src/HOL/Codatatype/Tools/bnf_wrap.ML
author blanchet
Mon Sep 03 11:54:21 2012 +0200 (2012-09-03)
changeset 49075 ed769978dc8d
parent 49074 d8af889dcbe3
child 49111 9d511132394e
permissions -rw-r--r--
rearrange dependencies
blanchet@49074
     1
(*  Title:      HOL/Codatatype/Tools/bnf_wrap.ML
blanchet@49017
     2
    Author:     Jasmin Blanchette, TU Muenchen
blanchet@49017
     3
    Copyright   2012
blanchet@49017
     4
blanchet@49074
     5
Wrapping existing datatypes.
blanchet@49017
     6
*)
blanchet@49017
     7
blanchet@49074
     8
signature BNF_WRAP =
blanchet@49017
     9
sig
blanchet@49017
    10
end;
blanchet@49017
    11
blanchet@49074
    12
structure BNF_Wrap : BNF_WRAP =
blanchet@49017
    13
struct
blanchet@49017
    14
blanchet@49017
    15
open BNF_Util
blanchet@49074
    16
open BNF_Wrap_Tactics
blanchet@49017
    17
blanchet@49046
    18
val is_N = "is_";
blanchet@49054
    19
val un_N = "un_";
blanchet@49054
    20
fun mk_un_N 1 1 suf = un_N ^ suf
blanchet@49054
    21
  | mk_un_N _ l suf = un_N ^ suf ^ string_of_int l;
blanchet@49046
    22
blanchet@49054
    23
val case_congN = "case_cong";
blanchet@49054
    24
val case_discsN = "case_discs";
blanchet@49054
    25
val casesN = "cases";
blanchet@49054
    26
val ctr_selsN = "ctr_sels";
blanchet@49054
    27
val disc_exclusN = "disc_exclus";
blanchet@49054
    28
val disc_exhaustN = "disc_exhaust";
blanchet@49054
    29
val discsN = "discs";
blanchet@49054
    30
val distinctN = "distinct";
blanchet@49075
    31
val exhaustN = "exhaust";
blanchet@49075
    32
val injectN = "inject";
blanchet@49075
    33
val nchotomyN = "nchotomy";
blanchet@49054
    34
val selsN = "sels";
blanchet@49054
    35
val splitN = "split";
blanchet@49054
    36
val split_asmN = "split_asm";
blanchet@49054
    37
val weak_case_cong_thmsN = "weak_case_cong";
blanchet@49019
    38
blanchet@49046
    39
val default_name = @{binding _};
blanchet@49046
    40
blanchet@49056
    41
fun pad_list x n xs = xs @ replicate (n - length xs) x;
blanchet@49056
    42
blanchet@49048
    43
fun mk_half_pairss' _ [] = []
blanchet@49056
    44
  | mk_half_pairss' indent (y :: ys) =
blanchet@49056
    45
    indent @ fold_rev (cons o single o pair y) ys (mk_half_pairss' ([] :: indent) ys);
blanchet@49027
    46
blanchet@49048
    47
fun mk_half_pairss ys = mk_half_pairss' [[]] ys;
blanchet@49027
    48
blanchet@49032
    49
val mk_Trueprop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq;
blanchet@49032
    50
blanchet@49055
    51
fun mk_undef T Ts = Const (@{const_name undefined}, Ts ---> T);
blanchet@49055
    52
blanchet@49043
    53
fun eta_expand_caseof_arg xs f_xs = fold_rev Term.lambda xs f_xs;
blanchet@49032
    54
blanchet@49046
    55
fun name_of_ctr t =
blanchet@49046
    56
  case head_of t of
blanchet@49046
    57
    Const (s, _) => s
blanchet@49046
    58
  | Free (s, _) => s
blanchet@49046
    59
  | _ => error "Cannot extract name of constructor";
blanchet@49046
    60
blanchet@49074
    61
fun prepare_wrap prep_term ((raw_ctrs, raw_caseof), (raw_disc_names, raw_sel_namess))
blanchet@49054
    62
  no_defs_lthy =
blanchet@49017
    63
  let
blanchet@49019
    64
    (* TODO: sanity checks on arguments *)
blanchet@49017
    65
blanchet@49025
    66
    (* TODO: normalize types of constructors w.r.t. each other *)
blanchet@49025
    67
blanchet@49025
    68
    val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
blanchet@49025
    69
    val caseof0 = prep_term no_defs_lthy raw_caseof;
blanchet@49017
    70
blanchet@49054
    71
    val n = length ctrs0;
blanchet@49054
    72
    val ks = 1 upto n;
blanchet@49054
    73
blanchet@49055
    74
    val (T_name, As0) = dest_Type (body_type (fastype_of (hd ctrs0)));
blanchet@49055
    75
    val b = Binding.qualified_name T_name;
blanchet@49055
    76
blanchet@49055
    77
    val (As, B) =
blanchet@49055
    78
      no_defs_lthy
blanchet@49055
    79
      |> mk_TFrees (length As0)
blanchet@49055
    80
      ||> the_single o fst o mk_TFrees 1;
blanchet@49055
    81
blanchet@49055
    82
    fun mk_ctr Ts ctr =
blanchet@49055
    83
