src/HOL/BNF/Tools/bnf_ctr_sugar.ML
author blanchet
Thu Sep 19 20:03:41 2013 +0200 (2013-09-19)
changeset 53740 c1911450b84a
parent 53704 657c89169d1a
child 53798 6a4e3299dfd1
permissions -rw-r--r--
cleaner handling of collapse theorems
blanchet@51797
     1
(*  Title:      HOL/BNF/Tools/bnf_ctr_sugar.ML
blanchet@49017
     2
    Author:     Jasmin Blanchette, TU Muenchen
blanchet@49017
     3
    Copyright   2012
blanchet@49017
     4
blanchet@51797
     5
Wrapping existing freely generated type's constructors.
blanchet@49017
     6
*)
blanchet@49017
     7
blanchet@51797
     8
signature BNF_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@53475
    28
     collapses: thm list,
blanchet@53475
    29
     expands: thm list,
blanchet@53475
    30
     case_convs: thm list};
blanchet@51809
    31
blanchet@51840
    32
  val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar
blanchet@51823
    33
blanchet@49633
    34
  val rep_compat_prefix: string
blanchet@49633
    35
blanchet@49585
    36
  val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
blanchet@49585
    37
  val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
blanchet@49585
    38
blanchet@49203
    39
  val mk_ctr: typ list -> term -> term
blanchet@49484
    40
  val mk_disc_or_sel: typ list -> term -> term
blanchet@49585
    41
blanchet@49622
    42
  val name_of_ctr: term -> string
blanchet@51777
    43
  val name_of_disc: term -> string
blanchet@49585
    44
blanchet@51781
    45
  val wrap_free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
blanchet@52968
    46
    (((bool * bool) * term list) * binding) *
blanchet@49280
    47
      (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
blanchet@51840
    48
    ctr_sugar * local_theory
blanchet@52823
    49
  val parse_wrap_free_constructors_options: (bool * bool) parser
blanchet@49286
    50
  val parse_bound_term: (binding * string) parser
blanchet@49017
    51
end;
blanchet@49017
    52
blanchet@51797
    53
structure BNF_Ctr_Sugar : BNF_CTR_SUGAR =
blanchet@49017
    54
struct
blanchet@49017
    55
blanchet@49017
    56
open BNF_Util
blanchet@51797
    57
open BNF_Ctr_Sugar_Tactics
blanchet@49017
    58
blanchet@51840
    59
type ctr_sugar =
blanchet@51839
    60
  {ctrs: term list,
blanchet@52375
    61
   casex: term,
blanchet@51839
    62
   discs: term list,
blanchet@51819
    63
   selss: term list list,
blanchet@51819
    64
   exhaust: thm,
blanchet@52375
    65
   nchotomy: thm,
blanchet@51819
    66
   injects: thm list,
blanchet@51819
    67
   distincts: thm list,
blanchet@51819
    68
   case_thms: thm list,
blanchet@52375
    69
   case_cong: thm,
blanchet@52375
    70
   weak_case_cong: thm,
blanchet@52375
    71
   split: thm,
blanchet@52375
    72
   split_asm: thm,
blanchet@51819
    73
   disc_thmss: thm list list,
blanchet@51819
    74
   discIs: thm list,
blanchet@53475
    75
   sel_thmss: thm list list,
blanchet@53475
    76
   disc_exhausts: thm list,
blanchet@53475
    77
   collapses: thm list,
blanchet@53475
    78
   expands: thm list,
blanchet@53475
    79
   case_convs: thm list};
blanchet@51809
    80
blanchet@52375
    81
fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
blanchet@53475
    82
    case_thms, case_cong, weak_case_cong, split, split_asm, disc_thmss, discIs, sel_thmss,
blanchet@53475
    83
    disc_exhausts, collapses, expands, case_convs} =
blanchet@51839
    84
  {ctrs = map (Morphism.term phi) ctrs,
blanchet@52375
    85
   casex = Morphism.term phi casex,
blanchet@51839
    86
   discs = map (Morphism.term phi) discs,
blanchet@51823
    87
   selss = map (map (Morphism.term phi)) selss,
blanchet@51823
    88
   exhaust = Morphism.thm phi exhaust,
blanchet@52375
    89
   nchotomy = Morphism.thm phi nchotomy,
blanchet@51823
    90
   injects = map (Morphism.thm phi) injects,
blanchet@51823
    91
   distincts = map (Morphism.thm phi) distincts,
blanchet@51823
    92
   case_thms = map (Morphism.thm phi) case_thms,
blanchet@52375
    93
   case_cong = Morphism.thm phi case_cong,
blanchet@52375
    94
   weak_case_cong = Morphism.thm phi weak_case_cong,
blanchet@52375
    95
   split = Morphism.thm phi split,
blanchet@52375
    96
   split_asm = Morphism.thm phi split_asm,
blanchet@51823
    97
   disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
blanchet@51823
    98
   discIs = map (Morphism.thm phi) discIs,
blanchet@53475
    99
   sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
blanchet@53475
   100
   disc_exhausts = map (Morphism.thm phi) disc_exhausts,
blanchet@53475
   101
   collapses = map (Morphism.thm phi) collapses,
blanchet@53475
   102
   expands = map (Morphism.thm phi) expands,
blanchet@53475
   103
   case_convs = map (Morphism.thm phi) case_convs};
blanchet@51823
   104
blanchet@49633
   105
val rep_compat_prefix = "new";
blanchet@49633
   106
blanchet@49223
   107
val isN = "is_";
blanchet@49223
   108
val unN = "un_";
blanchet@49223
   109
fun mk_unN 1 1 suf = unN ^ suf
blanchet@49223
   110
  | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
blanchet@49046
   111
blanchet@49594
   112
val caseN = "case";
blanchet@49054
   113
val case_congN = "case_cong";
blanchet@49594
   114
val case_convN = "case_conv";
blanchet@49118
   115
val collapseN = "collapse";
blanchet@49122
   116
val disc_excludeN = "disc_exclude";
blanchet@49054
   117
val disc_exhaustN = "disc_exhaust";
blanchet@53694
   118
val discN = "disc";
blanchet@53700
   119
val discIN = "discI";
blanchet@49054
   120
val distinctN = "distinct";
blanchet@49075
   121
val exhaustN = "exhaust";
blanchet@49486
   122
val expandN = "expand";
blanchet@49075
   123
val injectN = "inject";
blanchet@49075
   124
val nchotomyN = "nchotomy";
blanchet@53694
   125
val selN = "sel";
blanchet@49054
   126
val splitN = "split";
blanchet@49633
   127
val splitsN = "splits";
blanchet@49054
   128
val split_asmN = "split_asm";
blanchet@49054
   129
val weak_case_cong_thmsN = "weak_case_cong";
blanchet@49019
   130
blanchet@53700
   131
val cong_attrs = @{attributes [cong]};
blanchet@53700
   132
val safe_elim_attrs = @{attributes [elim!]};
blanchet@53700
   133
