src/HOL/Tools/ATP/atp_translate.ML
author blanchet
Wed Jun 01 10:29:43 2011 +0200 (2011-06-01)
changeset 43130 d73fc2e55308
parent 43129 4301f1c123d6
child 43136 cf5cda219058
permissions -rw-r--r--
implemented missing hAPP and ti cases of new path finder
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@43085
     9
signature ATP_TRANSLATE =
blanchet@38282
    10
sig
blanchet@42227
    11
  type 'a fo_term = 'a ATP_Problem.fo_term
blanchet@42939
    12
  type format = ATP_Problem.format
blanchet@42709
    13
  type formula_kind = ATP_Problem.formula_kind
blanchet@38282
    14
  type 'a problem = 'a ATP_Problem.problem
blanchet@43085
    15
blanchet@43085
    16
  type name = string * string
blanchet@43085
    17
blanchet@43085
    18
  datatype type_literal =
blanchet@43085
    19
    TyLitVar of name * name |
blanchet@43085
    20
    TyLitFree of name * name
blanchet@43085
    21
blanchet@43085
    22
  datatype arity_literal =
blanchet@43085
    23
    TConsLit of name * name * name list |
blanchet@43085
    24
    TVarLit of name * name
blanchet@43085
    25
blanchet@43086
    26
  type arity_clause =
blanchet@43086
    27
    {name: string,
blanchet@43086
    28
     prem_lits: arity_literal list,
blanchet@43086
    29
     concl_lits: arity_literal}
blanchet@43085
    30
blanchet@43086
    31
  type class_rel_clause =
blanchet@43086
    32
    {name: string,
blanchet@43086
    33
     subclass: name,
blanchet@43086
    34
     superclass: name}
blanchet@43085
    35
blanchet@43085
    36
  datatype combterm =
blanchet@43085
    37
    CombConst of name * typ * typ list |
blanchet@43085
    38
    CombVar of name * typ |
blanchet@43085
    39
    CombApp of combterm * combterm
blanchet@43085
    40
blanchet@43085
    41
  datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
blanchet@42613
    42
blanchet@42613
    43
  datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
blanchet@42613
    44
  datatype type_level =
blanchet@42613
    45
    All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
blanchet@43128
    46
  datatype type_heaviness = Heavyweight | Lightweight
blanchet@42613
    47
blanchet@43102
    48
  datatype type_sys =
blanchet@42722
    49
    Simple_Types of type_level |
blanchet@42837
    50
    Preds of polymorphism * type_level * type_heaviness |
blanchet@42837
    51
    Tags of polymorphism * type_level * type_heaviness
blanchet@42613
    52
blanchet@40114
    53
  type translated_formula
blanchet@38282
    54
blanchet@43085
    55
  val bound_var_prefix : string
blanchet@43085
    56
  val schematic_var_prefix: string
blanchet@43085
    57
  val fixed_var_prefix: string
blanchet@43085
    58
  val tvar_prefix: string
blanchet@43085
    59
  val tfree_prefix: string
blanchet@43085
    60
  val const_prefix: string
blanchet@43085
    61
  val type_const_prefix: string
blanchet@43085
    62
  val class_prefix: string
blanchet@43085
    63
  val skolem_const_prefix : string
blanchet@43085
    64
  val old_skolem_const_prefix : string
blanchet@43085
    65
  val new_skolem_const_prefix : string
blanchet@43125
    66
  val type_decl_prefix : string
blanchet@43125
    67
  val sym_decl_prefix : string
blanchet@43125
    68
  val preds_sym_formula_prefix : string
blanchet@43129
    69
  val lightweight_tags_sym_formula_prefix : string
blanchet@40204
    70
  val fact_prefix : string
blanchet@38282
    71
  val conjecture_prefix : string
blanchet@42881
    72
  val helper_prefix : string
blanchet@43125
    73
  val class_rel_clause_prefix : string
blanchet@43125
    74
  val arity_clause_prefix : string
blanchet@43125
    75
  val tfree_clause_prefix : string
blanchet@42881
    76
  val typed_helper_suffix : string
blanchet@43125
    77
  val untyped_helper_suffix : string
blanchet@42966
    78
  val predicator_name : string
blanchet@42966
    79
  val app_op_name : string
blanchet@43104
    80
  val type_tag_name : string
blanchet@42966
    81
  val type_pred_name : string
blanchet@42962
    82
  val simple_type_prefix : string
blanchet@43130
    83
  val prefixed_app_op_name : string
blanchet@43130
    84
  val prefixed_type_tag_name : string
blanchet@43085
    85
  val ascii_of: string -> string
blanchet@43085
    86
  val unascii_of: string -> string
blanchet@43085
    87
  val strip_prefix_and_unascii : string -> string -> string option
blanchet@43085
    88
  val proxify_const : string -> (int * (string * string)) option
blanchet@43085
    89
  val invert_const: string -> string
blanchet@43085
    90
  val unproxify_const: string -> string
blanchet@43085
    91
  val make_bound_var : string -> string
blanchet@43085
    92
  val make_schematic_var : string * int -> string
blanchet@43085
    93
  val make_fixed_var : string -> string
blanchet@43085
    94
  val make_schematic_type_var : string * int -> string
blanchet@43085
    95
  val make_fixed_type_var : string -> string
blanchet@43085
    96
  val make_fixed_const : string -> string
blanchet@43085
    97
  val make_fixed_type_const : string -> string
blanchet@43085
    98
  val make_type_class : string -> string
blanchet@43093
    99
  val new_skolem_var_name_from_const : string -> string
blanchet@43093
   100
  val num_type_args : theory -> string -> int
blanchet@43085
   101
  val make_arity_clauses :
blanchet@43085
   102
    theory -> string list -> class list -> class list * arity_clause list
blanchet@43085
   103
  val make_class_rel_clauses :
blanchet@43085
   104
    theory -> class list -> class list -> class_rel_clause list
blanchet@43085
   105
  val combtyp_of : combterm -> typ
blanchet@43085
   106
  val strip_combterm_comb : combterm -> combterm * combterm list
blanchet@43085
   107
  val atyps_of : typ -> typ list
blanchet@43085
   108
  val combterm_from_term :
blanchet@43085
   109
    theory -> (string * typ) list -> term -> combterm * typ list
blanchet@43085
   110
  val is_locality_global : locality -> bool
blanchet@43102
   111
  val type_sys_from_string : string -> type_sys
blanchet@43102
   112
  val polymorphism_of_type_sys : type_sys -> polymorphism
blanchet@43102
   113
  val level_of_type_sys : type_sys -> type_level
blanchet@43102
   114
  val is_type_sys_virtually_sound : type_sys -> bool
blanchet@43102
   115
  val is_type_sys_fairly_sound : type_sys -> bool
blanchet@43102
   116
  val choose_format : format list -> type_sys -> format * type_sys
blanchet@43085
   117
  val raw_type_literals_for_types : typ list -> type_literal list
blanchet@43130
   118
  val unmangled_const_name : string -> string
blanchet@42542
   119
  val unmangled_const : string -> string * string fo_term list
blanchet@41088
   120
  val translate_atp_fact :
blanchet@43102
   121
    Proof.context -> format -> type_sys -> bool -> (string * locality) * thm
blanchet@42640
   122
    -> translated_formula option * ((string * locality) * thm)
blanchet@43085
   123
  val helper_table : (string * (bool * thm list)) list
blanchet@43085
   124
  val tfree_classes_of_terms : term list -> string list
blanchet@43085
   125
  val tvar_classes_of_terms : term list -> string list
blanchet@43085
   126
  val type_consts_of_terms : theory -> term list -> string list
blanchet@40059
   127
  val prepare_atp_problem :
blanchet@43102
   128
    Proof.context -> format -> formula_kind -> formula_kind -> type_sys
blanchet@43096
   129
    -> bool option -> bool -> bool -> term list -> term
blanchet@41091
   130
    -> (translated_formula option * ((string * 'a) * thm)) list
blanchet@42541
   131
    -> string problem * string Symtab.table * int * int
blanchet@42881
   132
       * (string * 'a) list vector * int list * int Symtab.table
blanchet@41313
   133
  val atp_problem_weights : string problem -> (string * real) list
blanchet@38282
   134
end;
blanchet@38282
   135
blanchet@43085
   136
structure ATP_Translate : ATP_TRANSLATE =
blanchet@38282
   137
struct
blanchet@38282
   138
blanchet@43085
   139
open ATP_Util
blanchet@38282
   140
open ATP_Problem
blanchet@43085
   141
blanchet@43085
   142
type name = string * string
blanchet@43085
   143
blanchet@43085
   144
(* FIXME: avoid *)
blanchet@43085
   145
fun union_all xss = fold (union (op =)) xss []
blanchet@42640
   146
blanchet@42640
   147
(* experimental *)
blanchet@42640
   148
val generate_useful_info = false
blanchet@38282
   149
blanchet@42879
   150
fun useful_isabelle_info s =
blanchet@42879
   151
  if generate_useful_info then
blanchet@42879
   152
    SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
blanchet@42879
   153
  else
blanchet@42879
   154
    NONE
blanchet@42879
   155
blanchet@42879
   156
val intro_info = useful_isabelle_info "intro"
blanchet@42879
   157
val elim_info = useful_isabelle_info "elim"
blanchet@42879
   158
val simp_info = useful_isabelle_info "simp"
blanchet@42879
   159
blanchet@43085
   160
val bound_var_prefix = "B_"
blanchet@43085
   161
val schematic_var_prefix = "V_"
blanchet@43085
   162
val fixed_var_prefix = "v_"
blanchet@43085
   163
blanchet@43085
   164
val tvar_prefix = "T_"
blanchet@43085
   165
val tfree_prefix = "t_"
blanchet@43085
   166
blanchet@43085
   167
val const_prefix = "c_"
blanchet@43085
   168
val type_const_prefix = "tc_"
blanchet@43085
   169
val class_prefix = "cl_"
blanchet@43085
   170
blanchet@43085
   171
val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
blanchet@43085
   172
val old_skolem_const_prefix = skolem_const_prefix ^ "o"
blanchet@43085
   173
val new_skolem_const_prefix = skolem_const_prefix ^ "n"
blanchet@43085
   174
blanchet@42998
   175
val type_decl_prefix = "ty_"
blanchet@42998
   176
val sym_decl_prefix = "sy_"
blanchet@43125
   177
val preds_sym_formula_prefix = "psy_"
blanchet@43129
   178
val lightweight_tags_sym_formula_prefix = "tsy_"
blanchet@40204
   179
val fact_prefix = "fact_"
blanchet@38282
   180
val conjecture_prefix = "conj_"
blanchet@38282
   181
val helper_prefix = "help_"
blanchet@43093
   182
val class_rel_clause_prefix = "crel_"
blanchet@38282
   183
val arity_clause_prefix = "arity_"
blanchet@43085
   184
val tfree_clause_prefix = "tfree_"
blanchet@38282
   185
blanchet@42881
   186
val typed_helper_suffix = "_T"
blanchet@42881
   187
val untyped_helper_suffix = "_U"
blanchet@42881
   188
blanchet@42966
   189
val predicator_name = "hBOOL"
blanchet@42966
   190
val app_op_name = "hAPP"
blanchet@43104
   191
val type_tag_name = "ti"
blanchet@42966
   192
val type_pred_name = "is"
blanchet@42962
   193
val simple_type_prefix = "ty_"
blanchet@42531
   194
blanchet@43130
   195
val prefixed_app_op_name = const_prefix ^ app_op_name
blanchet@43130
   196
val prefixed_type_tag_name = const_prefix ^ type_tag_name
blanchet@43130
   197
blanchet@38282
   198
(* Freshness almost guaranteed! *)
blanchet@38282
   199
val sledgehammer_weak_prefix = "Sledgehammer:"
blanchet@38282
   200
blanchet@43085
   201
(*Escaping of special characters.
blanchet@43085
   202
  Alphanumeric characters are left unchanged.
blanchet@43085
   203
  The character _ goes to __
blanchet@43085
   204
  Characters in the range ASCII space to / go to _A to _P, respectively.
