys = is_type_system_sound type_sys
blanchet@41138
    85
blanchet@42524
    86
fun dont_need_type_args type_sys s =
blanchet@42531
    87
  s <> is_base andalso
blanchet@42531
    88
  (member (op =) [@{const_name HOL.eq}, @{const_name Metis.fequal}] s orelse
blanchet@42531
    89
   case type_sys of
blanchet@42533
    90
     Many_Typed => false
blanchet@42531
    91
   | Tags full_types => full_types
blanchet@42533
    92
   | Args _ => false
blanchet@42533
    93
   | Mangled _ => false
blanchet@42531
    94
   | No_Types => true)
blanchet@41136
    95
blanchet@42227
    96
datatype type_arg_policy = No_Type_Args | Explicit_Type_Args | Mangled_Types
blanchet@42227
    97
blanchet@42524
    98
fun type_arg_policy type_sys s =
blanchet@42533
    99
  if dont_need_type_args type_sys s then
blanchet@42533
   100
    No_Type_Args
blanchet@42533
   101
  else
blanchet@42533
   102
    case type_sys of
blanchet@42533
   103
      Many_Typed => Mangled_Types
blanchet@42533
   104
    | Mangled _ => Mangled_Types
blanchet@42533
   105
    | _ => Explicit_Type_Args
blanchet@42227
   106
blanchet@41136
   107
fun num_atp_type_args thy type_sys s =
blanchet@42531
   108
  if type_arg_policy type_sys s = Explicit_Type_Args then
blanchet@42531
   109
    if s = is_base then 1 else num_type_args thy s
blanchet@42531
   110
  else
blanchet@42531
   111
    0
blanchet@41136
   112
blanchet@42353
   113
fun atp_type_literals_for_types type_sys kind Ts =
blanchet@42353
   114
  if type_sys = No_Types then
blanchet@42353
   115
    []
blanchet@42353
   116
  else
blanchet@42353
   117
    Ts |> type_literals_for_types
blanchet@42353
   118
       |> filter (fn TyLitVar _ => kind <> Conjecture
blanchet@42353
   119
                   | TyLitFree _ => kind = Conjecture)
blanchet@41137
   120
blanchet@38282
   121
fun mk_anot phi = AConn (ANot, [phi])
blanchet@38282
   122
fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
blanchet@42534
   123
fun mk_aconns c phis =
blanchet@42534
   124
  let val (phis', phi') = split_last phis in
blanchet@42534
   125
    fold_rev (mk_aconn c) phis' phi'
blanchet@42534
   126
  end
blanchet@38282
   127
fun mk_ahorn [] phi = phi
blanchet@42534
   128
  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
blanchet@42522
   129
fun mk_aquant _ [] phi = phi
blanchet@42522
   130
  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
blanchet@42522
   131
    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
blanchet@42522
   132
  | mk_aquant q xs phi = AQuant (q, xs, phi)
blanchet@38282
   133
blanchet@42522
   134
fun close_universally atom_vars phi =
blanchet@41145
   135
  let
blanchet@41145
   136
    fun formula_vars bounds (AQuant (_, xs, phi)) =
blanchet@42526
   137
        formula_vars (map fst xs @ bounds) phi
blanchet@41145
   138
      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
blanchet@42522
   139
      | formula_vars bounds (AAtom tm) =
blanchet@42526
   140
        union (op =) (atom_vars tm []
blanchet@42526
   141
                      |> filter_out (member (op =) bounds o fst))
blanchet@42522
   142
  in mk_aquant AForall (formula_vars [] phi []) phi end
blanchet@42522
   143
blanchet@42531
   144
fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
blanchet@42522
   145
  | combterm_vars (CombConst _) = I
blanchet@42531
   146
  | combterm_vars (CombVar (name, ty)) = insert (op =) (name, SOME ty)
blanchet@42522
   147
val close_combformula_universally = close_universally combterm_vars
blanchet@42522
   148
blanchet@42522
   149
fun term_vars (ATerm (name as (s, _), tms)) =
blanchet@42531
   150
  is_atp_variable s ? insert (op =) (name, NONE)
blanchet@42526
   151
  #> fold term_vars tms
blanchet@42522
   152
val close_formula_universally = close_universally term_vars
blanchet@41145
   153
blanchet@41140
   154
fun combformula_for_prop thy eq_as_iff =
blanchet@38282
   155
  let
blanchet@41140
   156
    fun do_term bs t ts =
blanchet@41140
   157
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@41140
   158
      |>> AAtom ||> union (op =) ts
blanchet@38282
   159
    fun do_quant bs q s T t' =
blanchet@38518
   160
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   161
        do_formula ((s, T) :: bs) t'
blanchet@42531
   162
        #>> mk_aquant q [(`make_bound_var s, SOME (combtyp_from_typ T))]
blanchet@38518
   163
      end
blanchet@38282
   164
    and do_conn bs c t1 t2 =
blanchet@38282
   165
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   166
      #>> uncurry (mk_aconn c)
blanchet@38282
   167
    and do_formula bs t =
blanchet@38282
   168
      case t of
blanchet@42531
   169
        @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   170
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   171
        do_quant bs AForall s T t'
blanchet@38282
   172
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   173
        do_quant bs AExists s T t'
haftmann@38795
   174
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   175
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   176
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   177
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   178
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   179
      | _ => do_term bs t
blanchet@38282
   180
  in do_formula [] end
blanchet@38282
   181
blanchet@38618
   182
val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
blanchet@38282
   183
wenzelm@41491
   184
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   185
fun conceal_bounds Ts t =
blanchet@38282
   186
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   187
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   188
fun reveal_bounds Ts =
blanchet@38282
   189
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   190
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   191
blanchet@38608
   192
(* Removes the lambdas from an equation of the form "t = (%x. u)".