val iff_attrs = @{attributes [iff]};
blanchet@49300
   134
val induct_simp_attrs = @{attributes [induct_simp]};
blanchet@49300
   135
val simp_attrs = @{attributes [simp]};
blanchet@49046
   136
blanchet@53040
   137
fun unflat_lookup eq xs ys = map (fn xs' => permute_like eq xs xs' ys);
blanchet@49258
   138
blanchet@49585
   139
fun mk_half_pairss' _ ([], []) = []
blanchet@49591
   140
  | mk_half_pairss' indent (x :: xs, _ :: ys) =
blanchet@49585
   141
    indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
blanchet@49486
   142
blanchet@49585
   143
fun mk_half_pairss p = mk_half_pairss' [[]] p;
blanchet@49027
   144
blanchet@49486
   145
fun join_halves n half_xss other_half_xss =
blanchet@49486
   146
  let
blanchet@49486
   147
    val xsss =
blanchet@49486
   148
      map2 (map2 append) (Library.chop_groups n half_xss)
blanchet@49486
   149
        (transpose (Library.chop_groups n other_half_xss))
blanchet@49668
   150
    val xs = splice (flat half_xss) (flat other_half_xss);
blanchet@49585
   151
  in (xs, xsss) end;
blanchet@49027
   152
blanchet@49280
   153
fun mk_undefined T = Const (@{const_name undefined}, T);
blanchet@49055
   154
blanchet@49500
   155
fun mk_ctr Ts t =
blanchet@49500
   156
  let val Type (_, Ts0) = body_type (fastype_of t) in
blanchet@49500
   157
    Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49203
   158
  end;
blanchet@49203
   159
blanchet@49484
   160
fun mk_disc_or_sel Ts t =
blanchet@49484
   161
  Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
blanchet@49484
   162
blanchet@49536
   163
fun mk_case Ts T t =
blanchet@49536
   164
  let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
blanchet@49536
   165
    Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) t
blanchet@49536
   166
  end;
blanchet@49536
   167
blanchet@51777
   168
fun name_of_const what t =
blanchet@51777
   169
  (case head_of t of
blanchet@49622
   170
    Const (s, _) => s
blanchet@49622
   171
  | Free (s, _) => s
blanchet@51777
   172
  | _ => error ("Cannot extract name of " ^ what));
blanchet@51777
   173
blanchet@51777
   174
val name_of_ctr = name_of_const "constructor";
blanchet@51777
   175
blanchet@51777
   176
val notN = "not_";
blanchet@51777
   177
val eqN = "eq_";
blanchet@51777
   178
val neqN = "neq_";
blanchet@51777
   179
blanchet@51777
   180
fun name_of_disc t =
blanchet@51777
   181
  (case head_of t of
blanchet@51777
   182
    Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
blanchet@51777
   183
    Long_Name.map_base_name (prefix notN) (name_of_disc t')
blanchet@51777
   184
  | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
blanchet@51777
   185
    Long_Name.map_base_name (prefix eqN) (name_of_disc t')
blanchet@51777
   186
  | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
blanchet@51777
   187
    Long_Name.map_base_name (prefix neqN) (name_of_disc t')
blanchet@51777
   188
  | t' => name_of_const "destructor" t');
blanchet@49622
   189
blanchet@49622
   190
val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
blanchet@49046
   191
blanchet@49437
   192
fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
blanchet@49437
   193
blanchet@52969
   194
fun prepare_wrap_free_constructors prep_term ((((no_discs_sels, rep_compat), raw_ctrs),
blanchet@52968
   195
    raw_case_binding), (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
blanchet@49017
   196
  let
blanchet@49019
   197
    (* TODO: sanity checks on arguments *)
blanchet@49025
   198
blanchet@49280
   199
    val n = length raw_ctrs;
blanchet@49054
   200
    val ks = 1 upto n;
blanchet@49054
   201
blanchet@49121
   202
    val _ = if n > 0 then () else error "No constructors specified";
blanchet@49121
   203
blanchet@49280
   204
    val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
blanchet@49280
   205
    val sel_defaultss =
blanchet@49280
   206
      pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
blanchet@49280
   207
blanchet@52968
   208
    val Type (dataT_name, As0) = body_type (fastype_of (hd ctrs0));
blanchet@52988
   209
    val data_b_name = Long_Name.base_name dataT_name;
blanchet@52988
   210
    val data_b = Binding.name data_b_name;
blanchet@49055
   211
blanchet@49633
   212
    fun qualify mandatory =
blanchet@49633
   213
      Binding.qualify mandatory data_b_name o
blanchet@49633
   214
      (rep_compat ? Binding.qualify false rep_compat_prefix);
blanchet@49633
   215
blanchet@53268
   216
    fun dest_TFree_or_TVar (TFree p) = p
blanchet@53268
   217
      | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
blanchet@53268
   218
      | dest_TFree_or_TVar _ = error "Invalid type argument";
blanchet@52965
   219
blanchet@53268
   220
    val (unsorted_As, B) =
blanchet@49055
   221
      no_defs_lthy
blanchet@53268
   222
      |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
blanchet@49055
   223
      ||> the_single o fst o mk_TFrees 1;
blanchet@49055
   224
blanchet@53268
   225
    val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
blanchet@53268
   226
blanchet@49300
   227
    val dataT = Type (dataT_name, As);
blanchet@49055
   228
    val ctrs = map (mk_ctr As) ctrs0;
blanchet@49055
   229
    val ctr_Tss = map (binder_types o fastype_of) ctrs;
blanchet@49055
   230
blanchet@49055
   231
    val ms = map length ctr_Tss;
blanchet@49055
   232
blanchet@51790
   233
    val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
blanchet@49120
   234
blanchet@51790
   235
    fun can_definitely_rely_on_disc k =
blanchet@51790
   236
      not (Binding.is_empty (nth raw_disc_bindings' (k - 1)));
blanchet@51790
   237
    fun can_rely_on_disc k =
blanchet@51790
   238
      can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
blanchet@51787
   239
    fun should_omit_disc_binding k =
blanchet@51790
   240
      n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
blanchet@51790
   241
blanchet@51790
   242
    fun is_disc_binding_valid b =
blanchet@51790
   243
      not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
blanchet@51787
   244
blanchet@52322
   245
    val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
blanchet@49120