blanchet@43085
   205
  Other characters go to _nnn where nnn is the decimal ASCII code.*)
blanchet@43093
   206
val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
blanchet@43085
   207
blanchet@43085
   208
fun stringN_of_int 0 _ = ""
blanchet@43085
   209
  | stringN_of_int k n =
blanchet@43085
   210
    stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
blanchet@43085
   211
blanchet@43085
   212
fun ascii_of_char c =
blanchet@43085
   213
  if Char.isAlphaNum c then
blanchet@43085
   214
    String.str c
blanchet@43085
   215
  else if c = #"_" then
blanchet@43085
   216
    "__"
blanchet@43085
   217
  else if #" " <= c andalso c <= #"/" then
blanchet@43085
   218
    "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
blanchet@43085
   219
  else
blanchet@43085
   220
    (* fixed width, in case more digits follow *)
blanchet@43085
   221
    "_" ^ stringN_of_int 3 (Char.ord c)
blanchet@43085
   222
blanchet@43085
   223
val ascii_of = String.translate ascii_of_char
blanchet@43085
   224
blanchet@43085
   225
(** Remove ASCII armoring from names in proof files **)
blanchet@43085
   226
blanchet@43085
   227
(* We don't raise error exceptions because this code can run inside a worker
blanchet@43085
   228
   thread. Also, the errors are impossible. *)
blanchet@43085
   229
val unascii_of =
blanchet@43085
   230
  let
blanchet@43085
   231
    fun un rcs [] = String.implode(rev rcs)
blanchet@43085
   232
      | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
blanchet@43085
   233
        (* Three types of _ escapes: __, _A to _P, _nnn *)
blanchet@43085
   234
      | un rcs (#"_" :: #"_" :: cs) = un (#"_"::rcs) cs
blanchet@43085
   235
      | un rcs (#"_" :: c :: cs) =
blanchet@43085
   236
        if #"A" <= c andalso c<= #"P" then
blanchet@43085
   237
          (* translation of #" " to #"/" *)
blanchet@43085
   238
          un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
blanchet@43085
   239
        else
blanchet@43085
   240
          let val digits = List.take (c::cs, 3) handle Subscript => [] in
blanchet@43085
   241
            case Int.fromString (String.implode digits) of
blanchet@43085
   242
              SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
blanchet@43085
   243
            | NONE => un (c:: #"_"::rcs) cs (* ERROR *)
blanchet@43085
   244
          end
blanchet@43085
   245
      | un rcs (c :: cs) = un (c :: rcs) cs
blanchet@43085
   246
  in un [] o String.explode end
blanchet@43085
   247
blanchet@43085
   248
(* If string s has the prefix s1, return the result of deleting it,
blanchet@43085
   249
   un-ASCII'd. *)
blanchet@43085
   250
fun strip_prefix_and_unascii s1 s =
blanchet@43085
   251
  if String.isPrefix s1 s then
blanchet@43085
   252
    SOME (unascii_of (String.extract (s, size s1, NONE)))
blanchet@43085
   253
  else
blanchet@43085
   254
    NONE
blanchet@43085
   255
blanchet@43085
   256
val proxies =
blanchet@43085
   257
  [("c_False",
blanchet@43085
   258
    (@{const_name False}, (0, ("fFalse", @{const_name ATP.fFalse})))),
blanchet@43085
   259
   ("c_True", (@{const_name True}, (0, ("fTrue", @{const_name ATP.fTrue})))),
blanchet@43085
   260
   ("c_Not", (@{const_name Not}, (1, ("fNot", @{const_name ATP.fNot})))),
blanchet@43085
   261
   ("c_conj", (@{const_name conj}, (2, ("fconj", @{const_name ATP.fconj})))),
blanchet@43085
   262
   ("c_disj", (@{const_name disj}, (2, ("fdisj", @{const_name ATP.fdisj})))),
blanchet@43085
   263
   ("c_implies",
blanchet@43085
   264
    (@{const_name implies}, (2, ("fimplies", @{const_name ATP.fimplies})))),
blanchet@43085
   265
   ("equal",
blanchet@43085
   266
    (@{const_name HOL.eq}, (2, ("fequal", @{const_name ATP.fequal}))))]
blanchet@43085
   267
blanchet@43085
   268
val proxify_const = AList.lookup (op =) proxies #> Option.map snd
blanchet@43085
   269
blanchet@43085
   270
(* Readable names for the more common symbolic functions. Do not mess with the
blanchet@43085
   271
   table unless you know what you are doing. *)
blanchet@43085
   272
val const_trans_table =
blanchet@43085
   273
  [(@{type_name Product_Type.prod}, "prod"),
blanchet@43085
   274
   (@{type_name Sum_Type.sum}, "sum"),
blanchet@43085
   275
   (@{const_name False}, "False"),
blanchet@43085
   276
   (@{const_name True}, "True"),
blanchet@43085
   277
   (@{const_name Not}, "Not"),
blanchet@43085
   278
   (@{const_name conj}, "conj"),
blanchet@43085
   279
   (@{const_name disj}, "disj"),
blanchet@43085
   280
   (@{const_name implies}, "implies"),
blanchet@43085
   281
   (@{const_name HOL.eq}, "equal"),
blanchet@43085
   282
   (@{const_name If}, "If"),
blanchet@43085
   283
   (@{const_name Set.member}, "member"),
blanchet@43085
   284
   (@{const_name Meson.COMBI}, "COMBI"),
blanchet@43085
   285
   (@{const_name Meson.COMBK}, "COMBK"),
blanchet@43085
   286
   (@{const_name Meson.COMBB}, "COMBB"),
blanchet@43085
   287
   (@{const_name Meson.COMBC}, "COMBC"),
blanchet@43085
   288
   (@{const_name Meson.COMBS}, "COMBS")]
blanchet@43085
   289
  |> Symtab.make
blanchet@43085
   290
  |> fold (Symtab.update o swap o snd o snd o snd) proxies
blanchet@43085
   291
blanchet@43085
   292
(* Invert the table of translations between Isabelle and ATPs. *)
blanchet@43085
   293
val const_trans_table_inv =
blanchet@43085
   294
  const_trans_table |> Symtab.dest |> map swap |> Symtab.make
blanchet@43085
   295
val const_trans_table_unprox =
blanchet@43085
   296
  Symtab.empty
blanchet@43085
   297
  |> fold (fn (_, (isa, (_, (_, metis)))) => Symtab.update (metis, isa)) proxies
blanchet@43085
   298
blanchet@43085
   299
val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
blanchet@43085
   300
val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
blanchet@43085
   301
blanchet@43085
   302
fun lookup_const c =
blanchet@43085
   303
  case Symtab.lookup const_trans_table c of
blanchet@43085
   304
    SOME c' => c'
blanchet@43085
   305
  | NONE => ascii_of c
blanchet@43085
   306
blanchet@43085
   307
(*Remove the initial ' character from a type variable, if it is present*)
blanchet@43085
   308
fun trim_type_var s =
blanchet@43085
   309
  if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
blanchet@43085
   310
  else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
blanchet@43085
   311
blanchet@43085
   312
fun ascii_of_indexname (v,0) = ascii_of v
blanchet@43085
   313
  | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i
blanchet@43085
   314
blanchet@43085
   315
fun make_bound_var x = bound_var_prefix ^ ascii_of x
blanchet@43085
   316
fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
blanchet@43085
   317
fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
blanchet@43085
   318
blanchet@43085
   319
fun make_schematic_type_var (x,i) =
blanchet@43085
   320
      tvar_prefix ^ (ascii_of_indexname (trim_type_var x, i))
blanchet@43085
   321
fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x))
blanchet@43085
   322
blanchet@43085
   323
(* HOL.eq MUST BE "equal" because it's built into ATPs. *)
blanchet@43085
   324
fun make_fixed_const @{const_name HOL.eq} = "equal"
blanchet@43085
   325
  | make_fixed_const c = const_prefix ^ lookup_const c
blanchet@43085
   326
blanchet@43085
   327
fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
blanchet@43085
   328
blanchet@43085
   329
fun make_type_class clas = class_prefix ^ ascii_of clas
blanchet@43085
   330
blanchet@43093
   331
fun new_skolem_var_name_from_const s =
blanchet@43093
   332
  let val ss = s |> space_explode Long_Name.separator in
blanchet@43093
   333
    nth ss (length ss - 2)
blanchet@43093
   334
  end
blanchet@43093
   335
blanchet@43093
   336
(* The number of type arguments of a constant, zero if it's monomorphic. For
blanchet@43093
   337
   (instances of) Skolem pseudoconstants, this information is encoded in the
blanchet@43093
   338
   constant name. *)
blanchet@43093
   339
fun num_type_args thy s =
blanchet@43093
   340
  if String.isPrefix skolem_const_prefix s then
blanchet@43093
   341
    s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
blanchet@43093
   342
  else
blanchet@43093
   343
    (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
blanchet@43093
   344
blanchet@43085
   345
(** Definitions and functions for FOL clauses and formulas for TPTP **)
blanchet@43085
   346
blanchet@43085
   347
(* The first component is the type class; the second is a "TVar" or "TFree". *)
blanchet@43085
   348
datatype type_literal =
blanchet@43085
   349
  TyLitVar of name * name |
blanchet@43085
   350
  TyLitFree of name * name
blanchet@43085
   351
blanchet@43085
   352
blanchet@43085
   353
(** Isabelle arities **)
blanchet@43085
   354
blanchet@43085
   355
datatype arity_literal =
blanchet@43085
   356
  TConsLit of name * name * name list |
blanchet@43085
   357
  TVarLit of name * name
blanchet@43085
   358
blanchet@43085
   359
fun gen_TVars 0 = []
blanchet@43093
   360
  | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
blanchet@43085
   361
blanchet@43085
   362
fun pack_sort (_,[])  = []
blanchet@43085
   363
  | pack_sort (tvar, "HOL.type" :: srt) =
blanchet@43085
   364
    pack_sort (tvar, srt) (* IGNORE sort "type" *)
blanchet@43085
   365
  | pack_sort (tvar, cls :: srt) =
blanchet@43085
   366
    (`make_type_class cls, `I tvar) :: pack_sort (tvar, srt)
blanchet@43085
   367
blanchet@43086
   368
type arity_clause =
blanchet@43086
   369
  {name: string,
blanchet@43086
   370
   prem_lits: arity_literal list,
blanchet@43086
   371
   concl_lits: arity_literal}
blanchet@43085
   372
blanchet@43085
   373
(* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
blanchet@43085
   374
fun make_axiom_arity_clause (tcons, name, (cls, args)) =
blanchet@43085
   375
  let
blanchet@43085
   376
    val tvars = gen_TVars (length args)
blanchet@43085
   377
    val tvars_srts = ListPair.zip (tvars, args)
blanchet@43085
   378
  in
blanchet@43086
   379
    {name = name,
blanchet@43086
   380
     prem_lits = map TVarLit (union_all (map pack_sort tvars_srts)),
blanchet@43086
   381
     concl_lits = TConsLit (`make_type_class cls,
blanchet@43086
   382
                            `make_fixed_type_const tcons,
blanchet@43086
   383
                            tvars ~~ tvars)}
blanchet@43085
   384
  end
blanchet@43085
   385
blanchet@43085
   386
fun arity_clause _ _ (_, []) = []
blanchet@43085
   387
  | arity_clause seen n (tcons, ("HOL.type",_)::ars) =  (*ignore*)
blanchet@43085
   388
      arity_clause seen n (tcons,ars)
blanchet@43085
   389
  | arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
blanchet@43085
   390
      if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
blanchet@43085
   391
          make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ string_of_int n, ar) ::
blanchet@43085
   392
          arity_clause seen (n+1) (tcons,ars)
blanchet@43085
   393
      else
blanchet@43085
   394
          make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
blanchet@43085
   395
          arity_clause (class::seen) n (tcons,ars)
blanchet@43085
   396
blanchet@43085
   397
fun multi_arity_clause [] = []
blanchet@43085
   398
  | multi_arity_clause ((tcons, ars) :: tc_arlists) =
blanchet@43085
   399
      arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
blanchet@43085
   400
blanchet@43085
   401
(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
blanchet@43085
   402
  provided its arguments have the corresponding sorts.*)
blanchet@43085
   403
fun type_class_pairs thy tycons classes =
blanchet@43093
   404
  let
blanchet@43093
   405
    val alg = Sign.classes_of thy
blanchet@43093
   406
    fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
blanchet@43093
   407
    fun add_class tycon class =
blanchet@43093
   408
      cons (class, domain_sorts tycon class)
blanchet@43093
   409
      handle Sorts.CLASS_ERROR _ => I
blanchet@43093
   410
    fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
blanchet@43093
   411
  in map try_classes tycons end
blanchet@43085
   412
blanchet@43085
   413
(*Proving one (tycon, class) membership may require proving others, so iterate.*)
blanchet@43085
   414
fun iter_type_class_pairs _ _ [] = ([], [])
blanchet@43085
   415
  | iter_type_class_pairs thy tycons classes =
blanchet@43085
   416
      let val cpairs = type_class_pairs thy tycons classes
blanchet@43085
   417
          val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs)))
blanchet@43085
   418
            |> subtract (op =) classes |> subtract (op =) HOLogic.typeS
blanchet@43085
   419
          val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
blanchet@43093
   420
      in (union (op =) classes' classes, union (op =) cpairs' cpairs) end
blanchet@43085
   421
blanchet@43085
   422
fun make_arity_clauses thy tycons =
blanchet@43085
   423
  iter_type_class_pairs thy tycons ##> multi_arity_clause
blanchet@43085
   424
blanchet@43085
   425
blanchet@43085
   426
(** Isabelle class relations **)
blanchet@43085
   427
blanchet@43086
   428
type class_rel_clause =
blanchet@43086
   429
  {name: string,
blanchet@43086
   430
   subclass: name,
blanchet@43086
   431
   superclass: name}
blanchet@43085
   432
blanchet@43085
   433
(*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
blanchet@43085
   434
fun class_pairs _ [] _ = []
blanchet@43085
   435
  | class_pairs thy subs supers =
blanchet@43085
   436
      let
blanchet@43085
   437
        val class_less = Sorts.class_less (Sign.classes_of thy)
blanchet@43085
   438
        fun add_super sub super = class_less (sub, super) ? cons (sub, super)
blanchet@43085
   439
        fun add_supers sub = fold (add_super sub) supers
blanchet@43085
   440
      in fold add_supers subs [] end
blanchet@43085
   441
blanchet@43085
   442
fun make_class_rel_clause (sub,super) =
blanchet@43086
   443
  {name = sub ^ "_" ^ super,
blanchet@43086
   444
   subclass = `make_type_class sub,
blanchet@43086
   445
   superclass = `make_type_class super}
blanchet@43085
   446
blanchet@43085
   447
fun make_class_rel_clauses thy subs supers =
blanchet@43093
   448
  map make_class_rel_clause (class_pairs thy subs supers)
blanchet@43085
   449
blanchet@43085
   450
datatype combterm =
blanchet@43085
   451
  CombConst of name * typ * typ list |
blanchet@43085
   452
  CombVar of name * typ |
blanchet@43085
   453
  CombApp of combterm * combterm
blanchet@43085
   454
blanchet@43085
   455
fun combtyp_of (CombConst (_, T, _)) = T
blanchet@43085
   456
  | combtyp_of (CombVar (_, T)) = T
blanchet@43085
   457
  | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
blanchet@43085
   458
blanchet@43085
   459
(*gets the head of a combinator application, along with the list of arguments*)
blanchet@43085
   460
fun strip_combterm_comb u =
blanchet@43085
   461
    let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
blanchet@43085
   462
        |   stripc  x =  x
blanchet@43085
   463
    in stripc(u,[]) end
blanchet@43085
   464
blanchet@43085
   465
fun atyps_of T = fold_atyps (insert (op =)) T []
blanchet@43085
   466
blanchet@43085
   467
fun new_skolem_const_name s num_T_args =
blanchet@43085
   468
  [new_skolem_const_prefix, s, string_of_int num_T_args]
blanchet@43085
   469
  |> space_implode Long_Name.separator
blanchet@43085
   470
blanchet@43085
   471
(* Converts a term (with combinators) into a combterm. Also accumulates sort
blanchet@43085
   472
   infomation. *)
blanchet@43085
   473
fun combterm_from_term thy bs (P $ Q) =
blanchet@43085
   474
    let
blanchet@43085
   475
      val (P', P_atomics_Ts) = combterm_from_term thy bs P
blanchet@43085
   476
      val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
blanchet@43085
   477
