src/HOL/Tools/ctr_sugar.ML
author blanchet
Tue Nov 12 13:47:24 2013 +0100 (2013-11-12)
changeset 54403 40382f65bc80
parent 54400 418a183fbe21
child 54422 4ca60c430147
permissions -rw-r--r--
added convenience function
blanchet@54397
     1
(*  Title:      HOL/Tools/ctr_sugar.ML
blanchet@49017
     2
    Author:     Jasmin Blanchette, TU Muenchen
blanchet@54397
     3
    Copyright   2012, 2013
blanchet@49017
     4
blanchet@51797
     5
Wrapping existing freely generated type's constructors.
blanchet@49017
     6
*)
blanchet@49017
     7
blanchet@54006
     8
signature CTR_SUGAR =
blanchet@49017
     9
sig
blanchet@51840
    10
  type ctr_sugar =
blanchet@51839
    11
    {ctrs: term list,
blanchet@52375
    12
     casex: term,
blanchet@51839
    13
     discs: term list,
blanchet@51819
    14
     selss: term list list,
blanchet@51819
    15
     exhaust: thm,
blanchet@52375
    16
     nchotomy: thm,
blanchet@51819
    17
     injects: thm list,
blanchet@51819
    18
     distincts: thm list,
blanchet@51819
    19
     case_thms: thm list,
blanchet@52375
    20
     case_cong: thm,
blanchet@52375
    21
     weak_case_cong: thm,
blanchet@52375
    22
     split: thm,
blanchet@52375
    23
     split_asm: thm,
blanchet@51819
    24
     disc_thmss: thm list list,
blanchet@51819
    25
     discIs: thm list,
blanchet@53475
    26
     sel_thmss: thm list list,
blanchet@53475
    27
     disc_exhausts: thm list,
blanchet@53916
    28
     sel_exhausts: thm list,
blanchet@53475
    29
     collapses: thm list,
blanchet@53475
    30
     expands: thm list,
blanchet@53917
    31
     sel_splits: thm list,
blanchet@53917
    32
     sel_split_asms: thm list,
blanchet@53857
    33
     case_conv_ifs: thm list};
blanchet@51809
    34
blanchet@51840
    35
  val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar
blanchet@54256
    36
  val transfer_ctr_sugar: Proof.context -> ctr_sugar -> ctr_sugar
blanchet@53867
    37
  val ctr_sugar_of: Proof.context -> string -> ctr_sugar option
blanchet@53906
    38
  val ctr_sugars_of: Proof.context -> ctr_sugar list
blanchet@54403
    39
  val ctr_sugar_of_case: Proof.context -> string -> ctr_sugar option
blanchet@54399
    40
  val register_ctr_sugar: string -> ctr_sugar -> local_theory -> local_theory
blanchet@54400
    41
  val register_ctr_sugar_global: string -> ctr_sugar -> theory -> theory
blanchet@51823
    42
blanchet@49633
    43
  val rep_compat_prefix: string
blanchet@49633
    44
blanchet@49585
    45
  val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
blanchet@49585
    46
  val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
blanchet@49585
    47
blanchet@49203
    48
  val mk_ctr: typ list -> term -> term
blanchet@53864
    49
  val mk_case: typ list -> typ -> term -> term
blanchet@49484
    50
  val mk_disc_or_sel: typ list -> term -> term
blanchet@49622
    51
  val name_of_ctr: term -> string
blanchet@51777
    52
  val name_of_disc: term -> string
blanchet@53888
    53
  val dest_ctr: Proof.context -> string -> term -> term * term list
blanchet@53870
    54
  val dest_case: Proof.context -> string -> typ list -> term -> (term list * term list) option
blanchet@49585
    55
blanchet@51781
    56
  val wrap_free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
blanchet@52968
    57
    (((bool * bool) * term list) * binding) *
blanchet@49280
    58
      (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
blanchet@51840
    59
    ctr_sugar * local_theory
blanchet@52823
    60
  val parse_wrap_free_constructors_options: (bool * bool) parser
blanchet@49286
    61
  val parse_bound_term: (binding * string) parser
blanchet@49017
    62
end;
blanchet@49017
    63
blanchet@54006
    64
structure Ctr_Sugar : CTR_SUGAR =
blanchet@49017
    65
struct
blanchet@49017
    66
blanchet@54008
    67
open Ctr_Sugar_Util
blanchet@54006
    68
open Ctr_Sugar_Tactics
blanchet@49017
    69
blanchet@51840
    70
type ctr_sugar =
blanchet@51839
    71
  {ctrs: term list,
blanchet@52375
    72
   casex: term,
blanchet@51839
    73
   discs: term list,
blanchet@51819
    74
   selss: term list list,
blanchet@51819
    75
   exhaust: thm,
blanchet@52375
    76
   nchotomy: thm,
blanchet@51819
    77
   injects: thm list,
blanchet@51819
    78
   distincts: thm list,
blanchet@51819
    79
   case_thms: thm list,
blanchet@52375
    80
   case_cong: thm,
blanchet@52375
    81
   weak_case_cong: thm,
blanchet@52375
    82
   split: thm,
blanchet@52375
    83
   split_asm: thm,
blanchet@51819
    84
   disc_thmss: thm list list,
blanchet@51819
    85
   discIs: thm list,
blanchet@53475
    86
   sel_thmss: thm list list,
blanchet@53475
    87
   disc_exhausts: thm list,
blanchet@53916
    88
   sel_exhausts: thm list,
blanchet@53475
    89
   collapses: thm list,
blanchet@53475
    90
   expands: thm list,
blanchet@53917
    91
   sel_splits: thm list,
blanchet@53917
    92
   sel_split_asms: thm list,
blanchet@53857
    93
   case_conv_ifs: thm list};
blanchet@51809
    94
blanchet@53906
    95
fun eq_ctr_sugar ({ctrs = ctrs1, casex = case1, discs = discs1, selss = selss1, ...} : ctr_sugar,
blanchet@53906
    96
    {ctrs = ctrs2, casex = case2, discs = discs2, selss = selss2, ...} : ctr_sugar) =
blanchet@53906
    97
  ctrs1 = ctrs2 andalso case1 = case2 andalso discs1 = discs2 andalso selss1 = selss2;
blanchet@53906
    98
blanchet@52375
    99
fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
blanchet@53475
   100
    case_thms, case_cong, weak_case_cong, split, split_asm, disc_thmss, discIs, sel_thmss,
blanchet@53917
   101
    disc_exhausts, sel_exhausts, collapses, expands, sel_splits, sel_split_asms, case_conv_ifs} =
blanchet@51839
   102
  {ctrs = map (Morphism.term phi) ctrs,
blanchet@52375
   103
   casex = Morphism.term phi casex,
blanchet@51839
   104
   discs = map (Morphism.term phi) discs,
blanchet@51823
   105
   selss = map (map (Morphism.term phi)) selss,
blanchet@51823
   106
   exhaust = Morphism.thm phi exhaust,
blanchet@52375
   107
   nchotomy = Morphism.thm phi nchotomy,
blanchet@51823
   108
   injects = map (Morphism.thm phi) injects,
blanchet@51823
   109
   distincts = map (Morphism.thm phi) distincts,
blanchet@51823
   110
   case_thms = map (Morphism.thm phi) case_thms,
blanchet@52375
   111
   case_cong = Morphism.thm phi case_cong,
blanchet@52375
   112
   weak_case_cong = Morphism.thm phi weak_case_cong,
blanchet@52375
   113
   split = Morphism.thm phi split,
blanchet@52375
   114
   split_asm = Morphism.thm phi split_asm,
blanchet@51823
   115
   disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
blanchet@51823
   116
   discIs = map (Morphism.thm phi) discIs,
blanchet@53475
   117
   sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
blanchet@53475
   118
   disc_exhausts = map (Morphism.thm phi) disc_exhausts,
blanchet@53916
   119
   sel_exhausts = map (Morphism.thm phi) sel_exhausts,
blanchet@53475
   120
   collapses = map (Morphism.thm phi) collapses,
blanchet@53475
   121
   expands = map (Morphism.thm phi) expands,
blanchet@53917
   122
   sel_splits = map (Morphism.thm phi) sel_splits,
blanchet@53917
   123
   sel_split_asms = map (Morphism.thm phi) sel_split_asms,
blanchet@53857
   124
   case_conv_ifs = map (Morphism.thm phi) case_conv_ifs};
blanchet@51823
   125
blanchet@53906
   126
