src/HOL/Tools/Nitpick/nitpick_hol.ML
author blanchet
Tue Mar 09 14:18:21 2010 +0100 (2010-03-09)
changeset 35671 ed2c3830d881
parent 35665 ff2bf50505ab
child 35711 548d3f16404b
permissions -rw-r--r--
improved Nitpick's precision for "card" and "setsum" + fix incorrect outcome code w.r.t. "bisim_depth = -1"
blanchet@33978
     1
(*  Title:      HOL/Tools/Nitpick/nitpick_hol.ML
blanchet@33192
     2
    Author:     Jasmin Blanchette, TU Muenchen
blanchet@34982
     3
    Copyright   2008, 2009, 2010
blanchet@33192
     4
blanchet@33192
     5
Auxiliary HOL-related functions used by Nitpick.
blanchet@33192
     6
*)
blanchet@33192
     7
blanchet@33192
     8
signature NITPICK_HOL =
blanchet@33192
     9
sig
blanchet@33705
    10
  type styp = Nitpick_Util.styp
blanchet@33192
    11
  type const_table = term list Symtab.table
blanchet@33192
    12
  type special_fun = (styp * int list * term list) * styp
blanchet@33192
    13
  type unrolled = styp * styp
blanchet@33192
    14
  type wf_cache = (styp * (bool * bool)) list
blanchet@33192
    15
blanchet@35070
    16
  type hol_context = {
blanchet@33192
    17
    thy: theory,
blanchet@33192
    18
    ctxt: Proof.context,
blanchet@33192
    19
    max_bisim_depth: int,
blanchet@33192
    20
    boxes: (typ option * bool option) list,
blanchet@34982
    21
    stds: (typ option * bool) list,
blanchet@33192
    22
    wfs: (styp option * bool option) list,
blanchet@33192
    23
    user_axioms: bool option,
blanchet@33192
    24
    debug: bool,
blanchet@34124
    25
    binary_ints: bool option,
blanchet@33192
    26
    destroy_constrs: bool,
blanchet@33192
    27
    specialize: bool,
blanchet@33192
    28
    skolemize: bool,
blanchet@33192
    29
    star_linear_preds: bool,
blanchet@33192
    30
    uncurry: bool,
blanchet@33192
    31
    fast_descrs: bool,
blanchet@33192
    32
    tac_timeout: Time.time option,
blanchet@33192
    33
    evals: term list,
blanchet@33192
    34
    case_names: (string * int) list,
blanchet@33192
    35
    def_table: const_table,
blanchet@33192
    36
    nondef_table: const_table,
blanchet@33192
    37
    user_nondefs: term list,
blanchet@33192
    38
    simp_table: const_table Unsynchronized.ref,
blanchet@33192
    39
    psimp_table: const_table,
blanchet@33192
    40
    intro_table: const_table,
blanchet@33192
    41
    ground_thm_table: term list Inttab.table,
blanchet@33192
    42
    ersatz_table: (string * string) list,
blanchet@33192
    43
    skolems: (string * string list) list Unsynchronized.ref,
blanchet@33192
    44
    special_funs: special_fun list Unsynchronized.ref,
blanchet@33192
    45
    unrolled_preds: unrolled list Unsynchronized.ref,
blanchet@33580
    46
    wf_cache: wf_cache Unsynchronized.ref,
blanchet@33580
    47
    constr_cache: (typ * styp list) list Unsynchronized.ref}
blanchet@33192
    48
blanchet@35070
    49
  datatype fixpoint_kind = Lfp | Gfp | NoFp
blanchet@35070
    50
  datatype boxability =
blanchet@35070
    51
    InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
blanchet@35070
    52
blanchet@33192
    53
  val name_sep : string
blanchet@33192
    54
  val numeral_prefix : string
blanchet@35070
    55
  val ubfp_prefix : string
blanchet@35070
    56
  val lbfp_prefix : string
blanchet@35311
    57
  val quot_normal_prefix : string
blanchet@33192
    58
  val skolem_prefix : string
blanchet@35070
    59
  val special_prefix : string
blanchet@35070
    60
  val uncurry_prefix : string
blanchet@33192
    61
  val eval_prefix : string
blanchet@33192
    62
  val original_name : string -> string
blanchet@34998
    63
  val s_conj : term * term -> term
blanchet@35070
    64
  val s_disj : term * term -> term
blanchet@35070
    65
  val strip_any_connective : term -> term list * term
blanchet@35070
    66
  val conjuncts_of : term -> term list
blanchet@35070
    67
  val disjuncts_of : term -> term list
blanchet@35665
    68
  val unarize_unbox_etc_type : typ -> typ
blanchet@35665
    69
  val uniterize_unarize_unbox_etc_type : typ -> typ
blanchet@33192
    70
  val string_for_type : Proof.context -> typ -> string
blanchet@33192
    71
  val prefix_name : string -> string -> string
blanchet@34121
    72
  val shortest_name : string -> string
blanchet@33192
    73
  val short_name : string -> string
blanchet@34121
    74
  val shorten_names_in_term : term -> term
blanchet@33192
    75
  val type_match : theory -> typ * typ -> bool
blanchet@33192
    76
  val const_match : theory -> styp * styp -> bool
blanchet@33192
    77
  val term_match : theory -> term * term -> bool
blanchet@33192
    78
  val is_TFree : typ -> bool
blanchet@33192
    79
  val is_higher_order_type : typ -> bool
blanchet@33192
    80
  val is_fun_type : typ -> bool
blanchet@33192
    81
  val is_set_type : typ -> bool
blanchet@33192
    82
  val is_pair_type : typ -> bool
blanchet@33192
    83
  val is_lfp_iterator_type : typ -> bool
blanchet@33192
    84
  val is_gfp_iterator_type : typ -> bool
blanchet@33192
    85
  val is_fp_iterator_type : typ -> bool
blanchet@35280
    86
  val is_iterator_type : typ -> bool
blanchet@33192
    87
  val is_boolean_type : typ -> bool
blanchet@33192
    88
  val is_integer_type : typ -> bool
blanchet@34124
    89
  val is_bit_type : typ -> bool
blanchet@34124
    90
  val is_word_type : typ -> bool
blanchet@35220
    91
  val is_integer_like_type : typ -> bool
blanchet@33192
    92
  val is_record_type : typ -> bool
blanchet@33192
    93
  val is_number_type : theory -> typ -> bool
blanchet@33192
    94
  val const_for_iterator_type : typ -> styp
blanchet@35070
    95
  val strip_n_binders : int -> typ -> typ list * typ
blanchet@33192
    96
  val nth_range_type : int -> typ -> typ
blanchet@33192
    97
  val num_factors_in_type : typ -> int
blanchet@33192
    98
  val num_binder_types : typ -> int
blanchet@33192
    99
  val curried_binder_types : typ -> typ list
blanchet@33192
   100
  val mk_flat_tuple : typ -> term list -> term
blanchet@33192
   101
  val dest_n_tuple : int -> term -> term list
blanchet@33978
   102
  val is_real_datatype : theory -> string -> bool
blanchet@35220
   103
  val is_standard_datatype : theory -> (typ option * bool) list -> typ -> bool
blanchet@34936
   104
  val is_quot_type : theory -> typ -> bool
blanchet@33192
   105
  val is_codatatype : theory -> typ -> bool
blanchet@33192
   106
  val is_pure_typedef : theory -> typ -> bool
blanchet@33192
   107
  val is_univ_typedef : theory -> typ -> bool
blanchet@35220
   108
  val is_datatype : theory -> (typ option * bool) list -> typ -> bool
blanchet@33192
   109
  val is_record_constr : styp -> bool
blanchet@33192
   110
  val is_record_get : theory -> styp -> bool
blanchet@33192
   111
  val is_record_update : theory -> styp -> bool
blanchet@33192
   112
  val is_abs_fun : theory -> styp -> bool
blanchet@33192
   113
  val is_rep_fun : theory -> styp -> bool
blanchet@34936
   114
  val is_quot_abs_fun : Proof.context -> styp -> bool
blanchet@34936
   115
  val is_quot_rep_fun : Proof.context -> styp -> bool
blanchet@35070
   116
  val mate_of_rep_fun : theory -> styp -> styp
blanchet@35070
   117
  val is_constr_like : theory -> styp -> bool
blanchet@35070
   118
  val is_stale_constr : theory -> styp -> bool
blanchet@35220
   119
  val is_constr : theory -> (typ option * bool) list -> styp -> bool
blanchet@33192
   120
  val is_sel : string -> bool
blanchet@34124
   121
  val is_sel_like_and_no_discr : string -> bool
blanchet@35070
   122
  val box_type : hol_context -> boxability -> typ -> typ
blanchet@35190
   123
  val binarize_nat_and_int_in_type : typ -> typ
blanchet@35190
   124
  val binarize_nat_and_int_in_term : term -> term
blanchet@33192
   125
  val discr_for_constr : styp -> styp
blanchet@33192
   126
  val num_sels_for_constr_type : typ -> int
blanchet@33192
   127
  val nth_sel_name_for_constr_name : string -> int -> string
blanchet@33192
   128
  val nth_sel_for_constr : styp -> int -> styp
blanchet@35190
   129
  val binarized_and_boxed_nth_sel_for_constr :
blanchet@35190
   130
    hol_context -> bool -> styp -> int -> styp
blanchet@33192
   131
  val sel_no_from_name : string -> int
blanchet@35078
   132
  val close_form : term -> term
blanchet@33192
   133
  val eta_expand : typ list -> term -> int -> term
blanchet@33192
   134
  val extensionalize : term -> term
blanchet@33192
   135
  val distinctness_formula : typ -> term list -> term
blanchet@33192
   136
  val register_frac_type : string -> (string * string) list -> theory -> theory
blanchet@33192
   137
  val unregister_frac_type : string -> theory -> theory
blanchet@33192
   138
  val register_codatatype : typ -> string -> styp list -> theory -> theory
blanchet@33192
   139
  val unregister_codatatype : typ -> theory -> theory
blanchet@35070
   140
  val datatype_constrs : hol_context -> typ -> styp list
blanchet@35190
   141
  val binarized_and_boxed_datatype_constrs :
blanchet@35190
   142
    hol_context -> bool -> typ -> styp list
blanchet@35070
   143
  val num_datatype_constrs : hol_context -> typ -> int
blanchet@33192
   144
  val constr_name_for_sel_like : string -> string
blanchet@35190
   145
  val binarized_and_boxed_constr_for_sel : hol_context -> bool -> styp -> styp
blanchet@35070
   146
  val discriminate_value : hol_context -> styp -> term -> term
blanchet@35220
   147
  val select_nth_constr_arg :
blanchet@35220
   148
    theory -> (typ option * bool) list -> styp -> term -> int -> typ -> term
blanchet@35220
   149
  val construct_value :
blanchet@35220
   150
    theory -> (typ option * bool) list -> styp -> term list -> term
blanchet@35665
   151
  val coerce_term : hol_context -> typ list -> typ -> typ -> term -> term
blanchet@33192
   152
  val card_of_type : (typ * int) list -> typ -> int
blanchet@33192
   153
  val bounded_card_of_type : int -> int -> (typ * int) list -> typ -> int
blanchet@34123
   154
  val bounded_exact_card_of_type :
blanchet@35385
   155
    hol_context -> typ list -> int -> int -> (typ * int) list -> typ -> int
blanchet@35070
   156
  val is_finite_type : hol_context -> typ -> bool
blanchet@35665
   157
  val is_small_finite_type : hol_context -> typ -> bool
blanchet@35070
   158
  val special_bounds : term list -> (indexname * typ) list
blanchet@35386
   159
  val abs_var : indexname * typ -> term -> term
blanchet@35070
   160
  val is_funky_typedef : theory -> typ -> bool
blanchet@35335
   161
  val all_axioms_of :
blanchet@35335
   162
    theory -> (term * term) list -> term list * term list * term list
blanchet@35220
   163
  val arity_of_built_in_const :
blanchet@35220
   164
    theory -> (typ option * bool) list -> bool -> styp -> int option
blanchet@35220
   165
  val is_built_in_const :
blanchet@35220
   166
    theory -> (typ option * bool) list -> bool -> styp -> bool
blanchet@35070
   167
  val term_under_def : term -> term
blanchet@35220
   168
  val case_const_names :
blanchet@35220
   169
    theory -> (typ option * bool) list -> (string * int) list
blanchet@35335
   170
  val const_def_table :
blanchet@35335
   171
    Proof.context -> (term * term) list -> term list -> const_table
blanchet@33192
   172
  val const_nondef_table : term list -> const_table
blanchet@35335
   173
  val const_simp_table : Proof.context -> (term * term) list -> const_table
blanchet@35335
   174
  val const_psimp_table : Proof.context -> (term * term) list -> const_table
blanchet@35335
   175
  val inductive_intro_table :
blanchet@35335
   176
    Proof.context -> (term * term) list -> const_table -> const_table
blanchet@33192
   177
  val ground_theorem_table : theory -> term list Inttab.table
blanchet@33192
   178
  val ersatz_table : theory -> (string * string) list
blanchet@35070
   179
  val add_simps : const_table Unsynchronized.ref -> string -> term list -> unit
blanchet@35070
   180
  val inverse_axioms_for_rep_fun : theory -> styp -> term list
blanchet@35070
   181
  val optimized_typedef_axioms : theory -> string * typ list -> term list
blanchet@35220
   182
  val optimized_quot_type_axioms :
blanchet@35311
   183
    Proof.context -> (typ option * bool) list -> string * typ list -> term list
blanchet@33192
   184
  val def_of_const : theory -> const_table -> styp -> term option
blanchet@35070
   185
  val fixpoint_kind_of_const :
blanchet@35070
   186
    theory -> const_table -> string * typ -> fixpoint_kind
blanchet@35070
   187
  val is_inductive_pred : hol_context -> styp -> bool
blanchet@35070
   188
  val is_equational_fun : hol_context -> styp -> bool
blanchet@33192
   189
  val is_constr_pattern_lhs : theory -> term -> bool
blanchet@33192
   190
  val is_constr_pattern_formula : theory -> term -> bool
blanchet@35070
   191
  val unfold_defs_in_term : hol_context -> term -> term
blanchet@35070
   192
  val codatatype_bisim_axioms : hol_context -> typ -> term list
blanchet@35070
   193
  val is_well_founded_inductive_pred : hol_context -> styp -> bool
blanchet@35070
   194
  val unrolled_inductive_pred_const : hol_context -> bool -> styp -> term
blanchet@35070
   195
  val equational_fun_axioms : hol_context -> styp -> term list
blanchet@35070
   196
  val is_equational_fun_surely_complete : hol_context -> styp -> bool
blanchet@33556
   197
  val merge_type_vars_in_terms : term list -> term list
blanchet@35190
   198
  val ground_types_in_type : hol_context -> bool -> typ -> typ list
blanchet@35190
   199
  val ground_types_in_terms : hol_context -> bool -> term list -> typ list
blanchet@33192
   200
  val format_type : int list -> int list -> typ -> typ
blanchet@33192
   201
  val format_term_type :
blanchet@33192
   202
    theory -> const_table -> (term option * int list) list -> term -> typ
blanchet@33192
   203
  val user_friendly_const :
blanchet@35070
   204
   hol_context -> string * string -> (term option * int list) list
blanchet@33192
   205
   -> styp -> term * typ
blanchet@33192
   206
  val assign_operator_for_const : styp -> string
blanchet@33192
   207
end;
blanchet@33192
   208
blanchet@33232
   209
structure Nitpick_HOL : NITPICK_HOL =
blanchet@33192
   210
struct
blanchet@33192
   211
blanchet@33232
   212
open Nitpick_Util
blanchet@33192
   213
blanchet@33192
   214
type const_table = term list Symtab.table
blanchet@33192
   215
type special_fun = (styp * int list * term list) * styp
blanchet@33192
   216
type unrolled = styp * styp
blanchet@33192
   217
type wf_cache = (styp * (bool * bool)) list
blanchet@33192
   218
blanchet@35070
   219
type hol_context = {
blanchet@33192
   220
  thy: theory,
blanchet@33192
   221
  ctxt: Proof.context,
blanchet@33192
   222
  max_bisim_depth: int,
blanchet@33192
   223
  boxes: (typ option * bool option) list,
blanchet@34982
   224
  stds: (typ option * bool) list,
blanchet@33192
   225
  wfs: (styp option * bool option) list,
blanchet@33192
   226
  user_axioms: bool option,
blanchet@33192
   227
  debug: bool,
blanchet@34124
   228
  binary_ints: bool option,
blanchet@33192
   229
  destroy_constrs: bool,
blanchet@33192
   230
  specialize: bool,
blanchet@33192
   231
  skolemize: bool,
blanchet@33192
   232
  star_linear_preds: bool,
blanchet@33192
   233
  uncurry: bool,
blanchet@33192
   234
  fast_descrs: bool,
blanchet@33192
   235
  tac_timeout: Time.time option,
blanchet@33192
   236
  evals: term list,
blanchet@33192
   237
  case_names: (string * int) list,
blanchet@33192
   238
  def_table: const_table,
blanchet@33192
   239
  nondef_table: const_table,
blanchet@33192
   240
  user_nondefs: term list,
blanchet@33192
   241
  simp_table: const_table Unsynchronized.ref,
blanchet@33192
   242
  psimp_table: const_table,
blanchet@33192
   243
  intro_table: const_table,
blanchet@33192
   244
  ground_thm_table: term list Inttab.table,
blanchet@33192
   245
  ersatz_table: (string * string) list,
blanchet@33192
   246
  skolems: (string * string list) list Unsynchronized.ref,
blanchet@33192
   247
  special_funs: special_fun list Unsynchronized.ref,
blanchet@33192
   248
  unrolled_preds: unrolled list Unsynchronized.ref,
blanchet@33580
   249
  wf_cache: wf_cache Unsynchronized.ref,
blanchet@33580
   250
  constr_cache: (typ * styp list) list Unsynchronized.ref}
blanchet@33192
   251
blanchet@35070
   252
datatype fixpoint_kind = Lfp | Gfp | NoFp
blanchet@35070
   253
datatype boxability =
blanchet@35070
   254
  InConstr | InSel | InExpr | InPair | InFunLHS | InFunRHS1 | InFunRHS2
blanchet@35070
   255
blanchet@33583
   256
structure Data = Theory_Data(
blanchet@33192
   257
  type T = {frac_types: (string * (string * string) list) list,
blanchet@33192
   258
            codatatypes: (string * (string * styp list)) list}
blanchet@33192
   259
  val empty = {frac_types = [], codatatypes = []}
blanchet@33192
   260
  val extend = I
wenzelm@33522
   261
  fun merge ({frac_types = fs1, codatatypes = cs1},
wenzelm@33522
   262
               {frac_types = fs2, codatatypes = cs2}) : T =
wenzelm@33699
   263
    {frac_types = AList.merge (op =) (K true) (fs1, fs2),
wenzelm@33699
   264
     codatatypes = AList.merge (op =) (K true) (cs1, cs2)})
blanchet@33192
   265
blanchet@33192
   266
val name_sep = "$"
blanchet@33192
   267
val numeral_prefix = nitpick_prefix ^ "num" ^ name_sep
blanchet@33192
   268
val sel_prefix = nitpick_prefix ^ "sel"
blanchet@33192
   269
val discr_prefix = nitpick_prefix ^ "is" ^ name_sep
blanchet@33192
   270
val set_prefix = nitpick_prefix ^ "set" ^ name_sep
blanchet@33192
   271
val lfp_iterator_prefix = nitpick_prefix ^ "lfpit" ^ name_sep
blanchet@33192
   272
val gfp_iterator_prefix = nitpick_prefix ^ "gfpit" ^ name_sep