    in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
blanchet@43085
   478
  | combterm_from_term thy _ (Const (c, T)) =
blanchet@43085
   479
    let
blanchet@43085
   480
      val tvar_list =
blanchet@43085
   481
        (if String.isPrefix old_skolem_const_prefix c then
blanchet@43085
   482
           [] |> Term.add_tvarsT T |> map TVar
blanchet@43085
   483
         else
blanchet@43085
   484
           (c, T) |> Sign.const_typargs thy)
blanchet@43085
   485
      val c' = CombConst (`make_fixed_const c, T, tvar_list)
blanchet@43085
   486
    in (c', atyps_of T) end
blanchet@43085
   487
  | combterm_from_term _ _ (Free (v, T)) =
blanchet@43085
   488
    (CombConst (`make_fixed_var v, T, []), atyps_of T)
blanchet@43085
   489
  | combterm_from_term _ _ (Var (v as (s, _), T)) =
blanchet@43085
   490
    (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
blanchet@43085
   491
       let
blanchet@43085
   492
         val Ts = T |> strip_type |> swap |> op ::
blanchet@43085
   493
         val s' = new_skolem_const_name s (length Ts)
blanchet@43085
   494
       in CombConst (`make_fixed_const s', T, Ts) end
blanchet@43085
   495
     else
blanchet@43085
   496
       CombVar ((make_schematic_var v, s), T), atyps_of T)
blanchet@43085
   497
  | combterm_from_term _ bs (Bound j) =
blanchet@43085
   498
    nth bs j
blanchet@43085
   499
    |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
blanchet@43085
   500
  | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
blanchet@43085
   501
blanchet@43085
   502
datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
blanchet@43085
   503
blanchet@43085
   504
(* (quasi-)underapproximation of the truth *)
blanchet@43085
   505
fun is_locality_global Local = false
blanchet@43085
   506
  | is_locality_global Assum = false
blanchet@43085
   507
  | is_locality_global Chained = false
blanchet@43085
   508
  | is_locality_global _ = true
blanchet@43085
   509
blanchet@42613
   510
datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
blanchet@42613
   511
datatype type_level =
blanchet@42613
   512
  All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
blanchet@43128
   513
datatype type_heaviness = Heavyweight | Lightweight
blanchet@42613
   514
blanchet@43102
   515
datatype type_sys =
blanchet@42722
   516
  Simple_Types of type_level |
blanchet@42837
   517
  Preds of polymorphism * type_level * type_heaviness |
blanchet@42837
   518
  Tags of polymorphism * type_level * type_heaviness
blanchet@42613
   519
blanchet@42689
   520
fun try_unsuffixes ss s =
blanchet@42689
   521
  fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
blanchet@42689
   522
blanchet@42613
   523
fun type_sys_from_string s =
blanchet@42722
   524
  (case try (unprefix "poly_") s of
blanchet@42722
   525
     SOME s => (SOME Polymorphic, s)
blanchet@42613
   526
   | NONE =>
blanchet@42613
   527
     case try (unprefix "mono_") s of
blanchet@42722
   528
       SOME s => (SOME Monomorphic, s)
blanchet@42722
   529
     | NONE =>
blanchet@42722
   530
       case try (unprefix "mangled_") s of
blanchet@42722
   531
         SOME s => (SOME Mangled_Monomorphic, s)
blanchet@42722
   532
       | NONE => (NONE, s))
blanchet@42613
   533
  ||> (fn s =>
blanchet@42689
   534
          (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
blanchet@42689
   535
          case try_unsuffixes ["?", "_query"] s of
blanchet@42613
   536
            SOME s => (Nonmonotonic_Types, s)
blanchet@42613
   537
          | NONE =>
blanchet@42689
   538
            case try_unsuffixes ["!", "_bang"] s of
blanchet@42613
   539
              SOME s => (Finite_Types, s)
blanchet@42613
   540
            | NONE => (All_Types, s))
blanchet@42828
   541
  ||> apsnd (fn s =>
blanchet@42837
   542
                case try (unsuffix "_heavy") s of
blanchet@43128
   543
                  SOME s => (Heavyweight, s)
blanchet@43128
   544
                | NONE => (Lightweight, s))
blanchet@42837
   545
  |> (fn (poly, (level, (heaviness, core))) =>
blanchet@42837
   546
         case (core, (poly, level, heaviness)) of
blanchet@43128
   547
           ("simple", (NONE, _, Lightweight)) => Simple_Types level
blanchet@42854
   548
         | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
blanchet@42851
   549
         | ("tags", (SOME Polymorphic, All_Types, _)) =>
blanchet@42854
   550
           Tags (Polymorphic, All_Types, heaviness)
blanchet@42886
   551
         | ("tags", (SOME Polymorphic, _, _)) =>
blanchet@42886
   552
           (* The actual light encoding is very unsound. *)
blanchet@43128
   553
           Tags (Polymorphic, level, Heavyweight)
blanchet@42854
   554
         | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
blanchet@43128
   555
         | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
blanchet@43128
   556
           Preds (poly, Const_Arg_Types, Lightweight)
blanchet@43128
   557
         | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
blanchet@43128
   558
           Preds (Polymorphic, No_Types, Lightweight)
blanchet@42753
   559
         | _ => raise Same.SAME)
blanchet@42753
   560
  handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
blanchet@42613
   561
blanchet@42722
   562
fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
blanchet@42828
   563
  | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
blanchet@42828
   564
  | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
blanchet@42613
   565
blanchet@42722
   566
fun level_of_type_sys (Simple_Types level) = level
blanchet@42828
   567
  | level_of_type_sys (Preds (_, level, _)) = level
blanchet@42828
   568
  | level_of_type_sys (Tags (_, level, _)) = level
blanchet@42828
   569
blanchet@43128
   570
fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
blanchet@42837
   571
  | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
blanchet@42837
   572
  | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
blanchet@42831
   573
blanchet@42687
   574
fun is_type_level_virtually_sound level =
blanchet@42687
   575
  level = All_Types orelse level = Nonmonotonic_Types
blanchet@42613
   576
val is_type_sys_virtually_sound =
blanchet@42613
   577
  is_type_level_virtually_sound o level_of_type_sys
blanchet@42613
   578
blanchet@42613
   579
fun is_type_level_fairly_sound level =
blanchet@42613
   580
  is_type_level_virtually_sound level orelse level = Finite_Types
blanchet@42613
   581
val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
blanchet@42613
   582
blanchet@42994
   583
fun is_setting_higher_order THF (Simple_Types _) = true
blanchet@42994
   584
  | is_setting_higher_order _ _ = false
blanchet@42994
   585
blanchet@43101
   586
fun choose_format formats (Simple_Types level) =
blanchet@43101
   587
    if member (op =) formats THF then (THF, Simple_Types level)
blanchet@43101
   588
    else if member (op =) formats TFF then (TFF, Simple_Types level)
blanchet@43128
   589
    else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
blanchet@43101
   590
  | choose_format formats type_sys =
blanchet@43101
   591
    (case hd formats of
blanchet@43101
   592
       CNF_UEQ =>
blanchet@43101
   593
       (CNF_UEQ, case type_sys of
blanchet@43101
   594
                   Preds stuff =>
blanchet@43101
   595
                   (if is_type_sys_fairly_sound type_sys then Preds else Tags)
blanchet@43101
   596
                       stuff
blanchet@43101
   597
                 | _ => type_sys)
blanchet@43101
   598
     | format => (format, type_sys))
blanchet@43101
   599
blanchet@40114
   600
type translated_formula =
blanchet@38752
   601
  {name: string,
blanchet@42640
   602
   locality: locality,
blanchet@42525
   603
   kind: formula_kind,
blanchet@42562
   604
   combformula: (name, typ, combterm) formula,
blanchet@42562
   605
   atomic_types: typ list}
blanchet@38282
   606
blanchet@42640
   607
fun update_combformula f ({name, locality, kind, combformula, atomic_types}
blanchet@42640
   608
                          : translated_formula) =
blanchet@42640
   609
  {name = name, locality = locality, kind = kind, combformula = f combformula,
blanchet@42562
   610
   atomic_types = atomic_types} : translated_formula
blanchet@42542
   611
blanchet@42558
   612
fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
blanchet@42558
   613
blanchet@43064
   614
val type_instance = Sign.typ_instance o Proof_Context.theory_of
blanchet@43064
   615
blanchet@43064
   616
fun insert_type ctxt get_T x xs =
blanchet@43064
   617
  let val T = get_T x in
blanchet@43064
   618
    if exists (curry (type_instance ctxt) T o get_T) xs then xs
blanchet@43064
   619
    else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
blanchet@43064
   620
  end
blanchet@42677
   621
blanchet@42753
   622
(* The Booleans indicate whether all type arguments should be kept. *)
blanchet@42753
   623
datatype type_arg_policy =
blanchet@42753
   624
  Explicit_Type_Args of bool |
blanchet@42753
   625
  Mangled_Type_Args of bool |
blanchet@42753
   626
  No_Type_Args
blanchet@41136
   627
blanchet@42836
   628
fun should_drop_arg_type_args (Simple_Types _) =
blanchet@42836
   629
    false (* since TFF doesn't support overloading *)
blanchet@42836
   630
  | should_drop_arg_type_args type_sys =
blanchet@42836
   631
    level_of_type_sys type_sys = All_Types andalso
blanchet@43128
   632
    heaviness_of_type_sys type_sys = Heavyweight
blanchet@42831
   633
blanchet@43128
   634
fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
blanchet@43105
   635
  | general_type_arg_policy type_sys =
blanchet@43105
   636
    if level_of_type_sys type_sys = No_Types then
blanchet@43105
   637
      No_Type_Args
blanchet@43105
   638
    else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
blanchet@43105
   639
      Mangled_Type_Args (should_drop_arg_type_args type_sys)
blanchet@43105
   640
    else
blanchet@43105
   641
      Explicit_Type_Args (should_drop_arg_type_args type_sys)
blanchet@42563
   642
blanchet@42951
   643
fun type_arg_policy type_sys s =
blanchet@42951
   644
  if s = @{const_name HOL.eq} orelse
blanchet@42966
   645
     (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
blanchet@42951
   646
    No_Type_Args
blanchet@43105
   647
  else if s = type_tag_name then
blanchet@43105
   648
    Explicit_Type_Args false
blanchet@42951
   649
  else
blanchet@42951
   650
    general_type_arg_policy type_sys
blanchet@42227
   651
blanchet@43085
   652
(*Make literals for sorted type variables*)
blanchet@43098
   653
fun generic_sorts_on_type (_, []) = []
blanchet@43098
   654
  | generic_sorts_on_type ((x, i), s :: ss) =
blanchet@43098
   655
    generic_sorts_on_type ((x, i), ss)
blanchet@43093
   656
    |> (if s = the_single @{sort HOL.type} then
blanchet@43093
   657
          I
blanchet@43093
   658
        else if i = ~1 then
blanchet@43093
   659
          cons (TyLitFree (`make_type_class s, `make_fixed_type_var x))
blanchet@43093
   660
        else
blanchet@43093
   661
          cons (TyLitVar (`make_type_class s,
blanchet@43093
   662
                          (make_schematic_type_var (x, i), x))))
blanchet@43098
   663
fun sorts_on_tfree (TFree (s, S)) = generic_sorts_on_type ((s, ~1), S)
blanchet@43098
   664
  | sorts_on_tfree _ = []
blanchet@43098
   665
fun sorts_on_tvar (TVar z) = generic_sorts_on_type z
blanchet@43098
   666
  | sorts_on_tvar _ = []
blanchet@43085
   667
blanchet@43098
   668
(* Given a list of sorted type variables, return a list of type literals. *)
blanchet@43098
   669
fun raw_type_literals_for_types Ts =
blanchet@43098
   670
  union_all (map sorts_on_tfree Ts @ map sorts_on_tvar Ts)
blanchet@43098
   671
blanchet@43098
   672
fun type_literals_for_types type_sys sorts_on_typ Ts =
blanchet@43098
   673
  if level_of_type_sys type_sys = No_Types then []
blanchet@43098
   674
  else union_all (map sorts_on_typ Ts)
blanchet@41137
   675
blanchet@42534
   676
fun mk_aconns c phis =
blanchet@42534
   677
  let val (phis', phi') = split_last phis in
blanchet@42534
   678
    fold_rev (mk_aconn c) phis' phi'
blanchet@42534
   679
  end
blanchet@38282
   680
fun mk_ahorn [] phi = phi
blanchet@42534
   681
  | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
blanchet@42522
   682
fun mk_aquant _ [] phi = phi
blanchet@42522
   683
  | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
blanchet@42522
   684
    if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
blanchet@42522
   685
  | mk_aquant q xs phi = AQuant (q, xs, phi)
blanchet@38282
   686
blanchet@42522
   687
fun close_universally atom_vars phi =
blanchet@41145
   688
  let
blanchet@41145
   689
    fun formula_vars bounds (AQuant (_, xs, phi)) =
blanchet@42526
   690
        formula_vars (map fst xs @ bounds) phi
blanchet@41145
   691
      | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
blanchet@42522
   692
      | formula_vars bounds (AAtom tm) =
blanchet@42526
   693
        union (op =) (atom_vars tm []
blanchet@42526
   694
                      |> filter_out (member (op =) bounds o fst))
blanchet@42522
   695
  in mk_aquant AForall (formula_vars [] phi []) phi end
blanchet@42522
   696
blanchet@42531
   697
fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
blanchet@42522
   698
  | combterm_vars (CombConst _) = I
blanchet@42574
   699
  | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
blanchet@42674
   700
fun close_combformula_universally phi = close_universally combterm_vars phi
blanchet@42522
   701
blanchet@42522
   702
fun term_vars (ATerm (name as (s, _), tms)) =
blanchet@42998
   703
  is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
blanchet@42674
   704
fun close_formula_universally phi = close_universally term_vars phi
blanchet@41145
   705
blanchet@42994
   706
val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
blanchet@42994
   707
val homo_infinite_type = Type (homo_infinite_type_name, [])
blanchet@42994
   708
blanchet@42994
   709
fun fo_term_from_typ higher_order =
blanchet@42994
   710
  let
blanchet@42994
   711
    fun term (Type (s, Ts)) =
blanchet@42994
   712
      ATerm (case (higher_order, s) of
blanchet@42994
   713
               (true, @{type_name bool}) => `I tptp_bool_type
blanchet@42994
   714
             | (true, @{type_name fun}) => `I tptp_fun_type
blanchet@42994
   715
             | _ => if s = homo_infinite_type_name then `I tptp_individual_type
blanchet@42994
   716
                    else `make_fixed_type_const s,
blanchet@42994
   717
             map term Ts)
blanchet@42994
   718
    | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
blanchet@42994
   719
    | term (TVar ((x as (s, _)), _)) =
blanchet@42994
   720
      ATerm ((make_schematic_type_var x, s), [])
blanchet@42994
   721
  in term end
blanchet@42562
   722
blanchet@42562
   723
(* This shouldn't clash with anything else. *)
blanchet@42542
   724
val mangled_type_sep = "\000"
blanchet@42542
   725
blanchet@42562
   726
fun generic_mangled_type_name f (ATerm (name, [])) = f name
blanchet@42562
   727
  | generic_mangled_type_name f (ATerm (name, tys)) =
blanchet@42761
   728
    f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
blanchet@42761
   729
    ^ ")"
blanchet@42542
   730
blanchet@42998
   731
val bool_atype = AType (`I tptp_bool_type)
blanchet@42998
   732
blanchet@43085
   733
fun make_simple_type s =
blanchet@43085
   734
  if s = tptp_bool_type orelse s = tptp_fun_type orelse
blanchet@43085
   735
     s = tptp_individual_type then
blanchet@43085
   736
    s
blanchet@43085
   737
  else
blanchet@43085
   738
    simple_type_prefix ^ ascii_of s
blanchet@43085
   739
blanchet@42994
   740
fun ho_type_from_fo_term higher_order pred_sym ary =
blanchet@42963
   741