      let val Ts0 = snd (dest_Type (body_type (fastype_of ctr))) in
blanchet@49055
    84
        Term.subst_atomic_types (Ts0 ~~ Ts) ctr
blanchet@49055
    85
      end;
blanchet@49055
    86
blanchet@49055
    87
    val T = Type (T_name, As);
blanchet@49055
    88
    val ctrs = map (mk_ctr As) ctrs0;
blanchet@49055
    89
    val ctr_Tss = map (binder_types o fastype_of) ctrs;
blanchet@49055
    90
blanchet@49055
    91
    val ms = map length ctr_Tss;
blanchet@49055
    92
blanchet@49046
    93
    val disc_names =
blanchet@49056
    94
      pad_list default_name n raw_disc_names
blanchet@49056
    95
      |> map2 (fn ctr => fn disc =>
blanchet@49046
    96
        if Binding.eq_name (disc, default_name) then
blanchet@49046
    97
          Binding.name (prefix is_N (Long_Name.base_name (name_of_ctr ctr)))
blanchet@49046
    98
        else
blanchet@49056
    99
          disc) ctrs0;
blanchet@49056
   100
blanchet@49054
   101
    val sel_namess =
blanchet@49056
   102
      pad_list [] n raw_sel_namess
blanchet@49056
   103
      |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
blanchet@49056
   104
        if Binding.eq_name (sel, default_name) then
blanchet@49056
   105
          Binding.name (mk_un_N m l (Long_Name.base_name (name_of_ctr ctr)))
blanchet@49056
   106
        else
blanchet@49056
   107
          sel) (1 upto m) o pad_list default_name m) ctrs0 ms;
blanchet@49020
   108
blanchet@49028
   109
    fun mk_caseof Ts T =
blanchet@49028
   110
      let val (binders, body) = strip_type (fastype_of caseof0) in
blanchet@49028
   111
        Term.subst_atomic_types ((body, T) :: (snd (dest_Type (List.last binders)) ~~ Ts)) caseof0
blanchet@49022
   112
      end;
blanchet@49022
   113
blanchet@49028
   114
    val caseofB = mk_caseof As B;
blanchet@49025
   115
    val caseofB_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
blanchet@49025
   116
blanchet@49043
   117
    fun mk_caseofB_term eta_fs = Term.list_comb (caseofB, eta_fs);
blanchet@49043
   118
blanchet@49043
   119
    val (((((((xss, yss), fs), gs), (v, v')), w), (p, p')), names_lthy) = no_defs_lthy |>
blanchet@49025
   120
      mk_Freess "x" ctr_Tss
blanchet@49025
   121
      ||>> mk_Freess "y" ctr_Tss
blanchet@49025
   122
      ||>> mk_Frees "f" caseofB_Ts
blanchet@49032
   123
      ||>> mk_Frees "g" caseofB_Ts
blanchet@49020
   124
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") T
blanchet@49032
   125
      ||>> yield_singleton (mk_Frees "w") T
blanchet@49043
   126
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
blanchet@49043
   127
blanchet@49043
   128
    val q = Free (fst p', B --> HOLogic.boolT);
blanchet@49020
   129
blanchet@49025
   130
    val xctrs = map2 (curry Term.list_comb) ctrs xss;
blanchet@49025
   131
    val yctrs = map2 (curry Term.list_comb) ctrs yss;
blanchet@49032
   132
blanchet@49043
   133
    val xfs = map2 (curry Term.list_comb) fs xss;
blanchet@49043
   134
    val xgs = map2 (curry Term.list_comb) gs xss;
blanchet@49043
   135
blanchet@49043
   136
    val eta_fs = map2 eta_expand_caseof_arg xss xfs;
blanchet@49043
   137
    val eta_gs = map2 eta_expand_caseof_arg xss xgs;
blanchet@49043
   138
blanchet@49043
   139
    val caseofB_fs = Term.list_comb (caseofB, eta_fs);
blanchet@49020
   140
blanchet@49025
   141
    val exist_xs_v_eq_ctrs =
blanchet@49025
   142
      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (v, xctr))) xctrs xss;
blanchet@49022
   143
blanchet@49032
   144
    fun mk_sel_caseof_args k xs x T =
blanchet@49025
   145
      map2 (fn Ts => fn i => if i = k then fold_rev Term.lambda xs x else mk_undef T Ts) ctr_Tss ks;
blanchet@49025
   146
blanchet@49025
   147
    fun disc_spec b exist_xs_v_eq_ctr =
blanchet@49032
   148
      mk_Trueprop_eq (Free (Binding.name_of b, T --> HOLogic.boolT) $ v, exist_xs_v_eq_ctr);
blanchet@49025
   149
blanchet@49028
   150
    fun sel_spec b x xs k =
blanchet@49025
   151
      let val T' = fastype_of x in
blanchet@49032
   152
        mk_Trueprop_eq (Free (Binding.name_of b, T --> T') $ v,
blanchet@49032
   153
          Term.list_comb (mk_caseof As T', mk_sel_caseof_args k xs x T') $ v)