val transfer_ctr_sugar =
blanchet@53906
   127
  morph_ctr_sugar o Morphism.thm_morphism o Thm.transfer o Proof_Context.theory_of;
blanchet@53867
   128
blanchet@53867
   129
structure Data = Generic_Data
blanchet@53867
   130
(
blanchet@53867
   131
  type T = ctr_sugar Symtab.table;
blanchet@53867
   132
  val empty = Symtab.empty;
blanchet@53867
   133
  val extend = I;
blanchet@53867
   134
  val merge = Symtab.merge eq_ctr_sugar;
blanchet@53867
   135
);
blanchet@53867
   136
blanchet@53867
   137
fun ctr_sugar_of ctxt =
blanchet@53867
   138
  Symtab.lookup (Data.get (Context.Proof ctxt))
blanchet@53906
   139
  #> Option.map (transfer_ctr_sugar ctxt);
blanchet@53906
   140
blanchet@53906
   141
fun ctr_sugars_of ctxt =
blanchet@53906
   142
  Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
blanchet@53867
   143
blanchet@54403
   144
fun ctr_sugar_of_case ctxt s =
blanchet@54403
   145
  find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false) (ctr_sugars_of ctxt);
blanchet@54403
   146
blanchet@53867
   147
fun register_ctr_sugar key ctr_sugar =
blanchet@54285
   148
  Local_Theory.declaration {syntax = false, pervasive = true}
blanchet@53867
   149
    (fn phi => Data.map (Symtab.default (key, morph_ctr_sugar phi ctr_sugar)));
blanchet@53867
   150
blanchet@54400
   151
fun register_ctr_sugar_global key ctr_sugar =
blanchet@54400
   152
  Context.theory_map (Data.map (Symtab.default (key, ctr_sugar)));
blanchet@54400
   153
blanchet@49633
   154
val rep_compat_prefix = "new";
blanchet@49633
   155
blanchet@49223
   156
val isN = "is_";
blanchet@49223
   157
val unN = "un_";
blanchet@49223
   158
fun mk_unN 1 1 suf = unN ^ suf
blanchet@49223
   159
  | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
blanchet@49046
   160
blanchet@49594
   161
val caseN = "case";
blanchet@49054
   162
val case_congN = "case_cong";
blanchet@53857
   163
val case_conv_ifN = "case_conv_if";
blanchet@49118
   164
val collapseN = "collapse";
blanchet@49122
   165
val disc_excludeN = "disc_exclude";
blanchet@49054
   166
val disc_exhaustN = "disc_exhaust";
blanchet@53694
   167
val discN = "disc";
blanchet@53700
   168
val discIN = "discI";
blanchet@49054
   169
val distinctN = "distinct";
blanchet@49075
   170
val exhaustN = "exhaust";
blanchet@49486
   171
val expandN = "expand";
blanchet@49075
   172
val injectN = "inject";
blanchet@49075
   173
val nchotomyN = "nchotomy";
blanchet@53694
   174
val selN = "sel";
blanchet@53916
   175
val sel_exhaustN = "sel_exhaust";
blanchet@53917
   176
val sel_splitN = "sel_split";
blanchet@53917
   177
val sel_split_asmN = "sel_split_asm";
blanchet@49054
   178
val splitN = "split";
blanchet@49633
   179
val splitsN = "splits";
blanchet@49054
   180
val split_asmN = "split_asm";
blanchet@49054
   181
val weak_case_cong_thmsN = "weak_case_cong";
blanchet@49019
   182
blanchet@53700
   183
val cong_attrs = @{attributes [cong]};
blanchet@53836
   184
val dest_attrs = @{attributes [dest]};
blanchet@53700
   185
val safe_elim_attrs = @{attributes [elim!]};
blanchet@53700
   186
val iff_attrs = @{attributes [iff]};
blanchet@54145
   187
val inductsimp_attrs = @{attributes [induct_simp]};
blanchet@54145
   188
val nitpicksimp_attrs = @{attributes [nitpick_simp]};
blanchet@49300
   189
val simp_attrs = @{attributes [simp]};
blanchet@54151
   190
val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
blanchet@54151
   191
val code_nitpicksimp_simp_attrs = code_nitpicksimp_attrs @ simp_attrs;
blanchet@49046
   192
blanchet@53040
   193
fun unflat_lookup eq xs ys = map (fn xs' => permute_like eq xs xs' ys);
blanchet@49258
   194
blanchet@49585
   195
fun mk_half_pairss' _ ([], []) = []
blanchet@49591
   196
  | mk_half_pairss' indent (x :: xs, _ :: ys) =
blanchet@49585
   197
    indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
blanchet@49486
   198
blanchet@49585
   199
fun mk_half_pairss p = mk_half_pairss' [[]] p;
blanchet@49027
   200
blanchet@49486
   201
fun join_halves n half_xss other_half_xss =
blanchet@49486
   202
  let
blanchet@49486
   203
    val xsss =
blanchet@49486
   204
      map2 (map2 append) (Library.chop_groups n half_xss)
blanchet@49486
   205
        (transpose (Library.chop_groups n other_half_xss))
blanchet@49668
   206
    val xs = splice (flat half_xss) (flat other_half_xss);
blanchet@49585
   207
  in (xs, xsss) end;
blanchet@49027
   208
blanchet@49280
   209
fun mk_undefined T = Const (@{const_name undefined}, T);
blanchet@49055
   210
blanchet@49500
   211
fun mk_ctr Ts t =
blanchet@49500
   212
  let val Type (_, Ts0) = body_type (fastype_of t) in
blanchet@49500
   213
    Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49203
   214
  end;
blanchet@49203
   215
blanchet@49536
   216
fun mk_case Ts T t =
blanchet@49536
   217
  let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
blanchet@49536
   218
    Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) t
blanchet@49536
   219
  end;
blanchet@49536
   220
blanchet@53864
   221
fun mk_disc_or_sel Ts t =
blanchet@53864
   222
  Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
blanchet@53864
   223
blanchet@51777
   224
fun name_of_const what t =
blanchet@51777
   225
  (case head_of t of
blanchet@49622
   226
    Const (s, _) => s
blanchet@49622
   227
  | Free (s, _) => s
blanchet@51777
   228
  | _ => error ("Cannot extract name of " ^ what));
blanchet@51777
   229
blanchet@51777
   230
val name_of_ctr = name_of_const "constructor";
blanchet@51777
   231
blanchet@51777
   232
val notN = "not_";
blanchet@51777
   233
val eqN = "eq_";
blanchet@51777
   234
val neqN = "neq_";
blanchet@51777
   235
blanchet@51777
   236
fun name_of_disc t =
blanchet@51777
   237
  (case head_of t of
blanchet@51777
   238
    Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
blanchet@51777
   239
    Long_Name.map_base_name (prefix notN) (name_of_disc t')
blanchet@51777
   240
  | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
blanchet@51777
   241
    Long_Name.map_base_name (prefix eqN) (name_of_disc t')
blanchet@51777
   242
  | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
blanchet@51777
   243
    Long_Name.map_base_name (prefix neqN) (name_of_disc t')
blanchet@51777
   244
  | t' => name_of_const "destructor" t');
blanchet@49622
   245
blanchet@49622
   246
val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
blanchet@49046
   247
blanchet@53888
   248
fun dest_ctr ctxt s t =
blanchet@53888
   249
  let
blanchet@53888
   250
    val (f, args) = Term.strip_comb t;
blanchet@53888
   251
  in
blanchet@53888
   252
    (case ctr_sugar_of ctxt s of
blanchet@53888
   253
      SOME {ctrs, ...} =>
blanchet@53888
   254
      (case find_first (can (fo_match ctxt f)) ctrs of
blanchet@53888
   255
        SOME f' => (f', args)
blanchet@53888
   256
      | NONE => raise Fail "dest_ctr")
blanchet@53888
   257
    | NONE => raise Fail "dest_ctr")
blanchet@53888
   258
  end;
blanchet@53888
   259
blanchet@53870
   260
fun dest_case ctxt s Ts t =
blanchet@53870
   261
  (case Term.strip_comb t of
blanchet@53870
   262
    (Const (c, _), args as _ :: _) =>
blanchet@53870
   263
    (case ctr_sugar_of ctxt s of
blanchet@53870
   264
      SOME {casex = Const (case_name, _), discs = discs0, selss = selss0, ...} =>
blanchet@53870
   265
      if case_name = c then
blanchet@53924