  let
blanchet@42963
   742
    fun to_atype ty =
blanchet@42963
   743
      AType ((make_simple_type (generic_mangled_type_name fst ty),
blanchet@42963
   744
              generic_mangled_type_name snd ty))
blanchet@42963
   745
    fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
blanchet@42998
   746
    fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
blanchet@42994
   747
      | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
blanchet@42994
   748
    fun to_ho (ty as ATerm ((s, _), tys)) =
blanchet@42994
   749
      if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
blanchet@42994
   750
  in if higher_order then to_ho else to_fo ary end
blanchet@42963
   751
blanchet@42994
   752
fun mangled_type higher_order pred_sym ary =
blanchet@42994
   753
  ho_type_from_fo_term higher_order pred_sym ary o fo_term_from_typ higher_order
blanchet@42963
   754
blanchet@42994
   755
fun mangled_const_name T_args (s, s') =
blanchet@42963
   756
  let
blanchet@42994
   757
    val ty_args = map (fo_term_from_typ false) T_args
blanchet@42963
   758
    fun type_suffix f g =
blanchet@42963
   759
      fold_rev (curry (op ^) o g o prefix mangled_type_sep
blanchet@42963
   760
                o generic_mangled_type_name f) ty_args ""
blanchet@42963
   761
  in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
blanchet@42542
   762
blanchet@42542
   763
val parse_mangled_ident =
blanchet@42542
   764
  Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
blanchet@42542
   765
blanchet@42542
   766
fun parse_mangled_type x =
blanchet@42542
   767
  (parse_mangled_ident
blanchet@42542
   768
   -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
blanchet@42542
   769
                    [] >> ATerm) x
blanchet@42542
   770
and parse_mangled_types x =
blanchet@42542
   771
  (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
blanchet@42542
   772
blanchet@42542
   773
fun unmangled_type s =
blanchet@42542
   774
  s |> suffix ")" |> raw_explode
blanchet@42542
   775
    |> Scan.finite Symbol.stopper
blanchet@42542
   776
           (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
blanchet@42542
   777
                                                quote s)) parse_mangled_type))
blanchet@42542
   778
    |> fst
blanchet@42542
   779
blanchet@42561
   780
val unmangled_const_name = space_explode mangled_type_sep #> hd
blanchet@42542
   781
fun unmangled_const s =
blanchet@42542
   782
  let val ss = space_explode mangled_type_sep s in
blanchet@42542
   783
    (hd ss, map unmangled_type (tl ss))
blanchet@42542
   784
  end
blanchet@42542
   785
blanchet@43017
   786
fun introduce_proxies format type_sys =
blanchet@42568
   787
  let
blanchet@43017
   788
    fun intro top_level (CombApp (tm1, tm2)) =
blanchet@43017
   789
        CombApp (intro top_level tm1, intro false tm2)
blanchet@43017
   790
      | intro top_level (CombConst (name as (s, _), T, T_args)) =
blanchet@42570
   791
        (case proxify_const s of
blanchet@43017
   792
           SOME (_, proxy_base) =>
blanchet@43000
   793
           if top_level orelse is_setting_higher_order format type_sys then
blanchet@43000
   794
             case (top_level, s) of
blanchet@43000
   795
               (_, "c_False") => (`I tptp_false, [])
blanchet@43000
   796
             | (_, "c_True") => (`I tptp_true, [])
blanchet@43000
   797
             | (false, "c_Not") => (`I tptp_not, [])
blanchet@43000
   798
             | (false, "c_conj") => (`I tptp_and, [])
blanchet@43000
   799
             | (false, "c_disj") => (`I tptp_or, [])
blanchet@43000
   800
             | (false, "c_implies") => (`I tptp_implies, [])
blanchet@43000
   801
             | (false, s) =>
blanchet@43017
   802
               if is_tptp_equal s then (`I tptp_equal, [])
blanchet@43017
   803
               else (proxy_base |>> prefix const_prefix, T_args)
blanchet@43000
   804
             | _ => (name, [])
blanchet@42569
   805
           else
blanchet@42574
   806
             (proxy_base |>> prefix const_prefix, T_args)
blanchet@42574
   807
          | NONE => (name, T_args))
blanchet@42574
   808
        |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@43017
   809
      | intro _ tm = tm
blanchet@43017
   810
  in intro true end
blanchet@42568
   811
blanchet@42994
   812
fun combformula_from_prop thy format type_sys eq_as_iff =
blanchet@38282
   813
  let
blanchet@42568
   814
    fun do_term bs t atomic_types =
blanchet@41140
   815
      combterm_from_term thy bs (Envir.eta_contract t)
blanchet@42994
   816
      |>> (introduce_proxies format type_sys #> AAtom)
blanchet@42568
   817
      ||> union (op =) atomic_types
blanchet@38282
   818
    fun do_quant bs q s T t' =
blanchet@38518
   819
      let val s = Name.variant (map fst bs) s in
blanchet@38518
   820
        do_formula ((s, T) :: bs) t'
blanchet@42562
   821
        #>> mk_aquant q [(`make_bound_var s, SOME T)]
blanchet@38518
   822
      end
blanchet@38282
   823
    and do_conn bs c t1 t2 =
blanchet@38282
   824
      do_formula bs t1 ##>> do_formula bs t2
blanchet@42531
   825
      #>> uncurry (mk_aconn c)
blanchet@38282
   826
    and do_formula bs t =
blanchet@38282
   827
      case t of
blanchet@43096
   828
        @{const Trueprop} $ t1 => do_formula bs t1
blanchet@43096
   829
      | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
blanchet@38282
   830
      | Const (@{const_name All}, _) $ Abs (s, T, t') =>
blanchet@38282
   831
        do_quant bs AForall s T t'
blanchet@38282
   832
      | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
blanchet@38282
   833
        do_quant bs AExists s T t'
haftmann@38795
   834
      | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
haftmann@38795
   835
      | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
haftmann@38786
   836
      | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
haftmann@38864
   837
      | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
blanchet@41140
   838
        if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
blanchet@41140
   839
      | _ => do_term bs t
blanchet@38282
   840
  in do_formula [] end
blanchet@38282
   841
blanchet@42750
   842
fun presimplify_term ctxt =
blanchet@42750
   843
  Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
blanchet@42750
   844
  #> Meson.presimplify ctxt
blanchet@42750
   845
  #> prop_of
blanchet@38282
   846
wenzelm@41491
   847
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
blanchet@38282
   848
fun conceal_bounds Ts t =
blanchet@38282
   849
  subst_bounds (map (Free o apfst concealed_bound_name)
blanchet@38282
   850
                    (0 upto length Ts - 1 ~~ Ts), t)
blanchet@38282
   851
fun reveal_bounds Ts =
blanchet@38282
   852
  subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
blanchet@38282
   853
                    (0 upto length Ts - 1 ~~ Ts))
blanchet@38282
   854
blanchet@42747
   855
fun extensionalize_term ctxt t =
blanchet@42747
   856
  let val thy = Proof_Context.theory_of ctxt in
blanchet@42747
   857
    t |> cterm_of thy |> Meson.extensionalize_conv ctxt
blanchet@42747
   858
      |> prop_of |> Logic.dest_equals |> snd
blanchet@42747
   859
  end
blanchet@38608
   860
blanchet@38282
   861
fun introduce_combinators_in_term ctxt kind t =
wenzelm@42361
   862
  let val thy = Proof_Context.theory_of ctxt in
blanchet@38491
   863
    if Meson.is_fol_term thy t then
blanchet@38491
   864
      t
blanchet@38491
   865
    else
blanchet@38491
   866
      let
blanchet@38491
   867
        fun aux Ts t =
blanchet@38491
   868
          case t of
blanchet@38491
   869
            @{const Not} $ t1 => @{const Not} $ aux Ts t1
blanchet@38491
   870
          | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
blanchet@38491
   871
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   872
          | (t0 as Const (@{const_name All}, _)) $ t1 =>
blanchet@38652
   873
            aux Ts (t0 $ eta_expand Ts t1 1)
blanchet@38491
   874
          | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
blanchet@38491
   875
            t0 $ Abs (s, T, aux (T :: Ts) t')
blanchet@38652
   876
          | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
blanchet@38652
   877
            aux Ts (t0 $ eta_expand Ts t1 1)
haftmann@38795
   878
          | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38795
   879
          | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38786
   880
          | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
haftmann@38864
   881
          | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
blanchet@38491
   882
              $ t1 $ t2 =>
blanchet@38491
   883
            t0 $ aux Ts t1 $ aux Ts t2
blanchet@38491
   884
          | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
blanchet@38491
   885
                   t
blanchet@38491
   886
                 else
blanchet@38491
   887
                   t |> conceal_bounds Ts
blanchet@38491
   888
                     |> Envir.eta_contract
blanchet@38491
   889
                     |> cterm_of thy
blanchet@39890
   890
                     |> Meson_Clausify.introduce_combinators_in_cterm
blanchet@38491
   891
                     |> prop_of |> Logic.dest_equals |> snd
blanchet@38491
   892
                     |> reveal_bounds Ts
blanchet@39370
   893
        val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
blanchet@38491
   894
      in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
blanchet@38491
   895
      handle THM _ =>
blanchet@38491
   896
             (* A type variable of sort "{}" will make abstraction fail. *)
blanchet@38613
   897
             if kind = Conjecture then HOLogic.false_const
blanchet@38613
   898
             else HOLogic.true_const
blanchet@38491
   899
  end
blanchet@38282
   900
blanchet@38282
   901
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
blanchet@42353
   902
   same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
blanchet@38282
   903
fun freeze_term t =
blanchet@38282
   904
  let
blanchet@38282
   905
    fun aux (t $ u) = aux t $ aux u
blanchet@38282
   906
      | aux (Abs (s, T, t)) = Abs (s, T, aux t)
blanchet@38282
   907
      | aux (Var ((s, i), T)) =
blanchet@38282
   908
        Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
blanchet@38282
   909
      | aux t = t
blanchet@38282
   910
  in t |> exists_subterm is_Var t ? aux end
blanchet@38282
   911
blanchet@43096
   912
fun preprocess_prop ctxt presimp kind t =
blanchet@38282
   913
  let
wenzelm@42361
   914
    val thy = Proof_Context.theory_of ctxt
blanchet@38608
   915
    val t = t |> Envir.beta_eta_contract
blanchet@42944
   916
              |> transform_elim_prop
blanchet@41211
   917
              |> Object_Logic.atomize_term thy
blanchet@42563
   918
    val need_trueprop = (fastype_of t = @{typ bool})
blanchet@43096
   919
  in
blanchet@43096
   920
    t |> need_trueprop ? HOLogic.mk_Trueprop
blanchet@43096
   921
      |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
blanchet@43096
   922
      |> extensionalize_term ctxt
blanchet@43096
   923
      |> presimp ? presimplify_term ctxt
blanchet@43120
   924
      |> perhaps (try (HOLogic.dest_Trueprop))
blanchet@43096
   925
      |> introduce_combinators_in_term ctxt kind
blanchet@43096
   926
  end
blanchet@43096
   927
blanchet@43096
   928
(* making fact and conjecture formulas *)
blanchet@43096
   929
fun make_formula thy format type_sys eq_as_iff name loc kind t =
blanchet@43096
   930
  let
blanchet@42962
   931
    val (combformula, atomic_types) =
blanchet@42994
   932
      combformula_from_prop thy format type_sys eq_as_iff t []
blanchet@38282
   933
  in
blanchet@42640
   934
    {name = name, locality = loc, kind = kind, combformula = combformula,
blanchet@42562
   935
     atomic_types = atomic_types}
blanchet@38282
   936
  end
blanchet@38282
   937
blanchet@43096
   938
fun make_fact ctxt format type_sys keep_trivial eq_as_iff preproc presimp
blanchet@42994
   939
              ((name, loc), t) =
blanchet@43096
   940
  let val thy = Proof_Context.theory_of ctxt in
blanchet@43096
   941
    case (keep_trivial,
blanchet@43096
   942
          t |> preproc ? preprocess_prop ctxt presimp Axiom
blanchet@43096
   943
            |> make_formula thy format type_sys eq_as_iff name loc Axiom) of
blanchet@43096
   944
      (false,
blanchet@43096
   945
       formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...}) =>
blanchet@43096
   946
      if s = tptp_true then NONE else SOME formula
blanchet@43096
   947
    | (_, formula) => SOME formula
blanchet@43096
   948
  end
blanchet@42561
   949
blanchet@43096
   950
fun make_conjecture ctxt format prem_kind type_sys preproc ts =
blanchet@43096
   951
  let
blanchet@43096
   952
    val thy = Proof_Context.theory_of ctxt
blanchet@43096
   953
    val last = length ts - 1
blanchet@43096
   954
  in
blanchet@42709
   955
    map2 (fn j => fn t =>
blanchet@42709
   956
             let
blanchet@42709
   957
               val (kind, maybe_negate) =
blanchet@42709
   958
                 if j = last then
blanchet@42709
   959
                   (Conjecture, I)
blanchet@42709
   960
                 else
blanchet@42709
   961
                   (prem_kind,
blanchet@42709
   962
                    if prem_kind = Conjecture then update_combformula mk_anot
blanchet@42709
   963
                    else I)
blanchet@42709
   964
              in
blanchet@43098
   965
                t |> preproc ? (preprocess_prop ctxt true kind #> freeze_term)
blanchet@43096
   966
                  |> make_formula thy format type_sys true (string_of_int j)
blanchet@43096
   967
                                  General kind
blanchet@42962
   968
                  |> maybe_negate
blanchet@42709
   969
              end)
blanchet@38613
   970
         (0 upto last) ts
blanchet@38613
   971
  end
blanchet@38282
   972
blanchet@42682
   973
(** Finite and infinite type inference **)
blanchet@42682
   974
blanchet@42886
   975
fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
blanchet@42886
   976
  | deep_freeze_atyp T = T
blanchet@42886
   977
val deep_freeze_type = map_atyps deep_freeze_atyp
blanchet@42886
   978
blanchet@42682
   979
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
blanchet@42682
   980
   dangerous because their "exhaust" properties can easily lead to unsound ATP
blanchet@42682
   981
   proofs. On the other hand, all HOL infinite types can be given the same
blanchet@42682
   982
   models in first-order logic (via Löwenheim-Skolem). *)
blanchet@42682
   983
blanchet@42886
   984
fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
blanchet@42886
   985
    exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
blanchet@42836
   986
  | should_encode_type _ _ All_Types _ = true
blanchet@42682
   987
  | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
blanchet@42682
   988
  | should_encode_type _ _ _ _ = false
blanchet@42682
   989
blanchet@42837
   990
fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
blanchet@42834
   991
                             should_predicate_on_var T =
blanchet@43128
   992
    (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
blanchet@42878
   993
    should_encode_type ctxt nonmono_Ts level T
blanchet@42834
   994
  | should_predicate_on_type _ _ _ _ _ = false
blanchet@42682
   995
blanchet@42836
   996
fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
blanchet@42836
   997
    String.isPrefix bound_var_prefix s
blanchet@42836
   998
  | is_var_or_bound_var (CombVar _) = true
blanchet@42836
   999
  | is_var_or_bound_var _ = false
blanchet@42836
  1000
blanchet@42829
  1001
datatype tag_site = Top_Level | Eq_Arg | Elsewhere