blanchet@49022
   154
      end;
blanchet@49022
   155
blanchet@49028
   156
    val (((raw_discs, (_, raw_disc_defs)), (raw_selss, (_, raw_sel_defss))), (lthy', lthy)) =
blanchet@49022
   157
      no_defs_lthy
blanchet@49025
   158
      |> apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn exist_xs_v_eq_ctr =>
blanchet@49022
   159
        Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49025
   160
          ((Thm.def_binding b, []), disc_spec b exist_xs_v_eq_ctr))) disc_names exist_xs_v_eq_ctrs
blanchet@49028
   161
      ||>> apfst (apsnd split_list o split_list) o fold_map3 (fn bs => fn xs => fn k =>
blanchet@49025
   162
        apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn x =>
blanchet@49022
   163
          Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49028
   164
            ((Thm.def_binding b, []), sel_spec b x xs k))) bs xs) sel_namess xss ks
blanchet@49022
   165
      ||> `Local_Theory.restore;
blanchet@49022
   166
blanchet@49025
   167
    (*transforms defined frees into consts (and more)*)
blanchet@49025
   168
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49025
   169
blanchet@49028
   170
    val disc_defs = map (Morphism.thm phi) raw_disc_defs;
blanchet@49028
   171
    val sel_defss = map (map (Morphism.thm phi)) raw_sel_defss;
blanchet@49028
   172
blanchet@49028
   173
    val discs0 = map (Morphism.term phi) raw_discs;
blanchet@49028
   174
    val selss0 = map (map (Morphism.term phi)) raw_selss;
blanchet@49025
   175
blanchet@49028
   176
    fun mk_disc_or_sel Ts t =
blanchet@49028
   177
      Term.subst_atomic_types (snd (dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
blanchet@49028
   178
blanchet@49028
   179
    val discs = map (mk_disc_or_sel As) discs0;
blanchet@49028
   180
    val selss = map (map (mk_disc_or_sel As)) selss0;
blanchet@49025
   181
blanchet@49032
   182
    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
blanchet@49029
   183
blanchet@49020
   184
    val goal_exhaust =
blanchet@49032
   185
      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (v, xctr)]) in
blanchet@49025
   186
        mk_imp_p (map2 mk_prem xctrs xss)
blanchet@49020
   187
      end;
blanchet@49019
   188
blanchet@49034
   189
    val goal_injectss =
blanchet@49017
   190
      let
blanchet@49034
   191
        fun mk_goal _ _ [] [] = []
blanchet@49025
   192
          | mk_goal xctr yctr xs ys =
blanchet@49034
   193
            [mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
blanchet@49034
   194
              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys))];
blanchet@49017
   195
      in
blanchet@49034
   196
        map4 mk_goal xctrs yctrs xss yss
blanchet@49017
   197
      end;
blanchet@49017
   198
blanchet@49048
   199
    val goal_half_distinctss =
blanchet@49048
   200
      map (map (HOLogic.mk_Trueprop o HOLogic.mk_not o HOLogic.mk_eq)) (mk_half_pairss xctrs);
blanchet@49019
   201
blanchet@49043
   202
    val goal_cases = map2 (fn xctr => fn xf => mk_Trueprop_eq (caseofB_fs $ xctr, xf)) xctrs xfs;
blanchet@49025
   203
blanchet@49048
   204
    val goals = [goal_exhaust] :: goal_injectss @ goal_half_distinctss @ [goal_cases];
blanchet@49019
   205
blanchet@49019
   206
    fun after_qed thmss lthy =
blanchet@49019
   207
      let
blanchet@49048
   208
        val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) =
blanchet@49048
   209
          (hd thmss, apsnd (chop (n * n)) (chop n (tl thmss)));
blanchet@49019
   210
blanchet@49032
   211
        val exhaust_thm' =
blanchet@49032
   212
          let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in
blanchet@49032
   213
            Drule.instantiate' [] [SOME (certify lthy v)]
blanchet@49032
   214
              (Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm))
blanchet@49032
   215
          end;
blanchet@49032
   216
blanchet@49048
   217
        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
blanchet@49048
   218
blanchet@49052
   219
        val (distinct_thmsss', distinct_thmsss) =
blanchet@49048
   220
          map2 (map2 append) (Library.chop_groups n half_distinct_thmss)