   266
        let val n = length discs0 in
blanchet@53924
   267
          if n < length args then
blanchet@53924
   268
            let
blanchet@53924
   269
              val (branches, obj :: leftovers) = chop n args;
blanchet@53924
   270
              val discs = map (mk_disc_or_sel Ts) discs0;
blanchet@53924
   271
              val selss = map (map (mk_disc_or_sel Ts)) selss0;
blanchet@53924
   272
              val conds = map (rapp obj) discs;
blanchet@53924
   273
              val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
blanchet@53924
   274
              val branches' = map2 (curry Term.betapplys) branches branch_argss;
blanchet@53924
   275
            in
blanchet@53924
   276
              SOME (conds, branches')
blanchet@53924
   277
            end
blanchet@53924
   278
          else
blanchet@53924
   279
            NONE
blanchet@53870
   280
        end
blanchet@53870
   281
      else
blanchet@53870
   282
        NONE
blanchet@53870
   283
    | _ => NONE)
blanchet@53870
   284
  | _ => NONE);
blanchet@53870
   285
blanchet@49437
   286
fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
blanchet@49437
   287
blanchet@52969
   288
fun prepare_wrap_free_constructors prep_term ((((no_discs_sels, rep_compat), raw_ctrs),
blanchet@52968
   289
    raw_case_binding), (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
blanchet@49017
   290
  let
blanchet@49019
   291
    (* TODO: sanity checks on arguments *)
blanchet@49025
   292
blanchet@49280
   293
    val n = length raw_ctrs;
blanchet@49054
   294
    val ks = 1 upto n;
blanchet@49054
   295
blanchet@49121
   296
    val _ = if n > 0 then () else error "No constructors specified";
blanchet@49121
   297
blanchet@49280
   298
    val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
blanchet@49280
   299
    val sel_defaultss =
blanchet@49280
   300
      pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
blanchet@49280
   301
blanchet@53908
   302
    val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
blanchet@53908
   303
    val fc_b_name = Long_Name.base_name fcT_name;
blanchet@53908
   304
    val fc_b = Binding.name fc_b_name;
blanchet@49055
   305
blanchet@49633
   306
    fun qualify mandatory =
blanchet@53908
   307
      Binding.qualify mandatory fc_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
blanchet@49633
   308
blanchet@54386
   309
    fun dest_TFree_or_TVar (TFree sS) = sS
blanchet@53268
   310
      | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
blanchet@53268
   311
      | dest_TFree_or_TVar _ = error "Invalid type argument";
blanchet@52965
   312
blanchet@53268
   313
    val (unsorted_As, B) =
blanchet@49055
   314
      no_defs_lthy
blanchet@53268
   315
      |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
blanchet@49055
   316
      ||> the_single o fst o mk_TFrees 1;
blanchet@49055
   317
blanchet@53268
   318
    val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
blanchet@53268
   319
blanchet@53908
   320
    val fcT = Type (fcT_name, As);
blanchet@49055
   321
    val ctrs = map (mk_ctr As) ctrs0;
blanchet@49055
   322
    val ctr_Tss = map (binder_types o fastype_of) ctrs;
blanchet@49055
   323
blanchet@49055
   324
    val ms = map length ctr_Tss;
blanchet@49055
   325
blanchet@51790
   326
    val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
blanchet@49120
   327
blanchet@53925
   328
    fun can_definitely_rely_on_disc k = not (Binding.is_empty (nth raw_disc_bindings' (k - 1)));
blanchet@51790
   329
    fun can_rely_on_disc k =
blanchet@51790
   330
      can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
blanchet@53925
   331
    fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
blanchet@51790
   332
blanchet@51790
   333
    fun is_disc_binding_valid b =
blanchet@51790
   334
      not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
blanchet@51787
   335
blanchet@52322
   336
    val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
blanchet@49120
   337
blanchet@49336
   338
    val disc_bindings =
blanchet@49336
   339
      raw_disc_bindings'
blanchet@49120
   340
      |> map4 (fn k => fn m => fn ctr => fn disc =>
blanchet@51790
   341
        qualify false
blanchet@51787
   342
          (if Binding.is_empty disc then
blanchet@51790
   343
             if should_omit_disc_binding k then disc else standard_disc_binding ctr
blanchet@51790
   344
           else if Binding.eq_name (disc, equal_binding) then
blanchet@51790
   345
             if m = 0 then disc
blanchet@51790
   346
             else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
blanchet@51790
   347
           else if Binding.eq_name (disc, standard_binding) then
blanchet@51790
   348
             standard_disc_binding ctr
blanchet@49302
   349
           else
blanchet@51790
   350
             disc)) ks ms ctrs0;
blanchet@49056
   351
blanchet@51787
   352
    fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
blanchet@49120
   353
blanchet@49336
   354
    val sel_bindingss =
blanchet@49336
   355
      pad_list [] n raw_sel_bindingss
blanchet@49056
   356
      |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
blanchet@49633
   357
        qualify false
blanchet@51790
   358
          (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
blanchet@51787
   359
            standard_sel_binding m l ctr
blanchet@49302
   360
          else
traytel@49434
   361
            sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
blanchet@49020
   362
blanchet@49201
   363
    val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
blanchet@49043
   364
blanchet@52968
   365
    val ((((((((xss, xss'), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) = no_defs_lthy |>
blanchet@49364
   366
      mk_Freess' "x" ctr_Tss
blanchet@49025
   367
      ||>> mk_Freess "y" ctr_Tss
blanchet@49201
   368
      ||>> mk_Frees "f" case_Ts
blanchet@49201
   369
      ||>> mk_Frees "g" case_Ts
blanchet@53908
   370
      ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
blanchet@52968
   371
      ||>> mk_Frees "z" [B]
blanchet@49043
   372
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
blanchet@49043
   373
blanchet@49498
   374
    val u = Free u';
blanchet@49498
   375
    val v = Free v';
blanchet@49463
   376
    val q = Free (fst p', mk_pred1T B);
blanchet@49020
   377
blanchet@49025
   378
    val xctrs = map2 (curry Term.list_comb) ctrs xss;
blanchet@49025
   379
    val yctrs = map2 (curry Term.list_comb) ctrs yss;
blanchet@49032
   380
blanchet@49043
   381
    val xfs = map2 (curry Term.list_comb) fs xss;
blanchet@49043
   382
    val xgs = map2 (curry Term.list_comb) gs xss;
blanchet@49043
   383
blanchet@52968
   384
    (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
blanchet@52968
   385
       nicer names). Consider removing. *)
blanchet@52968
   386
    val eta_fs = map2 eta_expand_arg xss xfs;
blanchet@52968
   387
    val eta_gs = map2 eta_expand_arg xss xgs;
blanchet@52968
   388
blanchet@52968
   389
    val case_binding =
blanchet@52968
   390
      qualify false
blanchet@52968
   391
        (if Binding.is_empty raw_case_binding orelse
blanchet@52968
   392
            Binding.eq_name (raw_case_binding, standard_binding) then
blanchet@53908
   393
           Binding.suffix_name ("_" ^ caseN) fc_b