   246
blanchet@49336
   247
    val disc_bindings =
blanchet@49336
   248
      raw_disc_bindings'
blanchet@49120
   249
      |> map4 (fn k => fn m => fn ctr => fn disc =>
blanchet@51790
   250
        qualify false
blanchet@51787
   251
          (if Binding.is_empty disc then
blanchet@51790
   252
             if should_omit_disc_binding k then disc else standard_disc_binding ctr
blanchet@51790
   253
           else if Binding.eq_name (disc, equal_binding) then
blanchet@51790
   254
             if m = 0 then disc
blanchet@51790
   255
             else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
blanchet@51790
   256
           else if Binding.eq_name (disc, standard_binding) then
blanchet@51790
   257
             standard_disc_binding ctr
blanchet@49302
   258
           else
blanchet@51790
   259
             disc)) ks ms ctrs0;
blanchet@49056
   260
blanchet@51787
   261
    fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
blanchet@49120
   262
blanchet@49336
   263
    val sel_bindingss =
blanchet@49336
   264
      pad_list [] n raw_sel_bindingss
blanchet@49056
   265
      |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
blanchet@49633
   266
        qualify false
blanchet@51790
   267
          (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
blanchet@51787
   268
            standard_sel_binding m l ctr
blanchet@49302
   269
          else
traytel@49434
   270
            sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
blanchet@49020
   271
blanchet@49201
   272
    val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
blanchet@49043
   273
blanchet@52968
   274
    val ((((((((xss, xss'), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) = no_defs_lthy |>
blanchet@49364
   275
      mk_Freess' "x" ctr_Tss
blanchet@49025
   276
      ||>> mk_Freess "y" ctr_Tss
blanchet@49201
   277
      ||>> mk_Frees "f" case_Ts
blanchet@49201
   278
      ||>> mk_Frees "g" case_Ts
blanchet@49498
   279
      ||>> (apfst (map (rpair dataT)) oo Variable.variant_fixes) [data_b_name, data_b_name ^ "'"]
blanchet@52968
   280
      ||>> mk_Frees "z" [B]
blanchet@49043
   281
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
blanchet@49043
   282
blanchet@49498
   283
    val u = Free u';
blanchet@49498
   284
    val v = Free v';
blanchet@49463
   285
    val q = Free (fst p', mk_pred1T B);
blanchet@49020
   286
blanchet@49025
   287
    val xctrs = map2 (curry Term.list_comb) ctrs xss;
blanchet@49025
   288
    val yctrs = map2 (curry Term.list_comb) ctrs yss;
blanchet@49032
   289
blanchet@49043
   290
    val xfs = map2 (curry Term.list_comb) fs xss;
blanchet@49043
   291
    val xgs = map2 (curry Term.list_comb) gs xss;
blanchet@49043
   292
blanchet@52968
   293
    (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
blanchet@52968
   294
       nicer names). Consider removing. *)
blanchet@52968
   295
    val eta_fs = map2 eta_expand_arg xss xfs;
blanchet@52968
   296
    val eta_gs = map2 eta_expand_arg xss xgs;
blanchet@52968
   297
blanchet@52968
   298
    val case_binding =
blanchet@52968
   299
      qualify false
blanchet@52968
   300
        (if Binding.is_empty raw_case_binding orelse
blanchet@52968
   301
            Binding.eq_name (raw_case_binding, standard_binding) then
blanchet@52968
   302
           Binding.suffix_name ("_" ^ caseN) data_b
blanchet@52968
   303
         else
blanchet@52968
   304
           raw_case_binding);
blanchet@52968
   305
blanchet@52968
   306
    fun mk_case_disj xctr xf xs =
blanchet@52968
   307
      list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
blanchet@52968
   308
blanchet@52968
   309
    val case_rhs =
blanchet@52968
   310
      fold_rev (fold_rev Term.lambda) [fs, [u]]
blanchet@52968
   311
        (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
blanchet@52968
   312
           Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
blanchet@52968
   313
blanchet@52968
   314
    val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
blanchet@52968
   315
      |> Local_Theory.define ((case_binding, NoSyn), ((Thm.def_binding case_binding, []), case_rhs))
blanchet@52968
   316
      ||> `Local_Theory.restore;
blanchet@52968
   317
blanchet@52968
   318
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@52968
   319
blanchet@52968
   320
    val case_def = Morphism.thm phi raw_case_def;
blanchet@52968
   321
blanchet@52968
   322
    val case0 = Morphism.term phi raw_case;
blanchet@52968
   323
    val casex = mk_case As B case0;
blanchet@52968
   324
blanchet@51759
   325
    val fcase = Term.list_comb (casex, fs);
blanchet@51759
   326
blanchet@51759
   327
    val ufcase = fcase $ u;
blanchet@51759
   328
    val vfcase = fcase $ v;
blanchet@51759
   329
blanchet@51759
   330
    val eta_fcase = Term.list_comb (casex, eta_fs);
blanchet@51759
   331
    val eta_gcase = Term.list_comb (casex, eta_gs);
blanchet@49020
   332
blanchet@51759
   333
    val eta_ufcase = eta_fcase $ u;
blanchet@51759
   334
    val eta_vgcase = eta_gcase $ v;
blanchet@49486
   335
blanchet@49591
   336
    fun mk_uu_eq () = HOLogic.mk_eq (u, u);
blanchet@49486
   337
blanchet@49591
   338
    val uv_eq = mk_Trueprop_eq (u, v);
blanchet@49486
   339
blanchet@49486
   340
    val exist_xs_u_eq_ctrs =
blanchet@49486
   341
      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
blanchet@49022
   342
blanchet@51743
   343
    val unique_disc_no_def = TrueI; (*arbitrary marker*)
blanchet@51743
   344
    val alternate_disc_no_def = FalseE; (*arbitrary marker*)
blanchet@51743
   345
blanchet@49486
   346
    fun alternate_disc_lhs get_udisc k =
blanchet@49116
   347
      HOLogic.mk_not
blanchet@51790
   348
        (let val b = nth disc_bindings (k - 1) in
blanchet@51790
   349
           if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
blanchet@51790
   350
         end);
blanchet@49116
   351
blanchet@49486
   352
    val (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
blanchet@49486
   353
         sel_defss, lthy') =
blanchet@52969
   354
      if no_discs_sels then
blanchet@52968
   355
        (true, [], [], [], [], [], [], [], [], [], lthy)