blanchet@33192
   273
val unrolled_prefix = nitpick_prefix ^ "unroll" ^ name_sep
blanchet@33192
   274
val base_prefix = nitpick_prefix ^ "base" ^ name_sep
blanchet@33192
   275
val step_prefix = nitpick_prefix ^ "step" ^ name_sep
blanchet@33192
   276
val ubfp_prefix = nitpick_prefix ^ "ubfp" ^ name_sep
blanchet@33192
   277
val lbfp_prefix = nitpick_prefix ^ "lbfp" ^ name_sep
blanchet@35311
   278
val quot_normal_prefix = nitpick_prefix ^ "qn" ^ name_sep
blanchet@33192
   279
val skolem_prefix = nitpick_prefix ^ "sk"
blanchet@33192
   280
val special_prefix = nitpick_prefix ^ "sp"
blanchet@33192
   281
val uncurry_prefix = nitpick_prefix ^ "unc"
blanchet@33192
   282
val eval_prefix = nitpick_prefix ^ "eval"
blanchet@33192
   283
val iter_var_prefix = "i"
blanchet@33192
   284
val arg_var_prefix = "x"
blanchet@33192
   285
blanchet@33192
   286
(* int -> string *)
blanchet@33192
   287
fun sel_prefix_for j = sel_prefix ^ string_of_int j ^ name_sep
blanchet@35311
   288
(* Proof.context -> typ -> string *)
blanchet@35311
   289
fun quot_normal_name_for_type ctxt T =
blanchet@35311
   290
  quot_normal_prefix ^ unyxml (Syntax.string_of_typ ctxt T)
blanchet@33192
   291
blanchet@33192
   292
(* string -> string * string *)
blanchet@33192
   293
val strip_first_name_sep =
blanchet@33192
   294
  Substring.full #> Substring.position name_sep ##> Substring.triml 1
blanchet@33192
   295
  #> pairself Substring.string
blanchet@33192
   296
(* string -> string *)
blanchet@33192
   297
fun original_name s =
blanchet@33192
   298
  if String.isPrefix nitpick_prefix s then
blanchet@33192
   299
    case strip_first_name_sep s of (s1, "") => s1 | (_, s2) => original_name s2
blanchet@33192
   300
  else
blanchet@33192
   301
    s
blanchet@33192
   302
val after_name_sep = snd o strip_first_name_sep
blanchet@33192
   303
blanchet@34998
   304
(* term * term -> term *)
blanchet@34998
   305
fun s_conj (t1, @{const True}) = t1
blanchet@34998
   306
  | s_conj (@{const True}, t2) = t2
blanchet@34998
   307
  | s_conj (t1, t2) =
blanchet@34998
   308
    if t1 = @{const False} orelse t2 = @{const False} then @{const False}
blanchet@34998
   309
    else HOLogic.mk_conj (t1, t2)
blanchet@34998
   310
fun s_disj (t1, @{const False}) = t1
blanchet@34998
   311
  | s_disj (@{const False}, t2) = t2
blanchet@34998
   312
  | s_disj (t1, t2) =
blanchet@34998
   313
    if t1 = @{const True} orelse t2 = @{const True} then @{const True}
blanchet@34998
   314
    else HOLogic.mk_disj (t1, t2)
blanchet@34998
   315
blanchet@34998
   316
(* term -> term -> term list *)
blanchet@34998
   317
fun strip_connective conn_t (t as (t0 $ t1 $ t2)) =
blanchet@34998
   318
    if t0 = conn_t then strip_connective t0 t2 @ strip_connective t0 t1 else [t]
blanchet@34998
   319
  | strip_connective _ t = [t]
blanchet@34998
   320
(* term -> term list * term *)
blanchet@35280
   321
fun strip_any_connective (t as (t0 $ _ $ _)) =
blanchet@34998
   322
    if t0 = @{const "op &"} orelse t0 = @{const "op |"} then
blanchet@34998
   323
      (strip_connective t0 t, t0)
blanchet@34998
   324
    else
blanchet@34998
   325
      ([t], @{const Not})
blanchet@34998
   326
  | strip_any_connective t = ([t], @{const Not})
blanchet@34998
   327
(* term -> term list *)
blanchet@35070
   328
val conjuncts_of = strip_connective @{const "op &"}
blanchet@35070
   329
val disjuncts_of = strip_connective @{const "op |"}
blanchet@34998
   330
blanchet@33192
   331
(* When you add constants to these lists, make sure to handle them in
blanchet@33232
   332
   "Nitpick_Nut.nut_from_term", and perhaps in "Nitpick_Mono.consider_term" as
blanchet@33192
   333
   well. *)
blanchet@33192
   334
val built_in_consts =
blanchet@33192
   335
  [(@{const_name all}, 1),
blanchet@33192
   336
   (@{const_name "=="}, 2),
blanchet@33192
   337
   (@{const_name "==>"}, 2),
blanchet@33192
   338
   (@{const_name Pure.conjunction}, 2),
blanchet@33192
   339
   (@{const_name Trueprop}, 1),
blanchet@33192
   340
   (@{const_name Not}, 1),
blanchet@33192
   341
   (@{const_name False}, 0),
blanchet@33192
   342
   (@{const_name True}, 0),
blanchet@33192
   343
   (@{const_name All}, 1),
blanchet@33192
   344
   (@{const_name Ex}, 1),
blanchet@33192
   345
   (@{const_name "op ="}, 2),
blanchet@33192
   346
   (@{const_name "op &"}, 2),
blanchet@33192
   347
   (@{const_name "op |"}, 2),
blanchet@33192
   348
   (@{const_name "op -->"}, 2),
blanchet@33192
   349
   (@{const_name If}, 3),
blanchet@33192
   350
   (@{const_name Let}, 2),
blanchet@33192
   351
   (@{const_name Unity}, 0),
blanchet@33192
   352
   (@{const_name Pair}, 2),
blanchet@33192
   353
   (@{const_name fst}, 1),
blanchet@33192
   354
   (@{const_name snd}, 1),
blanchet@33192
   355
   (@{const_name Id}, 0),
blanchet@33192
   356
   (@{const_name insert}, 2),
blanchet@33192
   357
   (@{const_name converse}, 1),
blanchet@33192
   358
   (@{const_name trancl}, 1),
blanchet@33192
   359
   (@{const_name rel_comp}, 2),
blanchet@33192
   360
   (@{const_name image}, 2),
blanchet@33192
   361
   (@{const_name finite}, 1),
blanchet@34936
   362
   (@{const_name unknown}, 0),
blanchet@34936
   363
   (@{const_name is_unknown}, 1),
blanchet@35671
   364
   (@{const_name safe_The}, 1),
blanchet@35671
   365
   (@{const_name safe_Eps}, 1),
blanchet@33192
   366
   (@{const_name Frac}, 0),
blanchet@33192
   367
   (@{const_name norm_frac}, 0)]
blanchet@35220
   368
val built_in_nat_consts =
blanchet@35220
   369
  [(@{const_name Suc}, 0),
blanchet@35220
   370
   (@{const_name nat}, 0),
blanchet@35220
   371
   (@{const_name nat_gcd}, 0),
blanchet@35220
   372
   (@{const_name nat_lcm}, 0)]
blanchet@33192
   373
val built_in_descr_consts =
blanchet@33192
   374
  [(@{const_name The}, 1),
blanchet@33192
   375
   (@{const_name Eps}, 1)]
blanchet@33192
   376
val built_in_typed_consts =
blanchet@35220
   377
  [((@{const_name zero_class.zero}, int_T), 0),
blanchet@35220
   378
   ((@{const_name one_class.one}, int_T), 0),
blanchet@35220
   379
   ((@{const_name plus_class.plus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   380
   ((@{const_name minus_class.minus}, int_T --> int_T --> int_T), 0),
blanchet@35220
   381
   ((@{const_name times_class.times}, int_T --> int_T --> int_T), 0),
blanchet@35220
   382
   ((@{const_name div_class.div}, int_T --> int_T --> int_T), 0),
blanchet@35220
   383
   ((@{const_name uminus_class.uminus}, int_T --> int_T), 0),
blanchet@35220
   384
   ((@{const_name ord_class.less}, int_T --> int_T --> bool_T), 2),
blanchet@35220
   385
   ((@{const_name ord_class.less_eq}, int_T --> int_T --> bool_T), 2)]
blanchet@35220
   386
val built_in_typed_nat_consts =
blanchet@35220
   387
  [((@{const_name zero_class.zero}, nat_T), 0),
blanchet@35220
   388
   ((@{const_name one_class.one}, nat_T), 0),
blanchet@35220
   389
   ((@{const_name plus_class.plus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   390
   ((@{const_name minus_class.minus}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   391
   ((@{const_name times_class.times}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   392
   ((@{const_name div_class.div}, nat_T --> nat_T --> nat_T), 0),
blanchet@35220
   393
   ((@{const_name ord_class.less}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   394
   ((@{const_name ord_class.less_eq}, nat_T --> nat_T --> bool_T), 2),
blanchet@35220
   395
   ((@{const_name of_nat}, nat_T --> int_T), 0)]
blanchet@33192
   396
val built_in_set_consts =
blanchet@35220
   397
  [(@{const_name semilattice_inf_class.inf}, 2),
blanchet@35220
   398
   (@{const_name semilattice_sup_class.sup}, 2),
blanchet@35220
   399
   (@{const_name minus_class.minus}, 2),
blanchet@35220
   400
   (@{const_name ord_class.less_eq}, 2)]
blanchet@33192
   401
blanchet@33192
   402
(* typ -> typ *)
blanchet@35190
   403
fun unarize_type @{typ "unsigned_bit word"} = nat_T
blanchet@35190
   404
  | unarize_type @{typ "signed_bit word"} = int_T
blanchet@35190
   405
  | unarize_type (Type (s, Ts as _ :: _)) = Type (s, map unarize_type Ts)
blanchet@35190
   406
  | unarize_type T = T
blanchet@35665
   407
fun unarize_unbox_etc_type (Type (@{type_name fin_fun}, Ts)) =
blanchet@35665
   408
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
blanchet@35665
   409
  | unarize_unbox_etc_type (Type (@{type_name fun_box}, Ts)) =
blanchet@35665
   410
    unarize_unbox_etc_type (Type (@{type_name fun}, Ts))
blanchet@35665
   411
  | unarize_unbox_etc_type (Type (@{type_name pair_box}, Ts)) =
blanchet@35665
   412
    Type (@{type_name "*"}, map unarize_unbox_etc_type Ts)
blanchet@35665
   413
  | unarize_unbox_etc_type @{typ "unsigned_bit word"} = nat_T
blanchet@35665
   414
  | unarize_unbox_etc_type @{typ "signed_bit word"} = int_T
blanchet@35665
   415
  | unarize_unbox_etc_type (Type (s, Ts as _ :: _)) =
blanchet@35665
   416
    Type (s, map unarize_unbox_etc_type Ts)
blanchet@35665
   417
  | unarize_unbox_etc_type T = T
blanchet@35280
   418
fun uniterize_type (Type (s, Ts as _ :: _)) = Type (s, map uniterize_type Ts)
blanchet@35280
   419
  | uniterize_type @{typ bisim_iterator} = nat_T
blanchet@35280
   420
  | uniterize_type T = T
blanchet@35665
   421
val uniterize_unarize_unbox_etc_type = uniterize_type o unarize_unbox_etc_type
blanchet@35280
   422
blanchet@33192
   423
(* Proof.context -> typ -> string *)
blanchet@35665
   424
fun string_for_type ctxt = Syntax.string_of_typ ctxt o unarize_unbox_etc_type
blanchet@33192
   425
blanchet@33192
   426
(* string -> string -> string *)
blanchet@33192
   427
val prefix_name = Long_Name.qualify o Long_Name.base_name
blanchet@33192
   428
(* string -> string *)
blanchet@34121
   429
fun shortest_name s = List.last (space_explode "." s) handle List.Empty => ""
blanchet@33192
   430
(* string -> term -> term *)
blanchet@33192
   431
val prefix_abs_vars = Term.map_abs_vars o prefix_name
blanchet@33192
   432
(* string -> string *)
blanchet@34121
   433
fun short_name s =
blanchet@33192
   434
  case space_explode name_sep s of
blanchet@33192
   435
    [_] => s |> String.isPrefix nitpick_prefix s ? unprefix nitpick_prefix
blanchet@34121
   436
  | ss => map shortest_name ss |> space_implode "_"
blanchet@34121
   437
(* typ -> typ *)
blanchet@34121
   438
fun shorten_names_in_type (Type (s, Ts)) =
blanchet@34121
   439
    Type (short_name s, map shorten_names_in_type Ts)
blanchet@34121
   440
  | shorten_names_in_type T = T
blanchet@33192
   441
(* term -> term *)
blanchet@34121
   442
val shorten_names_in_term =
blanchet@34121
   443
  map_aterms (fn Const (s, T) => Const (short_name s, T) | t => t)
blanchet@34121
   444
  #> map_types shorten_names_in_type
blanchet@33192
   445
blanchet@33192
   446
(* theory -> typ * typ -> bool *)
blanchet@35665
   447
fun strict_type_match thy (T1, T2) =
blanchet@33192
   448
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
blanchet@33192
   449
  handle Type.TYPE_MATCH => false
blanchet@35665
   450
fun type_match thy = strict_type_match thy o pairself unarize_unbox_etc_type
blanchet@33192
   451
(* theory -> styp * styp -> bool *)
blanchet@33192
   452
fun const_match thy ((s1, T1), (s2, T2)) =
blanchet@33192
   453
  s1 = s2 andalso type_match thy (T1, T2)
blanchet@33192
   454
(* theory -> term * term -> bool *)
blanchet@33192
   455
fun term_match thy (Const x1, Const x2) = const_match thy (x1, x2)
blanchet@33192
   456
  | term_match thy (Free (s1, T1), Free (s2, T2)) =
blanchet@34121
   457
    const_match thy ((shortest_name s1, T1), (shortest_name s2, T2))
blanchet@35280
   458
  | term_match _ (t1, t2) = t1 aconv t2
blanchet@33192
   459
blanchet@33192
   460
(* typ -> bool *)
blanchet@33192
   461
fun is_TFree (TFree _) = true
blanchet@33192
   462
  | is_TFree _ = false
blanchet@35665
   463
fun is_higher_order_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   464
  | is_higher_order_type (Type (_, Ts)) = exists is_higher_order_type Ts
blanchet@33192
   465
  | is_higher_order_type _ = false
blanchet@35665
   466
fun is_fun_type (Type (@{type_name fun}, _)) = true
blanchet@33192
   467
  | is_fun_type _ = false
blanchet@35665
   468
fun is_set_type (Type (@{type_name fun}, [_, @{typ bool}])) = true
blanchet@33192
   469
  | is_set_type _ = false
blanchet@35665
   470
fun is_pair_type (Type (@{type_name "*"}, _)) = true
blanchet@33192
   471
  | is_pair_type _ = false
blanchet@33192
   472
fun is_lfp_iterator_type (Type (s, _)) = String.isPrefix lfp_iterator_prefix s
blanchet@33192
   473
  | is_lfp_iterator_type _ = false
blanchet@33192
   474
fun is_gfp_iterator_type (Type (s, _)) = String.isPrefix gfp_iterator_prefix s
blanchet@33192
   475
  | is_gfp_iterator_type _ = false
blanchet@33192
   476
val is_fp_iterator_type = is_lfp_iterator_type orf is_gfp_iterator_type
blanchet@35280
   477
fun is_iterator_type T =
blanchet@35280
   478
  (T = @{typ bisim_iterator} orelse is_fp_iterator_type T)
blanchet@34121
   479
fun is_boolean_type T = (T = prop_T orelse T = bool_T)
blanchet@35220
   480
fun is_integer_type T = (T = nat_T orelse T = int_T)
blanchet@34124
   481
fun is_bit_type T = (T = @{typ unsigned_bit} orelse T = @{typ signed_bit})
blanchet@34124
   482
fun is_word_type (Type (@{type_name word}, _)) = true
blanchet@34124
   483
  | is_word_type _ = false
blanchet@35280
   484
val is_integer_like_type = is_iterator_type orf is_integer_type orf is_word_type
blanchet@33192
   485
val is_record_type = not o null o Record.dest_recTs
blanchet@33192
   486
(* theory -> typ -> bool *)
blanchet@33192
   487
fun is_frac_type thy (Type (s, [])) =
blanchet@33583
   488
    not (null (these (AList.lookup (op =) (#frac_types (Data.get thy)) s)))
blanchet@33192
   489
  | is_frac_type _ _ = false
blanchet@35220
   490
fun is_number_type thy = is_integer_like_type orf is_frac_type thy
blanchet@33192
   491
blanchet@33192
   492
(* bool -> styp -> typ *)
blanchet@33192
   493
fun iterator_type_for_const gfp (s, T) =
blanchet@33192
   494
  Type ((if gfp then gfp_iterator_prefix else lfp_iterator_prefix) ^ s,
blanchet@33192
   495
        binder_types T)
blanchet@33192
   496
(* typ -> styp *)
blanchet@33192
   497
fun const_for_iterator_type (Type (s, Ts)) = (after_name_sep s, Ts ---> bool_T)
blanchet@33192
   498
  | const_for_iterator_type T =
blanchet@33232
   499
    raise TYPE ("Nitpick_HOL.const_for_iterator_type", [T], [])
blanchet@33192
   500
blanchet@35070
   501
(* int -> typ -> typ list * typ *)
blanchet@33192
   502
fun strip_n_binders 0 T = ([], T)
blanchet@35665
   503
  | strip_n_binders n (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
   504
    strip_n_binders (n - 1) T2 |>> cons T1
blanchet@33192
   505
  | strip_n_binders n (Type (@{type_name fun_box}, Ts)) =
blanchet@35665
   506
    strip_n_binders n (Type (@{type_name fun}, Ts))
blanchet@33232
   507
  | strip_n_binders _ T = raise TYPE ("Nitpick_HOL.strip_n_binders", [T], [])
blanchet@33192
   508
(* typ -> typ *)
blanchet@33192
   509
val nth_range_type = snd oo strip_n_binders
blanchet@33192
   510
blanchet@33192
   511
(* typ -> int *)
blanchet@35665
   512
fun num_factors_in_type (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
   513
    fold (Integer.add o num_factors_in_type) [T1, T2] 0
blanchet@33192
   514
  | num_factors_in_type _ = 1
blanchet@35665
   515
fun num_binder_types (Type (@{type_name fun}, [_, T2])) =
blanchet@35665
   516
    1 + num_binder_types T2
blanchet@33192
   517
  | num_binder_types _ = 0
blanchet@33192
   518
(* typ -> typ list *)
blanchet@33192
   519
val curried_binder_types = maps HOLogic.flatten_tupleT o binder_types
blanchet@33192
   520
fun maybe_curried_binder_types T =
blanchet@33192
   521
  (if is_pair_type (body_type T) then binder_types else curried_binder_types) T
blanchet@33192
   522
blanchet@33192
   523
(* typ -> term list -> term *)
blanchet@33192
   524
fun mk_flat_tuple _ [t] = t
blanchet@35665
   525
  | mk_flat_tuple (Type (@{type_name "*"}, [T1, T2])) (t :: ts) =
blanchet@33192
   526
    HOLogic.pair_const T1 T2 $ t $ (mk_flat_tuple T2 ts)
blanchet@33232
   527
  | mk_flat_tuple T ts = raise TYPE ("Nitpick_HOL.mk_flat_tuple", [T], ts)
blanchet@33192
   528
(* int -> term -> term list *)
blanchet@33192
   529
fun dest_n_tuple 1 t = [t]
blanchet@33192
   530
  | dest_n_tuple n t = HOLogic.dest_prod t ||> dest_n_tuple (n - 1) |> op ::
blanchet@33192
   531
blanchet@33192
   532
(* int -> typ -> typ list *)
blanchet@33192
   533
fun dest_n_tuple_type 1 T = [T]
blanchet@33192
   534
  | dest_n_tuple_type n (Type (_, [T1, T2])) =
blanchet@33192
   535
    T1 :: dest_n_tuple_type (n - 1) T2
blanchet@33232
   536
  | dest_n_tuple_type _ T =
blanchet@33232
   537
    raise TYPE ("Nitpick_HOL.dest_n_tuple_type", [T], [])
blanchet@33192
   538
blanchet@35220
   539
type typedef_info =
blanchet@35220
   540
  {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
blanchet@35220
   541
   set_def: thm option, prop_of_Rep: thm, set_name: string,
blanchet@35220
   542
   Abs_inverse: thm option, Rep_inverse: thm option}
blanchet@35220
   543
blanchet@35220
   544
(* theory -> string -> typedef_info *)
blanchet@35220
   545
fun typedef_info thy s =
blanchet@35220
   546
  if is_frac_type thy (Type (s, [])) then
blanchet@35220
   547
    SOME {abs_type = Type (s, []), rep_type = @{typ "int * int"},
blanchet@35220
   548
          Abs_name = @{const_name Abs_Frac}, Rep_name = @{const_name Rep_Frac},
blanchet@35220
   549
          set_def = NONE, prop_of_Rep = @{prop "Rep_Frac x \<in> Frac"}
blanchet@35220
   550
                          |> Logic.varify,