blanchet@49052
   221
            (transpose (Library.chop_groups n other_half_distinct_thmss))
blanchet@49052
   222
          |> `transpose;
blanchet@49048
   223
        val distinct_thms = interleave (flat half_distinct_thmss) (flat other_half_distinct_thmss);
blanchet@49019
   224
blanchet@49020
   225
        val nchotomy_thm =
blanchet@49020
   226
          let
blanchet@49020
   227
            val goal =
blanchet@49022
   228
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v',
blanchet@49029
   229
                Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs));
blanchet@49020
   230
          in
blanchet@49020
   231
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
blanchet@49020
   232
          end;
blanchet@49020
   233
blanchet@49030
   234
        val sel_thmss =
blanchet@49025
   235
          let
blanchet@49028
   236
            fun mk_thm k xs goal_case case_thm x sel_def =
blanchet@49025
   237
              let
blanchet@49025
   238
                val T = fastype_of x;
blanchet@49025
   239
                val cTs =
blanchet@49025
   240
                  map ((fn T' => certifyT lthy (if T' = B then T else T')) o TFree)
blanchet@49025
   241
                    (rev (Term.add_tfrees goal_case []));
blanchet@49032
   242
                val cxs = map (certify lthy) (mk_sel_caseof_args k xs x T);
blanchet@49025
   243
              in
blanchet@49025
   244
                Local_Defs.fold lthy [sel_def]
blanchet@49025
   245
                  (Drule.instantiate' (map SOME cTs) (map SOME cxs) case_thm)
blanchet@49025
   246
              end;
blanchet@49028
   247
            fun mk_thms k xs goal_case case_thm sel_defs =
blanchet@49028
   248
              map2 (mk_thm k xs goal_case case_thm) xs sel_defs;
blanchet@49025
   249
          in
blanchet@49030
   250
            map5 mk_thms ks xss goal_cases case_thms sel_defss
blanchet@49025
   251
          end;
blanchet@49025
   252
blanchet@49030
   253
        val discD_thms = map (fn def => def RS iffD1) disc_defs;
blanchet@49028
   254
        val discI_thms =
blanchet@49030
   255
          map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms disc_defs;
blanchet@49028
   256
        val not_disc_thms =
blanchet@49030
   257
          map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49030
   258
                  (Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49028
   259
            ms disc_defs;
blanchet@49028
   260
blanchet@49050
   261
        val (disc_thmss', disc_thmss) =
blanchet@49027
   262
          let
blanchet@49048
   263
            fun mk_thm discI _ [] = refl RS discI
blanchet@49048
   264
              | mk_thm _ not_disc [distinct] = distinct RS not_disc;
blanchet@49048
   265
            fun mk_thms discI not_disc distinctss = map (mk_thm discI not_disc) distinctss;
blanchet@49027
   266
          in
blanchet@49052
   267
            map3 mk_thms discI_thms not_disc_thms distinct_thmsss'
blanchet@49050
   268
            |> `transpose
blanchet@49027
   269
          end;
blanchet@49025
   270
blanchet@49053
   271
        val disc_exclus_thms =
blanchet@49028
   272
          let
blanchet@49028
   273
            fun mk_goal ((_, disc), (_, disc')) =
blanchet@49029
   274
              Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v),
blanchet@49029
   275
                HOLogic.mk_Trueprop (HOLogic.mk_not (disc' $ v))));
blanchet@49028
   276
            fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);
blanchet@49028
   277
blanchet@49048
   278
            val bundles = ms ~~ discD_thms ~~ discs;
blanchet@49048
   279
            val half_pairss = mk_half_pairss bundles;
blanchet@49028
   280
blanchet@49048
   281
            val goal_halvess = map (map mk_goal) half_pairss;
blanchet@49048
   282
            val half_thmss =
blanchet@49048
   283
              map3 (fn [] => K (K [])
blanchet@49048
   284
                     | [(((m, discD), _), _)] => fn disc_thm => fn [goal] =>
blanchet@49053
   285
                [prove (mk_half_disc_exclus_tac m discD disc_thm) goal])
blanchet@49050
   286