blanchet@42829
  1002
blanchet@42829
  1003
fun should_tag_with_type _ _ _ Top_Level _ _ = false
blanchet@42837
  1004
  | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
blanchet@42837
  1005
    (case heaviness of
blanchet@43128
  1006
       Heavyweight => should_encode_type ctxt nonmono_Ts level T
blanchet@43128
  1007
     | Lightweight =>
blanchet@42836
  1008
       case (site, is_var_or_bound_var u) of
blanchet@42836
  1009
         (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
blanchet@42829
  1010
       | _ => false)
blanchet@42829
  1011
  | should_tag_with_type _ _ _ _ _ _ = false
blanchet@42682
  1012
blanchet@42994
  1013
fun homogenized_type ctxt nonmono_Ts level =
blanchet@42994
  1014
  let
blanchet@42994
  1015
    val should_encode = should_encode_type ctxt nonmono_Ts level
blanchet@42994
  1016
    fun homo 0 T = if should_encode T then T else homo_infinite_type
blanchet@42994
  1017
      | homo ary (Type (@{type_name fun}, [T1, T2])) =
blanchet@42994
  1018
        homo 0 T1 --> homo (ary - 1) T2
blanchet@42994
  1019
      | homo _ _ = raise Fail "expected function type"
blanchet@42994
  1020
  in homo end
blanchet@42682
  1021
blanchet@42573
  1022
(** "hBOOL" and "hAPP" **)
blanchet@41313
  1023
blanchet@42574
  1024
type sym_info =
blanchet@43064
  1025
  {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
blanchet@42563
  1026
blanchet@43064
  1027
fun add_combterm_syms_to_table ctxt explicit_apply =
blanchet@42558
  1028
  let
blanchet@43064
  1029
    fun consider_var_arity const_T var_T max_ary =
blanchet@43064
  1030
      let
blanchet@43064
  1031
        fun iter ary T =
blanchet@43064
  1032
          if ary = max_ary orelse type_instance ctxt (var_T, T) then ary
blanchet@43064
  1033
          else iter (ary + 1) (range_type T)
blanchet@43064
  1034
      in iter 0 const_T end
blanchet@43064
  1035
    fun add top_level tm (accum as (ho_var_Ts, sym_tab)) =
blanchet@42558
  1036
      let val (head, args) = strip_combterm_comb tm in
blanchet@42558
  1037
        (case head of
blanchet@42563
  1038
           CombConst ((s, _), T, _) =>
blanchet@42558
  1039
           if String.isPrefix bound_var_prefix s then
blanchet@43064
  1040
             if explicit_apply = NONE andalso can dest_funT T then
blanchet@43064
  1041
               let
blanchet@43064
  1042
                 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
blanchet@43064
  1043
                   {pred_sym = pred_sym,
blanchet@43064
  1044
                    min_ary =
blanchet@43064
  1045
                      fold (fn T' => consider_var_arity T' T) types min_ary,
blanchet@43064
  1046
                    max_ary = max_ary, types = types}
blanchet@43064
  1047
                 val ho_var_Ts' = ho_var_Ts |> insert_type ctxt I T
blanchet@43064
  1048
               in
blanchet@43064
  1049
                 if pointer_eq (ho_var_Ts', ho_var_Ts) then accum
blanchet@43064
  1050
                 else (ho_var_Ts', Symtab.map (K repair_min_arity) sym_tab)
blanchet@43064
  1051
               end
blanchet@43064
  1052
             else
blanchet@43064
  1053
               accum
blanchet@42558
  1054
           else
blanchet@43064
  1055
             let
blanchet@43064
  1056
               val ary = length args
blanchet@43064
  1057
             in
blanchet@43064
  1058
               (ho_var_Ts,
blanchet@43064
  1059
                case Symtab.lookup sym_tab s of
blanchet@43064
  1060
                  SOME {pred_sym, min_ary, max_ary, types} =>
blanchet@43064
  1061
                  let
blanchet@43064
  1062
                    val types' = types |> insert_type ctxt I T
blanchet@43064
  1063
                    val min_ary =
blanchet@43064
  1064
                      if is_some explicit_apply orelse
blanchet@43064
  1065
                         pointer_eq (types', types) then
blanchet@43064
  1066
                        min_ary
blanchet@43064
  1067
                      else
blanchet@43064
  1068
                        fold (consider_var_arity T) ho_var_Ts min_ary
blanchet@43064
  1069
                  in
blanchet@43064
  1070
                    Symtab.update (s, {pred_sym = pred_sym andalso top_level,
blanchet@43064
  1071
                                       min_ary = Int.min (ary, min_ary),
blanchet@43064
  1072
                                       max_ary = Int.max (ary, max_ary),
blanchet@43064
  1073
                                       types = types'})
blanchet@43064
  1074
                                  sym_tab
blanchet@43064
  1075
                  end
blanchet@43064
  1076
                | NONE =>
blanchet@43064
  1077
                  let
blanchet@43064
  1078
                    val min_ary =
blanchet@43064
  1079
                      case explicit_apply of
blanchet@43064
  1080
                        SOME true => 0
blanchet@43064
  1081
                      | SOME false => ary
blanchet@43064
  1082
                      | NONE => fold (consider_var_arity T) ho_var_Ts ary
blanchet@43064
  1083
                  in
blanchet@43064
  1084
                    Symtab.update_new (s, {pred_sym = top_level,
blanchet@43064
  1085
                                           min_ary = min_ary, max_ary = ary,
blanchet@43064
  1086
                                           types = [T]})
blanchet@43064
  1087
                                      sym_tab
blanchet@43064
  1088
                  end)
blanchet@43064
  1089
             end
blanchet@43064
  1090
         | _ => accum)
blanchet@43064
  1091
        |> fold (add false) args
blanchet@42558
  1092
      end
blanchet@43064
  1093
  in add true end
blanchet@43064
  1094
fun add_fact_syms_to_table ctxt explicit_apply =
blanchet@43064
  1095
  fact_lift (formula_fold NONE
blanchet@43064
  1096
                          (K (add_combterm_syms_to_table ctxt explicit_apply)))
blanchet@38282
  1097
blanchet@42675
  1098
val default_sym_table_entries : (string * sym_info) list =
blanchet@43064
  1099
  [(tptp_equal, {pred_sym = true, min_ary = 2, max_ary = 2, types = []}),
blanchet@43064
  1100
   (tptp_old_equal, {pred_sym = true, min_ary = 2, max_ary = 2, types = []}),
blanchet@42966
  1101
   (make_fixed_const predicator_name,
blanchet@43064
  1102
    {pred_sym = true, min_ary = 1, max_ary = 1, types = []})] @
blanchet@42568
  1103
  ([tptp_false, tptp_true]
blanchet@43064
  1104
   |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []}))
blanchet@41140
  1105
blanchet@43064
  1106
fun sym_table_for_facts ctxt explicit_apply facts =
blanchet@43064
  1107
  Symtab.empty
blanchet@43064
  1108
  |> fold Symtab.default default_sym_table_entries
blanchet@43064
  1109
  |> pair [] |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
blanchet@38282
  1110
blanchet@42558
  1111
fun min_arity_of sym_tab s =
blanchet@42558
  1112
  case Symtab.lookup sym_tab s of
blanchet@42574
  1113
    SOME ({min_ary, ...} : sym_info) => min_ary
blanchet@42558
  1114
  | NONE =>
blanchet@42558
  1115
    case strip_prefix_and_unascii const_prefix s of
blanchet@42547
  1116
      SOME s =>
blanchet@42570
  1117
      let val s = s |> unmangled_const_name |> invert_const in
blanchet@42966
  1118
        if s = predicator_name then 1
blanchet@42966
  1119
        else if s = app_op_name then 2
blanchet@42966
  1120
        else if s = type_pred_name then 1
blanchet@42557
  1121
        else 0
blanchet@42547
  1122
      end
blanchet@42544
  1123
    | NONE => 0
blanchet@38282
  1124
blanchet@38282
  1125
(* True if the constant ever appears outside of the top-level position in
blanchet@38282
  1126
   literals, or if it appears with different arities (e.g., because of different
blanchet@38282
  1127
   type instantiations). If false, the constant always receives all of its
blanchet@38282
  1128
   arguments and is used as a predicate. *)
blanchet@42558
  1129
fun is_pred_sym sym_tab s =
blanchet@42558
  1130
  case Symtab.lookup sym_tab s of
blanchet@42574
  1131
    SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
blanchet@42574
  1132
    pred_sym andalso min_ary = max_ary
blanchet@42558
  1133
  | NONE => false
blanchet@38282
  1134
blanchet@42568
  1135
val predicator_combconst =
blanchet@42966
  1136
  CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
blanchet@42568
  1137
fun predicator tm = CombApp (predicator_combconst, tm)
blanchet@42542
  1138
blanchet@42568
  1139
fun introduce_predicators_in_combterm sym_tab tm =
blanchet@42542
  1140
  case strip_combterm_comb tm of
blanchet@42542
  1141
    (CombConst ((s, _), _, _), _) =>
blanchet@42568
  1142
    if is_pred_sym sym_tab s then tm else predicator tm
blanchet@42568
  1143
  | _ => predicator tm
blanchet@42542
  1144
blanchet@42544
  1145
fun list_app head args = fold (curry (CombApp o swap)) args head
blanchet@42544
  1146
blanchet@43130
  1147
val app_op = `make_fixed_const app_op_name
blanchet@43130
  1148
blanchet@42544
  1149
fun explicit_app arg head =
blanchet@42544
  1150
  let
blanchet@42562
  1151
    val head_T = combtyp_of head
blanchet@42693
  1152
    val (arg_T, res_T) = dest_funT head_T
blanchet@42544
  1153
    val explicit_app =
blanchet@43130
  1154
      CombConst (app_op, head_T --> head_T, [arg_T, res_T])
blanchet@42544
  1155
  in list_app explicit_app [head, arg] end
blanchet@42544
  1156
fun list_explicit_app head args = fold explicit_app args head
blanchet@38282
  1157
blanchet@42565
  1158
fun introduce_explicit_apps_in_combterm sym_tab =
blanchet@42544
  1159
  let
blanchet@42544
  1160
    fun aux tm =
blanchet@42544
  1161
      case strip_combterm_comb tm of
blanchet@42544
  1162
        (head as CombConst ((s, _), _, _), args) =>
blanchet@42544
  1163
        args |> map aux
blanchet@42557
  1164
             |> chop (min_arity_of sym_tab s)
blanchet@42544
  1165
             |>> list_app head
blanchet@42544
  1166
             |-> list_explicit_app
blanchet@42544
  1167
      | (head, args) => list_explicit_app head (map aux args)
blanchet@42544
  1168
  in aux end
blanchet@38282
  1169
blanchet@42753
  1170
fun chop_fun 0 T = ([], T)
blanchet@42753
  1171
  | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
blanchet@42753
  1172
    chop_fun (n - 1) ran_T |>> cons dom_T
blanchet@42753
  1173
  | chop_fun _ _ = raise Fail "unexpected non-function"
blanchet@42753
  1174
blanchet@42780
  1175
fun filter_type_args _ _ _ [] = []
blanchet@42780
  1176
  | filter_type_args thy s arity T_args =
blanchet@42834
  1177
    let
blanchet@42834
  1178
      (* will throw "TYPE" for pseudo-constants *)
blanchet@42966
  1179
      val U = if s = app_op_name then
blanchet@42834
  1180
                @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
blanchet@42834
  1181
              else
blanchet@42834
  1182
                s |> Sign.the_const_type thy
blanchet@42834
  1183
    in
blanchet@42781
  1184
      case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
blanchet@42781
  1185
        [] => []
blanchet@42781
  1186
      | res_U_vars =>
blanchet@42781
  1187
        let val U_args = (s, U) |> Sign.const_typargs thy in
blanchet@42781
  1188
          U_args ~~ T_args
blanchet@42781
  1189
          |> map_filter (fn (U, T) =>
blanchet@42781
  1190
                            if member (op =) res_U_vars (dest_TVar U) then
blanchet@42781
  1191
                              SOME T
blanchet@42781
  1192
                            else
blanchet@42781
  1193
                              NONE)
blanchet@42781
  1194
        end
blanchet@42780
  1195
    end
blanchet@42780
  1196
    handle TYPE _ => T_args
blanchet@42753
  1197
blanchet@42994
  1198
fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
blanchet@42753
  1199
  let
blanchet@42753
  1200
    val thy = Proof_Context.theory_of ctxt
blanchet@42753
  1201
    fun aux arity (CombApp (tm1, tm2)) =
blanchet@42753
  1202
        CombApp (aux (arity + 1) tm1, aux 0 tm2)
blanchet@42753
  1203
      | aux arity (CombConst (name as (s, _), T, T_args)) =
blanchet@42701
  1204
        let
blanchet@42701
  1205
          val level = level_of_type_sys type_sys
blanchet@42701
  1206
          val (T, T_args) =
blanchet@42701
  1207
            (* Aggressively merge most "hAPPs" if the type system is unsound
blanchet@42701
  1208
               anyway, by distinguishing overloads only on the homogenized
blanchet@42837
  1209
               result type. Don't do it for lightweight type systems, though,
blanchet@42837
  1210
               since it leads to too many unsound proofs. *)
blanchet@43130
  1211
            if s = prefixed_app_op_name andalso length T_args = 2 andalso
blanchet@42836
  1212
               not (is_type_sys_virtually_sound type_sys) andalso
blanchet@43128
  1213
               heaviness_of_type_sys type_sys = Heavyweight then
blanchet@42994
  1214
              T_args |> map (homogenized_type ctxt nonmono_Ts level 0)
blanchet@42701
  1215
                     |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
blanchet@42831
  1216
                                    (T --> T, tl Ts)
blanchet@42701
  1217
                                  end)
blanchet@42701
  1218
            else
blanchet@42701
  1219
              (T, T_args)
blanchet@42701
  1220
        in
blanchet@42701
  1221
          (case strip_prefix_and_unascii const_prefix s of
blanchet@42701
  1222
             NONE => (name, T_args)
blanchet@42701
  1223
           | SOME s'' =>
blanchet@42753
  1224
             let
blanchet@42753
  1225
               val s'' = invert_const s''
blanchet@42831
  1226
               fun filtered_T_args false = T_args
blanchet@42831
  1227
                 | filtered_T_args true = filter_type_args thy s'' arity T_args
blanchet@42753
  1228
             in
blanchet@42701
  1229
               case type_arg_policy type_sys s'' of
blanchet@42831
  1230
                 Explicit_Type_Args drop_args =>
blanchet@42831
  1231
                 (name, filtered_T_args drop_args)
blanchet@42831
  1232
               | Mangled_Type_Args drop_args =>
blanchet@42994
  1233
                 (mangled_const_name (filtered_T_args drop_args) name, [])
blanchet@42753
  1234
               | No_Type_Args => (name, [])
blanchet@42701
  1235
             end)
blanchet@42701
  1236
          |> (fn (name, T_args) => CombConst (name, T, T_args))
blanchet@42701
  1237
        end
blanchet@42753
  1238
      | aux _ tm = tm
blanchet@42753
  1239
  in aux 0 end
blanchet@42573
  1240
blanchet@42962
  1241
fun repair_combterm ctxt format nonmono_Ts type_sys sym_tab =
blanchet@42994
  1242
  not (is_setting_higher_order format type_sys)
blanchet@42994
  1243
  ? (introduce_explicit_apps_in_combterm sym_tab
blanchet@42994
  1244
     #> introduce_predicators_in_combterm sym_tab)
blanchet@42994
  1245
  #> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42962
  1246
fun repair_fact ctxt format nonmono_Ts type_sys sym_tab =
blanchet@42701
  1247
  update_combformula (formula_map
blanchet@42962
  1248
      (repair_combterm ctxt format nonmono_Ts type_sys sym_tab))
blanchet@42573
  1249
blanchet@42573
  1250
(** Helper facts **)
blanchet@42573
  1251
blanchet@43085
  1252
(* The Boolean indicates that a fairly sound type encoding is needed. *)
blanchet@43085
  1253
val helper_table =
blanchet@43085
  1254
  [("COMBI", (false, @{thms Meson.COMBI_def})),
blanchet@43085
  1255
   ("COMBK", (false, @{thms Meson.COMBK_def})),
blanchet@43085
  1256
   ("COMBB", (false, @{thms Meson.COMBB_def})),
blanchet@43085
  1257
   ("COMBC", (false, @{thms Meson.COMBC_def})),
blanchet@43085
  1258
   ("COMBS", (false, @{thms Meson.COMBS_def})),
blanchet@43085
  1259
   ("fequal",
blanchet@43085
  1260
    (* This is a lie: Higher-order equality doesn't need a sound type encoding.