blanchet@49278
   356
      else
blanchet@49278
   357
        let
blanchet@49463
   358
          fun disc_free b = Free (Binding.name_of b, mk_pred1T dataT);
blanchet@49025
   359
blanchet@49486
   360
          fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
blanchet@49278
   361
blanchet@49500
   362
          fun alternate_disc k =
blanchet@49500
   363
            Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
blanchet@49278
   364
blanchet@49280
   365
          fun mk_sel_case_args b proto_sels T =
blanchet@49280
   366
            map2 (fn Ts => fn k =>
blanchet@49280
   367
              (case AList.lookup (op =) proto_sels k of
blanchet@49280
   368
                NONE =>
blanchet@49364
   369
                (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
blanchet@49364
   370
                  NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
blanchet@52968
   371
                | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
blanchet@49280
   372
              | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
blanchet@49258
   373
blanchet@49278
   374
          fun sel_spec b proto_sels =
blanchet@49278
   375
            let
blanchet@49278
   376
              val _ =
blanchet@49278
   377
                (case duplicates (op =) (map fst proto_sels) of
blanchet@49278
   378
                   k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
blanchet@49278
   379
                     " for constructor " ^
blanchet@52968
   380
                     quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
blanchet@49278
   381
                 | [] => ())
blanchet@49278
   382
              val T =
blanchet@49278
   383
                (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
blanchet@49278
   384
                  [T] => T
blanchet@49278
   385
                | T :: T' :: _ => error ("Inconsistent range type for selector " ^
blanchet@52968
   386
                    quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
blanchet@52968
   387
                    ^ quote (Syntax.string_of_typ lthy T')));
blanchet@49278
   388
            in
blanchet@49486
   389
              mk_Trueprop_eq (Free (Binding.name_of b, dataT --> T) $ u,
blanchet@49536
   390
                Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
blanchet@49278
   391
            end;
blanchet@49116
   392
blanchet@49336
   393
          val sel_bindings = flat sel_bindingss;
blanchet@49336
   394
          val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
blanchet@49336
   395
          val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
blanchet@49285
   396
blanchet@49336
   397
          val sel_binding_index =
blanchet@49336
   398
            if all_sels_distinct then 1 upto length sel_bindings
blanchet@49336
   399
            else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
blanchet@49285
   400
blanchet@49285
   401
          val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
blanchet@49300
   402
          val sel_infos =
blanchet@49336
   403
            AList.group (op =) (sel_binding_index ~~ proto_sels)
blanchet@49285
   404
            |> sort (int_ord o pairself fst)
blanchet@49336
   405
            |> map snd |> curry (op ~~) uniq_sel_bindings;
blanchet@49336
   406
          val sel_bindings = map fst sel_infos;
blanchet@49258
   407
blanchet@49336
   408
          fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
blanchet@49258
   409
blanchet@49278
   410
          val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
blanchet@52968
   411
            lthy
blanchet@51809
   412
            |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
blanchet@51790
   413
                if Binding.is_empty b then
blanchet@51790
   414
                  if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
blanchet@51790
   415
                  else pair (alternate_disc k, alternate_disc_no_def)
blanchet@51790
   416
                else if Binding.eq_name (b, equal_binding) then
blanchet@51790
   417
                  pair (Term.lambda u exist_xs_u_eq_ctr, refl)
blanchet@51790
   418
                else
blanchet@51790
   419
                  Specification.definition (SOME (b, NONE, NoSyn),
blanchet@51790
   420
                    ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
blanchet@51809
   421
              ks exist_xs_u_eq_ctrs disc_bindings
blanchet@49278
   422
            ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
blanchet@49278
   423
              Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49300
   424
                ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
blanchet@49278
   425
            ||> `Local_Theory.restore;
blanchet@49022
   426
blanchet@49278
   427
          val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49025
   428
blanchet@49278
   429
          val disc_defs = map (Morphism.thm phi) raw_disc_defs;
blanchet@49281
   430
          val sel_defs = map (Morphism.thm phi) raw_sel_defs;
blanchet@49281
   431
          val sel_defss = unflat_selss sel_defs;
blanchet@49278
   432
blanchet@49278
   433
          val discs0 = map (Morphism.term phi) raw_discs;
blanchet@49278
   434
          val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
blanchet@49028
   435
blanchet@49278
   436
          val discs = map (mk_disc_or_sel As) discs0;
blanchet@49278
   437
          val selss = map (map (mk_disc_or_sel As)) selss0;
blanchet@49486
   438
blanchet@49500
   439
          val udiscs = map (rapp u) discs;
blanchet@49500
   440
          val uselss = map (map (rapp u)) selss;
blanchet@49486
   441
blanchet@49500
   442
          val vdiscs = map (rapp v) discs;
blanchet@49500
   443
          val vselss = map (map (rapp v)) selss;
blanchet@49278
   444
        in
blanchet@49486
   445
          (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
blanchet@49486
   446
           sel_defss, lthy')
blanchet@49278
   447
        end;
blanchet@49025
   448
blanchet@49032
   449
    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
blanchet@49029
   450
blanchet@49458