blanchet@35220
   551
          set_name = @{const_name Frac}, Abs_inverse = NONE, Rep_inverse = NONE}
blanchet@35220
   552
  else case Typedef.get_info thy s of
blanchet@35220
   553
    SOME {abs_type, rep_type, Abs_name, Rep_name, set_def, Rep, Abs_inverse,
blanchet@35220
   554
          Rep_inverse, ...} =>
blanchet@35220
   555
    SOME {abs_type = abs_type, rep_type = rep_type, Abs_name = Abs_name,
blanchet@35220
   556
          Rep_name = Rep_name, set_def = set_def, prop_of_Rep = prop_of Rep,
blanchet@35220
   557
          set_name = set_prefix ^ s, Abs_inverse = SOME Abs_inverse,
blanchet@35220
   558
          Rep_inverse = SOME Rep_inverse}
blanchet@35220
   559
  | NONE => NONE
blanchet@35220
   560
blanchet@35220
   561
(* theory -> string -> bool *)
blanchet@35220
   562
val is_typedef = is_some oo typedef_info
blanchet@35220
   563
val is_real_datatype = is_some oo Datatype.get_info
blanchet@35220
   564
(* theory -> (typ option * bool) list -> typ -> bool *)
blanchet@35220
   565
fun is_standard_datatype thy = the oo triple_lookup (type_match thy)
blanchet@35220
   566
blanchet@34121
   567
(* FIXME: Use antiquotation for "code_numeral" below or detect "rep_datatype",
blanchet@34121
   568
   e.g., by adding a field to "Datatype_Aux.info". *)
blanchet@35220
   569
(* theory -> (typ option * bool) list -> string -> bool *)
blanchet@35220
   570
fun is_basic_datatype thy stds s =
blanchet@35220
   571
  member (op =) [@{type_name "*"}, @{type_name bool}, @{type_name unit},
blanchet@35220
   572
                 @{type_name int}, "Code_Numeral.code_numeral"] s orelse
blanchet@35220
   573
  (s = @{type_name nat} andalso is_standard_datatype thy stds nat_T)
blanchet@34121
   574
blanchet@33192
   575
(* theory -> typ -> typ -> typ -> typ *)
blanchet@33192
   576
fun instantiate_type thy T1 T1' T2 =
blanchet@33192
   577
  Same.commit (Envir.subst_type_same
blanchet@35311
   578
                   (Sign.typ_match thy (T1, T1') Vartab.empty)) T2
blanchet@33192
   579
  handle Type.TYPE_MATCH =>
blanchet@33232
   580
         raise TYPE ("Nitpick_HOL.instantiate_type", [T1, T1'], [])
blanchet@35311
   581
fun varify_and_instantiate_type thy T1 T1' T2 =
blanchet@35311
   582
  instantiate_type thy (Logic.varifyT T1) T1' (Logic.varifyT T2)
blanchet@33192
   583
blanchet@33192
   584
(* theory -> typ -> typ -> styp *)
blanchet@33192
   585
fun repair_constr_type thy body_T' T =
blanchet@35311
   586
  varify_and_instantiate_type thy (body_type T) body_T' T
blanchet@33192
   587
blanchet@33192
   588
(* string -> (string * string) list -> theory -> theory *)
blanchet@33192
   589
fun register_frac_type frac_s ersaetze thy =
blanchet@33192
   590
  let
blanchet@33583
   591
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   592
    val frac_types = AList.update (op =) (frac_s, ersaetze) frac_types
blanchet@33583
   593
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   594
(* string -> theory -> theory *)
blanchet@33192
   595
fun unregister_frac_type frac_s = register_frac_type frac_s []
blanchet@33192
   596
blanchet@33192
   597
(* typ -> string -> styp list -> theory -> theory *)
blanchet@33192
   598
fun register_codatatype co_T case_name constr_xs thy =
blanchet@33192
   599
  let
blanchet@33583
   600
    val {frac_types, codatatypes} = Data.get thy
blanchet@33192
   601
    val constr_xs = map (apsnd (repair_constr_type thy co_T)) constr_xs
blanchet@33192
   602
    val (co_s, co_Ts) = dest_Type co_T
blanchet@33192
   603
    val _ =
blanchet@34936
   604
      if forall is_TFree co_Ts andalso not (has_duplicates (op =) co_Ts) andalso
blanchet@35665
   605
         co_s <> @{type_name fun} andalso
blanchet@35220
   606
         not (is_basic_datatype thy [(NONE, true)] co_s) then
blanchet@34121
   607
        ()
blanchet@34121
   608
      else
blanchet@34121
   609
        raise TYPE ("Nitpick_HOL.register_codatatype", [co_T], [])
blanchet@33192
   610
    val codatatypes = AList.update (op =) (co_s, (case_name, constr_xs))
blanchet@33192
   611
                                   codatatypes
blanchet@33583
   612
  in Data.put {frac_types = frac_types, codatatypes = codatatypes} thy end
blanchet@33192
   613
(* typ -> theory -> theory *)
blanchet@33192
   614
fun unregister_codatatype co_T = register_codatatype co_T "" []
blanchet@33192
   615
blanchet@33192
   616
(* theory -> typ -> bool *)
blanchet@35284
   617
fun is_quot_type thy (Type (s, _)) =
blanchet@35284
   618
    is_some (Quotient_Info.quotdata_lookup_raw thy s)
blanchet@34936
   619
  | is_quot_type _ _ = false
blanchet@35280
   620
fun is_codatatype thy (Type (s, _)) =
blanchet@33583
   621
    not (null (AList.lookup (op =) (#codatatypes (Data.get thy)) s
blanchet@33192
   622
               |> Option.map snd |> these))
blanchet@33192
   623
  | is_codatatype _ _ = false
blanchet@33192
   624
fun is_pure_typedef thy (T as Type (s, _)) =
blanchet@33192
   625
    is_typedef thy s andalso
blanchet@34936
   626
    not (is_real_datatype thy s orelse is_quot_type thy T orelse
blanchet@35220
   627
         is_codatatype thy T orelse is_record_type T orelse
blanchet@35220
   628
         is_integer_like_type T)
blanchet@33192
   629
  | is_pure_typedef _ _ = false
blanchet@33192
   630
fun is_univ_typedef thy (Type (s, _)) =
blanchet@33192
   631
    (case typedef_info thy s of
blanchet@33192
   632
       SOME {set_def, prop_of_Rep, ...} =>
blanchet@35332
   633
       let
blanchet@35332
   634
         val t_opt =
blanchet@35332
   635
           case set_def of
blanchet@35332
   636
             SOME thm => try (snd o Logic.dest_equals o prop_of) thm
blanchet@35332
   637
           | NONE => try (snd o HOLogic.dest_mem o HOLogic.dest_Trueprop)
blanchet@35332
   638
                         prop_of_Rep
blanchet@35332
   639
       in
blanchet@35332
   640
         case t_opt of
blanchet@35332
   641
           SOME (Const (@{const_name top}, _)) => true
blanchet@35386
   642
           (* "Multiset.multiset" *)
blanchet@35332
   643
         | SOME (Const (@{const_name Collect}, _)
blanchet@35332
   644
                 $ Abs (_, _, Const (@{const_name finite}, _) $ _)) => true
blanchet@35386
   645
           (* "FinFun.finfun" *)
blanchet@35386
   646
         | SOME (Const (@{const_name Collect}, _) $ Abs (_, _,
blanchet@35386
   647
                     Const (@{const_name Ex}, _) $ Abs (_, _,
blanchet@35386
   648
                         Const (@{const_name finite}, _) $ _))) => true
blanchet@35332
   649
         | _ => false
blanchet@35332
   650
       end
blanchet@33192
   651
     | NONE => false)
blanchet@33192
   652
  | is_univ_typedef _ _ = false
blanchet@35220
   653
(* theory -> (typ option * bool) list -> typ -> bool *)
blanchet@35220
   654
fun is_datatype thy stds (T as Type (s, _)) =
blanchet@34936
   655
    (is_typedef thy s orelse is_codatatype thy T orelse T = @{typ ind} orelse
blanchet@35220
   656
     is_quot_type thy T) andalso not (is_basic_datatype thy stds s)
blanchet@35220
   657
  | is_datatype _ _ _ = false
blanchet@33192
   658
blanchet@33192
   659
(* theory -> typ -> (string * typ) list * (string * typ) *)
blanchet@33192
   660
fun all_record_fields thy T =
blanchet@33192
   661
  let val (recs, more) = Record.get_extT_fields thy T in
blanchet@33192
   662
    recs @ more :: all_record_fields thy (snd more)
blanchet@33192
   663
  end
blanchet@33192
   664
  handle TYPE _ => []
blanchet@33192
   665
(* styp -> bool *)
blanchet@35280
   666
fun is_record_constr (s, T) =
blanchet@33192
   667
  String.isSuffix Record.extN s andalso
blanchet@33192
   668
  let val dataT = body_type T in
blanchet@33192
   669
    is_record_type dataT andalso
blanchet@33192
   670
    s = unsuffix Record.ext_typeN (fst (dest_Type dataT)) ^ Record.extN
blanchet@33192
   671
  end
blanchet@33192
   672
(* theory -> typ -> int *)
blanchet@33192
   673
val num_record_fields = Integer.add 1 o length o fst oo Record.get_extT_fields
blanchet@33192
   674
(* theory -> string -> typ -> int *)
blanchet@33192
   675
fun no_of_record_field thy s T1 =
blanchet@34121
   676
  find_index (curry (op =) s o fst)
blanchet@34121
   677
             (Record.get_extT_fields thy T1 ||> single |> op @)
blanchet@33192
   678
(* theory -> styp -> bool *)
blanchet@35665
   679
fun is_record_get thy (s, Type (@{type_name fun}, [T1, _])) =
blanchet@34121
   680
    exists (curry (op =) s o fst) (all_record_fields thy T1)
blanchet@33192
   681
  | is_record_get _ _ = false
blanchet@33192
   682
fun is_record_update thy (s, T) =
blanchet@33192
   683
  String.isSuffix Record.updateN s andalso
blanchet@34121
   684
  exists (curry (op =) (unsuffix Record.updateN s) o fst)
blanchet@33192
   685
         (all_record_fields thy (body_type T))
blanchet@33192
   686
  handle TYPE _ => false
blanchet@35665
   687
fun is_abs_fun thy (s, Type (@{type_name fun}, [_, Type (s', _)])) =
blanchet@33192
   688
    (case typedef_info thy s' of
blanchet@33192
   689
       SOME {Abs_name, ...} => s = Abs_name
blanchet@33192
   690
     | NONE => false)
blanchet@33192
   691
  | is_abs_fun _ _ = false
blanchet@35665
   692
fun is_rep_fun thy (s, Type (@{type_name fun}, [Type (s', _), _])) =
blanchet@33192
   693
    (case typedef_info thy s' of
blanchet@33192
   694
       SOME {Rep_name, ...} => s = Rep_name
blanchet@33192
   695
     | NONE => false)
blanchet@33192
   696
  | is_rep_fun _ _ = false
blanchet@34936
   697
(* Proof.context -> styp -> bool *)
blanchet@35665
   698
fun is_quot_abs_fun ctxt
blanchet@35665
   699
                    (x as (_, Type (@{type_name fun}, [_, Type (s', _)]))) =
blanchet@35284
   700
    (try (Quotient_Term.absrep_const_chk Quotient_Term.AbsF ctxt) s'
blanchet@35284
   701
     = SOME (Const x))
blanchet@34936
   702
  | is_quot_abs_fun _ _ = false
blanchet@35665
   703
fun is_quot_rep_fun ctxt
blanchet@35665
   704
                    (x as (_, Type (@{type_name fun}, [Type (s', _), _]))) =
blanchet@35284
   705
    (try (Quotient_Term.absrep_const_chk Quotient_Term.RepF ctxt) s'
blanchet@35284
   706
     = SOME (Const x))
blanchet@34936
   707
  | is_quot_rep_fun _ _ = false
blanchet@33192
   708
blanchet@33192
   709
(* theory -> styp -> styp *)
blanchet@35665
   710
fun mate_of_rep_fun thy (x as (_, Type (@{type_name fun},
blanchet@35665
   711
                                        [T1 as Type (s', _), T2]))) =
blanchet@33192
   712
    (case typedef_info thy s' of
blanchet@35665
   713
       SOME {Abs_name, ...} => (Abs_name, Type (@{type_name fun}, [T2, T1]))
blanchet@33232
   714
     | NONE => raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x]))
blanchet@33232
   715
  | mate_of_rep_fun _ x = raise TERM ("Nitpick_HOL.mate_of_rep_fun", [Const x])
blanchet@34936
   716
(* theory -> typ -> typ *)
blanchet@35284
   717
fun rep_type_for_quot_type thy (T as Type (s, _)) =
blanchet@35284
   718
  let val {qtyp, rtyp, ...} = Quotient_Info.quotdata_lookup thy s in
blanchet@35284
   719
    instantiate_type thy qtyp T rtyp
blanchet@35284
   720
  end
blanchet@34936
   721
(* theory -> typ -> term *)
blanchet@35284
   722
fun equiv_relation_for_quot_type thy (Type (s, Ts)) =
blanchet@35284
   723
    let
blanchet@35284
   724
      val {qtyp, equiv_rel, ...} = Quotient_Info.quotdata_lookup thy s
blanchet@35284
   725
      val Ts' = qtyp |> dest_Type |> snd
blanchet@35284
   726
    in subst_atomic_types (Ts' ~~ Ts) equiv_rel end
blanchet@34936
   727
  | equiv_relation_for_quot_type _ T =
blanchet@34936
   728
    raise TYPE ("Nitpick_HOL.equiv_relation_for_quot_type", [T], [])
blanchet@33192
   729
blanchet@33192
   730
(* theory -> styp -> bool *)
blanchet@33192
   731
fun is_coconstr thy (s, T) =
blanchet@33192
   732
  let
blanchet@33583
   733
    val {codatatypes, ...} = Data.get thy
blanchet@33192
   734
    val co_T = body_type T
blanchet@33192
   735
    val co_s = dest_Type co_T |> fst
blanchet@33192
   736
  in
blanchet@33192
   737
    exists (fn (s', T') => s = s' andalso repair_constr_type thy co_T T' = T)
blanchet@33192
   738
           (AList.lookup (op =) codatatypes co_s |> Option.map snd |> these)
blanchet@33192
   739
  end
blanchet@33192
   740
  handle TYPE ("dest_Type", _, _) => false
blanchet@33192
   741
fun is_constr_like thy (s, T) =
blanchet@35665
   742
  member (op =) [@{const_name FinFun}, @{const_name FunBox},
blanchet@35665
   743
                 @{const_name PairBox}, @{const_name Quot},
blanchet@35665
   744
                 @{const_name Zero_Rep}, @{const_name Suc_Rep}] s orelse
blanchet@35665
   745
  let val (x as (_, T)) = (s, unarize_unbox_etc_type T) in
blanchet@34936
   746
    Refute.is_IDT_constructor thy x orelse is_record_constr x orelse
blanchet@34936
   747
    (is_abs_fun thy x andalso is_pure_typedef thy (range_type T)) orelse
blanchet@34936
   748
    is_coconstr thy x
blanchet@33192
   749
  end
blanchet@33581
   750
fun is_stale_constr thy (x as (_, T)) =
blanchet@34936
   751
  is_codatatype thy (body_type T) andalso is_constr_like thy x andalso
blanchet@34936
   752
  not (is_coconstr thy x)
blanchet@35220
   753
(* theory -> (typ option * bool) list -> styp -> bool *)
blanchet@35220
   754
fun is_constr thy stds (x as (_, T)) =
blanchet@34936
   755
  is_constr_like thy x andalso
blanchet@35220
   756
  not (is_basic_datatype thy stds
blanchet@35220
   757
                         (fst (dest_Type (unarize_type (body_type T))))) andalso
blanchet@34936
   758
  not (is_stale_constr thy x)
blanchet@33192
   759
(* string -> bool *)
blanchet@33192
   760
val is_sel = String.isPrefix discr_prefix orf String.isPrefix sel_prefix
blanchet@33192
   761
val is_sel_like_and_no_discr =
blanchet@35665
   762
  String.isPrefix sel_prefix orf
blanchet@35665
   763
  (member (op =) [@{const_name fst}, @{const_name snd}])
blanchet@33192
   764
blanchet@33192
   765
(* boxability -> boxability *)
blanchet@33192
   766
fun in_fun_lhs_for InConstr = InSel
blanchet@33192
   767
  | in_fun_lhs_for _ = InFunLHS
blanchet@33192
   768
fun in_fun_rhs_for InConstr = InConstr
blanchet@33192
   769
  | in_fun_rhs_for InSel = InSel
blanchet@33192
   770
  | in_fun_rhs_for InFunRHS1 = InFunRHS2
blanchet@33192
   771
  | in_fun_rhs_for _ = InFunRHS1
blanchet@33192
   772
blanchet@35070
   773
(* hol_context -> boxability -> typ -> bool *)
blanchet@35070
   774
fun is_boxing_worth_it (hol_ctxt : hol_context) boxy T =
blanchet@33192
   775
  case T of
blanchet@35665
   776
    Type (@{type_name fun}, _) =>
blanchet@34936
   777
    (boxy = InPair orelse boxy = InFunLHS) andalso
blanchet@34936
   778
    not (is_boolean_type (body_type T))
blanchet@35665
   779
  | Type (@{type_name "*"}, Ts) =>
blanchet@34936
   780
    boxy = InPair orelse boxy = InFunRHS1 orelse boxy = InFunRHS2 orelse
blanchet@34936
   781
    ((boxy = InExpr orelse boxy = InFunLHS) andalso
blanchet@35070
   782
     exists (is_boxing_worth_it hol_ctxt InPair)
blanchet@35070
   783
            (map (box_type hol_ctxt InPair) Ts))
blanchet@33192
   784
  | _ => false
blanchet@35070
   785
(* hol_context -> boxability -> string * typ list -> string *)
blanchet@35280
   786
and should_box_type (hol_ctxt as {thy, boxes, ...}) boxy z =
blanchet@33192
   787
  case triple_lookup (type_match thy) boxes (Type z) of
blanchet@33192
   788
    SOME (SOME box_me) => box_me
blanchet@35070
   789
  | _ => is_boxing_worth_it hol_ctxt boxy (Type z)
blanchet@35070
   790
(* hol_context -> boxability -> typ -> typ *)
blanchet@35070
   791
and box_type hol_ctxt boxy T =
blanchet@33192
   792
  case T of
blanchet@35665
   793
    Type (z as (@{type_name fun}, [T1, T2])) =>
blanchet@34936
   794
    if boxy <> InConstr andalso boxy <> InSel andalso
blanchet@35070
   795
       should_box_type hol_ctxt boxy z then
blanchet@33192
   796
      Type (@{type_name fun_box},
blanchet@35070
   797
            [box_type hol_ctxt InFunLHS T1, box_type hol_ctxt InFunRHS1 T2])
blanchet@33192
   798
    else
blanchet@35070
   799
      box_type hol_ctxt (in_fun_lhs_for boxy) T1
blanchet@35070
   800
      --> box_type hol_ctxt (in_fun_rhs_for boxy) T2
blanchet@35665
   801
  | Type (z as (@{type_name "*"}, Ts)) =>
blanchet@34982
   802
    if boxy <> InConstr andalso boxy <> InSel
blanchet@35070
   803
       andalso should_box_type hol_ctxt boxy z then
blanchet@35070
   804
      Type (@{type_name pair_box}, map (box_type hol_ctxt InSel) Ts)
blanchet@33192
   805
    else
blanchet@35665
   806
      Type (@{type_name "*"},
blanchet@35665
   807
            map (box_type hol_ctxt
blanchet@34121
   808
                          (if boxy = InConstr orelse boxy = InSel then boxy
blanchet@34121
   809
                           else InPair)) Ts)
blanchet@33192
   810
  | _ => T
blanchet@33192
   811
blanchet@35190
   812
(* typ -> typ *)
blanchet@35190
   813
fun binarize_nat_and_int_in_type @{typ nat} = @{typ "unsigned_bit word"}
blanchet@35190
   814
  | binarize_nat_and_int_in_type @{typ int} = @{typ "signed_bit word"}
blanchet@35190
   815
  | binarize_nat_and_int_in_type (Type (s, Ts)) =
blanchet@35190
   816
    Type (s, map binarize_nat_and_int_in_type Ts)
blanchet@35190
   817
  | binarize_nat_and_int_in_type T = T
blanchet@35190
   818
(* term -> term *)
blanchet@35190
   819
val binarize_nat_and_int_in_term = map_types binarize_nat_and_int_in_type
blanchet@35190
   820
blanchet@33192
   821
(* styp -> styp *)
blanchet@33192
   822
fun discr_for_constr (s, T) = (discr_prefix ^ s, body_type T --> bool_T)
blanchet@33192
   823
blanchet@33192
   824
(* typ -> int *)
blanchet@33192