blanchet@39890
   193
   (Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
blanchet@38608
   194
fun extensionalize_term t =
blanchet@38608
   195
  let
blanchet@38608
   196
    fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
blanchet@38608
   197
      | aux j (t as Const (s, Type (_, [Type (_, [_, T']),
blanchet@38608
   198
                                        Type (_, [_, res_T])]))
blanchet@38608
   199
                    $ t2 $ Abs (var_s, var_T, t')) =
haftmann@38864
   200
        if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
blanchet@38608
   201
          let val var_t = Var ((var_s, j), var_T) in
blanchet@38608
   202
            Const (s, T' --> T' --> res_T)
blanchet@38608
   203
              $ betapply (t2, var_t) $ subst_bound (var_t, t')
blanchet@38608
   204
            |> aux (j + 1)
blanchet@38608
   205
          end
blanchet@38608
   206
        else
blanchet@38608
   207
          t
blanchet@38608
   208
      | aux _ t = t
blanchet@38608
   209
  in aux (maxidx_of_term t + 1) t end
blanchet@38608
   210
blanchet@38282
   211
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   212
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   213
    if Meson.is_fol_term thy t then
blanchet@38491
   214
      t
blanchet@38491
   215
    else
blanchet@38491
   216
      let
blanchet@38491
   217
        fun aux Ts t =
blanchet@38491
   218
          case t of
blanchet@38491
   219
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   220
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   221
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   222
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   223
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   224
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   225
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   226
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   227
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   228
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   229
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   230
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   231
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   232
              $ t1 $ t2 =>
blanchet@38491
   233
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   234
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   235
                   t
blanchet@38491
   236
                 else
blanchet@38491
   237
                   t |> conceal_bounds Ts
blanchet@38491
   238
                     |> Envir.eta_contract
blanchet@38491
   239
                     |> cterm_of thy
blanchet@39890
   240
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   241
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   242
                     |> reveal_bounds Ts
blanchet@39370
   243
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   244
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   245
      handle THM _ =>
blanchet@38491
   246
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   247
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   248
             else HOLogic.true_const
blanchet@38491
   249
  end
blanchet@38282
   250
blanchet@38282
   251
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   252
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   253
fun freeze_term t =
blanchet@38282
   254
  let
blanchet@38282
   255
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   256
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   257
      | aux (Var ((s, i), T)) =
blanchet@38282
   258
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   259
      | aux t = t
blanchet@38282
   260
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   261
blanchet@40204
   262
(* making fact and conjecture formulas *)
blanchet@41140
   263
fun make_formula ctxt eq_as_iff presimp name kind t =
blanchet@38282
   264
  let
wenzelm@42361
   265
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   266
    val t = t |> Envir.beta_eta_contract
blanchet@38652
   267
              |> transform_elim_term
blanchet@41211
   268
              |> Object_Logic.atomize_term thy
blanchet@38652
   269
    val need_trueprop = (fastype_of t = HOLogic.boolT)
blanchet@38652
   270
    val t = t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@38282
   271
              |> extensionalize_term
blanchet@38282
   272
              |> presimp ? presimplify_term thy
blanchet@38282
   273
              |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@38282
   274
              |> introduce_combinators_in_term ctxt kind
blanchet@38613
   275
              |> kind <> Axiom ? freeze_term
blanchet@41140
   276
    val (combformula, ctypes_sorts) = combformula_for_prop thy eq_as_iff t []
blanchet@38282
   277
  in
blanchet@38752
   278
    {name = name, combformula = combformula, kind = kind,
blanchet@38752
   279
     ctypes_sorts = ctypes_sorts}
blanchet@38282
   280
  end
blanchet@38282
   281
blanchet@41990
   282
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, _), th) =
blanchet@41990
   283
  case (keep_trivial,
blanchet@41990
   284
        make_formula ctxt eq_as_iff presimp name Axiom (prop_of th)) of
blanchet@41990
   285
    (false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
blanchet@41990
   286
    NONE
blanchet@41990
   287
  | (_, formula) => SOME formula
blanchet@38613
   288
fun make_conjecture ctxt ts =
blanchet@38613
   289
  let val last = length ts - 1 in
wenzelm@41491
   290
    map2 (fn j => make_formula ctxt true true (string_of_int j)
blanchet@38613
   291
                               (if j = last then Conjecture else Hypothesis))
blanchet@38613
   292
         (0 upto last) ts
blanchet@38613
   293
  end
blanchet@38282
   294
blanchet@38282
   295
(** Helper facts **)
blanchet@38282
   296
blanchet@41313
   297
fun fold_formula f (AQuant (_, _, phi)) = fold_formula f phi
blanchet@41313
   298