blanchet@43085
  1261
       However, this is done so for backward compatibility: Including the
blanchet@43085
  1262
       equality helpers by default in Metis breaks a few existing proofs. *)
blanchet@43085
  1263
    (true, @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
blanchet@43085
  1264
                  fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]})),
blanchet@43085
  1265
   ("fFalse", (true, @{thms True_or_False})),
blanchet@43085
  1266
   ("fFalse", (false, [@{lemma "~ fFalse" by (unfold fFalse_def) fast}])),
blanchet@43085
  1267
   ("fTrue", (true, @{thms True_or_False})),
blanchet@43085
  1268
   ("fTrue", (false, [@{lemma "fTrue" by (unfold fTrue_def) fast}])),
blanchet@43085
  1269
   ("fNot",
blanchet@43085
  1270
    (false, @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
blanchet@43085
  1271
                   fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]})),
blanchet@43085
  1272
   ("fconj",
blanchet@43085
  1273
    (false,
blanchet@43085
  1274
     @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
blanchet@43085
  1275
         by (unfold fconj_def) fast+})),
blanchet@43085
  1276
   ("fdisj",
blanchet@43085
  1277
    (false,
blanchet@43085
  1278
     @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
blanchet@43085
  1279
         by (unfold fdisj_def) fast+})),
blanchet@43085
  1280
   ("fimplies",
blanchet@43085
  1281
    (false, @{lemma "P | fimplies P Q" "~ Q | fimplies P Q"
blanchet@43085
  1282
                    "~ fimplies P Q | ~ P | Q"
blanchet@43085
  1283
                by (unfold fimplies_def) fast+})),
blanchet@43085
  1284
   ("If", (true, @{thms if_True if_False True_or_False}))]
blanchet@43085
  1285
blanchet@43130
  1286
val type_tag = `make_fixed_const type_tag_name
blanchet@43130
  1287
blanchet@42573
  1288
fun ti_ti_helper_fact () =
blanchet@42573
  1289
  let
blanchet@42573
  1290
    fun var s = ATerm (`I s, [])
blanchet@43130
  1291
    fun tag tm = ATerm (type_tag, [var "X", tm])
blanchet@42573
  1292
  in
blanchet@42612
  1293
    Formula (helper_prefix ^ "ti_ti", Axiom,
blanchet@43000
  1294
             AAtom (ATerm (`I tptp_equal, [tag (tag (var "Y")), tag (var "Y")]))
blanchet@42879
  1295
             |> close_formula_universally, simp_info, NONE)
blanchet@42573
  1296
  end
blanchet@42573
  1297
blanchet@43064
  1298
fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
blanchet@42573
  1299
  case strip_prefix_and_unascii const_prefix s of
blanchet@42573
  1300
    SOME mangled_s =>
blanchet@42573
  1301
    let
blanchet@42573
  1302
      val thy = Proof_Context.theory_of ctxt
blanchet@42573
  1303
      val unmangled_s = mangled_s |> unmangled_const_name
blanchet@42893
  1304
      fun dub_and_inst c needs_fairly_sound (th, j) =
blanchet@42881
  1305
        ((c ^ "_" ^ string_of_int j ^
blanchet@42893
  1306
          (if needs_fairly_sound then typed_helper_suffix
blanchet@42881
  1307
           else untyped_helper_suffix),
blanchet@42881
  1308
          General),
blanchet@42573
  1309
         let val t = th |> prop_of in
blanchet@42753
  1310
           t |> ((case general_type_arg_policy type_sys of
blanchet@42753
  1311
                    Mangled_Type_Args _ => true
blanchet@42753
  1312
                  | _ => false) andalso
blanchet@42573
  1313
                 not (null (Term.hidden_polymorphism t)))
blanchet@43064
  1314
                ? (case types of
blanchet@43064
  1315
                     [T] => specialize_type thy (invert_const unmangled_s, T)
blanchet@43064
  1316
                   | _ => I)
blanchet@42573
  1317
         end)
blanchet@42573
  1318
      fun make_facts eq_as_iff =
blanchet@43096
  1319
        map_filter (make_fact ctxt format type_sys true false eq_as_iff false)
blanchet@42893
  1320
      val fairly_sound = is_type_sys_fairly_sound type_sys
blanchet@42573
  1321
    in
blanchet@43085
  1322
      helper_table
blanchet@42894
  1323
      |> maps (fn (metis_s, (needs_fairly_sound, ths)) =>
blanchet@42573
  1324
                  if metis_s <> unmangled_s orelse
blanchet@42894
  1325
                     (needs_fairly_sound andalso not fairly_sound) then
blanchet@42573
  1326
                    []
blanchet@42573
  1327
                  else
blanchet@42573
  1328
                    ths ~~ (1 upto length ths)
blanchet@42893
  1329
                    |> map (dub_and_inst mangled_s needs_fairly_sound)
blanchet@42893
  1330
                    |> make_facts (not needs_fairly_sound))
blanchet@42573
  1331
    end
blanchet@42573
  1332
  | NONE => []
blanchet@42962
  1333
fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
blanchet@42962
  1334
  Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
blanchet@42962
  1335
                  []
blanchet@42573
  1336
blanchet@42994
  1337
fun translate_atp_fact ctxt format type_sys keep_trivial =
blanchet@43096
  1338
  `(make_fact ctxt format type_sys keep_trivial true true true o apsnd prop_of)
blanchet@42573
  1339
blanchet@43085
  1340
(***************************************************************)
blanchet@43085
  1341
(* Type Classes Present in the Axiom or Conjecture Clauses     *)
blanchet@43085
  1342
(***************************************************************)
blanchet@43085
  1343
blanchet@43085
  1344
fun set_insert (x, s) = Symtab.update (x, ()) s
blanchet@43085
  1345
blanchet@43085
  1346
fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
blanchet@43085
  1347
blanchet@43085
  1348
(* Remove this trivial type class (FIXME: similar code elsewhere) *)
blanchet@43085
  1349
fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
blanchet@43085
  1350
blanchet@43093
  1351
fun classes_of_terms get_Ts =
blanchet@43121
  1352
  map (map snd o get_Ts)
blanchet@43093
  1353
  #> List.foldl add_classes Symtab.empty
blanchet@43093
  1354
  #> delete_type #> Symtab.keys
blanchet@43085
  1355
blanchet@43093
  1356
val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
blanchet@43093
  1357
val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
blanchet@43085
  1358
blanchet@43085
  1359
(*fold type constructors*)
blanchet@43085
  1360
fun fold_type_consts f (Type (a, Ts)) x = fold (fold_type_consts f) Ts (f (a,x))
blanchet@43093
  1361
  | fold_type_consts _ _ x = x
blanchet@43085
  1362
blanchet@43085
  1363
(*Type constructors used to instantiate overloaded constants are the only ones needed.*)
blanchet@43085
  1364
fun add_type_consts_in_term thy =
blanchet@43085
  1365
  let
blanchet@43085
  1366
    fun aux (Const (@{const_name Meson.skolem}, _) $ _) = I
blanchet@43085
  1367
      | aux (t $ u) = aux t #> aux u
blanchet@43085
  1368
      | aux (Const x) =
blanchet@43085
  1369
        fold (fold_type_consts set_insert) (Sign.const_typargs thy x)
blanchet@43085
  1370
      | aux (Abs (_, _, u)) = aux u
blanchet@43085
  1371
      | aux _ = I
blanchet@43085
  1372
  in aux end
blanchet@43085
  1373
blanchet@43085
  1374
fun type_consts_of_terms thy ts =
blanchet@43093
  1375
  Symtab.keys (fold (add_type_consts_in_term thy) ts Symtab.empty)
blanchet@43085
  1376
blanchet@43096
  1377
fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
blanchet@42962
  1378
                       rich_facts =
blanchet@42573
  1379
  let
blanchet@42573
  1380
    val thy = Proof_Context.theory_of ctxt
blanchet@42573
  1381
    val fact_ts = map (prop_of o snd o snd) rich_facts
blanchet@42573
  1382
    val (facts, fact_names) =
blanchet@42573
  1383
      rich_facts
blanchet@42573
  1384
      |> map_filter (fn (NONE, _) => NONE
blanchet@42573
  1385
                      | (SOME fact, (name, _)) => SOME (fact, name))
blanchet@42573
  1386
      |> ListPair.unzip
blanchet@42573
  1387
    (* Remove existing facts from the conjecture, as this can dramatically
blanchet@42573
  1388
       boost an ATP's performance (for some reason). *)
blanchet@42573
  1389
    val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
blanchet@42573
  1390
    val goal_t = Logic.list_implies (hyp_ts, concl_t)
blanchet@42573
  1391
    val all_ts = goal_t :: fact_ts
blanchet@42573
  1392
    val subs = tfree_classes_of_terms all_ts
blanchet@42573
  1393
    val supers = tvar_classes_of_terms all_ts
blanchet@42573
  1394
    val tycons = type_consts_of_terms thy all_ts
blanchet@42994
  1395
    val conjs =
blanchet@43096
  1396
      hyp_ts @ [concl_t]
blanchet@43096
  1397
      |> make_conjecture ctxt format prem_kind type_sys preproc
blanchet@42573
  1398
    val (supers', arity_clauses) =
blanchet@42589
  1399
      if level_of_type_sys type_sys = No_Types then ([], [])
blanchet@42573
  1400
      else make_arity_clauses thy tycons supers
blanchet@42573
  1401
    val class_rel_clauses = make_class_rel_clauses thy subs supers'
blanchet@42573
  1402
  in
blanchet@42573
  1403
    (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
blanchet@42573
  1404
  end
blanchet@42573
  1405
blanchet@42573
  1406
fun fo_literal_from_type_literal (TyLitVar (class, name)) =
blanchet@42573
  1407
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
  1408
  | fo_literal_from_type_literal (TyLitFree (class, name)) =
blanchet@42573
  1409
    (true, ATerm (class, [ATerm (name, [])]))
blanchet@42573
  1410
blanchet@42573
  1411
fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
blanchet@42573
  1412
blanchet@43130
  1413
val type_pred = `make_fixed_const type_pred_name
blanchet@43130
  1414
blanchet@42994
  1415
fun type_pred_combterm ctxt nonmono_Ts type_sys T tm =
blanchet@43130
  1416
  CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
blanchet@42994
  1417
           |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys,
blanchet@42573
  1418
           tm)
blanchet@42573
  1419
blanchet@42878
  1420
fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
blanchet@42878
  1421
  | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
blanchet@43000
  1422
    accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
blanchet@42878
  1423
fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
blanchet@42878
  1424
  | is_var_nonmonotonic_in_formula pos phi _ name =
blanchet@42878
  1425
    formula_fold pos (var_occurs_positively_naked_in_term name) phi false
blanchet@42834
  1426
blanchet@42994
  1427
fun mk_const_aterm x T_args args =
blanchet@42994
  1428
  ATerm (x, map (fo_term_from_typ false) T_args @ args)
blanchet@42994
  1429
blanchet@42962
  1430
fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
blanchet@43130
  1431
  CombConst (type_tag, T --> T, [T])
blanchet@42994
  1432
  |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
blanchet@42962
  1433
  |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
blanchet@42829
  1434
  |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
blanchet@42962
  1435
and term_from_combterm ctxt format nonmono_Ts type_sys =
blanchet@42573
  1436
  let
blanchet@42962
  1437
    fun aux site u =
blanchet@42962
  1438
      let
blanchet@42962
  1439
        val (head, args) = strip_combterm_comb u
blanchet@42962
  1440
        val (x as (s, _), T_args) =
blanchet@42962
  1441
          case head of
blanchet@42962
  1442
            CombConst (name, _, T_args) => (name, T_args)
blanchet@42962
  1443
          | CombVar (name, _) => (name, [])
blanchet@42962
  1444
          | CombApp _ => raise Fail "impossible \"CombApp\""
blanchet@43000
  1445
        val arg_site = if site = Top_Level andalso is_tptp_equal s then Eq_Arg
blanchet@42962
  1446
                       else Elsewhere
blanchet@42994
  1447
        val t = mk_const_aterm x T_args (map (aux arg_site) args)
blanchet@42962
  1448
        val T = combtyp_of u
blanchet@42962
  1449
      in
blanchet@42962
  1450
        t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
blanchet@42962
  1451
                tag_with_type ctxt format nonmono_Ts type_sys T
blanchet@42962
  1452
              else
blanchet@42962
  1453
                I)
blanchet@42962
  1454
      end
blanchet@42962
  1455
  in aux end
blanchet@42962
  1456
and formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42962
  1457
                             should_predicate_on_var =
blanchet@42829
  1458
  let
blanchet@42994
  1459
    val higher_order = is_setting_higher_order format type_sys
blanchet@42962
  1460
    val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
blanchet@42573
  1461
    val do_bound_type =
blanchet@42682
  1462
      case type_sys of
blanchet@42722
  1463
        Simple_Types level =>
blanchet@42994
  1464
        homogenized_type ctxt nonmono_Ts level 0
blanchet@42994
  1465
        #> mangled_type higher_order false 0 #> SOME
blanchet@42682
  1466
      | _ => K NONE
blanchet@42878
  1467
    fun do_out_of_bound_type pos phi universal (name, T) =
blanchet@42834
  1468
      if should_predicate_on_type ctxt nonmono_Ts type_sys
blanchet@42878
  1469
             (fn () => should_predicate_on_var pos phi universal name) T then
blanchet@42834
  1470
        CombVar (name, T)
blanchet@42994
  1471
        |> type_pred_combterm ctxt nonmono_Ts type_sys T
blanchet@42878
  1472
        |> do_term |> AAtom |> SOME
blanchet@42573
  1473
      else
blanchet@42573
  1474
        NONE
blanchet@42878
  1475
    fun do_formula pos (AQuant (q, xs, phi)) =
blanchet@42878
  1476
        let
blanchet@42878
  1477
          val phi = phi |> do_formula pos
blanchet@42878
  1478
          val universal = Option.map (q = AExists ? not) pos
blanchet@42878
  1479
        in
blanchet@42834
  1480