   825
fun num_sels_for_constr_type T = length (maybe_curried_binder_types T)
blanchet@33192
   826
(* string -> int -> string *)
blanchet@33192
   827
fun nth_sel_name_for_constr_name s n =
blanchet@33192
   828
  if s = @{const_name Pair} then
blanchet@33192
   829
    if n = 0 then @{const_name fst} else @{const_name snd}
blanchet@33192
   830
  else
blanchet@33192
   831
    sel_prefix_for n ^ s
blanchet@33192
   832
(* styp -> int -> styp *)
blanchet@33192
   833
fun nth_sel_for_constr x ~1 = discr_for_constr x
blanchet@33192
   834
  | nth_sel_for_constr (s, T) n =
blanchet@33192
   835
    (nth_sel_name_for_constr_name s n,
blanchet@33192
   836
     body_type T --> nth (maybe_curried_binder_types T) n)
blanchet@35190
   837
(* hol_context -> bool -> styp -> int -> styp *)
blanchet@35190
   838
fun binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize =
blanchet@35190
   839
  apsnd ((binarize ? binarize_nat_and_int_in_type) o box_type hol_ctxt InSel)
blanchet@35190
   840
  oo nth_sel_for_constr
blanchet@33192
   841
blanchet@33192
   842
(* string -> int *)
blanchet@33192
   843
fun sel_no_from_name s =
blanchet@33192
   844
  if String.isPrefix discr_prefix s then
blanchet@33192
   845
    ~1
blanchet@33192
   846
  else if String.isPrefix sel_prefix s then
blanchet@33192
   847
    s |> unprefix sel_prefix |> Int.fromString |> the
blanchet@33192
   848
  else if s = @{const_name snd} then
blanchet@33192
   849
    1
blanchet@33192
   850
  else
blanchet@33192
   851
    0
blanchet@33192
   852
blanchet@35078
   853
(* term -> term *)
blanchet@35078
   854
val close_form =
blanchet@35078
   855
  let
blanchet@35078
   856
    (* (indexname * typ) list -> (indexname * typ) list -> term -> term *)
blanchet@35078
   857
    fun close_up zs zs' =
blanchet@35078
   858
      fold (fn (z as ((s, _), T)) => fn t' =>
blanchet@35078
   859
               Term.all T $ Abs (s, T, abstract_over (Var z, t')))
blanchet@35078
   860
           (take (length zs' - length zs) zs')
blanchet@35078
   861
    (* (indexname * typ) list -> term -> term *)
blanchet@35078
   862
    fun aux zs (@{const "==>"} $ t1 $ t2) =
blanchet@35078
   863
        let val zs' = Term.add_vars t1 zs in
blanchet@35078
   864
          close_up zs zs' (Logic.mk_implies (t1, aux zs' t2))
blanchet@35078
   865
        end
blanchet@35078
   866
      | aux zs t = close_up zs (Term.add_vars t zs) t
blanchet@35078
   867
  in aux [] end
blanchet@35078
   868
blanchet@33192
   869
(* typ list -> term -> int -> term *)
blanchet@33192
   870
fun eta_expand _ t 0 = t
blanchet@33192
   871
  | eta_expand Ts (Abs (s, T, t')) n =
blanchet@33192
   872
    Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
blanchet@33192
   873
  | eta_expand Ts t n =
blanchet@33192
   874
    fold_rev (curry3 Abs ("x\<^isub>\<eta>" ^ nat_subscript n))
blanchet@33192
   875
             (List.take (binder_types (fastype_of1 (Ts, t)), n))
blanchet@33192
   876
             (list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
blanchet@33192
   877
blanchet@33192
   878
(* term -> term *)
blanchet@33192
   879
fun extensionalize t =
blanchet@33192
   880
  case t of
blanchet@33192
   881
    (t0 as @{const Trueprop}) $ t1 => t0 $ extensionalize t1
blanchet@33192
   882
  | Const (@{const_name "op ="}, _) $ t1 $ Abs (s, T, t2) =>
blanchet@33192
   883
    let val v = Var ((s, maxidx_of_term t + 1), T) in
blanchet@33192
   884
      extensionalize (HOLogic.mk_eq (t1 $ v, subst_bound (v, t2)))
blanchet@33192
   885
    end
blanchet@33192
   886
  | _ => t
blanchet@33192
   887
blanchet@33192
   888
(* typ -> term list -> term *)
blanchet@33192
   889
fun distinctness_formula T =
blanchet@33192
   890
  all_distinct_unordered_pairs_of
blanchet@33192
   891
  #> map (fn (t1, t2) => @{const Not} $ (HOLogic.eq_const T $ t1 $ t2))
blanchet@33192
   892
  #> List.foldr (s_conj o swap) @{const True}
blanchet@33192
   893
blanchet@33192
   894
(* typ -> term *)
blanchet@35220
   895
fun zero_const T = Const (@{const_name zero_class.zero}, T)
blanchet@33192
   896
fun suc_const T = Const (@{const_name Suc}, T --> T)
blanchet@33192
   897
blanchet@35220
   898
(* hol_context -> typ -> styp list *)
blanchet@35220
   899
fun uncached_datatype_constrs ({thy, stds, ...} : hol_context)
blanchet@35220
   900
                              (T as Type (s, Ts)) =
blanchet@33583
   901
    (case AList.lookup (op =) (#codatatypes (Data.get thy)) s of
blanchet@34982
   902
       SOME (_, xs' as (_ :: _)) => map (apsnd (repair_constr_type thy T)) xs'
blanchet@33581
   903
     | _ =>
blanchet@35220
   904
       if is_datatype thy stds T then
blanchet@33581
   905
         case Datatype.get_info thy s of
blanchet@33581
   906
           SOME {index, descr, ...} =>
blanchet@33581
   907
           let
blanchet@33581
   908
             val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the
blanchet@33581
   909
           in
blanchet@33581
   910
             map (fn (s', Us) =>
blanchet@33581
   911
                     (s', map (Refute.typ_of_dtyp descr (dtyps ~~ Ts)) Us
blanchet@33581
   912
                          ---> T)) constrs
blanchet@33581
   913
           end
blanchet@33581
   914
         | NONE =>
blanchet@33581
   915
           if is_record_type T then
blanchet@33581
   916
             let
blanchet@33581
   917
               val s' = unsuffix Record.ext_typeN s ^ Record.extN
blanchet@33581
   918
               val T' = (Record.get_extT_fields thy T
blanchet@33581
   919
                        |> apsnd single |> uncurry append |> map snd) ---> T
blanchet@33581
   920
             in [(s', T')] end
blanchet@34936
   921
           else if is_quot_type thy T then
blanchet@34936
   922
             [(@{const_name Quot}, rep_type_for_quot_type thy T --> T)]
blanchet@33581
   923
           else case typedef_info thy s of
blanchet@33581
   924
             SOME {abs_type, rep_type, Abs_name, ...} =>
blanchet@35311
   925
             [(Abs_name,
blanchet@35311
   926
               varify_and_instantiate_type thy abs_type T rep_type --> T)]
blanchet@33581
   927
           | NONE =>
blanchet@33581
   928
             if T = @{typ ind} then
blanchet@33581
   929
               [dest_Const @{const Zero_Rep}, dest_Const @{const Suc_Rep}]
blanchet@33581
   930
             else
blanchet@33581
   931
               []
blanchet@33581
   932
       else
blanchet@33581
   933
         [])
blanchet@33580
   934
  | uncached_datatype_constrs _ _ = []
blanchet@35070
   935
(* hol_context -> typ -> styp list *)
blanchet@35220
   936
fun datatype_constrs (hol_ctxt as {constr_cache, ...}) T =
blanchet@33580
   937
  case AList.lookup (op =) (!constr_cache) T of
blanchet@33580
   938
    SOME xs => xs
blanchet@33580
   939
  | NONE =>
blanchet@35220
   940
    let val xs = uncached_datatype_constrs hol_ctxt T in
blanchet@33580
   941
      (Unsynchronized.change constr_cache (cons (T, xs)); xs)
blanchet@33580
   942
    end
blanchet@35190
   943
(* hol_context -> bool -> typ -> styp list *)
blanchet@35190
   944
fun binarized_and_boxed_datatype_constrs hol_ctxt binarize =
blanchet@35190
   945
  map (apsnd ((binarize ? binarize_nat_and_int_in_type)
blanchet@35190
   946
              o box_type hol_ctxt InConstr)) o datatype_constrs hol_ctxt
blanchet@35070
   947
(* hol_context -> typ -> int *)
blanchet@33192
   948
val num_datatype_constrs = length oo datatype_constrs
blanchet@33192
   949
blanchet@33192
   950
(* string -> string *)
blanchet@33192
   951
fun constr_name_for_sel_like @{const_name fst} = @{const_name Pair}
blanchet@33192
   952
  | constr_name_for_sel_like @{const_name snd} = @{const_name Pair}
blanchet@33192
   953
  | constr_name_for_sel_like s' = original_name s'
blanchet@35190
   954
(* hol_context -> bool -> styp -> styp *)
blanchet@35190
   955
fun binarized_and_boxed_constr_for_sel hol_ctxt binarize (s', T') =
blanchet@33192
   956
  let val s = constr_name_for_sel_like s' in
blanchet@35190
   957
    AList.lookup (op =)
blanchet@35190
   958
        (binarized_and_boxed_datatype_constrs hol_ctxt binarize (domain_type T'))
blanchet@35190
   959
        s
blanchet@33192
   960
    |> the |> pair s
blanchet@33192
   961
  end
blanchet@34982
   962
blanchet@35070
   963
(* hol_context -> styp -> term *)
blanchet@35070
   964
fun discr_term_for_constr hol_ctxt (x as (s, T)) =
blanchet@33192
   965
  let val dataT = body_type T in
blanchet@33192
   966
    if s = @{const_name Suc} then
blanchet@33192
   967
      Abs (Name.uu, dataT,
blanchet@33192
   968
           @{const Not} $ HOLogic.mk_eq (zero_const dataT, Bound 0))
blanchet@35070
   969
    else if num_datatype_constrs hol_ctxt dataT >= 2 then
blanchet@33192
   970
      Const (discr_for_constr x)
blanchet@33192
   971
    else
blanchet@33192
   972
      Abs (Name.uu, dataT, @{const True})
blanchet@33192
   973
  end
blanchet@35070
   974
(* hol_context -> styp -> term -> term *)
blanchet@35280
   975
fun discriminate_value (hol_ctxt as {thy, ...}) x t =
blanchet@35280
   976
  case head_of t of
blanchet@35280
   977
    Const x' =>
blanchet@33192
   978
    if x = x' then @{const True}
blanchet@33192
   979
    else if is_constr_like thy x' then @{const False}
blanchet@35070
   980
    else betapply (discr_term_for_constr hol_ctxt x, t)
blanchet@35070
   981
  | _ => betapply (discr_term_for_constr hol_ctxt x, t)
blanchet@33192
   982
blanchet@35220
   983
(* theory -> (typ option * bool) list -> styp -> term -> term *)
blanchet@35220
   984
fun nth_arg_sel_term_for_constr thy stds (x as (s, T)) n =
blanchet@33192
   985
  let val (arg_Ts, dataT) = strip_type T in
blanchet@35220
   986
    if dataT = nat_T andalso is_standard_datatype thy stds nat_T then
blanchet@35220
   987
      @{term "%n::nat. n - 1"}
blanchet@33192
   988
    else if is_pair_type dataT then
blanchet@33192
   989
      Const (nth_sel_for_constr x n)
blanchet@33192
   990
    else
blanchet@33192
   991
      let
blanchet@33192
   992
        (* int -> typ -> int * term *)
blanchet@35665
   993
        fun aux m (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
   994
            let
blanchet@33192
   995
              val (m, t1) = aux m T1
blanchet@33192
   996
              val (m, t2) = aux m T2
blanchet@33192
   997
            in (m, HOLogic.mk_prod (t1, t2)) end
blanchet@33192
   998
          | aux m T =
blanchet@33192
   999
            (m + 1, Const (nth_sel_name_for_constr_name s m, dataT --> T)
blanchet@33192
  1000
                    $ Bound 0)
blanchet@33192
  1001
        val m = fold (Integer.add o num_factors_in_type)
blanchet@33192
  1002
                     (List.take (arg_Ts, n)) 0
blanchet@33192
  1003
      in Abs ("x", dataT, aux m (nth arg_Ts n) |> snd) end
blanchet@33192
  1004
  end
blanchet@35220
  1005
(* theory -> (typ option * bool) list -> styp -> term -> int -> typ -> term *)
blanchet@35220
  1006
fun select_nth_constr_arg thy stds x t n res_T =
blanchet@35220
  1007
  (case strip_comb t of
blanchet@35220
  1008
     (Const x', args) =>
blanchet@35220
  1009
     if x = x' then nth args n
blanchet@35220
  1010
     else if is_constr_like thy x' then Const (@{const_name unknown}, res_T)
blanchet@35220
  1011
     else raise SAME ()
blanchet@35220
  1012
   | _ => raise SAME())
blanchet@35220
  1013
  handle SAME () => betapply (nth_arg_sel_term_for_constr thy stds x n, t)
blanchet@33192
  1014
blanchet@35220
  1015
(* theory -> (typ option * bool) list -> styp -> term list -> term *)
blanchet@35220
  1016
fun construct_value _ _ x [] = Const x
blanchet@35220
  1017
  | construct_value thy stds (x as (s, _)) args =
blanchet@33192
  1018
    let val args = map Envir.eta_contract args in
blanchet@33192
  1019
      case hd args of
blanchet@35280
  1020
        Const (s', _) $ t =>
blanchet@34936
  1021
        if is_sel_like_and_no_discr s' andalso
blanchet@34936
  1022
           constr_name_for_sel_like s' = s andalso
blanchet@35220
  1023
           forall (fn (n, t') =>
blanchet@35220
  1024
                      select_nth_constr_arg thy stds x t n dummyT = t')
blanchet@34936
  1025
                  (index_seq 0 (length args) ~~ args) then
blanchet@33192
  1026
          t
blanchet@33192
  1027
        else
blanchet@33192
  1028
          list_comb (Const x, args)
blanchet@33192
  1029
      | _ => list_comb (Const x, args)
blanchet@33192
  1030
    end
blanchet@33192
  1031
blanchet@35665
  1032
(* hol_context -> typ -> term -> term *)
blanchet@35665
  1033
fun constr_expand (hol_ctxt as {thy, stds, ...}) T t =
blanchet@35665
  1034
  (case head_of t of
blanchet@35665
  1035
     Const x => if is_constr_like thy x then t else raise SAME ()
blanchet@35665
  1036
   | _ => raise SAME ())
blanchet@35665
  1037
  handle SAME () =>
blanchet@35665
  1038
         let
blanchet@35665
  1039
           val x' as (_, T') =
blanchet@35665
  1040
             if is_pair_type T then
blanchet@35665
  1041
               let val (T1, T2) = HOLogic.dest_prodT T in
blanchet@35665
  1042
                 (@{const_name Pair}, T1 --> T2 --> T)
blanchet@35665
  1043
               end
blanchet@35665
  1044
             else
blanchet@35665
  1045
               datatype_constrs hol_ctxt T |> hd
blanchet@35665
  1046
           val arg_Ts = binder_types T'
blanchet@35665
  1047
         in
blanchet@35665
  1048
           list_comb (Const x', map2 (select_nth_constr_arg thy stds x' t)
blanchet@35665
  1049
                                     (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@35665
  1050
         end
blanchet@35665
  1051
blanchet@35665
  1052
(* (term -> term) -> int -> term -> term *)
blanchet@35665
  1053
fun coerce_bound_no f j t =
blanchet@35665
  1054
  case t of
blanchet@35665
  1055
    t1 $ t2 => coerce_bound_no f j t1 $ coerce_bound_no f j t2
blanchet@35665
  1056
  | Abs (s, T, t') => Abs (s, T, coerce_bound_no f (j + 1) t')
blanchet@35665
  1057
  | Bound j' => if j' = j then f t else t
blanchet@35665
  1058
  | _ => t
blanchet@35665
  1059
(* hol_context -> typ -> typ -> term -> term *)
blanchet@35665
  1060
fun coerce_bound_0_in_term hol_ctxt new_T old_T =
blanchet@35665
  1061
  old_T <> new_T ? coerce_bound_no (coerce_term hol_ctxt [new_T] old_T new_T) 0
blanchet@35665
  1062
(* hol_context -> typ list -> typ -> typ -> term -> term *)
blanchet@35665
  1063
and coerce_term (hol_ctxt as {thy, stds, fast_descrs, ...}) Ts new_T old_T t =
blanchet@35665
  1064
  if old_T = new_T then
blanchet@35665
  1065
    t
blanchet@35665
  1066
  else
blanchet@35665
  1067
    case (new_T, old_T) of
blanchet@35665
  1068
      (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1069
       Type (@{type_name fun}, [old_T1, old_T2])) =>
blanchet@35665
  1070
      (case eta_expand Ts t 1 of
blanchet@35665
  1071
         Abs (s, _, t') =>
blanchet@35665
  1072
         Abs (s, new_T1,
blanchet@35665
  1073
              t' |> coerce_bound_0_in_term hol_ctxt new_T1 old_T1
blanchet@35665
  1074
                 |> coerce_term hol_ctxt (new_T1 :: Ts) new_T2 old_T2)
blanchet@35665
  1075
         |> Envir.eta_contract
blanchet@35665
  1076
         |> new_s <> @{type_name fun}
blanchet@35665
  1077
            ? construct_value thy stds
blanchet@35665
  1078
                  (if new_s = @{type_name fin_fun} then @{const_name FinFun}
blanchet@35665
  1079
                   else @{const_name FunBox},
blanchet@35665
  1080
                   Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1081
              o single
blanchet@35665
  1082
       | t' => raise TERM ("Nitpick_HOL.coerce_term", [t']))
blanchet@35665
  1083
    | (Type (new_s, new_Ts as [new_T1, new_T2]),
blanchet@35665
  1084
       Type (old_s, old_Ts as [old_T1, old_T2])) =>
blanchet@35665
  1085
      if old_s = @{type_name fin_fun} orelse old_s = @{type_name fun_box} orelse
blanchet@35665
  1086
         old_s = @{type_name pair_box} orelse old_s = @{type_name "*"} then
blanchet@35665
  1087
        case constr_expand hol_ctxt old_T t of
blanchet@35665
  1088
          Const (old_s, _) $ t1 =>
blanchet@35665
  1089
          if new_s = @{type_name fun} then
blanchet@35665
  1090
            coerce_term hol_ctxt Ts new_T (Type (@{type_name fun}, old_Ts)) t1
blanchet@35665
  1091
          else
blanchet@35665
  1092
            construct_value thy stds
blanchet@35665
  1093
                (old_s, Type (@{type_name fun}, new_Ts) --> new_T)
blanchet@35665
  1094
                [coerce_term hol_ctxt Ts (Type (@{type_name fun}, new_Ts))
blanchet@35665
  1095
                             (Type (@{type_name fun}, old_Ts)) t1]
blanchet@35665
  1096
        | Const _ $ t1 $ t2 =>
blanchet@35665
  1097
          construct_value thy stds
blanchet@35665
  1098
              (if new_s = @{type_name "*"} then @{const_name Pair}
blanchet@35665
  1099
               else @{const_name PairBox}, new_Ts ---> new_T)
blanchet@35665
  1100
              (map3 (coerce_term hol_ctxt Ts) [new_T1, new_T2] [old_T1, old_T2]
blanchet@35665
  1101
                    [t1, t2])
blanchet@35665
  1102
        | t' => raise TERM ("Nitpick_HOL.coerce_term", [t'])
blanchet@35665
  1103
      else
blanchet@35665
  1104
        raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1105
    | _ => raise TYPE ("Nitpick_HOL.coerce_term", [new_T, old_T], [t])
blanchet@35665
  1106
blanchet@33192
  1107
(* (typ * int) list -> typ -> int *)
blanchet@35665
  1108
fun card_of_type assigns (Type (@{type_name fun}, [T1, T2])) =
blanchet@34123
  1109
    reasonable_power (card_of_type assigns T2) (card_of_type assigns T1)