  | fold_formula f (AConn (_, phis)) = fold (fold_formula f) phis
blanchet@41313
   299
  | fold_formula f (AAtom tm) = f tm
blanchet@41313
   300
blanchet@41140
   301
fun count_term (ATerm ((s, _), tms)) =
blanchet@41140
   302
  (if is_atp_variable s then I
blanchet@41140
   303
   else Symtab.map_entry s (Integer.add 1))
blanchet@41140
   304
  #> fold count_term tms
wenzelm@41406
   305
fun count_formula x = fold_formula count_term x
blanchet@38282
   306
blanchet@38282
   307
val init_counters =
blanchet@41140
   308
  metis_helpers |> map fst |> sort_distinct string_ord |> map (rpair 0)
blanchet@41140
   309
  |> Symtab.make
blanchet@38282
   310
blanchet@42521
   311
fun get_helper_facts ctxt type_sys formulas =
blanchet@38282
   312
  let
blanchet@42449
   313
    val no_dangerous_types = type_system_types_dangerous_types type_sys
blanchet@41140
   314
    val ct = init_counters |> fold count_formula formulas
blanchet@41140
   315
    fun is_used s = the (Symtab.lookup ct s) > 0
blanchet@41140
   316
    fun dub c needs_full_types (th, j) =
blanchet@41140
   317
      ((c ^ "_" ^ string_of_int j ^ (if needs_full_types then "ft" else ""),
blanchet@41140
   318
        false), th)
blanchet@41990
   319
    fun make_facts eq_as_iff = map_filter (make_fact ctxt false eq_as_iff false)
blanchet@38282
   320
  in
blanchet@41145
   321
    (metis_helpers
blanchet@41145
   322
     |> filter (is_used o fst)
blanchet@41145
   323
     |> maps (fn (c, (needs_full_types, ths)) =>
blanchet@41145
   324
                 if needs_full_types andalso not no_dangerous_types then
blanchet@41145
   325
                   []
blanchet@41145
   326
                 else
blanchet@41145
   327
                   ths ~~ (1 upto length ths)
blanchet@41145
   328
                   |> map (dub c needs_full_types)
blanchet@41145
   329
                   |> make_facts (not needs_full_types)),
blanchet@41145
   330
     if type_sys = Tags false then
blanchet@41145
   331
       let
blanchet@41145
   332
         fun var s = ATerm (`I s, [])
blanchet@41145
   333
         fun tag tm = ATerm (`I type_tag_name, [var "X", tm])
blanchet@41145
   334
       in
blanchet@42538
   335
         [Formula (Fof, helper_prefix ^ ascii_of "ti_ti", Axiom,
blanchet@42527
   336
                   AAtom (ATerm (`I "equal",
blanchet@42527
   337
                                 [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42529
   338
                   |> close_formula_universally, NONE, NONE)]
blanchet@41145
   339
       end
blanchet@41145
   340
     else
blanchet@41145
   341
       [])
blanchet@38282
   342
  end
blanchet@38282
   343
blanchet@41990
   344
fun translate_atp_fact ctxt keep_trivial =
blanchet@41990
   345
  `(make_fact ctxt keep_trivial true true)
blanchet@39004
   346
blanchet@41134
   347
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
blanchet@38282
   348
  let
wenzelm@42361
   349
    val thy = Proof_Context.theory_of ctxt
blanchet@41091
   350
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@41091
   351
    val (facts, fact_names) =
blanchet@41091
   352
      rich_facts
blanchet@41091
   353
      |> map_filter (fn (NONE, _) => NONE
blanchet@41091
   354
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@41091
   355
      |> ListPair.unzip
blanchet@40204
   356
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@39005
   357
       boost an ATP's performance (for some reason). *)
blanchet@40204
   358
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@38282
   359
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42353
   360
    val all_ts = goal_t :: fact_ts
blanchet@42353
   361
    val subs = tfree_classes_of_terms all_ts
blanchet@42353
   362
    val supers = tvar_classes_of_terms all_ts
blanchet@42353
   363
    val tycons = type_consts_of_terms thy all_ts
blanchet@41313
   364
    val conjs = make_conjecture ctxt (hyp_ts @ [concl_t])
blanchet@41137
   365
    val (supers', arity_clauses) =
blanchet@41137
   366
      if type_sys = No_Types then ([], [])
blanchet@41137
   367
      else make_arity_clauses thy tycons supers
blanchet@38282
   368
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@38282
   369
  in
blanchet@41313
   370
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@38282
   371
  end
blanchet@38282
   372
blanchet@41138
   373
fun tag_with_type ty t = ATerm (`I type_tag_name, [ty, t])
blanchet@38282
   374
blanchet@38282
   375
fun fo_term_for_combtyp (CombTVar name) = ATerm (name, [])
blanchet@38282
   376
  | fo_term_for_combtyp (CombTFree name) = ATerm (name, [])
blanchet@38282
   377
  | fo_term_for_combtyp (CombType (name, tys)) =
blanchet@38282
   378
    ATerm (name, map fo_term_for_combtyp tys)
blanchet@38282
   379
blanchet@38282
   380
fun fo_literal_for_type_literal (TyLitVar (class, name)) =
blanchet@38282
   381
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@38282
   382
  | fo_literal_for_type_literal (TyLitFree (class, name)) =
blanchet@38282
   383
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@38282
   384
blanchet@38282
   385
fun formula_for_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@38282
   386
blanchet@41138
   387
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@41138
   388
   considered dangerous because their "exhaust" properties can easily lead to
blanchet@41138
   389
   unsound ATP proofs. The checks below are an (unsound) approximation of
blanchet@41138
   390
   finiteness. *)
blanchet@41138
   391
blanchet@41138
   392
fun is_dtyp_dangerous _ (Datatype_Aux.DtTFree _) = true
blanchet@41138
   393
  | is_dtyp_dangerous ctxt (Datatype_Aux.DtType (s, Us)) =
blanchet@41138
   394
    is_type_constr_dangerous ctxt s andalso forall (is_dtyp_dangerous ctxt) Us
blanchet@41138
   395
  | is_dtyp_dangerous _ (Datatype_Aux.DtRec _) = false
blanchet@41138
   396
and is_type_dangerous ctxt (Type (s, Ts)) =
blanchet@41138
   397
    is_type_constr_dangerous ctxt s andalso forall (is_type_dangerous ctxt) Ts
blanchet@41140