              half_pairss (flat disc_thmss') goal_halvess;
blanchet@49028
   287
blanchet@49048
   288
            val goal_other_halvess = map (map (mk_goal o swap)) half_pairss;
blanchet@49048
   289
            val other_half_thmss =
blanchet@49053
   290
              map2 (map2 (prove o mk_other_half_disc_exclus_tac)) half_thmss goal_other_halvess;
blanchet@49028
   291
          in
blanchet@49048
   292
            interleave (flat half_thmss) (flat other_half_thmss)
blanchet@49028
   293
          end;
blanchet@49025
   294
blanchet@49029
   295
        val disc_exhaust_thm =
blanchet@49029
   296
          let
blanchet@49029
   297
            fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (disc $ v)];
blanchet@49029
   298
            val goal = fold Logic.all [p, v] (mk_imp_p (map mk_prem discs));
blanchet@49029
   299
          in
blanchet@49029
   300
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_disc_exhaust_tac n exhaust_thm discI_thms)
blanchet@49029
   301
          end;
blanchet@49025
   302
blanchet@49030
   303
        val ctr_sel_thms =
blanchet@49030
   304
          let
blanchet@49030
   305
            fun mk_goal ctr disc sels =
blanchet@49030
   306
              Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v),
blanchet@49032
   307
                mk_Trueprop_eq ((null sels ? swap)
blanchet@49032
   308
                  (Term.list_comb (ctr, map (fn sel => sel $ v) sels), v))));
blanchet@49030
   309
            val goals = map3 mk_goal ctrs discs selss;
blanchet@49030
   310
          in
blanchet@49030
   311
            map4 (fn goal => fn m => fn discD => fn sel_thms =>
blanchet@49030
   312
              Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49030
   313
                mk_ctr_sel_tac ctxt m discD sel_thms))
blanchet@49030
   314
              goals ms discD_thms sel_thmss
blanchet@49030
   315
          end;
blanchet@49025
   316
blanchet@49031
   317
        val case_disc_thm =
blanchet@49031
   318
          let
blanchet@49031
   319
            fun mk_core f sels = Term.list_comb (f, map (fn sel => sel $ v) sels);
blanchet@49031
   320
            fun mk_rhs _ [f] [sels] = mk_core f sels
blanchet@49031
   321
              | mk_rhs (disc :: discs) (f :: fs) (sels :: selss) =
blanchet@49031
   322
                Const (@{const_name If}, HOLogic.boolT --> B --> B --> B) $
blanchet@49031
   323
                  (disc $ v) $ mk_core f sels $ mk_rhs discs fs selss;
blanchet@49043
   324
            val goal = mk_Trueprop_eq (caseofB_fs $ v, mk_rhs discs fs selss);
blanchet@49031
   325
          in
blanchet@49031
   326
            Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49050
   327
              mk_case_disc_tac ctxt exhaust_thm' case_thms disc_thmss' sel_thmss)
blanchet@49031
   328
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49031
   329
          end;
blanchet@49025
   330
blanchet@49033
   331
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   332
          let
blanchet@49032
   333
            fun mk_prem xctr xs f g =
blanchet@49045
   334
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr),
blanchet@49032
   335
                mk_Trueprop_eq (f, g)));
blanchet@49033
   336
blanchet@49033
   337
            val v_eq_w = mk_Trueprop_eq (v, w);
blanchet@49043
   338
            val caseof_fs = mk_caseofB_term eta_fs;
blanchet@49043
   339
            val caseof_gs = mk_caseofB_term eta_gs;
blanchet@49032
   340
blanchet@49032
   341
            val goal =
blanchet@49033
   342
              Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs,
blanchet@49033
   343
                 mk_Trueprop_eq (caseof_fs $ v, caseof_gs $ w));
blanchet@49033
   344
            val goal_weak =
blanchet@49033
   345
              Logic.mk_implies (v_eq_w, mk_Trueprop_eq (caseof_fs $ v, caseof_fs $ w));
blanchet@49032
   346
          in
blanchet@49049
   347
            (Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms),
blanchet@49033
   348
             Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1)))
blanchet@49033
   349