blanchet@35665
  1110
  | card_of_type assigns (Type (@{type_name "*"}, [T1, T2])) =
blanchet@34123
  1111
    card_of_type assigns T1 * card_of_type assigns T2
blanchet@33192
  1112
  | card_of_type _ (Type (@{type_name itself}, _)) = 1
blanchet@33192
  1113
  | card_of_type _ @{typ prop} = 2
blanchet@33192
  1114
  | card_of_type _ @{typ bool} = 2
blanchet@33192
  1115
  | card_of_type _ @{typ unit} = 1
blanchet@34123
  1116
  | card_of_type assigns T =
blanchet@34123
  1117
    case AList.lookup (op =) assigns T of
blanchet@33192
  1118
      SOME k => k
blanchet@33192
  1119
    | NONE => if T = @{typ bisim_iterator} then 0
blanchet@33232
  1120
              else raise TYPE ("Nitpick_HOL.card_of_type", [T], [])
blanchet@33192
  1121
(* int -> (typ * int) list -> typ -> int *)
blanchet@35665
  1122
fun bounded_card_of_type max default_card assigns
blanchet@35665
  1123
                         (Type (@{type_name fun}, [T1, T2])) =
blanchet@33192
  1124
    let
blanchet@34123
  1125
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1126
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1127
    in
blanchet@33192
  1128
      if k1 = max orelse k2 = max then max
blanchet@33192
  1129
      else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1130
    end
blanchet@35665
  1131
  | bounded_card_of_type max default_card assigns
blanchet@35665
  1132
                         (Type (@{type_name "*"}, [T1, T2])) =
blanchet@33192
  1133
    let
blanchet@34123
  1134
      val k1 = bounded_card_of_type max default_card assigns T1
blanchet@34123
  1135
      val k2 = bounded_card_of_type max default_card assigns T2
blanchet@33192
  1136
    in if k1 = max orelse k2 = max then max else Int.min (max, k1 * k2) end
blanchet@34123
  1137
  | bounded_card_of_type max default_card assigns T =
blanchet@33192
  1138
    Int.min (max, if default_card = ~1 then
blanchet@34123
  1139
                    card_of_type assigns T
blanchet@33192
  1140
                  else
blanchet@34123
  1141
                    card_of_type assigns T
blanchet@33232
  1142
                    handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>
blanchet@33192
  1143
                           default_card)
blanchet@35385
  1144
(* hol_context -> typ list -> int -> (typ * int) list -> typ -> int *)
blanchet@35385
  1145
fun bounded_exact_card_of_type hol_ctxt finitizable_dataTs max default_card
blanchet@35385
  1146
                               assigns T =
blanchet@33192
  1147
  let
blanchet@33192
  1148
    (* typ list -> typ -> int *)
blanchet@33192
  1149
    fun aux avoid T =
blanchet@34121
  1150
      (if member (op =) avoid T then
blanchet@33192
  1151
         0
blanchet@35385
  1152
       else if member (op =) finitizable_dataTs T then
blanchet@35385
  1153
         raise SAME ()
blanchet@33192
  1154
       else case T of
blanchet@35665
  1155
         Type (@{type_name fun}, [T1, T2]) =>
blanchet@33192
  1156
         let
blanchet@33192
  1157
           val k1 = aux avoid T1
blanchet@33192
  1158
           val k2 = aux avoid T2
blanchet@33192
  1159
         in
blanchet@33192
  1160
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1161
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1162
           else Int.min (max, reasonable_power k2 k1)
blanchet@33192
  1163
         end
blanchet@35665
  1164
       | Type (@{type_name "*"}, [T1, T2]) =>
blanchet@33192
  1165
         let
blanchet@33192
  1166
           val k1 = aux avoid T1
blanchet@33192
  1167
           val k2 = aux avoid T2
blanchet@33192
  1168
         in
blanchet@33192
  1169
           if k1 = 0 orelse k2 = 0 then 0
blanchet@33192
  1170
           else if k1 >= max orelse k2 >= max then max
blanchet@33192
  1171
           else Int.min (max, k1 * k2)
blanchet@33192
  1172
         end
blanchet@33192
  1173
       | Type (@{type_name itself}, _) => 1
blanchet@33192
  1174
       | @{typ prop} => 2
blanchet@33192
  1175
       | @{typ bool} => 2
blanchet@33192
  1176
       | @{typ unit} => 1
blanchet@33192
  1177
       | Type _ =>
blanchet@35070
  1178
         (case datatype_constrs hol_ctxt T of
blanchet@34126
  1179
            [] => if is_integer_type T orelse is_bit_type T then 0
blanchet@34126
  1180
                  else raise SAME ()
blanchet@33192
  1181
          | constrs =>
blanchet@33192
  1182
            let
blanchet@33192
  1183
              val constr_cards =
blanchet@35280
  1184
                map (Integer.prod o map (aux (T :: avoid)) o binder_types o snd)
blanchet@35280
  1185
                    constrs
blanchet@33192
  1186
            in
blanchet@34121
  1187
              if exists (curry (op =) 0) constr_cards then 0
blanchet@33192
  1188
              else Integer.sum constr_cards
blanchet@33192
  1189
            end)
blanchet@33192
  1190
       | _ => raise SAME ())
blanchet@34123
  1191
      handle SAME () =>
blanchet@34123
  1192
             AList.lookup (op =) assigns T |> the_default default_card
blanchet@33192
  1193
  in Int.min (max, aux [] T) end
blanchet@33192
  1194
blanchet@35665
  1195
val small_type_max_card = 5
blanchet@35665
  1196
blanchet@35070
  1197
(* hol_context -> typ -> bool *)
blanchet@35384
  1198
fun is_finite_type hol_ctxt T =
blanchet@35665
  1199
  bounded_exact_card_of_type hol_ctxt [] 1 2 [] T > 0
blanchet@35665
  1200
(* hol_context -> typ -> bool *)
blanchet@35665
  1201
fun is_small_finite_type hol_ctxt T =
blanchet@35665
  1202
  let val n = bounded_exact_card_of_type hol_ctxt [] 1 2 [] T in
blanchet@35665
  1203
    n > 0 andalso n <= small_type_max_card
blanchet@35665
  1204
  end
blanchet@33192
  1205
blanchet@33192
  1206
(* term -> bool *)
blanchet@33192
  1207
fun is_ground_term (t1 $ t2) = is_ground_term t1 andalso is_ground_term t2
blanchet@33192
  1208
  | is_ground_term (Const _) = true
blanchet@33192
  1209
  | is_ground_term _ = false
blanchet@33192
  1210
blanchet@33192
  1211
(* term -> word -> word *)
blanchet@33192
  1212
fun hashw_term (t1 $ t2) = Polyhash.hashw (hashw_term t1, hashw_term t2)
blanchet@33192
  1213
  | hashw_term (Const (s, _)) = Polyhash.hashw_string (s, 0w0)
blanchet@33192
  1214
  | hashw_term _ = 0w0
blanchet@33192
  1215
(* term -> int *)
blanchet@33192
  1216
val hash_term = Word.toInt o hashw_term
blanchet@33192
  1217
blanchet@33192
  1218
(* term list -> (indexname * typ) list *)
blanchet@33192
  1219
fun special_bounds ts =
wenzelm@35408
  1220
  fold Term.add_vars ts [] |> sort (Term_Ord.fast_indexname_ord o pairself fst)
blanchet@33192
  1221
blanchet@33192
  1222
(* indexname * typ -> term -> term *)
blanchet@33192
  1223
fun abs_var ((s, j), T) body = Abs (s, T, abstract_over (Var ((s, j), T), body))
blanchet@33192
  1224
blanchet@33571
  1225
(* theory -> string -> bool *)
blanchet@33571
  1226
fun is_funky_typedef_name thy s =
blanchet@34121
  1227
  member (op =) [@{type_name unit}, @{type_name "*"}, @{type_name "+"},
blanchet@34936
  1228
                 @{type_name int}] s orelse
blanchet@34936
  1229
  is_frac_type thy (Type (s, []))
blanchet@35070
  1230
(* theory -> typ -> bool *)
blanchet@33571
  1231
fun is_funky_typedef thy (Type (s, _)) = is_funky_typedef_name thy s
blanchet@33571
  1232
  | is_funky_typedef _ _ = false
blanchet@33192
  1233
(* term -> bool *)
blanchet@33192
  1234
fun is_arity_type_axiom (Const (@{const_name HOL.type_class}, _)
blanchet@33192
  1235
                         $ Const (@{const_name TYPE}, _)) = true
blanchet@33192
  1236
  | is_arity_type_axiom _ = false
blanchet@33192
  1237
(* theory -> bool -> term -> bool *)
blanchet@33197
  1238
fun is_typedef_axiom thy boring (@{const "==>"} $ _ $ t2) =
blanchet@33197
  1239
    is_typedef_axiom thy boring t2
blanchet@33197
  1240
  | is_typedef_axiom thy boring
blanchet@33192
  1241
        (@{const Trueprop} $ (Const (@{const_name Typedef.type_definition}, _)
blanchet@35665
  1242
         $ Const (_, Type (@{type_name fun}, [Type (s, _), _]))
blanchet@35665
  1243
         $ Const _ $ _)) =
blanchet@33571
  1244
    boring <> is_funky_typedef_name thy s andalso is_typedef thy s
blanchet@33192
  1245
  | is_typedef_axiom _ _ _ = false
blanchet@33192
  1246
blanchet@33192
  1247
(* Distinguishes between (1) constant definition axioms, (2) type arity and
blanchet@33192
  1248
   typedef axioms, and (3) other axioms, and returns the pair ((1), (3)).
blanchet@33192
  1249
   Typedef axioms are uninteresting to Nitpick, because it can retrieve them
blanchet@33192
  1250
   using "typedef_info". *)
blanchet@33192
  1251
(* theory -> (string * term) list -> string list -> term list * term list *)
blanchet@33192
  1252
fun partition_axioms_by_definitionality thy axioms def_names =
blanchet@33192
  1253
  let
blanchet@33192
  1254
    val axioms = sort (fast_string_ord o pairself fst) axioms
blanchet@33192
  1255
    val defs = OrdList.inter (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1256
    val nondefs =
blanchet@33192
  1257
      OrdList.subtract (fast_string_ord o apsnd fst) def_names axioms
blanchet@33192
  1258
      |> filter_out ((is_arity_type_axiom orf is_typedef_axiom thy true) o snd)
blanchet@33192
  1259
  in pairself (map snd) (defs, nondefs) end
blanchet@33192
  1260
blanchet@33197
  1261
(* Ideally we would check against "Complex_Main", not "Refute", but any theory
blanchet@33197
  1262
   will do as long as it contains all the "axioms" and "axiomatization"
blanchet@33192
  1263
   commands. *)
blanchet@33192
  1264
(* theory -> bool *)
blanchet@33192
  1265
fun is_built_in_theory thy = Theory.subthy (thy, @{theory Refute})
blanchet@33192
  1266
blanchet@33192
  1267
(* term -> bool *)
blanchet@35283
  1268
val is_trivial_definition =
blanchet@35283
  1269
  the_default false o try (op aconv o Logic.dest_equals)
blanchet@33192
  1270
val is_plain_definition =
blanchet@33192
  1271
  let
blanchet@33192
  1272
    (* term -> bool *)
blanchet@33192
  1273
    fun do_lhs t1 =
blanchet@33192
  1274
      case strip_comb t1 of
blanchet@34936
  1275
        (Const _, args) =>
blanchet@34936
  1276
        forall is_Var args andalso not (has_duplicates (op =) args)
blanchet@33192
  1277
      | _ => false
blanchet@33192
  1278
    fun do_eq (Const (@{const_name "=="}, _) $ t1 $ _) = do_lhs t1
blanchet@33192
  1279
      | do_eq (@{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ _)) =
blanchet@33192
  1280
        do_lhs t1
blanchet@33192
  1281
      | do_eq _ = false
blanchet@33192
  1282
  in do_eq end
blanchet@33192
  1283
blanchet@35335
  1284
(* theory -> (term * term) list -> term list * term list * term list *)
blanchet@35335
  1285
fun all_axioms_of thy subst =
blanchet@33192
  1286
  let
blanchet@33192
  1287
    (* theory list -> term list *)
blanchet@35335
  1288
    val axioms_of_thys =
blanchet@35335
  1289
      maps Thm.axioms_of #> map (apsnd (subst_atomic subst o prop_of))
blanchet@33192
  1290
    val specs = Defs.all_specifications_of (Theory.defs_of thy)
wenzelm@33701
  1291
    val def_names = specs |> maps snd |> map_filter #def
blanchet@33197
  1292
                    |> OrdList.make fast_string_ord
blanchet@33192
  1293
    val thys = thy :: Theory.ancestors_of thy
blanchet@33192
  1294
    val (built_in_thys, user_thys) = List.partition is_built_in_theory thys
blanchet@33192
  1295
    val built_in_axioms = axioms_of_thys built_in_thys
blanchet@33192
  1296
    val user_axioms = axioms_of_thys user_thys
blanchet@33192
  1297
    val (built_in_defs, built_in_nondefs) =
blanchet@33192
  1298
      partition_axioms_by_definitionality thy built_in_axioms def_names
blanchet@33197
  1299
      ||> filter (is_typedef_axiom thy false)
blanchet@33192
  1300
    val (user_defs, user_nondefs) =
blanchet@33192
  1301
      partition_axioms_by_definitionality thy user_axioms def_names
blanchet@33197
  1302
    val (built_in_nondefs, user_nondefs) =
blanchet@33197
  1303
      List.partition (is_typedef_axiom thy false) user_nondefs
blanchet@33197
  1304
      |>> append built_in_nondefs
blanchet@34121
  1305
    val defs =
blanchet@34121
  1306
      (thy |> PureThy.all_thms_of
blanchet@34121
  1307
           |> filter (curry (op =) Thm.definitionK o Thm.get_kind o snd)
blanchet@35283
  1308
           |> map (prop_of o snd)
blanchet@35283
  1309
           |> filter_out is_trivial_definition
blanchet@35283
  1310
           |> filter is_plain_definition) @
blanchet@34121
  1311
      user_defs @ built_in_defs
blanchet@33192
  1312
  in (defs, built_in_nondefs, user_nondefs) end
blanchet@33192
  1313
blanchet@35220
  1314
(* theory -> (typ option * bool) list -> bool -> styp -> int option *)
blanchet@35220
  1315
fun arity_of_built_in_const thy stds fast_descrs (s, T) =
blanchet@33192
  1316
  if s = @{const_name If} then
blanchet@33192
  1317
    if nth_range_type 3 T = @{typ bool} then NONE else SOME 3
blanchet@35220
  1318
  else
blanchet@35220
  1319
    let val std_nats = is_standard_datatype thy stds nat_T in
blanchet@35220
  1320
      case AList.lookup (op =)
blanchet@35220
  1321
                    (built_in_consts
blanchet@35220
  1322
                     |> std_nats ? append built_in_nat_consts
blanchet@35220
  1323
                     |> fast_descrs ? append built_in_descr_consts) s of
blanchet@35220
  1324
        SOME n => SOME n
blanchet@35220
  1325
      | NONE =>
blanchet@35220
  1326
        case AList.lookup (op =)
blanchet@35220
  1327
                 (built_in_typed_consts
blanchet@35220
  1328
                  |> std_nats ? append built_in_typed_nat_consts)
blanchet@35220
  1329
                 (s, unarize_type T) of
blanchet@35220
  1330
          SOME n => SOME n
blanchet@35220
  1331
        | NONE =>
blanchet@35280
  1332
          case s of
blanchet@35280
  1333
            @{const_name zero_class.zero} =>
blanchet@35280
  1334
            if is_iterator_type T then SOME 0 else NONE
blanchet@35280
  1335
          | @{const_name Suc} =>
blanchet@35280
  1336
            if is_iterator_type (domain_type T) then SOME 0 else NONE
blanchet@35280
  1337
          | _ => if is_fun_type T andalso is_set_type (domain_type T) then
blanchet@35280
  1338
                   AList.lookup (op =) built_in_set_consts s
blanchet@35280
  1339
                 else
blanchet@35280
  1340
                   NONE
blanchet@35220
  1341
    end
blanchet@35220
  1342
(* theory -> (typ option * bool) list -> bool -> styp -> bool *)
blanchet@35220
  1343
val is_built_in_const = is_some oooo arity_of_built_in_const
blanchet@33192
  1344
blanchet@33192
  1345
(* This function is designed to work for both real definition axioms and
blanchet@33192
  1346
   simplification rules (equational specifications). *)
blanchet@33192
  1347
(* term -> term *)
blanchet@33192
  1348
fun term_under_def t =
blanchet@33192
  1349
  case t of
blanchet@33192
  1350
    @{const "==>"} $ _ $ t2 => term_under_def t2
blanchet@33192
  1351
  | Const (@{const_name "=="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1352
  | @{const Trueprop} $ t1 => term_under_def t1
blanchet@33192
  1353
  | Const (@{const_name "op ="}, _) $ t1 $ _ => term_under_def t1
blanchet@33192
  1354
  | Abs (_, _, t') => term_under_def t'
blanchet@33192
  1355
  | t1 $ _ => term_under_def t1
blanchet@33192
  1356
  | _ => t
blanchet@33192
  1357
blanchet@33192
  1358
(* Here we crucially rely on "Refute.specialize_type" performing a preorder
blanchet@33192
  1359
   traversal of the term, without which the wrong occurrence of a constant could
blanchet@33192
  1360
   be matched in the face of overloading. *)
blanchet@35220
  1361
(* theory -> (typ option * bool) list -> bool -> const_table -> styp
blanchet@35220
  1362
   -> term list *)
blanchet@35220
  1363
fun def_props_for_const thy stds fast_descrs table (x as (s, _)) =
blanchet@35220
  1364
  if is_built_in_const thy stds fast_descrs x then
blanchet@33192
  1365
    []
blanchet@33192
  1366
  else
blanchet@33192
  1367
    these (Symtab.lookup table s)
blanchet@33192
  1368
    |> map_filter (try (Refute.specialize_type thy x))
blanchet@34121
  1369
    |> filter (curry (op =) (Const x) o term_under_def)
blanchet@33192
  1370
blanchet@35280
  1371
(* term -> term option *)
blanchet@35280
  1372
fun normalized_rhs_of t =
blanchet@33192
  1373
  let
blanchet@33743
  1374
    (* term option -> term option *)
blanchet@33743
  1375
    fun aux (v as Var _) (SOME t) = SOME (lambda v t)
blanchet@35280
  1376
      | aux (c as Const (@{const_name TYPE}, _)) (SOME t) = SOME (lambda c t)
blanchet@33743
  1377
      | aux _ _ = NONE
blanchet@33192
  1378
    val (lhs, rhs) =
blanchet@33192
  1379
      case t of
blanchet@33192
  1380
        Const (@{const_name "=="}, _) $ t1 $ t2 => (t1, t2)
blanchet@33192
  1381
      | @{const Trueprop} $ (Const (@{const_name "op ="}, _) $ t1 $ t2) =>
blanchet@33192
  1382
        (t1, t2)
blanchet@33232
  1383
      | _ => raise TERM ("Nitpick_HOL.normalized_rhs_of", [t])
blanchet@33192
  1384
    val args = strip_comb lhs |> snd
blanchet@33743
  1385
  in fold_rev aux args (SOME rhs) end
blanchet@33192
  1386
blanchet@33192
  1387
(* theory -> const_table -> styp -> term option *)
blanchet@33192
  1388
fun def_of_const thy table (x as (s, _)) =
blanchet@35220
  1389
  if is_built_in_const thy [(NONE, false)] false x orelse
blanchet@35220
  1390
     original_name s <> s then
blanchet@33192
  1391
    NONE
blanchet@33192
  1392
  else
blanchet@35220
  1393
    x |> def_props_for_const thy [(NONE, false)] false table |> List.last
blanchet@35280
  1394
      |> normalized_rhs_of |> Option.map (prefix_abs_vars s)
blanchet@33192