   398
  | is_type_dangerous _ _ = false
blanchet@41138
   399
and is_type_constr_dangerous ctxt s =
wenzelm@42361
   400
  let val thy = Proof_Context.theory_of ctxt in
blanchet@41138
   401
    case Datatype_Data.get_info thy s of
blanchet@41138
   402
      SOME {descr, ...} =>
blanchet@41138
   403
      forall (fn (_, (_, _, constrs)) =>
blanchet@41138
   404
                 forall (forall (is_dtyp_dangerous ctxt) o snd) constrs) descr
blanchet@41138
   405
    | NONE =>
blanchet@41138
   406
      case Typedef.get_info ctxt s of
blanchet@41138
   407
        ({rep_type, ...}, _) :: _ => is_type_dangerous ctxt rep_type
blanchet@41138
   408
      | [] => true
blanchet@41138
   409
  end
blanchet@41138
   410
blanchet@41138
   411
fun is_combtyp_dangerous ctxt (CombType ((s, _), tys)) =
blanchet@41138
   412
    (case strip_prefix_and_unascii type_const_prefix s of
blanchet@41138
   413
       SOME s' => forall (is_combtyp_dangerous ctxt) tys andalso
blanchet@41138
   414
                  is_type_constr_dangerous ctxt (invert_const s')
blanchet@41138
   415
     | NONE => false)
blanchet@41138
   416
  | is_combtyp_dangerous _ _ = false
blanchet@41138
   417
blanchet@41138
   418
fun should_tag_with_type ctxt (Tags full_types) ty =
blanchet@41138
   419
    full_types orelse is_combtyp_dangerous ctxt ty
blanchet@41138
   420
  | should_tag_with_type _ _ _ = false
blanchet@41138
   421
blanchet@41140
   422
val fname_table =
blanchet@41140
   423
  [("c_False", (0, ("c_fFalse", @{const_name Metis.fFalse}))),
blanchet@41140
   424
   ("c_True", (0, ("c_fTrue", @{const_name Metis.fTrue}))),
blanchet@41140
   425
   ("c_Not", (1, ("c_fNot", @{const_name Metis.fNot}))),
blanchet@41140
   426
   ("c_conj", (2, ("c_fconj", @{const_name Metis.fconj}))),
blanchet@41140
   427
   ("c_disj", (2, ("c_fdisj", @{const_name Metis.fdisj}))),
blanchet@41140
   428
   ("c_implies", (2, ("c_fimplies", @{const_name Metis.fimplies}))),
blanchet@41140
   429
   ("equal", (2, ("c_fequal", @{const_name Metis.fequal})))]
blanchet@41140
   430
blanchet@42227
   431
(* We are crossing our fingers that it doesn't clash with anything else. *)
blanchet@42227
   432
val mangled_type_sep = "\000"
blanchet@42227
   433
blanchet@42531
   434
fun mangled_combtyp_component f (CombTFree name) = f name
blanchet@42531
   435
  | mangled_combtyp_component f (CombTVar name) =
blanchet@42236
   436
    f name (* FIXME: shouldn't happen *)
blanchet@42236
   437
    (* raise Fail "impossible schematic type variable" *)
blanchet@42531
   438
  | mangled_combtyp_component f (CombType (name, tys)) =
blanchet@42531
   439
    "(" ^ commas (map (mangled_combtyp_component f) tys) ^ ")" ^ f name
blanchet@42531
   440
blanchet@42531
   441
fun mangled_combtyp ty =
blanchet@42531
   442
  (make_type (mangled_combtyp_component fst ty),
blanchet@42531
   443
   mangled_combtyp_component snd ty)
blanchet@42227
   444
blanchet@42227
   445
fun mangled_type_suffix f g tys =
blanchet@42531
   446
  fold_rev (curry (op ^) o g o prefix mangled_type_sep
blanchet@42531
   447
            o mangled_combtyp_component f) tys ""
blanchet@42227
   448
blanchet@42534
   449
fun mangled_const_fst ty_args s = s ^ mangled_type_suffix fst ascii_of ty_args
blanchet@42534
   450
fun mangled_const_snd ty_args s' = s' ^ mangled_type_suffix snd I ty_args
blanchet@42534
   451
fun mangled_const ty_args (s, s') =
blanchet@42534
   452
  (mangled_const_fst ty_args s, mangled_const_snd ty_args s')
blanchet@42533
   453
blanchet@42227
   454
val parse_mangled_ident =
blanchet@42227
   455
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42227
   456
blanchet@42227
   457
fun parse_mangled_type x =
blanchet@42227
   458
  ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")"
blanchet@42227
   459
      -- parse_mangled_ident >> (ATerm o swap)
blanchet@42227
   460
   || parse_mangled_ident >> (ATerm o rpair [])) x
blanchet@42227
   461
and parse_mangled_types x =
blanchet@42227
   462
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42227
   463
blanchet@42227
   464
fun unmangled_type s =
blanchet@42227
   465
  s |> suffix ")" |> raw_explode
blanchet@42227
   466
    |> Scan.finite Symbol.stopper
blanchet@42227
   467
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42227
   468
                                                quote s)) parse_mangled_type))
blanchet@42227
   469
    |> fst
blanchet@42227
   470
blanchet@42227
   471
fun unmangled_const s =
blanchet@42227
   472
  let val ss = space_explode mangled_type_sep s in
blanchet@42227
   473
    (hd ss, map unmangled_type (tl ss))
blanchet@42227
   474
  end
blanchet@42227
   475
blanchet@42531
   476
fun pred_combtyp ty =
blanchet@42531
   477
  case combtyp_from_typ @{typ "unit => bool"} of
blanchet@42531
   478
    CombType (name, [_, bool_ty]) => CombType (name, [ty, bool_ty])
blanchet@42531
   479
  | _ => raise Fail "expected two-argument type constructor"
blanchet@42531
   480
blanchet@42534
   481
fun has_type_combatom ty tm =
blanchet@42534
   482
  CombApp (CombConst ((const_prefix ^ is_base, is_base), pred_combtyp ty, [ty]),
blanchet@42534
   483
           tm)
blanchet@42534
   484
  |> AAtom
blanchet@42534
   485
blanchet@42530
   486
fun formula_for_combformula ctxt type_sys =
blanchet@38282
   487
  let
blanchet@42530
   488
    fun do_term top_level u =
blanchet@38282
   489
      let
blanchet@38282
   490
        val (head, args) = strip_combterm_comb u
blanchet@38282
   491
        val (x, ty_args) =
blanchet@38282
   492
          case head of
blanchet@38282
   493
            CombConst (name as (s, s'), _, ty_args) =>
blanchet@41140
   494
            (case AList.lookup (op =) fname_table s of
blanchet@41140
   495
               SOME (n, fname) =>
blanchet@41150
   496
               (if top_level andalso length args = n then
blanchet@41150
   497
                  case s of
blanchet@41150
   498
                    "c_False" => ("$false", s')
blanchet@41150
   499