   451
    val exhaust_goal =
blanchet@49486
   452
      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (u, xctr)]) in
blanchet@49486
   453
        fold_rev Logic.all [p, u] (mk_imp_p (map2 mk_prem xctrs xss))
blanchet@49020
   454
      end;
blanchet@49019
   455
blanchet@49484
   456
    val inject_goalss =
blanchet@49017
   457
      let
blanchet@49034
   458
        fun mk_goal _ _ [] [] = []
blanchet@49025
   459
          | mk_goal xctr yctr xs ys =
blanchet@49121
   460
            [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
blanchet@49121
   461
              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
blanchet@49017
   462
      in
blanchet@49034
   463
        map4 mk_goal xctrs yctrs xss yss
blanchet@49017
   464
      end;
blanchet@49017
   465
blanchet@49484
   466
    val half_distinct_goalss =
blanchet@49121
   467
      let
blanchet@49203
   468
        fun mk_goal ((xs, xc), (xs', xc')) =
blanchet@49121
   469
          fold_rev Logic.all (xs @ xs')
blanchet@49203
   470
            (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
blanchet@49121
   471
      in
blanchet@49585
   472
        map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
blanchet@49121
   473
      end;
blanchet@49019
   474
blanchet@52968
   475
    val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
blanchet@49019
   476
blanchet@49019
   477
    fun after_qed thmss lthy =
blanchet@49019
   478
      let
blanchet@52968
   479
        val ([exhaust_thm], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
blanchet@49019
   480
blanchet@49438
   481
        val inject_thms = flat inject_thmss;
blanchet@49438
   482
blanchet@53210
   483
        val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
blanchet@49486
   484
blanchet@49486
   485
        fun inst_thm t thm =
blanchet@49486
   486
          Drule.instantiate' [] [SOME (certify lthy t)]
blanchet@53210
   487
            (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
blanchet@49486
   488
blanchet@49486
   489
        val uexhaust_thm = inst_thm u exhaust_thm;
blanchet@49032
   490
blanchet@49300
   491
        val exhaust_cases = map base_name_of_ctr ctrs;
blanchet@49300
   492
blanchet@49048
   493
        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
blanchet@49048
   494
blanchet@49486
   495
        val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
blanchet@49585
   496
          join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
blanchet@49019
   497
blanchet@49020
   498
        val nchotomy_thm =
blanchet@49020
   499
          let
blanchet@49020
   500
            val goal =
blanchet@49486
   501
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
blanchet@49486
   502
                Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
blanchet@49020
   503
          in
wenzelm@51551
   504
            Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
traytel@49667
   505
            |> Thm.close_derivation
blanchet@49020
   506
          end;
blanchet@49020
   507
blanchet@52968
   508
        val case_thms =
blanchet@52968
   509
          let
blanchet@52968
   510
            val goals =
blanchet@52968
   511
              map3 (fn xctr => fn xf => fn xs =>
blanchet@52968
   512
                fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
blanchet@52968
   513
          in
blanchet@52968
   514
            map4 (fn k => fn goal => fn injects => fn distinctss =>
blanchet@52968
   515
                Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@52968
   516
                  mk_case_tac ctxt n k case_def injects distinctss)
blanchet@52968
   517
                |> Thm.close_derivation)
blanchet@52968
   518
              ks goals inject_thmss distinct_thmsss
blanchet@52968
   519
          end;
blanchet@52968
   520
blanchet@53704
   521
        val (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms, nontriv_discI_thms,
blanchet@53740
   522
             disc_exclude_thms, disc_exhaust_thms, all_collapse_thms, safe_collapse_thms,
blanchet@53740
   523
             expand_thms, case_conv_thms) =
blanchet@52969
   524
          if no_discs_sels then
blanchet@53740
   525
            ([], [], [], [], [], [], [], [], [], [], [], [])
blanchet@49116
   526
          else
blanchet@49116
   527
            let
blanchet@49364
   528
              fun make_sel_thm xs' case_thm sel_def =
blanchet@49364
   529
                zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
blanchet@49364
   530
                    (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
blanchet@49281
   531
blanchet@53704
   532
              val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
blanchet@53704
   533
blanchet@49281
   534
              fun has_undefined_rhs thm =
blanchet@49281
   535
                (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
blanchet@49281
   536
                  Const (@{const_name undefined}, _) => true
blanchet@49281
   537
                | _ => false);
blanchet@49281
   538
blanchet@49281
   539
              val all_sel_thms =
blanchet@49285
   540
                (if all_sels_distinct andalso forall null sel_defaultss then
blanchet@49285
   541
                   flat sel_thmss
blanchet@49285
   542
                 else
blanchet@49364
   543
                   map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
blanchet@49364
   544
                     (xss' ~~ case_thms))
blanchet@49285
   545
                |> filter_out has_undefined_rhs;
blanchet@49278
   546
blanchet@49278
   547
              fun mk_unique_disc_def () =
blanchet@49278
   548
                let
blanchet@49278
   549
                  val m = the_single ms;
blanchet@49591
   550
                  val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
blanchet@49278
   551
                in
wenzelm@51551
   552
                  Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
blanchet@49692
   553
                  |> Thm.close_derivation
blanchet@49278
   554
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   555
                end;
blanchet@49278