  1395
    handle List.Empty => NONE
blanchet@33192
  1396
blanchet@33192
  1397
(* term -> fixpoint_kind *)
blanchet@33192
  1398
fun fixpoint_kind_of_rhs (Abs (_, _, t)) = fixpoint_kind_of_rhs t
blanchet@33192
  1399
  | fixpoint_kind_of_rhs (Const (@{const_name lfp}, _) $ Abs _) = Lfp
blanchet@33192
  1400
  | fixpoint_kind_of_rhs (Const (@{const_name gfp}, _) $ Abs _) = Gfp
blanchet@33192
  1401
  | fixpoint_kind_of_rhs _ = NoFp
blanchet@33192
  1402
blanchet@33192
  1403
(* theory -> const_table -> term -> bool *)
blanchet@33192
  1404
fun is_mutually_inductive_pred_def thy table t =
blanchet@33192
  1405
  let
blanchet@33192
  1406
    (* term -> bool *)
blanchet@33192
  1407
    fun is_good_arg (Bound _) = true
blanchet@33192
  1408
      | is_good_arg (Const (s, _)) =
blanchet@34936
  1409
        s = @{const_name True} orelse s = @{const_name False} orelse
blanchet@34936
  1410
        s = @{const_name undefined}
blanchet@33192
  1411
      | is_good_arg _ = false
blanchet@33192
  1412
  in
blanchet@33192
  1413
    case t |> strip_abs_body |> strip_comb of
blanchet@33192
  1414
      (Const x, ts as (_ :: _)) =>
blanchet@33192
  1415
      (case def_of_const thy table x of
blanchet@33192
  1416
         SOME t' => fixpoint_kind_of_rhs t' <> NoFp andalso forall is_good_arg ts
blanchet@33192
  1417
       | NONE => false)
blanchet@33192
  1418
    | _ => false
blanchet@33192
  1419
  end
blanchet@33192
  1420
(* theory -> const_table -> term -> term *)
blanchet@33192
  1421
fun unfold_mutually_inductive_preds thy table =
blanchet@33192
  1422
  map_aterms (fn t as Const x =>
blanchet@33192
  1423
                 (case def_of_const thy table x of
blanchet@33192
  1424
                    SOME t' =>
blanchet@33192
  1425
                    let val t' = Envir.eta_contract t' in
blanchet@33192
  1426
                      if is_mutually_inductive_pred_def thy table t' then t'
blanchet@33192
  1427
                      else t
blanchet@33192
  1428
                    end
blanchet@33192
  1429
                 | NONE => t)
blanchet@33192
  1430
               | t => t)
blanchet@33192
  1431
blanchet@33192
  1432
(* term -> string * term *)
blanchet@33192
  1433
fun pair_for_prop t =
blanchet@33192
  1434
  case term_under_def t of
blanchet@33192
  1435
    Const (s, _) => (s, t)
blanchet@33232
  1436
  | t' => raise TERM ("Nitpick_HOL.pair_for_prop", [t, t'])
blanchet@33192
  1437
blanchet@35335
  1438
(* (Proof.context -> term list) -> Proof.context -> (term * term) list
blanchet@35335
  1439
   -> const_table *)
blanchet@35335
  1440
fun table_for get ctxt subst =
blanchet@35335
  1441
  ctxt |> get |> map (pair_for_prop o subst_atomic subst)
blanchet@35335
  1442
       |> AList.group (op =) |> Symtab.make
blanchet@33192
  1443
blanchet@35220
  1444
(* theory -> (typ option * bool) list -> (string * int) list *)
blanchet@35220
  1445
fun case_const_names thy stds =
blanchet@33192
  1446
  Symtab.fold (fn (dtype_s, {index, descr, case_name, ...}) =>
blanchet@35220
  1447
                  if is_basic_datatype thy stds dtype_s then
blanchet@33192
  1448
                    I
blanchet@33192
  1449
                  else
blanchet@33192
  1450
                    cons (case_name, AList.lookup (op =) descr index
blanchet@33192
  1451
                                     |> the |> #3 |> length))
blanchet@33192
  1452
              (Datatype.get_all thy) [] @
blanchet@33583
  1453
  map (apsnd length o snd) (#codatatypes (Data.get thy))
blanchet@33192
  1454
blanchet@35335
  1455
(* Proof.context -> (term * term) list -> term list -> const_table *)
blanchet@35335
  1456
fun const_def_table ctxt subst ts =
blanchet@35335
  1457
  table_for (map prop_of o Nitpick_Defs.get) ctxt subst
blanchet@33192
  1458
  |> fold (fn (s, t) => Symtab.map_default (s, []) (cons t))
blanchet@33192
  1459
          (map pair_for_prop ts)
blanchet@33192
  1460
(* term list -> const_table *)
blanchet@33192
  1461
fun const_nondef_table ts =
blanchet@33192
  1462
  fold (fn t => append (map (fn s => (s, t)) (Term.add_const_names t []))) ts []
blanchet@33192
  1463
  |> AList.group (op =) |> Symtab.make
blanchet@35335
  1464
(* Proof.context -> (term * term) list -> const_table *)
blanchet@33192
  1465
val const_simp_table = table_for (map prop_of o Nitpick_Simps.get)
blanchet@33192
  1466
val const_psimp_table = table_for (map prop_of o Nitpick_Psimps.get)
blanchet@35335
  1467
(* Proof.context -> (term * term) list -> const_table -> const_table *)
blanchet@35335
  1468
fun inductive_intro_table ctxt subst def_table =
blanchet@33192
  1469
  table_for (map (unfold_mutually_inductive_preds (ProofContext.theory_of ctxt)
blanchet@33192
  1470
                                                  def_table o prop_of)
blanchet@35335
  1471
             o Nitpick_Intros.get) ctxt subst
blanchet@33192
  1472
(* theory -> term list Inttab.table *)
blanchet@33192
  1473
fun ground_theorem_table thy =
blanchet@33192
  1474
  fold ((fn @{const Trueprop} $ t1 =>
blanchet@33192
  1475
            is_ground_term t1 ? Inttab.map_default (hash_term t1, []) (cons t1)
blanchet@33192
  1476
          | _ => I) o prop_of o snd) (PureThy.all_thms_of thy) Inttab.empty
blanchet@33192
  1477
blanchet@33192
  1478
val basic_ersatz_table =
blanchet@33192
  1479
  [(@{const_name prod_case}, @{const_name split}),
blanchet@33192
  1480
   (@{const_name card}, @{const_name card'}),
blanchet@33192
  1481
   (@{const_name setsum}, @{const_name setsum'}),
blanchet@33192
  1482
   (@{const_name fold_graph}, @{const_name fold_graph'}),
blanchet@33192
  1483
   (@{const_name wf}, @{const_name wf'}),
blanchet@33192
  1484
   (@{const_name wf_wfrec}, @{const_name wf_wfrec'}),
blanchet@33192
  1485
   (@{const_name wfrec}, @{const_name wfrec'})]
blanchet@33192
  1486
blanchet@33192
  1487
(* theory -> (string * string) list *)
blanchet@33192
  1488
fun ersatz_table thy =
blanchet@33583
  1489
  fold (append o snd) (#frac_types (Data.get thy)) basic_ersatz_table
blanchet@33192
  1490
blanchet@33192
  1491
(* const_table Unsynchronized.ref -> string -> term list -> unit *)
blanchet@33192
  1492
fun add_simps simp_table s eqs =
blanchet@33192
  1493
  Unsynchronized.change simp_table
blanchet@33192
  1494
      (Symtab.update (s, eqs @ these (Symtab.lookup (!simp_table) s)))
blanchet@33192
  1495
blanchet@34936
  1496
(* theory -> styp -> term list *)
blanchet@34936
  1497
fun inverse_axioms_for_rep_fun thy (x as (_, T)) =
blanchet@34936
  1498
  let val abs_T = domain_type T in
blanchet@34936
  1499
    typedef_info thy (fst (dest_Type abs_T)) |> the
blanchet@34936
  1500
    |> pairf #Abs_inverse #Rep_inverse
blanchet@34936
  1501
    |> pairself (Refute.specialize_type thy x o prop_of o the)
blanchet@34936
  1502
    ||> single |> op ::
blanchet@34936
  1503
  end
blanchet@35070
  1504
(* theory -> string * typ list -> term list *)
blanchet@35280
  1505
fun optimized_typedef_axioms thy (abs_z as (abs_s, _)) =
blanchet@34936
  1506
  let val abs_T = Type abs_z in
blanchet@33192
  1507
    if is_univ_typedef thy abs_T then
blanchet@33192
  1508
      []
blanchet@33192
  1509
    else case typedef_info thy abs_s of
blanchet@35280
  1510
      SOME {abs_type, rep_type, Rep_name, prop_of_Rep, set_name, ...} =>
blanchet@33192
  1511
      let
blanchet@35311
  1512
        val rep_T = varify_and_instantiate_type thy abs_type abs_T rep_type
blanchet@33192
  1513
        val rep_t = Const (Rep_name, abs_T --> rep_T)
blanchet@33192
  1514
        val set_t = Const (set_name, rep_T --> bool_T)
blanchet@33192
  1515
        val set_t' =
blanchet@33192
  1516
          prop_of_Rep |> HOLogic.dest_Trueprop
blanchet@33192
  1517
                      |> Refute.specialize_type thy (dest_Const rep_t)
blanchet@33192
  1518
                      |> HOLogic.dest_mem |> snd
blanchet@33192
  1519
      in
blanchet@33192
  1520
        [HOLogic.all_const abs_T
blanchet@33192
  1521
         $ Abs (Name.uu, abs_T, set_t $ (rep_t $ Bound 0))]
blanchet@33192
  1522
        |> set_t <> set_t' ? cons (HOLogic.mk_eq (set_t, set_t'))
blanchet@33192
  1523
        |> map HOLogic.mk_Trueprop
blanchet@33192
  1524
      end
blanchet@33192
  1525
    | NONE => []
blanchet@33192
  1526
  end
blanchet@35311
  1527
(* Proof.context -> string * typ list -> term list *)
blanchet@35311
  1528
fun optimized_quot_type_axioms ctxt stds abs_z =
blanchet@34936
  1529
  let
blanchet@35311
  1530
    val thy = ProofContext.theory_of ctxt
blanchet@34936
  1531
    val abs_T = Type abs_z
blanchet@34936
  1532
    val rep_T = rep_type_for_quot_type thy abs_T
blanchet@34936
  1533
    val equiv_rel = equiv_relation_for_quot_type thy abs_T
blanchet@34936
  1534
    val a_var = Var (("a", 0), abs_T)
blanchet@34936
  1535
    val x_var = Var (("x", 0), rep_T)
blanchet@34936
  1536
    val y_var = Var (("y", 0), rep_T)
blanchet@34936
  1537
    val x = (@{const_name Quot}, rep_T --> abs_T)
blanchet@35220
  1538
    val sel_a_t = select_nth_constr_arg thy stds x a_var 0 rep_T
blanchet@35311
  1539
    val normal_t = Const (quot_normal_name_for_type ctxt abs_T, rep_T --> rep_T)
blanchet@34936
  1540
    val normal_x = normal_t $ x_var
blanchet@34936
  1541
    val normal_y = normal_t $ y_var
blanchet@34936
  1542
    val is_unknown_t = Const (@{const_name is_unknown}, rep_T --> bool_T)
blanchet@34936
  1543
  in
blanchet@34982
  1544
    [Logic.mk_equals (normal_t $ sel_a_t, sel_a_t),
blanchet@34936
  1545
     Logic.list_implies
blanchet@34982
  1546
         ([@{const Not} $ (is_unknown_t $ normal_x),
blanchet@34936
  1547
           @{const Not} $ (is_unknown_t $ normal_y),
blanchet@34936
  1548
           equiv_rel $ x_var $ y_var] |> map HOLogic.mk_Trueprop,
blanchet@34936
  1549
           Logic.mk_equals (normal_x, normal_y)),
blanchet@35388
  1550
     Logic.list_implies
blanchet@35388
  1551
         ([HOLogic.mk_Trueprop (@{const Not} $ (is_unknown_t $ normal_x)),
blanchet@35388
  1552
           HOLogic.mk_Trueprop (@{const Not} $ HOLogic.mk_eq (normal_x, x_var))],
blanchet@35388
  1553
          HOLogic.mk_Trueprop (equiv_rel $ x_var $ normal_x))]
blanchet@33864
  1554
  end
blanchet@33192
  1555
blanchet@35220
  1556
(* theory -> (typ option * bool) list -> int * styp -> term *)
blanchet@35220
  1557
fun constr_case_body thy stds (j, (x as (_, T))) =
blanchet@33192
  1558
  let val arg_Ts = binder_types T in
blanchet@35220
  1559
    list_comb (Bound j, map2 (select_nth_constr_arg thy stds x (Bound 0))
blanchet@33192
  1560
                             (index_seq 0 (length arg_Ts)) arg_Ts)
blanchet@33192
  1561
  end
blanchet@35070
  1562
(* hol_context -> typ -> int * styp -> term -> term *)
blanchet@35220
  1563
fun add_constr_case (hol_ctxt as {thy, stds, ...}) res_T (j, x) res_t =
blanchet@34124
  1564
  Const (@{const_name If}, bool_T --> res_T --> res_T --> res_T)
blanchet@35220
  1565
  $ discriminate_value hol_ctxt x (Bound 0) $ constr_case_body thy stds (j, x)
blanchet@33580
  1566
  $ res_t
blanchet@35070
  1567
(* hol_context -> typ -> typ -> term *)
blanchet@35220
  1568
fun optimized_case_def (hol_ctxt as {thy, stds, ...}) dataT res_T =
blanchet@33192
  1569
  let
blanchet@35070
  1570
    val xs = datatype_constrs hol_ctxt dataT
blanchet@35179
  1571
    val func_Ts = map ((fn T => binder_types T ---> res_T) o snd) xs
blanchet@35179
  1572
    val (xs', x) = split_last xs
blanchet@33192
  1573
  in
blanchet@35220
  1574
    constr_case_body thy stds (1, x)
blanchet@35179
  1575
    |> fold_rev (add_constr_case hol_ctxt res_T) (length xs downto 2 ~~ xs')
blanchet@33192
  1576
    |> fold_rev (curry absdummy) (func_Ts @ [dataT])
blanchet@33192
  1577
  end
blanchet@33192
  1578
blanchet@35070
  1579
(* hol_context -> string -> typ -> typ -> term -> term *)
blanchet@35220
  1580
fun optimized_record_get (hol_ctxt as {thy, stds, ...}) s rec_T res_T t =
blanchet@35070
  1581
  let val constr_x = hd (datatype_constrs hol_ctxt rec_T) in
blanchet@33192
  1582
    case no_of_record_field thy s rec_T of
blanchet@33192
  1583
      ~1 => (case rec_T of
blanchet@33192
  1584
               Type (_, Ts as _ :: _) =>
blanchet@33192
  1585
               let
blanchet@33192
  1586
                 val rec_T' = List.last Ts
blanchet@33192
  1587
                 val j = num_record_fields thy rec_T - 1
blanchet@33192
  1588
               in
blanchet@35220
  1589
                 select_nth_constr_arg thy stds constr_x t j res_T
blanchet@35070
  1590
                 |> optimized_record_get hol_ctxt s rec_T' res_T
blanchet@33192
  1591
               end
blanchet@33232
  1592
             | _ => raise TYPE ("Nitpick_HOL.optimized_record_get", [rec_T],
blanchet@33232
  1593
                                []))
blanchet@35220
  1594
    | j => select_nth_constr_arg thy stds constr_x t j res_T
blanchet@33192
  1595
  end
blanchet@35070
  1596
(* hol_context -> string -> typ -> term -> term -> term *)
blanchet@35220
  1597
fun optimized_record_update (hol_ctxt as {thy, stds, ...}) s rec_T fun_t rec_t =
blanchet@33192
  1598
  let
blanchet@35070
  1599
    val constr_x as (_, constr_T) = hd (datatype_constrs hol_ctxt rec_T)
blanchet@33192
  1600
    val Ts = binder_types constr_T
blanchet@33192
  1601
    val n = length Ts
blanchet@33192
  1602
    val special_j = no_of_record_field thy s rec_T
blanchet@35220
  1603
    val ts =
blanchet@35220
  1604
      map2 (fn j => fn T =>
blanchet@35220
  1605
               let val t = select_nth_constr_arg thy stds constr_x rec_t j T in
blanchet@35220
  1606
                 if j = special_j then
blanchet@35220
  1607
                   betapply (fun_t, t)
blanchet@35220
  1608
                 else if j = n - 1 andalso special_j = ~1 then
blanchet@35220
  1609
                   optimized_record_update hol_ctxt s
blanchet@35220
  1610
                       (rec_T |> dest_Type |> snd |> List.last) fun_t t
blanchet@35220
  1611
                 else
blanchet@35220
  1612
                   t
blanchet@35220
  1613
               end) (index_seq 0 n) Ts
blanchet@33192
  1614
  in list_comb (Const constr_x, ts) end
blanchet@33192
  1615
blanchet@33192
  1616
(* theory -> const_table -> string * typ -> fixpoint_kind *)
blanchet@33192
  1617
fun fixpoint_kind_of_const thy table x =
blanchet@35220
  1618
  if is_built_in_const thy [(NONE, false)] false x then
blanchet@33192
  1619
    NoFp
blanchet@33192
  1620
  else
blanchet@33192
  1621
    fixpoint_kind_of_rhs (the (def_of_const thy table x))
blanchet@33192
  1622
    handle Option.Option => NoFp
blanchet@33192
  1623
blanchet@35070
  1624
(* hol_context -> styp -> bool *)
blanchet@35220
  1625
fun is_real_inductive_pred ({thy, stds, fast_descrs, def_table, intro_table,
blanchet@35220
  1626
                             ...} : hol_context) x =
blanchet@35220
  1627
  fixpoint_kind_of_const thy def_table x <> NoFp andalso
blanchet@35220
  1628
  not (null (def_props_for_const thy stds fast_descrs intro_table x))
blanchet@35220
  1629
fun is_real_equational_fun ({thy, stds, fast_descrs, simp_table, psimp_table,
blanchet@35220
  1630
                             ...} : hol_context) x =
blanchet@35220
  1631
  exists (fn table => not (null (def_props_for_const thy stds fast_descrs table
blanchet@35220
  1632
                                                     x)))
blanchet@33192
  1633
         [!simp_table, psimp_table]
blanchet@35070
  1634
fun is_inductive_pred hol_ctxt =
blanchet@35070
  1635
  is_real_inductive_pred hol_ctxt andf (not o is_real_equational_fun hol_ctxt)
blanchet@35280
  1636
fun is_equational_fun hol_ctxt =
blanchet@35665
  1637
  (is_real_equational_fun hol_ctxt orf is_real_inductive_pred hol_ctxt orf
blanchet@35665
  1638
   (String.isPrefix ubfp_prefix orf String.isPrefix lbfp_prefix) o fst)
blanchet@33192
  1639
blanchet@33192
  1640
(* term * term -> term *)
blanchet@33192
  1641
fun s_betapply (Const (@{const_name If}, _) $ @{const True} $ t, _) = t
blanchet@33192
  1642
  | s_betapply (Const (@{const_name If}, _) $ @{const False} $ _, t) = t
blanchet@33192
  1643
  | s_betapply p = betapply p
blanchet@33192
  1644
(* term * term list -> term *)
blanchet@33192
  1645
val s_betapplys = Library.foldl s_betapply
blanchet@33192
  1646
blanchet@33192
  1647
(* term -> term *)
blanchet@33192
  1648
fun lhs_of_equation t =
blanchet@33192
  1649
  case t of
blanchet@33192
  1650
    Const (@{const_name all}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1651
  | Const (@{const_name "=="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1652
  | @{const "==>"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1653
  | @{const Trueprop} $ t1 => lhs_of_equation t1
blanchet@33192
  1654
  | Const (@{const_name All}, _) $ Abs (_, _, t1) => lhs_of_equation t1
blanchet@33192
  1655
  | Const (@{const_name "op ="}, _) $ t1 $ _ => SOME t1
blanchet@33192
  1656
  | @{const "op -->"} $ _ $ t2 => lhs_of_equation t2
blanchet@33192
  1657
  | _ => NONE
blanchet@33192
  1658
(* theory -> term -> bool *)
blanchet@33192
  1659
fun is_constr_pattern _ (Bound _) = true
blanchet@33864
  1660
  | is_constr_pattern _ (Var _) = true
blanchet@33192
  1661
  | is_constr_pattern thy t =
blanchet@33192
  1662
    case strip_comb t of
blanchet@35280
  1663
      (Const x, args) =>
blanchet@33192
  1664
      is_constr_like thy x andalso forall (is_constr_pattern thy) args
blanchet@33192
  1665
    | _ => false
blanchet@33192
  1666
fun is_constr_pattern_lhs thy t =
blanchet@33192
  1667
  forall (is_constr_pattern thy) (snd (strip_comb t))
blanchet@33192
  1668
fun is_constr_pattern_formula thy t =