            |> pairself (singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   350
          end;
blanchet@49025
   351
blanchet@49044
   352
        val (split_thm, split_asm_thm) =
blanchet@49043
   353
          let
blanchet@49044
   354
            fun mk_conjunct xctr xs f_xs =
blanchet@49043
   355
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs));
blanchet@49044
   356
            fun mk_disjunct xctr xs f_xs =
blanchet@49044
   357
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr),
blanchet@49044
   358
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   359
blanchet@49044
   360
            val lhs = q $ (mk_caseofB_term eta_fs $ v);
blanchet@49044
   361
blanchet@49043
   362
            val goal =
blanchet@49044
   363
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49044
   364
            val goal_asm =
blanchet@49044
   365
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   366
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   367
blanchet@49044
   368
            val split_thm =
blanchet@49049
   369
              Skip_Proof.prove lthy [] [] goal
blanchet@49052
   370
                (fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss)
blanchet@49044
   371
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49044
   372
            val split_asm_thm =
blanchet@49044
   373
              Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} =>
blanchet@49044
   374
                mk_split_asm_tac ctxt split_thm)
blanchet@49044
   375
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49043
   376
          in
blanchet@49044
   377
            (split_thm, split_asm_thm)
blanchet@49043
   378
          end;
blanchet@49025
   379
blanchet@49043
   380
        (* TODO: case syntax *)
blanchet@49043
   381
        (* TODO: attributes (simp, case_names, etc.) *)
blanchet@49025
   382
blanchet@49052
   383
        val notes =
blanchet@49052
   384
          [(case_congN, [case_cong_thm]),
blanchet@49052
   385
           (case_discsN, [case_disc_thm]),
blanchet@49052
   386
           (casesN, case_thms),
blanchet@49052
   387
           (ctr_selsN, ctr_sel_thms),
blanchet@49052
   388
           (discsN, (flat disc_thmss)),
blanchet@49053
   389
           (disc_exclusN, disc_exclus_thms),
blanchet@49052
   390
           (disc_exhaustN, [disc_exhaust_thm]),
blanchet@49052
   391
           (distinctN, distinct_thms),
blanchet@49052
   392
           (exhaustN, [exhaust_thm]),
blanchet@49052
   393
           (injectN, (flat inject_thmss)),
blanchet@49052
   394
           (nchotomyN, [nchotomy_thm]),
blanchet@49052
   395
           (selsN, (flat sel_thmss)),
blanchet@49052
   396
           (splitN, [split_thm]),
blanchet@49052
   397
           (split_asmN, [split_asm_thm]),
blanchet@49052
   398
           (weak_case_cong_thmsN, [weak_case_cong_thm])]
blanchet@49052
   399
          |> map (fn (thmN, thms) =>
blanchet@49052
   400
            ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
blanchet@49019
   401
      in
blanchet@49052
   402
        lthy |> Local_Theory.notes notes |> snd
blanchet@49019
   403
      end;
blanchet@49017
   404
  in
blanchet@49025
   405
    (goals, after_qed, lthy')
blanchet@49017
   406
  end;
blanchet@49017
   407
blanchet@49057
   408
val parse_bindings = Parse.$$$ "[" |--  Parse.list Parse.binding --| Parse.$$$ "]";
blanchet@49057
   409
blanchet@49057
   410
val parse_bindingss = Parse.$$$ "[" |-- Parse.list parse_bindings --| Parse.$$$ "]";
blanchet@49017
   411
blanchet@49074
   412
val wrap_data_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49019
   413
  Proof.theorem NONE after_qed (map (map (rpair [])) goalss) lthy) oo
blanchet@49074
   414
  prepare_wrap Syntax.read_term;
blanchet@49017
   415
blanchet@49017
   416
val _ =
blanchet@49074
   417
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype"
blanchet@49023
   418
    (((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term --
blanchet@49057
   419
      Scan.optional (parse_bindings -- Scan.optional parse_bindingss []) ([], []))
blanchet@49074
   420
     >> wrap_data_cmd);
blanchet@49017
   421
blanchet@49017
   422
end;