   556
blanchet@49278
   557
              fun mk_alternate_disc_def k =
blanchet@49278
   558
                let
blanchet@49278
   559
                  val goal =
blanchet@49486
   560
                    mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
blanchet@49486
   561
                      nth exist_xs_u_eq_ctrs (k - 1));
blanchet@49278
   562
                in
wenzelm@51551
   563
                  Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49278
   564
                    mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
blanchet@49486
   565
                      (nth distinct_thms (2 - k)) uexhaust_thm)
blanchet@49692
   566
                  |> Thm.close_derivation
blanchet@49278
   567
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   568
                end;
blanchet@49028
   569
blanchet@49278
   570
              val has_alternate_disc_def =
blanchet@49278
   571
                exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
blanchet@49278
   572
blanchet@49278
   573
              val disc_defs' =
blanchet@49278
   574
                map2 (fn k => fn def =>
blanchet@49278
   575
                  if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
blanchet@49278
   576
                  else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
blanchet@49278
   577
                  else def) ks disc_defs;
blanchet@49278
   578
blanchet@49278
   579
              val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49278
   580
              val discI_thms =
blanchet@49278
   581
                map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
blanchet@49278
   582
                  disc_defs';
blanchet@49278
   583
              val not_discI_thms =
blanchet@49278
   584
                map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49504
   585
                    (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49278
   586
                  ms disc_defs';
blanchet@49278
   587
blanchet@49278
   588
              val (disc_thmss', disc_thmss) =
blanchet@49278
   589
                let
blanchet@49278
   590
                  fun mk_thm discI _ [] = refl RS discI
blanchet@49278
   591
                    | mk_thm _ not_discI [distinct] = distinct RS not_discI;
blanchet@49278
   592
                  fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
blanchet@49278
   593
                in
blanchet@49278
   594
                  map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
blanchet@49278
   595
                end;
blanchet@49278
   596
blanchet@53704
   597
              val nontriv_disc_thms =
blanchet@53704
   598
                flat (map2 (fn b => if is_disc_binding_valid b then I else K [])
blanchet@53704
   599
                  disc_bindings disc_thmss);
blanchet@53704
   600
blanchet@53704
   601
              fun is_discI_boring b =
blanchet@53704
   602
                (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
blanchet@53704
   603
blanchet@53704
   604
              val nontriv_discI_thms =
blanchet@53704
   605
                flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
blanchet@53704
   606
                  discI_thms);
blanchet@49028
   607
blanchet@49486
   608
              val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
blanchet@49486
   609
                let
blanchet@49486
   610
                  fun mk_goal [] = []
blanchet@49486
   611
                    | mk_goal [((_, udisc), (_, udisc'))] =
blanchet@49486
   612
                      [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
blanchet@49486
   613
                         HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
blanchet@49486
   614
traytel@49667
   615
                  fun prove tac goal =
wenzelm@51551
   616
                    Goal.prove_sorry lthy [] [] goal (K tac)
traytel@49667
   617
                    |> Thm.close_derivation;
blanchet@49486
   618
blanchet@49585
   619
                  val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
blanchet@49486
   620
blanchet@49486
   621
                  val half_goalss = map mk_goal half_pairss;
blanchet@49486
   622
                  val half_thmss =
blanchet@49486
   623
                    map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
wenzelm@51798
   624
                        fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
blanchet@49486
   625
                      half_goalss half_pairss (flat disc_thmss');
blanchet@49278
   626
blanchet@49486
   627
                  val other_half_goalss = map (mk_goal o map swap) half_pairss;
blanchet@49486
   628
                  val other_half_thmss =
blanchet@49486
   629
                    map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
blanchet@49486
   630
                      other_half_goalss;
blanchet@49486
   631
                in
blanchet@49585
   632
                  join_halves n half_thmss other_half_thmss ||> `transpose
blanchet@49486
   633
                  |>> has_alternate_disc_def ? K []
blanchet@49486
   634
                end;
blanchet@49278
   635
blanchet@49486
   636
              val disc_exhaust_thm =
blanchet@49486
   637
                let
blanchet@49486
   638
                  fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
blanchet@49486
   639
                  val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
blanchet@49486
   640
                in
wenzelm@51551
   641
                  Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@49486
   642
                    mk_disc_exhaust_tac n exhaust_thm discI_thms)
traytel@49667
   643
                  |> Thm.close_derivation
blanchet@49486
   644
                end;
blanchet@49028
   645
blanchet@53740
   646
              val (safe_collapse_thms, all_collapse_thms) =
blanchet@49486
   647
                let
blanchet@49486
   648
                  fun mk_goal ctr udisc usels =
blanchet@49486
   649
                    let
blanchet@49486
   650
                      val prem = HOLogic.mk_Trueprop udisc;
blanchet@49486
   651
                      val concl =