blanchet@33192
  1669
  case lhs_of_equation t of
blanchet@33192
  1670
    SOME t' => is_constr_pattern_lhs thy t'
blanchet@33192
  1671
  | NONE => false
blanchet@33192
  1672
blanchet@35070
  1673
(* Prevents divergence in case of cyclic or infinite definition dependencies. *)
blanchet@33747
  1674
val unfold_max_depth = 255
blanchet@33192
  1675
blanchet@35070
  1676
(* hol_context -> term -> term *)
blanchet@35284
  1677
fun unfold_defs_in_term (hol_ctxt as {thy, ctxt, stds, fast_descrs, case_names,
blanchet@35280
  1678
                                      def_table, ground_thm_table, ersatz_table,
blanchet@35280
  1679
                                      ...}) =
blanchet@33192
  1680
  let
blanchet@33192
  1681
    (* int -> typ list -> term -> term *)
blanchet@33192
  1682
    fun do_term depth Ts t =
blanchet@33192
  1683
      case t of
blanchet@33192
  1684
        (t0 as Const (@{const_name Int.number_class.number_of},
blanchet@35665
  1685
                      Type (@{type_name fun}, [_, ran_T]))) $ t1 =>
blanchet@33192
  1686
        ((if is_number_type thy ran_T then
blanchet@33192
  1687
            let
blanchet@33192
  1688
              val j = t1 |> HOLogic.dest_numeral
blanchet@33882
  1689
                         |> ran_T = nat_T ? Integer.max 0
blanchet@33192
  1690
              val s = numeral_prefix ^ signed_string_of_int j
blanchet@33192
  1691
            in
blanchet@35220
  1692
              if is_integer_like_type ran_T then
blanchet@35220
  1693
                if is_standard_datatype thy stds ran_T then
blanchet@35220
  1694
                  Const (s, ran_T)
blanchet@35220
  1695
                else
blanchet@35220
  1696
                  funpow j (curry (op $) (suc_const ran_T)) (zero_const ran_T)
blanchet@33192
  1697
              else
blanchet@33192
  1698
                do_term depth Ts (Const (@{const_name of_int}, int_T --> ran_T)
blanchet@33192
  1699
                                  $ Const (s, int_T))
blanchet@33192
  1700
            end
blanchet@33192
  1701
            handle TERM _ => raise SAME ()
blanchet@33192
  1702
          else
blanchet@33192
  1703
            raise SAME ())
blanchet@33192
  1704
         handle SAME () => betapply (do_term depth Ts t0, do_term depth Ts t1))
blanchet@33864
  1705
      | Const (@{const_name refl_on}, T) $ Const (@{const_name top}, _) $ t2 =>
blanchet@33192
  1706
        do_const depth Ts t (@{const_name refl'}, range_type T) [t2]
blanchet@35280
  1707
      | (t0 as Const (@{const_name Sigma}, _)) $ t1 $ (t2 as Abs (_, _, t2')) =>
blanchet@33192
  1708
        betapplys (t0 |> loose_bvar1 (t2', 0) ? do_term depth Ts,
blanchet@33192
  1709
                   map (do_term depth Ts) [t1, t2])
blanchet@33192
  1710
      | Const (x as (@{const_name distinct},
blanchet@35665
  1711
               Type (@{type_name fun}, [Type (@{type_name list}, [T']), _])))
blanchet@33192
  1712
        $ (t1 as _ $ _) =>
blanchet@33192
  1713
        (t1 |> HOLogic.dest_list |> distinctness_formula T'
blanchet@33192
  1714
         handle TERM _ => do_const depth Ts t x [t1])
blanchet@35280
  1715
      | Const (x as (@{const_name If}, _)) $ t1 $ t2 $ t3 =>
blanchet@34936
  1716
        if is_ground_term t1 andalso
blanchet@34936
  1717
           exists (Pattern.matches thy o rpair t1)
blanchet@34936
  1718
                  (Inttab.lookup_list ground_thm_table (hash_term t1)) then
blanchet@33192
  1719
          do_term depth Ts t2
blanchet@33192
  1720
        else
blanchet@33192
  1721
          do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1722
      | Const x $ t1 $ t2 $ t3 => do_const depth Ts t x [t1, t2, t3]
blanchet@33192
  1723
      | Const x $ t1 $ t2 => do_const depth Ts t x [t1, t2]
blanchet@33192
  1724
      | Const x $ t1 => do_const depth Ts t x [t1]
blanchet@33192
  1725
      | Const x => do_const depth Ts t x []
blanchet@33192
  1726
      | t1 $ t2 => betapply (do_term depth Ts t1, do_term depth Ts t2)
blanchet@33192
  1727
      | Free _ => t
blanchet@33192
  1728
      | Var _ => t
blanchet@33192
  1729
      | Bound _ => t
blanchet@33192
  1730
      | Abs (s, T, body) => Abs (s, T, do_term depth (T :: Ts) body)
blanchet@33192
  1731
    (* int -> typ list -> styp -> term list -> int -> typ -> term * term list *)
blanchet@33192
  1732
    and select_nth_constr_arg_with_args _ _ (x as (_, T)) [] n res_T =
blanchet@33192
  1733
        (Abs (Name.uu, body_type T,
blanchet@35220
  1734
              select_nth_constr_arg thy stds x (Bound 0) n res_T), [])
blanchet@33192
  1735
      | select_nth_constr_arg_with_args depth Ts x (t :: ts) n res_T =
blanchet@35220
  1736
        (select_nth_constr_arg thy stds x (do_term depth Ts t) n res_T, ts)
blanchet@33192
  1737
    (* int -> typ list -> term -> styp -> term list -> term *)
blanchet@33192
  1738
    and do_const depth Ts t (x as (s, T)) ts =
blanchet@33192
  1739
      case AList.lookup (op =) ersatz_table s of
blanchet@33192
  1740
        SOME s' =>
blanchet@33192
  1741
        do_const (depth + 1) Ts (list_comb (Const (s', T), ts)) (s', T) ts
blanchet@33192
  1742
      | NONE =>
blanchet@33192
  1743
        let
blanchet@33192
  1744
          val (const, ts) =
blanchet@35220
  1745
            if is_built_in_const thy stds fast_descrs x then
blanchet@33877
  1746
              (Const x, ts)
blanchet@33192
  1747
            else case AList.lookup (op =) case_names s of
blanchet@33192
  1748
              SOME n =>
blanchet@33192
  1749
              let
blanchet@33192
  1750
                val (dataT, res_T) = nth_range_type n T
blanchet@33705
  1751
                                     |> pairf domain_type range_type
blanchet@33192
  1752
              in
blanchet@35070
  1753
                (optimized_case_def hol_ctxt dataT res_T
blanchet@33192
  1754
                 |> do_term (depth + 1) Ts, ts)
blanchet@33192
  1755
              end
blanchet@33192
  1756
            | _ =>
blanchet@35220
  1757
              if is_constr thy stds x then
blanchet@33192
  1758
                (Const x, ts)
blanchet@33581
  1759
              else if is_stale_constr thy x then
blanchet@34936
  1760
                raise NOT_SUPPORTED ("(non-co)constructors of codatatypes \
blanchet@33581
  1761
                                     \(\"" ^ s ^ "\")")
blanchet@35284
  1762
              else if is_quot_abs_fun ctxt x then
blanchet@34936
  1763
                let
blanchet@34936
  1764
                  val rep_T = domain_type T
blanchet@34936
  1765
                  val abs_T = range_type T
blanchet@34936
  1766
                in
blanchet@34936
  1767
                  (Abs (Name.uu, rep_T,
blanchet@34936
  1768
                        Const (@{const_name Quot}, rep_T --> abs_T)
blanchet@35311
  1769
                               $ (Const (quot_normal_name_for_type ctxt abs_T,
blanchet@34936
  1770
                                         rep_T --> rep_T) $ Bound 0)), ts)
blanchet@34936
  1771
                end
blanchet@35284
  1772
              else if is_quot_rep_fun ctxt x then
blanchet@34936
  1773
                let
blanchet@34936
  1774
                  val abs_T = domain_type T
blanchet@34936
  1775
                  val rep_T = range_type T
blanchet@34936
  1776
                  val x' = (@{const_name Quot}, rep_T --> abs_T)
blanchet@34936
  1777
                in select_nth_constr_arg_with_args depth Ts x' ts 0 rep_T end
blanchet@33192
  1778
              else if is_record_get thy x then
blanchet@33192
  1779
                case length ts of
blanchet@33192
  1780
                  0 => (do_term depth Ts (eta_expand Ts t 1), [])
blanchet@35070
  1781
                | _ => (optimized_record_get hol_ctxt s (domain_type T)
blanchet@34982
  1782
                            (range_type T) (do_term depth Ts (hd ts)), tl ts)
blanchet@33192
  1783
              else if is_record_update thy x then
blanchet@33192
  1784
                case length ts of
blanchet@35070
  1785
                  2 => (optimized_record_update hol_ctxt
blanchet@33580
  1786
                            (unsuffix Record.updateN s) (nth_range_type 2 T)
blanchet@33580
  1787
                            (do_term depth Ts (hd ts))
blanchet@33580
  1788
                            (do_term depth Ts (nth ts 1)), [])
blanchet@33192
  1789
                | n => (do_term depth Ts (eta_expand Ts t (2 - n)), [])
blanchet@33192
  1790
              else if is_rep_fun thy x then
blanchet@33192
  1791
                let val x' = mate_of_rep_fun thy x in
blanchet@35220
  1792
                  if is_constr thy stds x' then
blanchet@33192
  1793
                    select_nth_constr_arg_with_args depth Ts x' ts 0
blanchet@33192
  1794
                                                    (range_type T)
blanchet@33192
  1795
                  else
blanchet@33192
  1796
                    (Const x, ts)
blanchet@33192
  1797
                end
blanchet@35070
  1798
              else if is_equational_fun hol_ctxt x then
blanchet@33192
  1799
                (Const x, ts)
blanchet@33192
  1800
              else case def_of_const thy def_table x of
blanchet@33192
  1801
                SOME def =>
blanchet@33192
  1802
                if depth > unfold_max_depth then
blanchet@34124
  1803
                  raise TOO_LARGE ("Nitpick_HOL.unfold_defs_in_term",
blanchet@34124
  1804
                                   "too many nested definitions (" ^
blanchet@34124
  1805
                                   string_of_int depth ^ ") while expanding " ^
blanchet@34124
  1806
                                   quote s)
blanchet@33192
  1807
                else if s = @{const_name wfrec'} then
blanchet@33192
  1808
                  (do_term (depth + 1) Ts (betapplys (def, ts)), [])
blanchet@33192
  1809
                else
blanchet@33192
  1810
                  (do_term (depth + 1) Ts def, ts)
blanchet@33192
  1811
              | NONE => (Const x, ts)
blanchet@33192
  1812
        in s_betapplys (const, map (do_term depth Ts) ts) |> Envir.beta_norm end
blanchet@33192
  1813
  in do_term 0 [] end
blanchet@33192
  1814
blanchet@35070
  1815
(* hol_context -> typ -> term list *)
blanchet@35220
  1816
fun codatatype_bisim_axioms (hol_ctxt as {thy, stds, ...}) T =
blanchet@33192
  1817
  let
blanchet@35070
  1818
    val xs = datatype_constrs hol_ctxt T
blanchet@33192
  1819
    val set_T = T --> bool_T
blanchet@33192
  1820
    val iter_T = @{typ bisim_iterator}
blanchet@34124
  1821
    val bisim_const = Const (@{const_name bisim}, iter_T --> T --> T --> bool_T)
blanchet@33192
  1822
    val bisim_max = @{const bisim_iterator_max}
blanchet@33192
  1823
    val n_var = Var (("n", 0), iter_T)
blanchet@33192
  1824
    val n_var_minus_1 =
blanchet@35671
  1825
      Const (@{const_name safe_The}, (iter_T --> bool_T) --> iter_T)
blanchet@33192
  1826
      $ Abs ("m", iter_T, HOLogic.eq_const iter_T
blanchet@33192
  1827
                          $ (suc_const iter_T $ Bound 0) $ n_var)
blanchet@33192
  1828
    val x_var = Var (("x", 0), T)
blanchet@33192
  1829
    val y_var = Var (("y", 0), T)
blanchet@33192
  1830
    (* styp -> int -> typ -> term *)
blanchet@33192
  1831
    fun nth_sub_bisim x n nth_T =
blanchet@33192
  1832
      (if is_codatatype thy nth_T then bisim_const $ n_var_minus_1
blanchet@33192
  1833
       else HOLogic.eq_const nth_T)
blanchet@35220
  1834
      $ select_nth_constr_arg thy stds x x_var n nth_T
blanchet@35220
  1835
      $ select_nth_constr_arg thy stds x y_var n nth_T
blanchet@33192
  1836
    (* styp -> term *)
blanchet@33192
  1837
    fun case_func (x as (_, T)) =
blanchet@33192
  1838
      let
blanchet@33192
  1839
        val arg_Ts = binder_types T
blanchet@33192
  1840
        val core_t =
blanchet@35070
  1841
          discriminate_value hol_ctxt x y_var ::
blanchet@33192
  1842
          map2 (nth_sub_bisim x) (index_seq 0 (length arg_Ts)) arg_Ts
blanchet@33192
  1843
          |> foldr1 s_conj
blanchet@33192
  1844
      in List.foldr absdummy core_t arg_Ts end
blanchet@33192
  1845
  in
blanchet@33192
  1846
    [HOLogic.eq_const bool_T $ (bisim_const $ n_var $ x_var $ y_var)
blanchet@33192
  1847
     $ (@{term "op |"} $ (HOLogic.eq_const iter_T $ n_var $ zero_const iter_T)
blanchet@35070
  1848
        $ (betapplys (optimized_case_def hol_ctxt T bool_T,
blanchet@33192
  1849
                      map case_func xs @ [x_var]))),
blanchet@33192
  1850
     HOLogic.eq_const set_T $ (bisim_const $ bisim_max $ x_var)
blanchet@34124
  1851
     $ (Const (@{const_name insert}, T --> set_T --> set_T)
blanchet@35220
  1852
        $ x_var $ Const (@{const_name bot_class.bot}, set_T))]
blanchet@33192
  1853
    |> map HOLogic.mk_Trueprop
blanchet@33192
  1854
  end
blanchet@33192
  1855
blanchet@33192
  1856
exception NO_TRIPLE of unit
blanchet@33192
  1857
blanchet@33192
  1858
(* theory -> styp -> term -> term list * term list * term *)
blanchet@33192
  1859
fun triple_for_intro_rule thy x t =
blanchet@33192
  1860
  let
wenzelm@35625
  1861
    val prems = Logic.strip_imp_prems t |> map (Object_Logic.atomize_term thy)
wenzelm@35625
  1862
    val concl = Logic.strip_imp_concl t |> Object_Logic.atomize_term thy
blanchet@34121
  1863
    val (main, side) = List.partition (exists_Const (curry (op =) x)) prems
blanchet@33192
  1864
    (* term -> bool *)
blanchet@34121
  1865
     val is_good_head = curry (op =) (Const x) o head_of
blanchet@33192
  1866
  in
blanchet@33192
  1867
    if forall is_good_head main then (side, main, concl) else raise NO_TRIPLE ()
blanchet@33192
  1868
  end
blanchet@33192
  1869
blanchet@33192
  1870
(* term -> term *)
blanchet@33192
  1871
val tuple_for_args = HOLogic.mk_tuple o snd o strip_comb
blanchet@33192
  1872
blanchet@33192
  1873
(* indexname * typ -> term list -> term -> term -> term *)
blanchet@33192
  1874
fun wf_constraint_for rel side concl main =
blanchet@33192
  1875
  let
blanchet@33192
  1876
    val core = HOLogic.mk_mem (HOLogic.mk_prod (tuple_for_args main,
blanchet@33192
  1877
                                                tuple_for_args concl), Var rel)
blanchet@33192
  1878
    val t = List.foldl HOLogic.mk_imp core side
blanchet@33192
  1879
    val vars = filter (not_equal rel) (Term.add_vars t [])
blanchet@33192
  1880
  in
blanchet@33192
  1881
    Library.foldl (fn (t', ((x, j), T)) =>
blanchet@33192
  1882
                      HOLogic.all_const T
blanchet@33192
  1883
                      $ Abs (x, T, abstract_over (Var ((x, j), T), t')))
blanchet@33192
  1884
                  (t, vars)
blanchet@33192
  1885
  end
blanchet@33192
  1886
blanchet@33192
  1887
(* indexname * typ -> term list * term list * term -> term *)
blanchet@33192
  1888
fun wf_constraint_for_triple rel (side, main, concl) =
blanchet@33192
  1889
  map (wf_constraint_for rel side concl) main |> foldr1 s_conj
blanchet@33192
  1890
blanchet@33192
  1891
(* Proof.context -> Time.time option -> thm
blanchet@33192
  1892
   -> (Proof.context -> tactic -> tactic) -> bool *)
blanchet@33192
  1893
fun terminates_by ctxt timeout goal tac =
blanchet@33192
  1894
  can (SINGLE (Classical.safe_tac (claset_of ctxt)) #> the
blanchet@33192
  1895
       #> SINGLE (DETERM_TIMEOUT timeout
blanchet@33192
  1896
                                 (tac ctxt (auto_tac (clasimpset_of ctxt))))
blanchet@33192
  1897
       #> the #> Goal.finish ctxt) goal
blanchet@33192
  1898
blanchet@35181
  1899
val max_cached_wfs = 50
blanchet@35181
  1900
val cached_timeout =
blanchet@35181
  1901
  Synchronized.var "Nitpick_HOL.cached_timeout" (SOME Time.zeroTime)
blanchet@35181
  1902
val cached_wf_props =
blanchet@35181
  1903
  Synchronized.var "Nitpick_HOL.cached_wf_props" ([] : (term * bool) list)
blanchet@33192
  1904
krauss@33351
  1905
val termination_tacs = [Lexicographic_Order.lex_order_tac true,
blanchet@33192
  1906
                        ScnpReconstruct.sizechange_tac]
blanchet@33192
  1907
blanchet@35070
  1908
(* hol_context -> const_table -> styp -> bool *)
blanchet@33580
  1909
fun uncached_is_well_founded_inductive_pred
blanchet@35220
  1910
        ({thy, ctxt, stds, debug, fast_descrs, tac_timeout, intro_table, ...}
blanchet@35070
  1911
         : hol_context) (x as (_, T)) =
blanchet@35220
  1912
  case def_props_for_const thy stds fast_descrs intro_table x of
blanchet@33580
  1913
    [] => raise TERM ("Nitpick_HOL.uncached_is_well_founded_inductive",
blanchet@33232
  1914
                      [Const x])
blanchet@33192
  1915
  | intro_ts =>
blanchet@33192
  1916
    (case map (triple_for_intro_rule thy x) intro_ts
blanchet@33192
  1917
          |> filter_out (null o #2) of
blanchet@33192
  1918
       [] => true
blanchet@33192
  1919
     | triples =>
blanchet@33192
  1920
       let
blanchet@33192
  1921
         val binders_T = HOLogic.mk_tupleT (binder_types T)
blanchet@33192
  1922
         val rel_T = HOLogic.mk_prodT (binders_T, binders_T) --> bool_T
blanchet@33882
  1923
         val j = fold Integer.max (map maxidx_of_term intro_ts) 0 + 1
blanchet@33192
  1924
         val rel = (("R", j), rel_T)
blanchet@33192
  1925
         val prop = Const (@{const_name wf}, rel_T --> bool_T) $ Var rel ::
blanchet@33192
  1926
                    map (wf_constraint_for_triple rel) triples
blanchet@33192
  1927
                    |> foldr1 s_conj |> HOLogic.mk_Trueprop
blanchet@33192
  1928
         val _ = if debug then
blanchet@33192
  1929
                   priority ("Wellfoundedness goal: " ^
blanchet@33192
  1930
                             Syntax.string_of_term ctxt prop ^ ".")