                  | "c_True" => ("$true", s')
blanchet@41150
   500
                  | _ => name
blanchet@41150
   501
                else
blanchet@41150
   502
                  fname, [])
blanchet@41140
   503
             | NONE =>
blanchet@41140
   504
               case strip_prefix_and_unascii const_prefix s of
blanchet@41140
   505
                 NONE => (name, ty_args)
blanchet@41140
   506
               | SOME s'' =>
blanchet@42227
   507
                 let val s'' = invert_const s'' in
blanchet@42524
   508
                   case type_arg_policy type_sys s'' of
blanchet@42227
   509
                     No_Type_Args => (name, [])
blanchet@42227
   510
                   | Explicit_Type_Args => (name, ty_args)
blanchet@42534
   511
                   | Mangled_Types => (mangled_const ty_args name, [])
blanchet@42227
   512
                 end)
blanchet@38282
   513
          | CombVar (name, _) => (name, [])
blanchet@38282
   514
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@42530
   515
        val t = ATerm (x, map fo_term_for_combtyp ty_args @
blanchet@42530
   516
                          map (do_term false) args)
blanchet@41138
   517
        val ty = combtyp_of u
blanchet@42530
   518
      in
blanchet@42530
   519
        t |> (if should_tag_with_type ctxt type_sys ty then
blanchet@42530
   520
                tag_with_type (fo_term_for_combtyp ty)
blanchet@42530
   521
              else
blanchet@42530
   522
                I)
blanchet@42530
   523
      end
blanchet@42531
   524
    val do_bound_type =
blanchet@42531
   525
      if type_sys = Many_Typed then SOME o mangled_combtyp else K NONE
blanchet@42531
   526
    val do_out_of_bound_type =
blanchet@42531
   527
      if member (op =) [Args true, Mangled true] type_sys then
blanchet@42531
   528
        (fn (s, ty) =>
blanchet@42534
   529
            has_type_combatom ty (CombVar (s, ty))
blanchet@42534
   530
            |> formula_for_combformula ctxt type_sys |> SOME)
blanchet@42531
   531
      else
blanchet@42531
   532
        K NONE
blanchet@42530
   533
    fun do_formula (AQuant (q, xs, phi)) =
blanchet@42531
   534
        AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42531
   535
                                      | SOME ty => do_bound_type ty)),
blanchet@42534
   536
                (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42531
   537
                    (map_filter
blanchet@42531
   538
                         (fn (_, NONE) => NONE
blanchet@42531
   539
                           | (s, SOME ty) => do_out_of_bound_type (s, ty)) xs)
blanchet@42531
   540
                    (do_formula phi))
blanchet@42530
   541
      | do_formula (AConn (c, phis)) = AConn (c, map do_formula phis)
blanchet@42530
   542
      | do_formula (AAtom tm) = AAtom (do_term true tm)
blanchet@42530
   543
  in do_formula end
blanchet@38282
   544
blanchet@41138
   545
fun formula_for_fact ctxt type_sys
blanchet@40204
   546
                     ({combformula, ctypes_sorts, ...} : translated_formula) =
blanchet@38282
   547
  mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal)
blanchet@42353
   548
                (atp_type_literals_for_types type_sys Axiom ctypes_sorts))
blanchet@42522
   549
           (formula_for_combformula ctxt type_sys
blanchet@42522
   550
                                    (close_combformula_universally combformula))
blanchet@38282
   551
blanchet@42538
   552
fun logic_for_type_sys Many_Typed = Tff
blanchet@42538
   553
  | logic_for_type_sys _ = Fof
blanchet@42538
   554
blanchet@42180
   555
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42180
   556
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42180
   557
   the remote provers might care. *)
blanchet@42180
   558
fun problem_line_for_fact ctxt prefix type_sys
blanchet@42180
   559
                          (j, formula as {name, kind, ...}) =
blanchet@42538
   560
  Formula (logic_for_type_sys type_sys,
blanchet@42538
   561
           prefix ^ string_of_int j ^ "_" ^ ascii_of name, kind,
blanchet@42538
   562
           formula_for_fact ctxt type_sys formula, NONE, NONE)
blanchet@38282
   563
blanchet@38282
   564
fun problem_line_for_class_rel_clause (ClassRelClause {name, subclass,
blanchet@38282
   565
                                                       superclass, ...}) =
blanchet@38282
   566
  let val ty_arg = ATerm (("T", "T"), []) in
blanchet@42538
   567
    Formula (Fof, class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42527
   568
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42529
   569
                               AAtom (ATerm (superclass, [ty_arg]))]),
blanchet@42529
   570
             NONE, NONE)
blanchet@38282
   571
  end
blanchet@38282
   572
blanchet@38282
   573
fun fo_literal_for_arity_literal (TConsLit (c, t, args)) =
blanchet@38282
   574
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@38282
   575
  | fo_literal_for_arity_literal (TVarLit (c, sort)) =
blanchet@38282
   576
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@38282
   577
blanchet@38282
   578
fun problem_line_for_arity_clause (ArityClause {name, conclLit, premLits,
blanchet@38282
   579
                                                ...}) =
blanchet@42538
   580
  Formula (Fof, arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42527
   581
           mk_ahorn (map (formula_for_fo_literal o apfst not
blanchet@42527
   582
                          o fo_literal_for_arity_literal) premLits)
blanchet@42527
   583
                    (formula_for_fo_literal
blanchet@42529
   584
                         (fo_literal_for_arity_literal conclLit)), NONE, NONE)
blanchet@38282
   585
blanchet@41138
   586
fun problem_line_for_conjecture ctxt type_sys
blanchet@40114
   587
        ({name, kind, combformula, ...} : translated_formula) =
blanchet@42538
   588
  Formula (logic_for_type_sys type_sys, conjecture_prefix ^ name, kind,
blanchet@42527
   589