blanchet@49486
   652
                        mk_Trueprop_eq ((null usels ? swap) (Term.list_comb (ctr, usels), u));
blanchet@49486
   653
                    in
blanchet@53740
   654
                      (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
blanchet@49486
   655
                    end;
blanchet@53740
   656
                  val (trivs, goals) = map3 mk_goal ctrs udiscs uselss |> split_list;
blanchet@53740
   657
                  val thms =
blanchet@53740
   658
                    map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
blanchet@53740
   659
                        Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@53740
   660
                          mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
blanchet@53740
   661
                        |> Thm.close_derivation
blanchet@53740
   662
                        |> not triv ? perhaps (try (fn thm => refl RS thm)))
blanchet@53740
   663
                      ms discD_thms sel_thmss trivs goals;
blanchet@49486
   664
                in
blanchet@53740
   665
                  (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
blanchet@53740
   666
                   thms)
blanchet@49486
   667
                end;
blanchet@49025
   668
blanchet@49486
   669
              val expand_thms =
blanchet@49486
   670
                let
blanchet@49486
   671
                  fun mk_prems k udisc usels vdisc vsels =
blanchet@49486
   672
                    (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
blanchet@49486
   673
                    (if null usels then
blanchet@49486
   674
                       []
blanchet@49486
   675
                     else
blanchet@49486
   676
                       [Logic.list_implies
blanchet@49486
   677
                          (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
blanchet@49486
   678
                             HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49486
   679
                               (map2 (curry HOLogic.mk_eq) usels vsels)))]);
blanchet@49486
   680
blanchet@49591
   681
                  val goal =
blanchet@49591
   682
                    Library.foldr Logic.list_implies
blanchet@49591
   683
                      (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
blanchet@49486
   684
                  val uncollapse_thms =
blanchet@53740
   685
                    map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
blanchet@49486
   686
                in
wenzelm@51551
   687
                  [Goal.prove_sorry lthy [] [] goal (fn _ =>
wenzelm@51717
   688
                     mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
blanchet@49486
   689
                       (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
blanchet@49486
   690
                       disc_exclude_thmsss')]
blanchet@49692
   691
                  |> map Thm.close_derivation
blanchet@49486
   692
                  |> Proof_Context.export names_lthy lthy
blanchet@49486
   693
                end;
blanchet@49278
   694
blanchet@49594
   695
              val case_conv_thms =
blanchet@49486
   696
                let
blanchet@49486
   697
                  fun mk_body f usels = Term.list_comb (f, usels);
blanchet@51770
   698
                  val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs (map2 mk_body fs uselss));
blanchet@49486
   699
                in
wenzelm@51551
   700
                  [Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49594
   701
                     mk_case_conv_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)]
blanchet@49692
   702
                  |> map Thm.close_derivation
blanchet@49486
   703
                  |> Proof_Context.export names_lthy lthy
blanchet@49486
   704
                end;
blanchet@49116
   705
            in
blanchet@53704
   706
              (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms,
blanchet@53740
   707
               nontriv_discI_thms, disc_exclude_thms, [disc_exhaust_thm], all_collapse_thms,
blanchet@53740
   708
               safe_collapse_thms, expand_thms, case_conv_thms)
blanchet@49116
   709
            end;
blanchet@49025
   710
blanchet@49033
   711
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   712
          let
blanchet@51763
   713
            fun mk_prem xctr xs xf xg =
blanchet@49486
   714
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
blanchet@51763
   715
                mk_Trueprop_eq (xf, xg)));
blanchet@49033
   716
blanchet@49032
   717
            val goal =
blanchet@51763
   718
              Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
blanchet@51759
   719
                 mk_Trueprop_eq (eta_ufcase, eta_vgcase));
blanchet@49591
   720
            val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
blanchet@49032
   721
          in
wenzelm@51717
   722
            (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
wenzelm@51551
   723
             Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
blanchet@49692
   724
            |> pairself (Thm.close_derivation #> singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   725
          end;
blanchet@49025
   726
blanchet@49044
   727
        val (split_thm, split_asm_thm) =
blanchet@49043
   728
          let
blanchet@49044
   729
            fun mk_conjunct xctr xs f_xs =
blanchet@49486
   730
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
blanchet@49044
   731
            fun mk_disjunct xctr xs f_xs =
blanchet@49486
   732
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
blanchet@49044
   733
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   734
blanchet@51770
   735
            val lhs = q $ ufcase;
blanchet@49044
   736
blanchet@49043
   737
            val goal =
blanchet@49044
   738
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49458
   739
            val asm_goal =
blanchet@49044
   740
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   741
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   742
blanchet@49044
   743
            val split_thm =
wenzelm@51551
   744
              Goal.prove_sorry lthy [] [] goal