blanchet@52968
   394
         else
blanchet@52968
   395
           raw_case_binding);
blanchet@52968
   396
blanchet@52968
   397
    fun mk_case_disj xctr xf xs =
blanchet@52968
   398
      list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
blanchet@52968
   399
blanchet@53925
   400
    val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
blanchet@53925
   401
      (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
blanchet@53925
   402
         Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
blanchet@52968
   403
blanchet@52968
   404
    val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
blanchet@54155
   405
      |> Local_Theory.define ((case_binding, NoSyn),
blanchet@54155
   406
        ((Binding.conceal (Thm.def_binding case_binding), []), case_rhs))
blanchet@52968
   407
      ||> `Local_Theory.restore;
blanchet@52968
   408
blanchet@52968
   409
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@52968
   410
blanchet@52968
   411
    val case_def = Morphism.thm phi raw_case_def;
blanchet@52968
   412
blanchet@52968
   413
    val case0 = Morphism.term phi raw_case;
blanchet@52968
   414
    val casex = mk_case As B case0;
blanchet@52968
   415
blanchet@51759
   416
    val fcase = Term.list_comb (casex, fs);
blanchet@51759
   417
blanchet@51759
   418
    val ufcase = fcase $ u;
blanchet@51759
   419
    val vfcase = fcase $ v;
blanchet@51759
   420
blanchet@51759
   421
    val eta_fcase = Term.list_comb (casex, eta_fs);
blanchet@51759
   422
    val eta_gcase = Term.list_comb (casex, eta_gs);
blanchet@49020
   423
blanchet@51759
   424
    val eta_ufcase = eta_fcase $ u;
blanchet@51759
   425
    val eta_vgcase = eta_gcase $ v;
blanchet@49486
   426
blanchet@49591
   427
    fun mk_uu_eq () = HOLogic.mk_eq (u, u);
blanchet@49486
   428
blanchet@49591
   429
    val uv_eq = mk_Trueprop_eq (u, v);
blanchet@49486
   430
blanchet@49486
   431
    val exist_xs_u_eq_ctrs =
blanchet@49486
   432
      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
blanchet@49022
   433
blanchet@51743
   434
    val unique_disc_no_def = TrueI; (*arbitrary marker*)
blanchet@51743
   435
    val alternate_disc_no_def = FalseE; (*arbitrary marker*)
blanchet@51743
   436
blanchet@49486
   437
    fun alternate_disc_lhs get_udisc k =
blanchet@49116
   438
      HOLogic.mk_not
blanchet@51790
   439
        (let val b = nth disc_bindings (k - 1) in
blanchet@51790
   440
           if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
blanchet@51790
   441
         end);
blanchet@49116
   442
blanchet@53917
   443
    val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
blanchet@52969
   444
      if no_discs_sels then
blanchet@53917
   445
        (true, [], [], [], [], [], lthy)
blanchet@49278
   446
      else
blanchet@49278
   447
        let
blanchet@53908
   448
          fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
blanchet@49025
   449
blanchet@49486
   450
          fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
blanchet@49278
   451
blanchet@49500
   452
          fun alternate_disc k =
blanchet@49500
   453
            Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
blanchet@49278
   454
blanchet@49280
   455
          fun mk_sel_case_args b proto_sels T =
blanchet@49280
   456
            map2 (fn Ts => fn k =>
blanchet@49280
   457
              (case AList.lookup (op =) proto_sels k of
blanchet@49280
   458
                NONE =>
blanchet@49364
   459
                (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
blanchet@49364
   460
                  NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
blanchet@52968
   461
                | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
blanchet@49280
   462
              | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
blanchet@49258
   463
blanchet@49278
   464
          fun sel_spec b proto_sels =
blanchet@49278
   465
            let
blanchet@49278
   466
              val _ =
blanchet@49278
   467
                (case duplicates (op =) (map fst proto_sels) of
blanchet@49278
   468
                   k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
blanchet@49278
   469
                     " for constructor " ^
blanchet@52968
   470
                     quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
blanchet@49278
   471
                 | [] => ())
blanchet@49278
   472
              val T =
blanchet@49278
   473
                (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
blanchet@49278
   474
                  [T] => T
blanchet@49278
   475
                | T :: T' :: _ => error ("Inconsistent range type for selector " ^
blanchet@52968
   476
                    quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
blanchet@52968
   477
                    ^ quote (Syntax.string_of_typ lthy T')));
blanchet@49278
   478
            in
blanchet@53908
   479
              mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
blanchet@49536
   480
                Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
blanchet@49278
   481
            end;
blanchet@49116
   482
blanchet@49336
   483
          val sel_bindings = flat sel_bindingss;
blanchet@49336
   484
          val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
blanchet@49336
   485
          val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
blanchet@49285
   486
blanchet@49336
   487
          val sel_binding_index =
blanchet@49336
   488
            if all_sels_distinct then 1 upto length sel_bindings
blanchet@49336
   489
            else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
blanchet@49285
   490
blanchet@49285
   491
          val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
blanchet@49300
   492
          val sel_infos =
blanchet@49336
   493
            AList.group (op =) (sel_binding_index ~~ proto_sels)
blanchet@49285
   494
            |> sort (int_ord o pairself fst)
blanchet@49336
   495
            |> map snd |> curry (op ~~) uniq_sel_bindings;
blanchet@49336
   496
          val sel_bindings = map fst sel_infos;
blanchet@49258
   497
blanchet@49336
   498
          fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
blanchet@49258
   499
blanchet@49278
   500
          val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
blanchet@52968
   501
            lthy
blanchet@51809
   502
            |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
blanchet@51790
   503
                if Binding.is_empty b then
blanchet@51790
   504
                  if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
blanchet@51790
   505
                  else pair (alternate_disc k, alternate_disc_no_def)
blanchet@51790
   506
                else if Binding.eq_name (b, equal_binding) then
blanchet@51790
   507
                  pair (Term.lambda u exist_xs_u_eq_ctr, refl)
blanchet@51790
   508
                else
blanchet@51790
   509
                  Specification.definition (SOME (b, NONE, NoSyn),
blanchet@51790
   510
                    ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
blanchet@51809
   511
              ks exist_xs_u_eq_ctrs disc_bindings
blanchet@49278
   512
            ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
blanchet@49278
   513
              Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49300
   514
                ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
blanchet@49278
   515
            ||> `Local_Theory.restore;
blanchet@49022
   516
blanchet@49278
   517
          val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49025
   518
blanchet@49278
   519
          val disc_defs = map (Morphism.thm phi) raw_disc_defs;
blanchet@49281
   520
          val sel_defs = map (Morphism.thm phi) raw_sel_defs;
blanchet@49281
   521
          val sel_defss = unflat_selss sel_defs;
blanchet@49278
   522
blanchet@49278
   523
          val discs0 = map (Morphism.term phi) raw_discs;
blanchet@49278
   524
          val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
blanchet@49028
   525
blanchet@49278
   526
          val discs = map (mk_disc_or_sel As) discs0;
blanchet@49278
   527
          val selss = map (map (mk_disc_or_sel As)) selss0;
blanchet@49278
   528
        in
blanchet@53917
   529
          (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
blanchet@49278
   530
        end;
blanchet@49025
   531
blanchet@49032
   532
    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
blanchet@49029
   533
blanchet@49458
   534
    val exhaust_goal =
blanchet@49486
   535
      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (u, xctr)]) in
blanchet@49486
   536
        fold_rev Logic.all [p, u] (mk_imp_p (map2 mk_prem xctrs xss))
blanchet@49020
   537
      end;
blanchet@49019
   538
blanchet@49484
   539
    val inject_goalss =
blanchet@49017
   540
      let
blanchet@49034
   541
        fun mk_goal _ _ [] [] = []
blanchet@49025
   542
          | mk_goal xctr yctr xs ys =
blanchet@49121
   543
            [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
blanchet@49121
   544
              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
blanchet@49017
   545
      in
blanchet@49034
   546
        map4 mk_goal xctrs yctrs xss yss
blanchet@49017
   547
      end;
blanchet@49017
   548
blanchet@49484
   549
    val half_distinct_goalss =
blanchet@49121
   550
      let
blanchet@49203
   551
        fun mk_goal ((xs, xc), (xs', xc')) =
blanchet@49121
   552
          fold_rev Logic.all (xs @ xs')
blanchet@49203
   553
            (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
blanchet@49121
   554
      in
blanchet@49585
   555
        map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
blanchet@49121
   556
      end;
blanchet@49019
   557
blanchet@52968
   558
    val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
blanchet@49019
   559
blanchet@49019
   560
    fun after_qed thmss lthy =
blanchet@49019
   561
      let
blanchet@52968
   562
        val ([exhaust_thm], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
blanchet@49019
   563
blanchet@49438
   564
        val inject_thms = flat inject_thmss;
blanchet@49438
   565
blanchet@53210
   566
        val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
blanchet@49486
   567
blanchet@49486
   568
        fun inst_thm t thm =
blanchet@49486
   569
          Drule.instantiate' [] [SOME (certify lthy t)]
blanchet@53210
   570
            (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
blanchet@49486
   571
blanchet@49486
   572
        val uexhaust_thm = inst_thm u exhaust_thm;
blanchet@49032
   573
blanchet@49300
   574
        val exhaust_cases = map base_name_of_ctr ctrs;
blanchet@49300
   575
blanchet@49048
   576
        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
blanchet@49048
   577
blanchet@49486
   578
        val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
blanchet@49585
   579
          join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
blanchet@49019
   580
blanchet@49020
   581
        val nchotomy_thm =
blanchet@49020
   582
          let
blanchet@49020
   583
            val goal =
blanchet@49486
   584
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
blanchet@49486
   585
                Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
blanchet@49020
   586
          in
wenzelm@51551
   587
            Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
traytel@49667
   588
            |> Thm.close_derivation
blanchet@49020
   589
          end;
blanchet@49020
   590
blanchet@52968
   591
        val case_thms =
blanchet@52968
   592
          let
blanchet@52968
   593
            val goals =
blanchet@52968
   594
              map3 (fn xctr => fn xf => fn xs =>
blanchet@52968
   595
                fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
blanchet@52968
   596
          in
blanchet@52968
   597
            map4 (fn k => fn goal => fn injects => fn distinctss =>
blanchet@52968
   598
                Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@52968
   599
                  mk_case_tac ctxt n k case_def injects distinctss)
blanchet@52968
   600
                |> Thm.close_derivation)
blanchet@52968
   601
              ks goals inject_thmss distinct_thmsss
blanchet@52968
   602
          end;
blanchet@52968
   603
blanchet@53917
   604
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@53917
   605
          let
blanchet@53917
   606
            fun mk_prem xctr xs xf xg =
blanchet@53917
   607
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
blanchet@53917
   608
                mk_Trueprop_eq (xf, xg)));
blanchet@53917
   609
blanchet@53917
   610
            val goal =
blanchet@53917
   611
              Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
blanchet@53917
   612
                 mk_Trueprop_eq (eta_ufcase, eta_vgcase));
blanchet@53917
   613
            val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
blanchet@53917
   614
          in
blanchet@53917
   615
            (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
blanchet@53917
   616
             Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
blanchet@53917
   617
            |> pairself (Thm.close_derivation #> singleton (Proof_Context.export names_lthy lthy))
blanchet@53917
   618
          end;
blanchet@53917
   619
blanchet@53917
   620
        val split_lhs = q $ ufcase;
blanchet@53917
   621
blanchet@53917
   622
        fun mk_split_conjunct xctr xs f_xs =
blanchet@53917
   623
          list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
blanchet@53917
   624
        fun mk_split_disjunct xctr xs f_xs =
blanchet@53917
   625
          list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
blanchet@53917
   626
            HOLogic.mk_not (q $ f_xs)));
blanchet@53917
   627
blanchet@53917
   628
        fun mk_split_goal xctrs xss xfs =
blanchet@53917
   629
          mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
blanchet@53917
   630
            (map3 mk_split_conjunct xctrs xss xfs));
blanchet@53917
   631
        fun mk_split_asm_goal xctrs xss xfs =
blanchet@53917
   632
          mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@53917
   633
            (map3 mk_split_disjunct xctrs xss xfs)));
blanchet@53917
   634
blanchet@53917
   635
        fun prove_split selss goal =
blanchet@53917
   636
          Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@53917
   637
            mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
blanchet@53917
   638
          |> Thm.close_derivation
blanchet@53917
   639