           formula_for_combformula ctxt type_sys
blanchet@42527
   590
                                   (close_combformula_universally combformula),
blanchet@42529
   591
           NONE, NONE)
blanchet@38282
   592
blanchet@42353
   593
fun free_type_literals type_sys ({ctypes_sorts, ...} : translated_formula) =
blanchet@42353
   594
  ctypes_sorts |> atp_type_literals_for_types type_sys Conjecture
blanchet@41137
   595
               |> map fo_literal_for_type_literal
blanchet@38282
   596
blanchet@39975
   597
fun problem_line_for_free_type j lit =
blanchet@42538
   598
  Formula (Fof, tfree_prefix ^ string_of_int j, Hypothesis,
blanchet@42529
   599
           formula_for_fo_literal lit, NONE, NONE)
blanchet@42353
   600
fun problem_lines_for_free_types type_sys facts =
blanchet@38282
   601
  let
blanchet@42353
   602
    val litss = map (free_type_literals type_sys) facts
blanchet@38282
   603
    val lits = fold (union (op =)) litss []
blanchet@39975
   604
  in map2 problem_line_for_free_type (0 upto length lits - 1) lits end
blanchet@38282
   605
blanchet@38282
   606
(** "hBOOL" and "hAPP" **)
blanchet@38282
   607
blanchet@42520
   608
type sym_info = {min_arity: int, max_arity: int, fun_sym: bool}
blanchet@38282
   609
blanchet@42533
   610
fun consider_term_syms top_level (ATerm ((s, _), ts)) =
blanchet@39452
   611
  (if is_atp_variable s then
blanchet@38282
   612
     I
blanchet@38282
   613
   else
blanchet@38282
   614
     let val n = length ts in
blanchet@38282
   615
       Symtab.map_default
blanchet@42520
   616
           (s, {min_arity = n, max_arity = 0, fun_sym = false})
blanchet@42520
   617
           (fn {min_arity, max_arity, fun_sym} =>
blanchet@38282
   618
               {min_arity = Int.min (n, min_arity),
blanchet@38282
   619
                max_arity = Int.max (n, max_arity),
blanchet@42520
   620
                fun_sym = fun_sym orelse not top_level})
blanchet@38282
   621
     end)
blanchet@42533
   622
  #> fold (consider_term_syms (top_level andalso s = type_tag_name)) ts
blanchet@42533
   623
val consider_formula_syms = fold_formula (consider_term_syms true)
blanchet@38282
   624
blanchet@42533
   625
fun consider_problem_line_syms (Type_Decl _) = I
blanchet@42538
   626
  | consider_problem_line_syms (Formula (_, _, _, phi, _, _)) =
blanchet@42533
   627
    consider_formula_syms phi
blanchet@42533
   628
fun consider_problem_syms problem =
blanchet@42533
   629
  fold (fold consider_problem_line_syms o snd) problem
blanchet@38282
   630
blanchet@41140
   631
(* needed for helper facts if the problem otherwise does not involve equality *)
blanchet@42520
   632
val equal_entry = ("equal", {min_arity = 2, max_arity = 2, fun_sym = false})
blanchet@41140
   633
blanchet@42520
   634
fun sym_table_for_problem explicit_apply problem =
blanchet@41140
   635
  if explicit_apply then
blanchet@41140
   636
    NONE
blanchet@41140
   637
  else
blanchet@42527
   638
    SOME (Symtab.empty |> Symtab.default equal_entry
blanchet@42533
   639
                       |> consider_problem_syms problem)
blanchet@38282
   640
blanchet@41134
   641
fun min_arity_of thy type_sys NONE s =
blanchet@41138
   642
    (if s = "equal" orelse s = type_tag_name orelse
blanchet@38282
   643
        String.isPrefix type_const_prefix s orelse
blanchet@38282
   644
        String.isPrefix class_prefix s then
blanchet@38282
   645
       16383 (* large number *)
blanchet@38748
   646
     else case strip_prefix_and_unascii const_prefix s of
blanchet@42524
   647
       SOME s' => s' |> unmangled_const |> fst |> invert_const
blanchet@42524
   648
                     |> num_atp_type_args thy type_sys
blanchet@38282
   649
     | NONE => 0)
blanchet@42520
   650
  | min_arity_of _ _ (SOME sym_tab) s =
blanchet@42520
   651
    case Symtab.lookup sym_tab s of
blanchet@42520
   652
      SOME ({min_arity, ...} : sym_info) => min_arity
blanchet@38282
   653
    | NONE => 0
blanchet@38282
   654
blanchet@38282
   655
fun full_type_of (ATerm ((s, _), [ty, _])) =
blanchet@41138
   656
    if s = type_tag_name then SOME ty else NONE
blanchet@41138
   657
  | full_type_of _ = NONE
blanchet@38282
   658
blanchet@38282
   659
fun list_hAPP_rev _ t1 [] = t1
blanchet@38282
   660
  | list_hAPP_rev NONE t1 (t2 :: ts2) =
blanchet@38282
   661
    ATerm (`I "hAPP", [list_hAPP_rev NONE t1 ts2, t2])
blanchet@38282
   662
  | list_hAPP_rev (SOME ty) t1 (t2 :: ts2) =
blanchet@41138
   663
    case full_type_of t2 of
blanchet@41138
   664
      SOME ty2 =>
blanchet@41138
   665
      let val ty' = ATerm (`make_fixed_type_const @{type_name fun},
blanchet@41138
   666
                           [ty2, ty]) in
blanchet@41138
   667
        ATerm (`I "hAPP",
blanchet@41138
   668
               [tag_with_type ty' (list_hAPP_rev (SOME ty') t1 ts2), t2])
blanchet@41138
   669
      end
blanchet@41138
   670
    | NONE => list_hAPP_rev NONE t1 (t2 :: ts2)
blanchet@38282
   671
blanchet@42520
   672
fun repair_applications_in_term thy type_sys sym_tab =
blanchet@38282
   673
  let
blanchet@38282
   674
    fun aux opt_ty (ATerm (name as (s, _), ts)) =
blanchet@41138
   675
      if s = type_tag_name then
blanchet@38282
   676
        case ts of
blanchet@38282
   677
          [t1, t2] => ATerm (name, [aux NONE t1, aux (SOME t1) t2])
blanchet@41138
   678
        | _ => raise Fail "malformed type tag"
blanchet@38282
   679
      else
blanchet@38282
   680
        let
blanchet@38282
   681
          val ts = map (aux NONE) ts
blanchet@42520
   682
          val (ts1, ts2) = chop (min_arity_of thy type_sys sym_tab s) ts
blanchet@38282
   683
        in list_hAPP_rev opt_ty (ATerm (name, ts1)) (rev ts2) end
blanchet@38282
   684
  in aux NONE end
blanchet@38282
   685
blanchet@38282
   686
fun boolify t = ATerm (`I "hBOOL", [t])
blanchet@38282
   687
blanchet@38282
   688
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
   689
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
   690
   type instantiations). If false, the constant always receives all of its