          AQuant (q, xs |> map (apsnd (fn NONE => NONE
blanchet@42834
  1481
                                        | SOME T => do_bound_type T)),
blanchet@42834
  1482
                  (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
blanchet@42834
  1483
                      (map_filter
blanchet@42834
  1484
                           (fn (_, NONE) => NONE
blanchet@42834
  1485
                             | (s, SOME T) =>
blanchet@42878
  1486
                               do_out_of_bound_type pos phi universal (s, T))
blanchet@42878
  1487
                           xs)
blanchet@42834
  1488
                      phi)
blanchet@42834
  1489
        end
blanchet@42878
  1490
      | do_formula pos (AConn conn) = aconn_map pos do_formula conn
blanchet@42878
  1491
      | do_formula _ (AAtom tm) = AAtom (do_term tm)
blanchet@42878
  1492
  in do_formula o SOME end
blanchet@42573
  1493
blanchet@43098
  1494
fun bound_tvars type_sys Ts =
blanchet@42727
  1495
  mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
blanchet@43098
  1496
                (type_literals_for_types type_sys sorts_on_tvar Ts))
blanchet@42727
  1497
blanchet@42956
  1498
fun formula_for_fact ctxt format nonmono_Ts type_sys
blanchet@42573
  1499
                     ({combformula, atomic_types, ...} : translated_formula) =
blanchet@42727
  1500
  combformula
blanchet@42727
  1501
  |> close_combformula_universally
blanchet@42962
  1502
  |> formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42878
  1503
                              is_var_nonmonotonic_in_formula true
blanchet@43098
  1504
  |> bound_tvars type_sys atomic_types
blanchet@42573
  1505
  |> close_formula_universally
blanchet@42573
  1506
blanchet@42573
  1507
(* Each fact is given a unique fact number to avoid name clashes (e.g., because
blanchet@42573
  1508
   of monomorphization). The TPTP explicitly forbids name clashes, and some of
blanchet@42573
  1509
   the remote provers might care. *)
blanchet@42956
  1510
fun formula_line_for_fact ctxt format prefix nonmono_Ts type_sys
blanchet@42640
  1511
                          (j, formula as {name, locality, kind, ...}) =
blanchet@42680
  1512
  Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
blanchet@42680
  1513
                     else string_of_int j ^ "_") ^
blanchet@42647
  1514
           ascii_of name,
blanchet@42956
  1515
           kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
blanchet@42879
  1516
           case locality of
blanchet@42879
  1517
             Intro => intro_info
blanchet@42879
  1518
           | Elim => elim_info
blanchet@42879
  1519
           | Simp => simp_info
blanchet@42879
  1520
           | _ => NONE)
blanchet@42573
  1521
blanchet@43086
  1522
fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
blanchet@43086
  1523
                                       : class_rel_clause) =
blanchet@42573
  1524
  let val ty_arg = ATerm (`I "T", []) in
blanchet@42577
  1525
    Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
  1526
             AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
blanchet@42573
  1527
                               AAtom (ATerm (superclass, [ty_arg]))])
blanchet@42879
  1528
             |> close_formula_universally, intro_info, NONE)
blanchet@42573
  1529
  end
blanchet@42573
  1530
blanchet@42573
  1531
fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
blanchet@42573
  1532
    (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
blanchet@42573
  1533
  | fo_literal_from_arity_literal (TVarLit (c, sort)) =
blanchet@42573
  1534
    (false, ATerm (c, [ATerm (sort, [])]))
blanchet@42573
  1535
blanchet@43086
  1536
fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
blanchet@43086
  1537
                                   : arity_clause) =
blanchet@42577
  1538
  Formula (arity_clause_prefix ^ ascii_of name, Axiom,
blanchet@42573
  1539
           mk_ahorn (map (formula_from_fo_literal o apfst not
blanchet@42895
  1540
                          o fo_literal_from_arity_literal) prem_lits)
blanchet@42573
  1541
                    (formula_from_fo_literal
blanchet@42895
  1542
                         (fo_literal_from_arity_literal concl_lits))
blanchet@42879
  1543
           |> close_formula_universally, intro_info, NONE)
blanchet@42573
  1544
blanchet@42962
  1545
fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
blanchet@43098
  1546
        ({name, kind, combformula, atomic_types, ...} : translated_formula) =
blanchet@42577
  1547
  Formula (conjecture_prefix ^ name, kind,
blanchet@42962
  1548
           formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42939
  1549
               is_var_nonmonotonic_in_formula false
blanchet@42939
  1550
               (close_combformula_universally combformula)
blanchet@43098
  1551
           |> bound_tvars type_sys atomic_types
blanchet@42573
  1552
           |> close_formula_universally, NONE, NONE)
blanchet@42573
  1553
blanchet@43098
  1554
fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
blanchet@43098
  1555
  atomic_types |> type_literals_for_types type_sys sorts_on_tfree
blanchet@42573
  1556
               |> map fo_literal_from_type_literal
blanchet@42573
  1557
blanchet@42573
  1558
fun formula_line_for_free_type j lit =
blanchet@43085
  1559
  Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
blanchet@42573
  1560
           formula_from_fo_literal lit, NONE, NONE)
blanchet@43098
  1561
fun formula_lines_for_free_types type_sys facts =
blanchet@42573
  1562
  let
blanchet@43098
  1563
    val litss = map (free_type_literals type_sys) facts
blanchet@42573
  1564
    val lits = fold (union (op =)) litss []
blanchet@42573
  1565
  in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
blanchet@42573
  1566
blanchet@42573
  1567
(** Symbol declarations **)
blanchet@42544
  1568
blanchet@42574
  1569
fun should_declare_sym type_sys pred_sym s =
blanchet@42998
  1570
  is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
blanchet@42894
  1571
  (case type_sys of
blanchet@42894
  1572
     Simple_Types _ => true
blanchet@43128
  1573
   | Tags (_, _, Lightweight) => true
blanchet@42894
  1574
   | _ => not pred_sym)
blanchet@38282
  1575
blanchet@42886
  1576
fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
blanchet@42574
  1577
  let
blanchet@42698
  1578
    fun add_combterm in_conj tm =
blanchet@42574
  1579
      let val (head, args) = strip_combterm_comb tm in
blanchet@42574
  1580
        (case head of
blanchet@42574
  1581
           CombConst ((s, s'), T, T_args) =>
blanchet@42574
  1582
           let val pred_sym = is_pred_sym repaired_sym_tab s in
blanchet@42574
  1583
             if should_declare_sym type_sys pred_sym s then
blanchet@42576
  1584
               Symtab.map_default (s, [])
blanchet@42886
  1585
                   (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
blanchet@42886
  1586
                                         in_conj))
blanchet@42574
  1587
             else
blanchet@42574
  1588
               I
blanchet@42574
  1589
           end
blanchet@42574
  1590
         | _ => I)
blanchet@42698
  1591
        #> fold (add_combterm in_conj) args
blanchet@42574
  1592
      end
blanchet@42698
  1593
    fun add_fact in_conj =
blanchet@42834
  1594
      fact_lift (formula_fold NONE (K (add_combterm in_conj)))
blanchet@42698
  1595
  in
blanchet@42698
  1596
    Symtab.empty
blanchet@42698
  1597
    |> is_type_sys_fairly_sound type_sys
blanchet@42698
  1598
       ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
blanchet@42698
  1599
  end
blanchet@42533
  1600
blanchet@42886
  1601
(* These types witness that the type classes they belong to allow infinite
blanchet@42886
  1602
   models and hence that any types with these type classes is monotonic. *)
blanchet@43085
  1603
val known_infinite_types =
blanchet@43085
  1604
  [@{typ nat}, Type ("Int.int", []), @{typ "nat => bool"}]
blanchet@42886
  1605
blanchet@42685
  1606
(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
blanchet@42685
  1607
   out with monotonicity" paper presented at CADE 2011. *)
blanchet@42886
  1608
fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
blanchet@42829
  1609
  | add_combterm_nonmonotonic_types ctxt level _
blanchet@43000
  1610
        (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1), tm2)) =
blanchet@43000
  1611
    (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
blanchet@42829
  1612
     (case level of
blanchet@42886
  1613
        Nonmonotonic_Types =>
blanchet@42886
  1614
        not (is_type_surely_infinite ctxt known_infinite_types T)
blanchet@42829
  1615
      | Finite_Types => is_type_surely_finite ctxt T
blanchet@42886
  1616
      | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
blanchet@42829
  1617
  | add_combterm_nonmonotonic_types _ _ _ _ = I
blanchet@42829
  1618
fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
blanchet@42829
  1619
                                            : translated_formula) =
blanchet@42834
  1620
  formula_fold (SOME (kind <> Conjecture))
blanchet@42829
  1621
               (add_combterm_nonmonotonic_types ctxt level) combformula
blanchet@42886
  1622
fun nonmonotonic_types_for_facts ctxt type_sys facts =
blanchet@42829
  1623
  let val level = level_of_type_sys type_sys in
blanchet@42886
  1624
    if level = Nonmonotonic_Types orelse level = Finite_Types then
blanchet@42886
  1625
      [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
blanchet@42886
  1626
         (* We must add "bool" in case the helper "True_or_False" is added
blanchet@42886
  1627
            later. In addition, several places in the code rely on the list of
blanchet@42886
  1628
            nonmonotonic types not being empty. *)
blanchet@42886
  1629
         |> insert_type ctxt I @{typ bool}
blanchet@42886
  1630
    else
blanchet@42886
  1631
      []
blanchet@42829
  1632
  end
blanchet@42677
  1633
blanchet@42994
  1634
fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
blanchet@42994
  1635
                      (s', T_args, T, pred_sym, ary, _) =
blanchet@42994
  1636
  let
blanchet@42994
  1637
    val (higher_order, T_arg_Ts, level) =
blanchet@42994
  1638
      case type_sys of
blanchet@42994
  1639
        Simple_Types level => (format = THF, [], level)
blanchet@42994
  1640
      | _ => (false, replicate (length T_args) homo_infinite_type, No_Types)
blanchet@42994
  1641
  in
blanchet@42998
  1642
    Decl (sym_decl_prefix ^ s, (s, s'),
blanchet@42994
  1643
          (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
blanchet@42994
  1644
          |> mangled_type higher_order pred_sym (length T_arg_Ts + ary))
blanchet@42994
  1645
  end
blanchet@42579
  1646
blanchet@42592
  1647
fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
blanchet@42592
  1648
blanchet@43125
  1649
fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
blanchet@43125
  1650
        type_sys n s j (s', T_args, T, _, ary, in_conj) =
blanchet@42579
  1651
  let
blanchet@42709
  1652
    val (kind, maybe_negate) =
blanchet@42709
  1653
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42709
  1654
      else (Axiom, I)
blanchet@42753
  1655
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42579
  1656
    val bound_names =
blanchet@42579
  1657
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1658
    val bounds =
blanchet@42579
  1659
      bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
blanchet@42579
  1660
    val bound_Ts =
blanchet@42592
  1661
      arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
blanchet@42592
  1662
                             else NONE)
blanchet@42579
  1663
  in
blanchet@43125
  1664
    Formula (preds_sym_formula_prefix ^ s ^
blanchet@42709
  1665
             (if n > 1 then "_" ^ string_of_int j else ""), kind,
blanchet@42579
  1666
             CombConst ((s, s'), T, T_args)
blanchet@42829
  1667
             |> fold (curry (CombApp o swap)) bounds
blanchet@42994
  1668
             |> type_pred_combterm ctxt nonmono_Ts type_sys res_T
blanchet@42963
  1669
             |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
blanchet@42962
  1670
             |> formula_from_combformula ctxt format nonmono_Ts type_sys
blanchet@42878
  1671
                                         (K (K (K (K true)))) true
blanchet@43098
  1672
             |> n > 1 ? bound_tvars type_sys (atyps_of T)
blanchet@42709
  1673
             |> close_formula_universally
blanchet@42709
  1674
             |> maybe_negate,
blanchet@42879
  1675
             intro_info, NONE)
blanchet@42579
  1676
  end
blanchet@42579
  1677
blanchet@43129
  1678
fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
blanchet@43129
  1679
        nonmono_Ts type_sys n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
blanchet@42829
  1680
  let
blanchet@42829
  1681
    val ident_base =
blanchet@43129
  1682
      lightweight_tags_sym_formula_prefix ^ s ^
blanchet@43125
  1683
      (if n > 1 then "_" ^ string_of_int j else "")
blanchet@42852
  1684
    val (kind, maybe_negate) =
blanchet@42852
  1685
      if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
blanchet@42852
  1686
      else (Axiom, I)
blanchet@42829
  1687
    val (arg_Ts, res_T) = chop_fun ary T
blanchet@42829
  1688
    val bound_names =
blanchet@42829
  1689
      1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
blanchet@42829
  1690
    val bounds = bound_names |> map (fn name => ATerm (name, []))
blanchet@42994
  1691
    val cst = mk_const_aterm (s, s') T_args