wenzelm@51717
   745
                (fn _ => mk_split_tac lthy uexhaust_thm case_thms inject_thmss distinct_thmsss)
blanchet@49692
   746
              |> Thm.close_derivation
blanchet@49692
   747
              |> singleton (Proof_Context.export names_lthy lthy);
blanchet@49044
   748
            val split_asm_thm =
wenzelm@51551
   749
              Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
blanchet@49044
   750
                mk_split_asm_tac ctxt split_thm)
blanchet@49692
   751
              |> Thm.close_derivation
blanchet@49692
   752
              |> singleton (Proof_Context.export names_lthy lthy);
blanchet@49043
   753
          in
blanchet@49044
   754
            (split_thm, split_asm_thm)
blanchet@49043
   755
          end;
blanchet@49025
   756
blanchet@49437
   757
        val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
blanchet@49300
   758
        val cases_type_attr = Attrib.internal (K (Induct.cases_type dataT_name));
blanchet@49300
   759
blanchet@49052
   760
        val notes =
blanchet@49594
   761
          [(caseN, case_thms, simp_attrs),
blanchet@49594
   762
           (case_congN, [case_cong_thm], []),
blanchet@49594
   763
           (case_convN, case_conv_thms, []),
blanchet@53740
   764
           (collapseN, safe_collapse_thms, simp_attrs),
blanchet@53704
   765
           (discN, nontriv_disc_thms, simp_attrs),
blanchet@53700
   766
           (discIN, nontriv_discI_thms, []),
blanchet@49300
   767
           (disc_excludeN, disc_exclude_thms, []),
blanchet@49300
   768
           (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
blanchet@49300
   769
           (distinctN, distinct_thms, simp_attrs @ induct_simp_attrs),
blanchet@49300
   770
           (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
blanchet@49486
   771
           (expandN, expand_thms, []),
blanchet@49438
   772
           (injectN, inject_thms, iff_attrs @ induct_simp_attrs),
blanchet@49300
   773
           (nchotomyN, [nchotomy_thm], []),
blanchet@53694
   774
           (selN, all_sel_thms, simp_attrs),
blanchet@49300
   775
           (splitN, [split_thm], []),
blanchet@49300
   776
           (split_asmN, [split_asm_thm], []),
blanchet@49633
   777
           (splitsN, [split_thm, split_asm_thm], []),
blanchet@49300
   778
           (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
blanchet@49300
   779
          |> filter_out (null o #2)
blanchet@49300
   780
          |> map (fn (thmN, thms, attrs) =>
blanchet@49633
   781
            ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49300
   782
blanchet@49300
   783
        val notes' =
blanchet@49300
   784
          [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs)]
blanchet@49300
   785
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49019
   786
      in
blanchet@52375
   787
        ({ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
blanchet@52375
   788
          nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
blanchet@52375
   789
          case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
blanchet@52375
   790
          split = split_thm, split_asm = split_asm_thm, disc_thmss = disc_thmss,
blanchet@53475
   791
          discIs = discI_thms, sel_thmss = sel_thmss, disc_exhausts = disc_exhaust_thms,
blanchet@53740
   792
          collapses = all_collapse_thms, expands = expand_thms, case_convs = case_conv_thms},
blanchet@51819
   793
         lthy
blanchet@51819
   794
         |> not rep_compat ?
blanchet@51819
   795
            (Local_Theory.declaration {syntax = false, pervasive = true}
traytel@51697
   796
               (fn phi => Case_Translation.register
blanchet@51819
   797
                  (Morphism.term phi casex) (map (Morphism.term phi) ctrs)))
blanchet@51819
   798
         |> Local_Theory.notes (notes' @ notes) |> snd)
blanchet@49019
   799
      end;
blanchet@49017
   800
  in
blanchet@49121
   801
    (goalss, after_qed, lthy')
blanchet@49017
   802
  end;
blanchet@49017
   803
blanchet@51781
   804
fun wrap_free_constructors tacss = (fn (goalss, after_qed, lthy) =>
wenzelm@51551
   805
  map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
blanchet@51781
   806
  |> (fn thms => after_qed thms lthy)) oo prepare_wrap_free_constructors (K I);
blanchet@49280
   807
blanchet@51781
   808
val wrap_free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49297
   809
  Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
blanchet@51781
   810
  prepare_wrap_free_constructors Syntax.read_term;
blanchet@49297
   811
blanchet@49280
   812
fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
blanchet@49111
   813
blanchet@51790
   814
val parse_bindings = parse_bracket_list parse_binding;
blanchet@49280
   815
val parse_bindingss = parse_bracket_list parse_bindings;
blanchet@49280
   816
blanchet@51790
   817
val parse_bound_term = (parse_binding --| @{keyword ":"}) -- Parse.term;
blanchet@49280
   818
val parse_bound_terms = parse_bracket_list parse_bound_term;
blanchet@49280
   819
val parse_bound_termss = parse_bracket_list parse_bound_terms;
blanchet@49017
   820
blanchet@52823
   821
val parse_wrap_free_constructors_options =
blanchet@52969
   822
  Scan.optional (@{keyword "("} |-- Parse.list1 ((@{keyword "no_discs_sels"} >> K (true, false)) ||
blanchet@49633
   823
      (@{keyword "rep_compat"} >> K (false, true))) --| @{keyword ")"}
blanchet@49633
   824
    >> (pairself (exists I) o split_list)) (false, false);
blanchet@49278
   825
blanchet@49017
   826
val _ =
blanchet@51781
   827
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_free_constructors"}
blanchet@51797
   828
    "wrap an existing freely generated type's constructors"
blanchet@52823
   829
    ((parse_wrap_free_constructors_options -- (@{keyword "["} |-- Parse.list Parse.term --|
blanchet@52823
   830
        @{keyword "]"}) --
blanchet@52968
   831
      parse_binding -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
blanchet@49280
   832
        Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
blanchet@51781
   833
     >> wrap_free_constructors_cmd);
blanchet@49017
   834
blanchet@49017
   835
end;