blanchet@38282
   691
   arguments and is used as a predicate. *)
blanchet@42520
   692
fun is_pred_sym NONE s =
blanchet@38589
   693
    s = "equal" orelse s = "$false" orelse s = "$true" orelse
blanchet@38589
   694
    String.isPrefix type_const_prefix s orelse String.isPrefix class_prefix s
blanchet@42520
   695
  | is_pred_sym (SOME sym_tab) s =
blanchet@42520
   696
    case Symtab.lookup sym_tab s of
blanchet@42520
   697
      SOME {min_arity, max_arity, fun_sym} =>
blanchet@42520
   698
      not fun_sym andalso min_arity = max_arity
blanchet@38282
   699
    | NONE => false
blanchet@38282
   700
blanchet@42520
   701
fun repair_predicates_in_term pred_sym_tab (t as ATerm ((s, _), ts)) =
blanchet@41138
   702
  if s = type_tag_name then
blanchet@38282
   703
    case ts of
blanchet@38282
   704
      [_, t' as ATerm ((s', _), _)] =>
blanchet@42520
   705
      if is_pred_sym pred_sym_tab s' then t' else boolify t
blanchet@41138
   706
    | _ => raise Fail "malformed type tag"
blanchet@38282
   707
  else
blanchet@42520
   708
    t |> not (is_pred_sym pred_sym_tab s) ? boolify
blanchet@38282
   709
blanchet@42521
   710
fun repair_formula thy type_sys sym_tab =
blanchet@38282
   711
  let
blanchet@42520
   712
    val pred_sym_tab = case type_sys of Tags _ => NONE | _ => sym_tab
blanchet@38282
   713
    fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
blanchet@38282
   714
      | aux (AConn (c, phis)) = AConn (c, map aux phis)
blanchet@38282
   715
      | aux (AAtom tm) =
blanchet@42520
   716
        AAtom (tm |> repair_applications_in_term thy type_sys sym_tab
blanchet@42520
   717
                  |> repair_predicates_in_term pred_sym_tab)
blanchet@42522
   718
  in aux #> close_formula_universally end
blanchet@38282
   719
blanchet@42527
   720
fun repair_problem_line thy type_sys sym_tab
blanchet@42538
   721
        (Formula (logic, ident, kind, phi, source, useful_info)) =
blanchet@42538
   722
    Formula (logic, ident, kind, repair_formula thy type_sys sym_tab phi,
blanchet@42538
   723
             source, useful_info)
blanchet@42528
   724
  | repair_problem_line _ _ _ _ = raise Fail "unexpected non-formula"
blanchet@42521
   725
fun repair_problem thy = map o apsnd o map oo repair_problem_line thy
blanchet@38282
   726
blanchet@42534
   727
fun is_const_relevant type_sys sym_tab unmangled_s s =
blanchet@42534
   728
  not (String.isPrefix bound_var_prefix unmangled_s) andalso
blanchet@42534
   729
  unmangled_s <> "equal" andalso
blanchet@42534
   730
  (type_sys = Many_Typed orelse not (is_pred_sym sym_tab s))
blanchet@42533
   731
blanchet@42534
   732
fun consider_combterm_consts type_sys sym_tab tm =
blanchet@42533
   733
  let val (head, args) = strip_combterm_comb tm in
blanchet@42533
   734
    (case head of
blanchet@42533
   735
       CombConst ((s, s'), ty, ty_args) =>
blanchet@42533
   736
       (* FIXME: exploit type subsumption *)
blanchet@42534
   737
       is_const_relevant type_sys sym_tab s
blanchet@42534
   738
                         (s |> member (op =) [Many_Typed, Mangled true] type_sys
blanchet@42534
   739
                               ? mangled_const_fst ty_args)
blanchet@42534
   740
       ? Symtab.insert_list (op =) (s, (s', ty_args, ty))
blanchet@42533
   741
     | _ => I) (* FIXME: hAPP on var *)
blanchet@42534
   742
    #> fold (consider_combterm_consts type_sys sym_tab) args
blanchet@42533
   743
  end
blanchet@42533
   744
blanchet@42534
   745
fun consider_fact_consts type_sys sym_tab
blanchet@42534
   746
                         ({combformula, ...} : translated_formula) =
blanchet@42534
   747
  fold_formula (consider_combterm_consts type_sys sym_tab) combformula
blanchet@42533
   748
blanchet@42533
   749
fun const_table_for_facts type_sys sym_tab facts =
blanchet@42533
   750
  Symtab.empty |> member (op =) [Many_Typed, Args true, Mangled true] type_sys
blanchet@42534
   751
                  ? fold (consider_fact_consts type_sys sym_tab) facts
blanchet@42533
   752
blanchet@42534
   753
fun strip_and_map_combtyp f (ty as CombType ((s, _), tys)) =
blanchet@42533
   754
    (case (strip_prefix_and_unascii type_const_prefix s, tys) of
blanchet@42533
   755
       (SOME @{type_name fun}, [dom_ty, ran_ty]) =>
blanchet@42534
   756
       strip_and_map_combtyp f ran_ty |>> cons (f dom_ty)
blanchet@42534
   757
     | _ => ([], f ty))
blanchet@42534
   758
  | strip_and_map_combtyp f ty = ([], f ty)
blanchet@42533
   759
blanchet@42534
   760
fun type_decl_line_for_const_entry ctxt type_sys sym_tab s (s', ty_args, ty) =
blanchet@42534
   761
  if type_sys = Many_Typed then
blanchet@42534
   762
    let
blanchet@42534
   763
      val (arg_tys, res_ty) = strip_and_map_combtyp mangled_combtyp ty
blanchet@42534
   764
      val (s, s') = (s, s') |> mangled_const ty_args
blanchet@42534
   765
    in
blanchet@42534
   766
      Type_Decl (type_decl_prefix ^ ascii_of s, (s, s'), arg_tys,
blanchet@42534
   767
                 if is_pred_sym sym_tab s then `I tff_bool_type else res_ty)
blanchet@42534
   768
    end
blanchet@42534
   769
  else
blanchet@42533
   770
    let
blanchet@42534
   771
      val (arg_tys, res_ty) = strip_and_map_combtyp I ty
blanchet@42534
   772
      val bounds =
blanchet@42534
   773
        map (`I o make_bound_var o string_of_int) (1 upto length arg_tys)
blanchet@42534
   774
        ~~ map SOME arg_tys
blanchet@42534
   775
      val bound_tms =
blanchet@42534
   776
        map (fn (name, ty) => CombConst (name, the ty, [])) bounds
blanchet@42534
   777
    in
blanchet@42538
   778
      Formula (Fof, type_decl_prefix ^ ascii_of s, Axiom,
blanchet@42534
   779
               mk_aquant AForall bounds
blanchet@42534
   780
                         (has_type_combatom res_ty
blanchet@42534
   781
                              (fold (curry (CombApp o swap)) bound_tms
blanchet@42534
   782
                                    (CombConst ((s, s'), ty, ty_args))))
blanchet@42534