          |> singleton (Proof_Context.export names_lthy lthy);
blanchet@53917
   640
blanchet@53917
   641
        fun prove_split_asm asm_goal split_thm =
blanchet@53917
   642
          Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
blanchet@53917
   643
            mk_split_asm_tac ctxt split_thm)
blanchet@53917
   644
          |> Thm.close_derivation
blanchet@53917
   645
          |> singleton (Proof_Context.export names_lthy lthy);
blanchet@53917
   646
blanchet@53917
   647
        val (split_thm, split_asm_thm) =
blanchet@53917
   648
          let
blanchet@53917
   649
            val goal = mk_split_goal xctrs xss xfs;
blanchet@53917
   650
            val asm_goal = mk_split_asm_goal xctrs xss xfs;
blanchet@53917
   651
blanchet@53917
   652
            val thm = prove_split (replicate n []) goal;
blanchet@53917
   653
            val asm_thm = prove_split_asm asm_goal thm;
blanchet@53917
   654
          in
blanchet@53917
   655
            (thm, asm_thm)
blanchet@53917
   656
          end;
blanchet@53917
   657
blanchet@53704
   658
        val (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms, nontriv_discI_thms,
blanchet@53916
   659
             disc_exclude_thms, disc_exhaust_thms, sel_exhaust_thms, all_collapse_thms,
blanchet@53917
   660
             safe_collapse_thms, expand_thms, sel_split_thms, sel_split_asm_thms,
blanchet@53917
   661
             case_conv_if_thms) =
blanchet@52969
   662
          if no_discs_sels then
blanchet@53917
   663
            ([], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
blanchet@49116
   664
          else
blanchet@49116
   665
            let
blanchet@53917
   666
              val udiscs = map (rapp u) discs;
blanchet@53917
   667
              val uselss = map (map (rapp u)) selss;
blanchet@53917
   668
              val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
blanchet@53917
   669
              val usel_fs = map2 (curry Term.list_comb) fs uselss;
blanchet@53917
   670
blanchet@53917
   671
              val vdiscs = map (rapp v) discs;
blanchet@53917
   672
              val vselss = map (map (rapp v)) selss;
blanchet@53917
   673
blanchet@49364
   674
              fun make_sel_thm xs' case_thm sel_def =
blanchet@49364
   675
                zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
blanchet@49364
   676
                    (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
blanchet@49281
   677
blanchet@53704
   678
              val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
blanchet@53704
   679
blanchet@49281
   680
              fun has_undefined_rhs thm =
blanchet@49281
   681
                (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
blanchet@49281
   682
                  Const (@{const_name undefined}, _) => true
blanchet@49281
   683
                | _ => false);
blanchet@49281
   684
blanchet@49281
   685
              val all_sel_thms =
blanchet@49285
   686
                (if all_sels_distinct andalso forall null sel_defaultss then
blanchet@49285
   687
                   flat sel_thmss
blanchet@49285
   688
                 else
blanchet@49364
   689
                   map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
blanchet@49364
   690
                     (xss' ~~ case_thms))
blanchet@49285
   691
                |> filter_out has_undefined_rhs;
blanchet@49278
   692
blanchet@49278
   693
              fun mk_unique_disc_def () =
blanchet@49278
   694
                let
blanchet@49278
   695
                  val m = the_single ms;
blanchet@49591
   696
                  val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
blanchet@49278
   697
                in
wenzelm@51551
   698
                  Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
blanchet@49692
   699
                  |> Thm.close_derivation
blanchet@49278
   700
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   701
                end;
blanchet@49278
   702
blanchet@49278
   703
              fun mk_alternate_disc_def k =
blanchet@49278
   704
                let
blanchet@49278
   705
                  val goal =
blanchet@49486
   706
                    mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
blanchet@49486
   707
                      nth exist_xs_u_eq_ctrs (k - 1));
blanchet@49278
   708
                in
wenzelm@51551
   709
                  Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49278
   710
                    mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
blanchet@49486
   711
                      (nth distinct_thms (2 - k)) uexhaust_thm)
blanchet@49692
   712
                  |> Thm.close_derivation
blanchet@49278
   713
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   714
                end;
blanchet@49028
   715
blanchet@49278
   716
              val has_alternate_disc_def =
blanchet@49278
   717
                exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
blanchet@49278
   718
blanchet@49278
   719
              val disc_defs' =
blanchet@49278
   720
                map2 (fn k => fn def =>
blanchet@49278
   721
                  if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
blanchet@49278
   722
                  else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
blanchet@49278
   723
                  else def) ks disc_defs;
blanchet@49278
   724
blanchet@49278
   725
              val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49278
   726
              val discI_thms =
blanchet@49278
   727
                map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
blanchet@49278
   728
                  disc_defs';
blanchet@49278
   729
              val not_discI_thms =
blanchet@49278
   730
                map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49504
   731
                    (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49278
   732
                  ms disc_defs';
blanchet@49278
   733
blanchet@49278
   734
              val (disc_thmss', disc_thmss) =
blanchet@49278
   735
                let
blanchet@49278
   736
                  fun mk_thm discI _ [] = refl RS discI
blanchet@49278
   737
                    | mk_thm _ not_discI [distinct] = distinct RS not_discI;
blanchet@49278
   738
                  fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
blanchet@49278
   739
                in
blanchet@49278
   740
                  map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
blanchet@49278
   741
                end;
blanchet@49278
   742
blanchet@53704
   743
              val nontriv_disc_thms =
blanchet@53704
   744
                flat (map2 (fn b => if is_disc_binding_valid b then I else K [])
blanchet@53704
   745
                  disc_bindings disc_thmss);
blanchet@53704
   746
blanchet@53704
   747
              fun is_discI_boring b =
blanchet@53704
   748
                (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
blanchet@53704
   749
blanchet@53704
   750
              val nontriv_discI_thms =
blanchet@53704
   751
                flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
blanchet@53704
   752
                  discI_thms);
blanchet@49028
   753
blanchet@49486
   754
              val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
blanchet@49486
   755