blanchet@33192
  1931
                 else
blanchet@33192
  1932
                   ()
blanchet@33192
  1933
       in
blanchet@35181
  1934
         if tac_timeout = Synchronized.value cached_timeout andalso
blanchet@35181
  1935
            length (Synchronized.value cached_wf_props) < max_cached_wfs then
blanchet@33557
  1936
           ()
blanchet@33557
  1937
         else
blanchet@35181
  1938
           (Synchronized.change cached_wf_props (K []);
blanchet@35181
  1939
            Synchronized.change cached_timeout (K tac_timeout));
blanchet@35181
  1940
         case AList.lookup (op =) (Synchronized.value cached_wf_props) prop of
blanchet@33192
  1941
           SOME wf => wf
blanchet@33192
  1942
         | NONE =>
blanchet@33192
  1943
           let
blanchet@33192
  1944
             val goal = prop |> cterm_of thy |> Goal.init
blanchet@33705
  1945
             val wf = exists (terminates_by ctxt tac_timeout goal)
blanchet@33705
  1946
                             termination_tacs
blanchet@35181
  1947
           in Synchronized.change cached_wf_props (cons (prop, wf)); wf end
blanchet@33192
  1948
       end)
blanchet@35309
  1949
    handle List.Empty => false | NO_TRIPLE () => false
blanchet@33192
  1950
blanchet@35070
  1951
(* The type constraint below is a workaround for a Poly/ML crash. *)
blanchet@33192
  1952
blanchet@35070
  1953
(* hol_context -> styp -> bool *)
blanchet@33192
  1954
fun is_well_founded_inductive_pred
blanchet@35070
  1955
        (hol_ctxt as {thy, wfs, def_table, wf_cache, ...} : hol_context)
blanchet@33192
  1956
        (x as (s, _)) =
blanchet@33192
  1957
  case triple_lookup (const_match thy) wfs x of
blanchet@33192
  1958
    SOME (SOME b) => b
blanchet@34936
  1959
  | _ => s = @{const_name Nats} orelse s = @{const_name fold_graph'} orelse
blanchet@34936
  1960
         case AList.lookup (op =) (!wf_cache) x of
blanchet@35181
  1961
           SOME (_, wf) => wf
blanchet@35181
  1962
         | NONE =>
blanchet@35181
  1963
           let
blanchet@35181
  1964
             val gfp = (fixpoint_kind_of_const thy def_table x = Gfp)
blanchet@35181
  1965
             val wf = uncached_is_well_founded_inductive_pred hol_ctxt x
blanchet@35181
  1966
           in
blanchet@35181
  1967
             Unsynchronized.change wf_cache (cons (x, (gfp, wf))); wf
blanchet@35181
  1968
           end
blanchet@33192
  1969
blanchet@35280
  1970
(* typ list -> typ -> term -> term *)
blanchet@35280
  1971
fun ap_curry [_] _ t = t
blanchet@35280
  1972
  | ap_curry arg_Ts tuple_T t =
blanchet@33192
  1973
    let val n = length arg_Ts in
blanchet@33192
  1974
      list_abs (map (pair "c") arg_Ts,
blanchet@33192
  1975
                incr_boundvars n t
blanchet@33192
  1976
                $ mk_flat_tuple tuple_T (map Bound (n - 1 downto 0)))
blanchet@33192
  1977
    end
blanchet@33192
  1978
blanchet@33192
  1979
(* int -> term -> int *)
blanchet@33192
  1980
fun num_occs_of_bound_in_term j (t1 $ t2) =
blanchet@33192
  1981
    op + (pairself (num_occs_of_bound_in_term j) (t1, t2))
blanchet@35280
  1982
  | num_occs_of_bound_in_term j (Abs (_, _, t')) =
blanchet@33192
  1983
    num_occs_of_bound_in_term (j + 1) t'
blanchet@33192
  1984
  | num_occs_of_bound_in_term j (Bound j') = if j' = j then 1 else 0
blanchet@33192
  1985
  | num_occs_of_bound_in_term _ _ = 0
blanchet@33192
  1986
blanchet@33192
  1987
(* term -> bool *)
blanchet@33192
  1988
val is_linear_inductive_pred_def =
blanchet@33192
  1989
  let
blanchet@33192
  1990
    (* int -> term -> bool *)
blanchet@33192
  1991
    fun do_disjunct j (Const (@{const_name Ex}, _) $ Abs (_, _, t2)) =
blanchet@33192
  1992
        do_disjunct (j + 1) t2
blanchet@33192
  1993
      | do_disjunct j t =
blanchet@33192
  1994
        case num_occs_of_bound_in_term j t of
blanchet@33192
  1995
          0 => true
blanchet@35070
  1996
        | 1 => exists (curry (op =) (Bound j) o head_of) (conjuncts_of t)
blanchet@33192
  1997
        | _ => false
blanchet@33192
  1998
    (* term -> bool *)
blanchet@33192
  1999
    fun do_lfp_def (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  2000
        let val (xs, body) = strip_abs t2 in
blanchet@33192
  2001
          case length xs of
blanchet@33192
  2002
            1 => false
blanchet@35070
  2003
          | n => forall (do_disjunct (n - 1)) (disjuncts_of body)
blanchet@33192
  2004
        end
blanchet@33192
  2005
      | do_lfp_def _ = false
blanchet@33192
  2006
  in do_lfp_def o strip_abs_body end
blanchet@33192
  2007
blanchet@33851
  2008
(* int -> int list list *)
blanchet@33851
  2009
fun n_ptuple_paths 0 = []
blanchet@33851
  2010
  | n_ptuple_paths 1 = []
blanchet@33851
  2011
  | n_ptuple_paths n = [] :: map (cons 2) (n_ptuple_paths (n - 1))
blanchet@33851
  2012
(* int -> typ -> typ -> term -> term *)
blanchet@33851
  2013
val ap_n_split = HOLogic.mk_psplits o n_ptuple_paths
blanchet@33192
  2014
blanchet@33192
  2015
(* term -> term * term *)
blanchet@33192
  2016
val linear_pred_base_and_step_rhss =
blanchet@33192
  2017
  let
blanchet@33192
  2018
    (* term -> term *)
blanchet@33192
  2019
    fun aux (Const (@{const_name lfp}, _) $ t2) =
blanchet@33192
  2020
        let
blanchet@33192
  2021
          val (xs, body) = strip_abs t2
blanchet@33192
  2022
          val arg_Ts = map snd (tl xs)
blanchet@33192
  2023
          val tuple_T = HOLogic.mk_tupleT arg_Ts
blanchet@33192
  2024
          val j = length arg_Ts
blanchet@33192
  2025
          (* int -> term -> term *)
blanchet@33192
  2026
          fun repair_rec j (Const (@{const_name Ex}, T1) $ Abs (s2, T2, t2')) =
blanchet@33192
  2027
              Const (@{const_name Ex}, T1)
blanchet@33192
  2028
              $ Abs (s2, T2, repair_rec (j + 1) t2')
blanchet@33192
  2029
            | repair_rec j (@{const "op &"} $ t1 $ t2) =
blanchet@33192
  2030
              @{const "op &"} $ repair_rec j t1 $ repair_rec j t2
blanchet@33192
  2031
            | repair_rec j t =
blanchet@33192
  2032
              let val (head, args) = strip_comb t in
blanchet@33192
  2033
                if head = Bound j then
blanchet@33192
  2034
                  HOLogic.eq_const tuple_T $ Bound j
blanchet@33192
  2035
                  $ mk_flat_tuple tuple_T args
blanchet@33192
  2036
                else
blanchet@33192
  2037
                  t
blanchet@33192
  2038
              end
blanchet@33192
  2039
          val (nonrecs, recs) =
blanchet@34121
  2040
            List.partition (curry (op =) 0 o num_occs_of_bound_in_term j)
blanchet@35070
  2041
                           (disjuncts_of body)
blanchet@33192
  2042
          val base_body = nonrecs |> List.foldl s_disj @{const False}
blanchet@33192
  2043
          val step_body = recs |> map (repair_rec j)
blanchet@33192
  2044
                               |> List.foldl s_disj @{const False} 
blanchet@33192
  2045
        in
blanchet@33192
  2046
          (list_abs (tl xs, incr_bv (~1, j, base_body))
blanchet@33851
  2047
           |> ap_n_split (length arg_Ts) tuple_T bool_T,
blanchet@33192
  2048
           Abs ("y", tuple_T, list_abs (tl xs, step_body)
blanchet@33851
  2049
                              |> ap_n_split (length arg_Ts) tuple_T bool_T))
blanchet@33192
  2050
        end
blanchet@33192
  2051
      | aux t =
blanchet@33232
  2052
        raise TERM ("Nitpick_HOL.linear_pred_base_and_step_rhss.aux", [t])
blanchet@33192
  2053
  in aux end
blanchet@33192
  2054
blanchet@35070
  2055
(* hol_context -> styp -> term -> term *)
blanchet@35280
  2056
fun starred_linear_pred_const (hol_ctxt as {simp_table, ...}) (s, T) def =
blanchet@33192
  2057
  let
blanchet@33192
  2058
    val j = maxidx_of_term def + 1
blanchet@33192
  2059
    val (outer, fp_app) = strip_abs def
blanchet@33192
  2060
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  2061
    val outer_vars = map (fn (s, T) => Var ((s, j), T)) outer
blanchet@33192
  2062
    val fp_app = subst_bounds (rev outer_vars, fp_app)
blanchet@33192
  2063
    val (outer_Ts, rest_T) = strip_n_binders (length outer) T
blanchet@33192
  2064
    val tuple_arg_Ts = strip_type rest_T |> fst
blanchet@33192
  2065
    val tuple_T = HOLogic.mk_tupleT tuple_arg_Ts
blanchet@33192
  2066
    val set_T = tuple_T --> bool_T
blanchet@33192
  2067
    val curried_T = tuple_T --> set_T
blanchet@35665
  2068
    val uncurried_T = Type (@{type_name "*"}, [tuple_T, tuple_T]) --> bool_T
blanchet@33192
  2069
    val (base_rhs, step_rhs) = linear_pred_base_and_step_rhss fp_app
blanchet@33192
  2070
    val base_x as (base_s, _) = (base_prefix ^ s, outer_Ts ---> set_T)
blanchet@33192
  2071
    val base_eq = HOLogic.mk_eq (list_comb (Const base_x, outer_vars), base_rhs)
blanchet@33192
  2072
                  |> HOLogic.mk_Trueprop
blanchet@33192
  2073
    val _ = add_simps simp_table base_s [base_eq]
blanchet@33192
  2074
    val step_x as (step_s, _) = (step_prefix ^ s, outer_Ts ---> curried_T)
blanchet@33192
  2075
    val step_eq = HOLogic.mk_eq (list_comb (Const step_x, outer_vars), step_rhs)
blanchet@33192
  2076
                  |> HOLogic.mk_Trueprop
blanchet@33192
  2077
    val _ = add_simps simp_table step_s [step_eq]
blanchet@33192
  2078
  in
blanchet@33192
  2079
    list_abs (outer,
blanchet@33192
  2080
              Const (@{const_name Image}, uncurried_T --> set_T --> set_T)
blanchet@33192
  2081
              $ (Const (@{const_name rtrancl}, uncurried_T --> uncurried_T)
blanchet@33192
  2082
                 $ (Const (@{const_name split}, curried_T --> uncurried_T)
blanchet@33192
  2083
                    $ list_comb (Const step_x, outer_bounds)))
blanchet@33192
  2084
              $ list_comb (Const base_x, outer_bounds)
blanchet@35280
  2085
              |> ap_curry tuple_arg_Ts tuple_T)
blanchet@35070
  2086
    |> unfold_defs_in_term hol_ctxt
blanchet@33192
  2087
  end
blanchet@33192
  2088
blanchet@35070
  2089
(* hol_context -> bool -> styp -> term *)
blanchet@35070
  2090
fun unrolled_inductive_pred_const (hol_ctxt as {thy, star_linear_preds,
blanchet@33192
  2091
                                                def_table, simp_table, ...})
blanchet@33192
  2092
                                  gfp (x as (s, T)) =
blanchet@33192
  2093
  let
blanchet@33192
  2094
    val iter_T = iterator_type_for_const gfp x
blanchet@33192
  2095
    val x' as (s', _) = (unrolled_prefix ^ s, iter_T --> T)
blanchet@33192
  2096
    val unrolled_const = Const x' $ zero_const iter_T
blanchet@33192
  2097
    val def = the (def_of_const thy def_table x)
blanchet@33192
  2098
  in
blanchet@35070
  2099
    if is_equational_fun hol_ctxt x' then
blanchet@33192
  2100
      unrolled_const (* already done *)
blanchet@34936
  2101
    else if not gfp andalso is_linear_inductive_pred_def def andalso
blanchet@34936
  2102
         star_linear_preds then
blanchet@35070
  2103
      starred_linear_pred_const hol_ctxt x def
blanchet@33192
  2104
    else
blanchet@33192
  2105
      let
blanchet@33192
  2106
        val j = maxidx_of_term def + 1
blanchet@33192
  2107
        val (outer, fp_app) = strip_abs def
blanchet@33192
  2108
        val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  2109
        val cur = Var ((iter_var_prefix, j + 1), iter_T)
blanchet@33192
  2110
        val next = suc_const iter_T $ cur
blanchet@33192
  2111
        val rhs = case fp_app of
blanchet@33192
  2112
                    Const _ $ t =>
blanchet@33192
  2113
                    betapply (t, list_comb (Const x', next :: outer_bounds))
blanchet@33232
  2114
                  | _ => raise TERM ("Nitpick_HOL.unrolled_inductive_pred_\
blanchet@33232
  2115
                                     \const", [fp_app])
blanchet@33192
  2116
        val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  2117
        val all = outer @ inner
blanchet@33192
  2118
        val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  2119
        val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  2120
        val eq = HOLogic.mk_eq (list_comb (Const x', cur :: bounds), naked_rhs)
blanchet@33192
  2121
                 |> HOLogic.mk_Trueprop |> curry subst_bounds (rev vars)
blanchet@33192
  2122
        val _ = add_simps simp_table s' [eq]
blanchet@33192
  2123
      in unrolled_const end
blanchet@33192
  2124
  end
blanchet@33192
  2125
blanchet@35070
  2126
(* hol_context -> styp -> term *)
blanchet@35070
  2127
fun raw_inductive_pred_axiom ({thy, def_table, ...} : hol_context) x =
blanchet@33192
  2128
  let
blanchet@33192
  2129
    val def = the (def_of_const thy def_table x)
blanchet@33192
  2130
    val (outer, fp_app) = strip_abs def
blanchet@33192
  2131
    val outer_bounds = map Bound (length outer - 1 downto 0)
blanchet@33192
  2132
    val rhs = case fp_app of
blanchet@33192
  2133
                Const _ $ t => betapply (t, list_comb (Const x, outer_bounds))
blanchet@33232
  2134
              | _ => raise TERM ("Nitpick_HOL.raw_inductive_pred_axiom",
blanchet@33192
  2135
                                 [fp_app])
blanchet@33192
  2136
    val (inner, naked_rhs) = strip_abs rhs
blanchet@33192
  2137
    val all = outer @ inner
blanchet@33192
  2138
    val bounds = map Bound (length all - 1 downto 0)
blanchet@33192
  2139
    val j = maxidx_of_term def + 1
blanchet@33192
  2140
    val vars = map (fn (s, T) => Var ((s, j), T)) all
blanchet@33192
  2141
  in
blanchet@33192
  2142
    HOLogic.mk_eq (list_comb (Const x, bounds), naked_rhs)
blanchet@33192