   783
               |> formula_for_combformula ctxt type_sys,
blanchet@42534
   784
               NONE, NONE)
blanchet@42534
   785
    end
blanchet@42534
   786
fun type_decl_lines_for_const ctxt type_sys sym_tab (s, xs) =
blanchet@42534
   787
  map (type_decl_line_for_const_entry ctxt type_sys sym_tab s) xs
blanchet@42533
   788
blanchet@41157
   789
val factsN = "Relevant facts"
blanchet@41157
   790
val class_relsN = "Class relationships"
blanchet@41157
   791
val aritiesN = "Arity declarations"
blanchet@41157
   792
val helpersN = "Helper facts"
blanchet@42533
   793
val type_declsN = "Type declarations"
blanchet@41157
   794
val conjsN = "Conjectures"
blanchet@41313
   795
val free_typesN = "Type variables"
blanchet@41157
   796
blanchet@41157
   797
fun offset_of_heading_in_problem _ [] j = j
blanchet@41157
   798
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@41157
   799
    if heading = needle then j
blanchet@41157
   800
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@41157
   801
blanchet@42521
   802
fun prepare_atp_problem ctxt readable_names type_sys explicit_apply hyp_ts
blanchet@42521
   803
                        concl_t facts =
blanchet@38282
   804
  let
wenzelm@42361
   805
    val thy = Proof_Context.theory_of ctxt
blanchet@41313
   806
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@41134
   807
      translate_formulas ctxt type_sys hyp_ts concl_t facts
blanchet@42522
   808
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@42522
   809
       Flotter hack. *)
blanchet@38282
   810
    val problem =
blanchet@42180
   811
      [(factsN, map (problem_line_for_fact ctxt fact_prefix type_sys)
blanchet@42180
   812
                    (0 upto length facts - 1 ~~ facts)),
blanchet@41157
   813
       (class_relsN, map problem_line_for_class_rel_clause class_rel_clauses),
blanchet@41157
   814
       (aritiesN, map problem_line_for_arity_clause arity_clauses),
blanchet@41157
   815
       (helpersN, []),
blanchet@42533
   816
       (type_declsN, []),
blanchet@41313
   817
       (conjsN, map (problem_line_for_conjecture ctxt type_sys) conjs),
blanchet@42353
   818
       (free_typesN, problem_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42520
   819
    val sym_tab = sym_table_for_problem explicit_apply problem
blanchet@42521
   820
    val problem = problem |> repair_problem thy type_sys sym_tab
blanchet@42521
   821
    val helper_facts =
blanchet@42538
   822
      problem |> maps (map_filter (fn Formula (_, _, _, phi, _, _) => SOME phi
blanchet@42528
   823
                                    | _ => NONE) o snd)
blanchet@42527
   824
              |> get_helper_facts ctxt type_sys
blanchet@42533
   825
    val const_tab = const_table_for_facts type_sys sym_tab (conjs @ facts)
blanchet@42533
   826
    val type_decl_lines =
blanchet@42534
   827
      Symtab.fold_rev (append o type_decl_lines_for_const ctxt type_sys sym_tab)
blanchet@42534
   828
                      const_tab []
blanchet@41157
   829
    val helper_lines =
blanchet@42521
   830
      helper_facts
blanchet@42180
   831
      |>> map (pair 0
blanchet@42180
   832
               #> problem_line_for_fact ctxt helper_prefix type_sys
blanchet@42521
   833
               #> repair_problem_line thy type_sys sym_tab)
blanchet@41157
   834
      |> op @
blanchet@41140
   835
    val (problem, pool) =
blanchet@42533
   836
      problem |> fold (AList.update (op =))
blanchet@42533
   837
                      [(helpersN, helper_lines), (type_declsN, type_decl_lines)]
blanchet@41140
   838
              |> nice_atp_problem readable_names
blanchet@38282
   839
  in
blanchet@38282
   840
    (problem,
blanchet@38282
   841
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@41157
   842
     offset_of_heading_in_problem conjsN problem 0,
blanchet@41157
   843
     fact_names |> Vector.fromList)
blanchet@38282
   844
  end
blanchet@38282
   845
blanchet@41313
   846
(* FUDGE *)
blanchet@41313
   847
val conj_weight = 0.0
blanchet@41770
   848
val hyp_weight = 0.1
blanchet@41770
   849
val fact_min_weight = 0.2
blanchet@41313
   850
val fact_max_weight = 1.0
blanchet@41313
   851
blanchet@41313
   852
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@41313
   853
  (not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
blanchet@41313
   854
  #> fold (add_term_weights weight) tms
blanchet@42538
   855
fun add_problem_line_weights weight (Formula (_, _, _, phi, _, _)) =
blanchet@42528
   856
    fold_formula (add_term_weights weight) phi
blanchet@42528
   857
  | add_problem_line_weights _ _ = I
blanchet@41313
   858
blanchet@41313
   859
fun add_conjectures_weights [] = I
blanchet@41313
   860
  | add_conjectures_weights conjs =
blanchet@41313
   861
    let val (hyps, conj) = split_last conjs in
blanchet@41313
   862
      add_problem_line_weights conj_weight conj
blanchet@41313
   863
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
   864
    end
blanchet@41313
   865
blanchet@41313
   866
fun add_facts_weights facts =
blanchet@41313
   867
  let
blanchet@41313
   868
    val num_facts = length facts
blanchet@41313
   869
    fun weight_of j =
blanchet@41313
   870
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
   871
                        / Real.fromInt num_facts
blanchet@41313
   872
  in
blanchet@41313
   873
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
   874
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
   875
  end
blanchet@41313
   876
blanchet@41313
   877
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
   878
fun atp_problem_weights problem =
blanchet@41313
   879
  Symtab.empty
blanchet@41313
   880
  |> add_conjectures_weights (these (AList.lookup (op =) problem conjsN))
blanchet@41313
   881
  |> add_facts_weights (these (AList.lookup (op =) problem factsN))
blanchet@41313
   882
  |> Symtab.dest
blanchet@41726
   883
  |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@41313
   884
blanchet@38282
   885
end;