                let
blanchet@49486
   756
                  fun mk_goal [] = []
blanchet@49486
   757
                    | mk_goal [((_, udisc), (_, udisc'))] =
blanchet@49486
   758
                      [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
blanchet@49486
   759
                         HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
blanchet@49486
   760
traytel@49667
   761
                  fun prove tac goal =
wenzelm@51551
   762
                    Goal.prove_sorry lthy [] [] goal (K tac)
traytel@49667
   763
                    |> Thm.close_derivation;
blanchet@49486
   764
blanchet@49585
   765
                  val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
blanchet@49486
   766
blanchet@49486
   767
                  val half_goalss = map mk_goal half_pairss;
blanchet@49486
   768
                  val half_thmss =
blanchet@49486
   769
                    map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
wenzelm@51798
   770
                        fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
blanchet@49486
   771
                      half_goalss half_pairss (flat disc_thmss');
blanchet@49278
   772
blanchet@49486
   773
                  val other_half_goalss = map (mk_goal o map swap) half_pairss;
blanchet@49486
   774
                  val other_half_thmss =
blanchet@49486
   775
                    map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
blanchet@49486
   776
                      other_half_goalss;
blanchet@49486
   777
                in
blanchet@49585
   778
                  join_halves n half_thmss other_half_thmss ||> `transpose
blanchet@49486
   779
                  |>> has_alternate_disc_def ? K []
blanchet@49486
   780
                end;
blanchet@49278
   781
blanchet@49486
   782
              val disc_exhaust_thm =
blanchet@49486
   783
                let
blanchet@49486
   784
                  fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
blanchet@49486
   785
                  val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
blanchet@49486
   786
                in
wenzelm@51551
   787
                  Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@49486
   788
                    mk_disc_exhaust_tac n exhaust_thm discI_thms)
traytel@49667
   789
                  |> Thm.close_derivation
blanchet@49486
   790
                end;
blanchet@49028
   791
blanchet@53740
   792
              val (safe_collapse_thms, all_collapse_thms) =
blanchet@49486
   793
                let
blanchet@54008
   794
                  fun mk_goal m udisc usel_ctr =
blanchet@49486
   795
                    let
blanchet@49486
   796
                      val prem = HOLogic.mk_Trueprop udisc;
blanchet@53916
   797
                      val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
blanchet@49486
   798
                    in
blanchet@53740
   799
                      (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
blanchet@49486
   800
                    end;
blanchet@54008
   801
                  val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
blanchet@53740
   802
                  val thms =
blanchet@53740
   803
                    map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
blanchet@53740
   804
                        Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@53740
   805
                          mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
blanchet@53740
   806
                        |> Thm.close_derivation
blanchet@53740
   807
                        |> not triv ? perhaps (try (fn thm => refl RS thm)))
blanchet@53740
   808
                      ms discD_thms sel_thmss trivs goals;
blanchet@49486
   809
                in
blanchet@53740
   810
                  (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
blanchet@53740
   811
                   thms)
blanchet@49486
   812
                end;
blanchet@49025
   813
blanchet@53916
   814
              val swapped_all_collapse_thms =
blanchet@53916
   815
                map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
blanchet@53916
   816
blanchet@53916
   817
              val sel_exhaust_thm =
blanchet@53916
   818
                let
blanchet@53916
   819
                  fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
blanchet@53916
   820
                  val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
blanchet@53916
   821
                in
blanchet@53916
   822
                  Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@53916
   823
                    mk_sel_exhaust_tac n disc_exhaust_thm swapped_all_collapse_thms)
blanchet@53916
   824
                  |> Thm.close_derivation
blanchet@53916
   825
                end;
blanchet@53916
   826
blanchet@53919
   827
              val expand_thm =
blanchet@49486
   828
                let
blanchet@49486
   829
                  fun mk_prems k udisc usels vdisc vsels =
blanchet@49486
   830
                    (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
blanchet@49486
   831
                    (if null usels then
blanchet@49486
   832
                       []
blanchet@49486
   833
                     else
blanchet@49486
   834
                       [Logic.list_implies
blanchet@49486
   835
                          (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
blanchet@49486
   836
                             HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49486
   837
                               (map2 (curry HOLogic.mk_eq) usels vsels)))]);
blanchet@49486
   838
blanchet@49591
   839
                  val goal =
blanchet@49591
   840
                    Library.foldr Logic.list_implies
blanchet@49591
   841
                      (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
blanchet@49486
   842
                  val uncollapse_thms =
blanchet@53740
   843
                    map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
blanchet@49486
   844
                in
blanchet@53919
   845
                  Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@53919
   846
                    mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
blanchet@53919
   847
                      (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
blanchet@53919
   848
                      disc_exclude_thmsss')
blanchet@53919
   849
                  |> Thm.close_derivation
blanchet@53919
   850
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49486
   851
                end;
blanchet@49278
   852
blanchet@53917
   853
              val (sel_split_thm, sel_split_asm_thm) =
blanchet@53917
   854
                let
blanchet@53917
   855
                  val zss = map (K []) xss;
blanchet@53917
   856
                  val goal = mk_split_goal usel_ctrs zss usel_fs;
blanchet@53917
   857
                  val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
blanchet@53917
   858
blanchet@53917
   859
                  val thm = prove_split sel_thmss goal;
blanchet@53917
   860
                  val asm_thm = prove_split_asm asm_goal thm;
blanchet@53917
   861
                in
blanchet@53917
   862
                  (thm, asm_thm)
blanchet@53917
   863
                end;
blanchet@53917
   864
blanchet@53919
   865