blanchet@42830
  1692
    val atomic_Ts = atyps_of T
blanchet@42834
  1693
    fun eq tms =
blanchet@42834
  1694
      (if pred_sym then AConn (AIff, map AAtom tms)
blanchet@43000
  1695
       else AAtom (ATerm (`I tptp_equal, tms)))
blanchet@43098
  1696
      |> bound_tvars type_sys atomic_Ts
blanchet@42830
  1697
      |> close_formula_universally
blanchet@42852
  1698
      |> maybe_negate
blanchet@42836
  1699
    val should_encode = should_encode_type ctxt nonmono_Ts All_Types
blanchet@42962
  1700
    val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
blanchet@42829
  1701
    val add_formula_for_res =
blanchet@42829
  1702
      if should_encode res_T then
blanchet@42852
  1703
        cons (Formula (ident_base ^ "_res", kind,
blanchet@42994
  1704
                       eq [tag_with res_T (cst bounds), cst bounds],
blanchet@42879
  1705
                       simp_info, NONE))
blanchet@42829
  1706
      else
blanchet@42829
  1707
        I
blanchet@42829
  1708
    fun add_formula_for_arg k =
blanchet@42829
  1709
      let val arg_T = nth arg_Ts k in
blanchet@42829
  1710
        if should_encode arg_T then
blanchet@42829
  1711
          case chop k bounds of
blanchet@42829
  1712
            (bounds1, bound :: bounds2) =>
blanchet@42852
  1713
            cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
blanchet@42994
  1714
                           eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
blanchet@42994
  1715
                               cst bounds],
blanchet@42879
  1716
                           simp_info, NONE))
blanchet@42829
  1717
          | _ => raise Fail "expected nonempty tail"
blanchet@42829
  1718
        else
blanchet@42829
  1719
          I
blanchet@42829
  1720
      end
blanchet@42829
  1721
  in
blanchet@42834
  1722
    [] |> not pred_sym ? add_formula_for_res
blanchet@42829
  1723
       |> fold add_formula_for_arg (ary - 1 downto 0)
blanchet@42829
  1724
  end
blanchet@42829
  1725
blanchet@42836
  1726
fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
blanchet@42836
  1727
blanchet@42956
  1728
fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
blanchet@42709
  1729
                                (s, decls) =
blanchet@42998
  1730
  case type_sys of
blanchet@42998
  1731
    Simple_Types _ =>
blanchet@42998
  1732
    decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
blanchet@42998
  1733
  | Preds _ =>
blanchet@42998
  1734
    let
blanchet@42998
  1735
      val decls =
blanchet@42998
  1736
        case decls of
blanchet@42998
  1737
          decl :: (decls' as _ :: _) =>
blanchet@42998
  1738
          let val T = result_type_of_decl decl in
blanchet@42998
  1739
            if forall (curry (type_instance ctxt o swap) T
blanchet@42998
  1740
                       o result_type_of_decl) decls' then
blanchet@42998
  1741
              [decl]
blanchet@42998
  1742
            else
blanchet@42998
  1743
              decls
blanchet@42998
  1744
          end
blanchet@42998
  1745
        | _ => decls
blanchet@42998
  1746
      val n = length decls
blanchet@42998
  1747
      val decls =
blanchet@42998
  1748
        decls
blanchet@42998
  1749
        |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
blanchet@42998
  1750
                   o result_type_of_decl)
blanchet@42998
  1751
    in
blanchet@42998
  1752
      (0 upto length decls - 1, decls)
blanchet@43125
  1753
      |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
blanchet@43125
  1754
                                                nonmono_Ts type_sys n s)
blanchet@42998
  1755
    end
blanchet@42998
  1756
  | Tags (_, _, heaviness) =>
blanchet@42998
  1757
    (case heaviness of
blanchet@43128
  1758
       Heavyweight => []
blanchet@43128
  1759
     | Lightweight =>
blanchet@42998
  1760
       let val n = length decls in
blanchet@42998
  1761
         (0 upto n - 1 ~~ decls)
blanchet@43129
  1762
         |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
blanchet@43129
  1763
                      conj_sym_kind nonmono_Ts type_sys n s)
blanchet@42998
  1764
       end)
blanchet@42579
  1765
blanchet@42956
  1766
fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
blanchet@42956
  1767
                                     type_sys sym_decl_tab =
blanchet@42998
  1768
  sym_decl_tab
blanchet@42998
  1769
  |> Symtab.dest
blanchet@42998
  1770
  |> sort_wrt fst
blanchet@42998
  1771
  |> rpair []
blanchet@42998
  1772
  |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
blanchet@42998
  1773
                                                     nonmono_Ts type_sys)
blanchet@42543
  1774
blanchet@43128
  1775
fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavyweight)) =
blanchet@42831
  1776
    level = Nonmonotonic_Types orelse level = Finite_Types
blanchet@42831
  1777
  | should_add_ti_ti_helper _ = false
blanchet@42831
  1778
blanchet@42939
  1779
fun offset_of_heading_in_problem _ [] j = j
blanchet@42939
  1780
  | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
blanchet@42939
  1781
    if heading = needle then j
blanchet@42939
  1782
    else offset_of_heading_in_problem needle problem (j + length lines)
blanchet@42939
  1783
blanchet@42998
  1784
val implicit_declsN = "Should-be-implicit typings"
blanchet@42998
  1785
val explicit_declsN = "Explicit typings"
blanchet@41157
  1786
val factsN = "Relevant facts"
blanchet@41157
  1787
val class_relsN = "Class relationships"
blanchet@42543
  1788
val aritiesN = "Arities"
blanchet@41157
  1789
val helpersN = "Helper facts"
blanchet@41157
  1790
val conjsN = "Conjectures"
blanchet@41313
  1791
val free_typesN = "Type variables"
blanchet@41157
  1792
blanchet@42939
  1793
fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
blanchet@43096
  1794
                        explicit_apply readable_names preproc hyp_ts concl_t
blanchet@43096
  1795
                        facts =
blanchet@38282
  1796
  let
blanchet@43101
  1797
    val (format, type_sys) = choose_format [format] type_sys
blanchet@41313
  1798
    val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
blanchet@43096
  1799
      translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
blanchet@43096
  1800
                         facts
blanchet@43064
  1801
    val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
blanchet@42886
  1802
    val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
blanchet@42962
  1803
    val repair = repair_fact ctxt format nonmono_Ts type_sys sym_tab
blanchet@42682
  1804
    val (conjs, facts) = (conjs, facts) |> pairself (map repair)
blanchet@43064
  1805
    val repaired_sym_tab =
blanchet@43064
  1806
      conjs @ facts |> sym_table_for_facts ctxt (SOME false)
blanchet@42573
  1807
    val helpers =
blanchet@42962
  1808
      repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
blanchet@42962
  1809
                       |> map repair
blanchet@42894
  1810
    val lavish_nonmono_Ts =
blanchet@42894
  1811
      if null nonmono_Ts orelse
blanchet@42894
  1812
         polymorphism_of_type_sys type_sys <> Polymorphic then
blanchet@42894
  1813
        nonmono_Ts
blanchet@42894
  1814
      else
blanchet@42894
  1815
        [TVar (("'a", 0), HOLogic.typeS)]
blanchet@42680
  1816
    val sym_decl_lines =
blanchet@42731
  1817
      (conjs, helpers @ facts)
blanchet@42886
  1818
      |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
blanchet@42956
  1819
      |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
blanchet@42956
  1820
                                          lavish_nonmono_Ts type_sys
blanchet@42881
  1821
    val helper_lines =
blanchet@42956
  1822
      0 upto length helpers - 1 ~~ helpers
blanchet@42956
  1823
      |> map (formula_line_for_fact ctxt format helper_prefix lavish_nonmono_Ts
blanchet@42956
  1824
                                    type_sys)
blanchet@42956
  1825
      |> (if should_add_ti_ti_helper type_sys then cons (ti_ti_helper_fact ())
blanchet@42956
  1826
          else I)
blanchet@42522
  1827
    (* Reordering these might confuse the proof reconstruction code or the SPASS
blanchet@43039
  1828
       FLOTTER hack. *)
blanchet@38282
  1829
    val problem =
blanchet@42998
  1830
      [(explicit_declsN, sym_decl_lines),
blanchet@42956
  1831
       (factsN,
blanchet@42956
  1832
        map (formula_line_for_fact ctxt format fact_prefix nonmono_Ts type_sys)
blanchet@42956
  1833
            (0 upto length facts - 1 ~~ facts)),
blanchet@42545
  1834
       (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
blanchet@42545
  1835
       (aritiesN, map formula_line_for_arity_clause arity_clauses),
blanchet@42881
  1836
       (helpersN, helper_lines),
blanchet@42962
  1837
       (conjsN,
blanchet@42962
  1838
        map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
blanchet@42962
  1839
            conjs),
blanchet@43098
  1840
       (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
blanchet@42543
  1841
    val problem =
blanchet@42561
  1842
      problem
blanchet@43092
  1843
      |> (case format of
blanchet@43092
  1844
            CNF => ensure_cnf_problem
blanchet@43092
  1845
          | CNF_UEQ => filter_cnf_ueq_problem
blanchet@43092
  1846
          | _ => I)
blanchet@42998
  1847
      |> (if is_format_typed format then
blanchet@42998
  1848
            declare_undeclared_syms_in_atp_problem type_decl_prefix
blanchet@42998
  1849
                                                   implicit_declsN
blanchet@42998
  1850
          else
blanchet@42998
  1851
            I)
blanchet@43092
  1852
    val (problem, pool) = problem |> nice_atp_problem readable_names
blanchet@42881
  1853
    val helpers_offset = offset_of_heading_in_problem helpersN problem 0
blanchet@42881
  1854
    val typed_helpers =
blanchet@42881
  1855
      map_filter (fn (j, {name, ...}) =>
blanchet@42881
  1856
                     if String.isSuffix typed_helper_suffix name then SOME j
blanchet@42881
  1857
                     else NONE)
blanchet@42881
  1858
                 ((helpers_offset + 1 upto helpers_offset + length helpers)
blanchet@42881
  1859
                  ~~ helpers)
blanchet@42778
  1860
    fun add_sym_arity (s, {min_ary, ...} : sym_info) =
blanchet@42755
  1861
      if min_ary > 0 then
blanchet@42755
  1862
        case strip_prefix_and_unascii const_prefix s of
blanchet@42755
  1863
          SOME s => Symtab.insert (op =) (s, min_ary)
blanchet@42755
  1864
        | NONE => I
blanchet@42755
  1865
      else
blanchet@42755
  1866
        I
blanchet@38282
  1867
  in
blanchet@38282
  1868
    (problem,
blanchet@38282
  1869
     case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
blanchet@42585
  1870
     offset_of_heading_in_problem conjsN problem 0,
blanchet@42541
  1871
     offset_of_heading_in_problem factsN problem 0,
blanchet@42755
  1872
     fact_names |> Vector.fromList,
blanchet@42881
  1873
     typed_helpers,
blanchet@42755
  1874
     Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
blanchet@38282
  1875
  end
blanchet@38282
  1876
blanchet@41313
  1877
(* FUDGE *)
blanchet@41313
  1878
val conj_weight = 0.0
blanchet@41770
  1879
val hyp_weight = 0.1
blanchet@41770
  1880
val fact_min_weight = 0.2
blanchet@41313
  1881
val fact_max_weight = 1.0
blanchet@42608
  1882
val type_info_default_weight = 0.8
blanchet@41313
  1883
blanchet@41313
  1884
fun add_term_weights weight (ATerm (s, tms)) =
blanchet@42998
  1885
  is_tptp_user_symbol s ? Symtab.default (s, weight)
blanchet@41313
  1886
  #> fold (add_term_weights weight) tms
blanchet@42577
  1887
fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
blanchet@42834
  1888
    formula_fold NONE (K (add_term_weights weight)) phi
blanchet@42528
  1889
  | add_problem_line_weights _ _ = I
blanchet@41313
  1890
blanchet@41313
  1891
fun add_conjectures_weights [] = I
blanchet@41313
  1892
  | add_conjectures_weights conjs =
blanchet@41313
  1893
    let val (hyps, conj) = split_last conjs in
blanchet@41313
  1894
      add_problem_line_weights conj_weight conj
blanchet@41313
  1895
      #> fold (add_problem_line_weights hyp_weight) hyps
blanchet@41313
  1896
    end
blanchet@41313
  1897
blanchet@41313
  1898
fun add_facts_weights facts =
blanchet@41313
  1899
  let
blanchet@41313
  1900
    val num_facts = length facts
blanchet@41313
  1901
    fun weight_of j =
blanchet@41313
  1902
      fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
blanchet@41313
  1903
                        / Real.fromInt num_facts
blanchet@41313
  1904
  in
blanchet@41313
  1905
    map weight_of (0 upto num_facts - 1) ~~ facts
blanchet@41313
  1906
    |> fold (uncurry add_problem_line_weights)
blanchet@41313
  1907
  end
blanchet@41313
  1908
blanchet@41313
  1909
(* Weights are from 0.0 (most important) to 1.0 (least important). *)
blanchet@41313
  1910
fun atp_problem_weights problem =
blanchet@42608
  1911
  let val get = these o AList.lookup (op =) problem in
blanchet@42608
  1912
    Symtab.empty
blanchet@42608
  1913
    |> add_conjectures_weights (get free_typesN @ get conjsN)
blanchet@42608
  1914
    |> add_facts_weights (get factsN)
blanchet@42608
  1915
    |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
blanchet@42998
  1916
            [explicit_declsN, class_relsN, aritiesN]
blanchet@42608
  1917
    |> Symtab.dest
blanchet@42608
  1918
    |> sort (prod_ord Real.compare string_ord o pairself swap)
blanchet@42608
  1919
  end
blanchet@41313
  1920
blanchet@38282
  1921
end;