              val case_conv_if_thm =
blanchet@49486
   866
                let
blanchet@53917
   867
                  val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
blanchet@49486
   868
                in
blanchet@53919
   869
                  Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@53919
   870
                    mk_case_conv_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
blanchet@53919
   871
                  |> Thm.close_derivation
blanchet@53919
   872
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49486
   873
                end;
blanchet@49116
   874
            in
blanchet@53704
   875
              (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms,
blanchet@53916
   876
               nontriv_discI_thms, disc_exclude_thms, [disc_exhaust_thm], [sel_exhaust_thm],
blanchet@53919
   877
               all_collapse_thms, safe_collapse_thms, [expand_thm], [sel_split_thm],
blanchet@53919
   878
               [sel_split_asm_thm], [case_conv_if_thm])
blanchet@49116
   879
            end;
blanchet@49025
   880
blanchet@49437
   881
        val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
blanchet@53908
   882
        val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
blanchet@49300
   883
blanchet@54151
   884
        val anonymous_notes =
blanchet@54151
   885
          [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs),
blanchet@54151
   886
           (map (fn th => th RS @{thm eq_False[THEN iffD2]}
blanchet@54151
   887
              handle THM _ => th RS @{thm eq_True[THEN iffD2]}) nontriv_disc_thms,
blanchet@54151
   888
            code_nitpicksimp_attrs)]
blanchet@54151
   889
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@54151
   890
blanchet@49052
   891
        val notes =
blanchet@54145
   892
          [(caseN, case_thms, code_nitpicksimp_simp_attrs),
blanchet@49594
   893
           (case_congN, [case_cong_thm], []),
blanchet@53857
   894
           (case_conv_ifN, case_conv_if_thms, []),
blanchet@53740
   895
           (collapseN, safe_collapse_thms, simp_attrs),
blanchet@53704
   896
           (discN, nontriv_disc_thms, simp_attrs),
blanchet@53700
   897
           (discIN, nontriv_discI_thms, []),
blanchet@53836
   898
           (disc_excludeN, disc_exclude_thms, dest_attrs),
blanchet@49300
   899
           (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
blanchet@54145
   900
           (distinctN, distinct_thms, simp_attrs @ inductsimp_attrs),
blanchet@49300
   901
           (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
blanchet@49486
   902
           (expandN, expand_thms, []),
blanchet@54145
   903
           (injectN, inject_thms, iff_attrs @ inductsimp_attrs),
blanchet@49300
   904
           (nchotomyN, [nchotomy_thm], []),
blanchet@54145
   905
           (selN, all_sel_thms, code_nitpicksimp_simp_attrs),
blanchet@53916
   906
           (sel_exhaustN, sel_exhaust_thms, [exhaust_case_names_attr]),
blanchet@53917
   907
           (sel_splitN, sel_split_thms, []),
blanchet@53917
   908
           (sel_split_asmN, sel_split_asm_thms, []),
blanchet@49300
   909
           (splitN, [split_thm], []),
blanchet@49300
   910
           (split_asmN, [split_asm_thm], []),
blanchet@49633
   911
           (splitsN, [split_thm, split_asm_thm], []),
blanchet@49300
   912
           (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
blanchet@49300
   913
          |> filter_out (null o #2)
blanchet@49300
   914
          |> map (fn (thmN, thms, attrs) =>
blanchet@49633
   915
            ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49300
   916
blanchet@53867
   917
        val ctr_sugar =
blanchet@53867
   918
          {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
blanchet@53867
   919
           nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
blanchet@53867
   920
           case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
blanchet@53867
   921
           split = split_thm, split_asm = split_asm_thm, disc_thmss = disc_thmss,
blanchet@53867
   922
           discIs = discI_thms, sel_thmss = sel_thmss, disc_exhausts = disc_exhaust_thms,
blanchet@53916
   923
           sel_exhausts = sel_exhaust_thms, collapses = all_collapse_thms, expands = expand_thms,
blanchet@53917
   924
           sel_splits = sel_split_thms, sel_split_asms = sel_split_asm_thms,
blanchet@53916
   925
           case_conv_ifs = case_conv_if_thms};
blanchet@49019
   926
      in
blanchet@53867
   927
        (ctr_sugar,
blanchet@51819
   928
         lthy
blanchet@51819
   929
         |> not rep_compat ?
blanchet@54285
   930
            (Local_Theory.declaration {syntax = false, pervasive = true}
traytel@51697
   931
               (fn phi => Case_Translation.register
blanchet@51819
   932
                  (Morphism.term phi casex) (map (Morphism.term phi) ctrs)))
blanchet@54145
   933
         |> Local_Theory.notes (anonymous_notes @ notes) |> snd
blanchet@53908
   934
         |> register_ctr_sugar fcT_name ctr_sugar)
blanchet@49019
   935
      end;
blanchet@49017
   936
  in
blanchet@49121
   937
    (goalss, after_qed, lthy')
blanchet@49017
   938
  end;
blanchet@49017
   939
blanchet@51781
   940
fun wrap_free_constructors tacss = (fn (goalss, after_qed, lthy) =>
wenzelm@51551
   941
  map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
blanchet@51781
   942
  |> (fn thms => after_qed thms lthy)) oo prepare_wrap_free_constructors (K I);
blanchet@49280
   943
blanchet@51781
   944
val wrap_free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49297
   945
  Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
blanchet@51781
   946
  prepare_wrap_free_constructors Syntax.read_term;
blanchet@49297
   947
blanchet@49280
   948
fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
blanchet@49111
   949
blanchet@51790
   950
val parse_bindings = parse_bracket_list parse_binding;
blanchet@49280
   951
val parse_bindingss = parse_bracket_list parse_bindings;
blanchet@49280
   952
blanchet@51790
   953
val parse_bound_term = (parse_binding --| @{keyword ":"}) -- Parse.term;
blanchet@49280
   954
val parse_bound_terms = parse_bracket_list parse_bound_term;
blanchet@49280
   955
val parse_bound_termss = parse_bracket_list parse_bound_terms;
blanchet@49017
   956
blanchet@52823
   957
val parse_wrap_free_constructors_options =
blanchet@52969
   958
  Scan.optional (@{keyword "("} |-- Parse.list1 ((@{keyword "no_discs_sels"} >> K (true, false)) ||
blanchet@49633
   959
      (@{keyword "rep_compat"} >> K (false, true))) --| @{keyword ")"}
blanchet@49633
   960
    >> (pairself (exists I) o split_list)) (false, false);
blanchet@49278
   961
blanchet@49017
   962
val _ =
blanchet@51781
   963
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_free_constructors"}
blanchet@51797
   964
    "wrap an existing freely generated type's constructors"
blanchet@52823
   965
    ((parse_wrap_free_constructors_options -- (@{keyword "["} |-- Parse.list Parse.term --|
blanchet@52823
   966
        @{keyword "]"}) --
blanchet@52968
   967
      parse_binding -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
blanchet@49280
   968
        Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
blanchet@51781
   969
     >> wrap_free_constructors_cmd);
blanchet@49017
   970
blanchet@49017
   971
end;