src/HOL/Codatatype/Tools/bnf_wrap.ML
author blanchet
Tue Sep 04 18:49:40 2012 +0200 (2012-09-04)
changeset 49130 3c26e17b2849
parent 49129 b5413cb7d860
child 49136 56a50871e25d
permissions -rw-r--r--
implemented "mk_case_tac" -- and got rid of "cheat_tac"
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@49129
    10
  val no_binder: binding
blanchet@49121
    11
  val mk_half_pairss: 'a list -> ('a * 'a) list list
blanchet@49121
    12
  val wrap_data: ({prems: thm list, context: Proof.context} -> tactic) list list ->
blanchet@49119
    13
    (term list * term) * (binding list * binding list list) -> local_theory -> local_theory
blanchet@49017
    14
end;
blanchet@49017
    15
blanchet@49074
    16
structure BNF_Wrap : BNF_WRAP =
blanchet@49017
    17
struct
blanchet@49017
    18
blanchet@49017
    19
open BNF_Util
blanchet@49074
    20
open BNF_Wrap_Tactics
blanchet@49017
    21
blanchet@49046
    22
val is_N = "is_";
blanchet@49054
    23
val un_N = "un_";
blanchet@49054
    24
fun mk_un_N 1 1 suf = un_N ^ suf
blanchet@49054
    25
  | mk_un_N _ l suf = un_N ^ suf ^ string_of_int l;
blanchet@49046
    26
blanchet@49054
    27
val case_congN = "case_cong";
blanchet@49116
    28
val case_eqN = "case_eq";
blanchet@49054
    29
val casesN = "cases";
blanchet@49118
    30
val collapseN = "collapse";
blanchet@49122
    31
val disc_excludeN = "disc_exclude";
blanchet@49054
    32
val disc_exhaustN = "disc_exhaust";
blanchet@49054
    33
val discsN = "discs";
blanchet@49054
    34
val distinctN = "distinct";
blanchet@49075
    35
val exhaustN = "exhaust";
blanchet@49075
    36
val injectN = "inject";
blanchet@49075
    37
val nchotomyN = "nchotomy";
blanchet@49054
    38
val selsN = "sels";
blanchet@49054
    39
val splitN = "split";
blanchet@49054
    40
val split_asmN = "split_asm";
blanchet@49054
    41
val weak_case_cong_thmsN = "weak_case_cong";
blanchet@49019
    42
blanchet@49129
    43
val no_binder = @{binding "*"};
blanchet@49129
    44
val fallback_binder = @{binding _};
blanchet@49046
    45
blanchet@49056
    46
fun pad_list x n xs = xs @ replicate (n - length xs) x;
blanchet@49056
    47
blanchet@49048
    48
fun mk_half_pairss' _ [] = []
blanchet@49056
    49
  | mk_half_pairss' indent (y :: ys) =
blanchet@49056
    50
    indent @ fold_rev (cons o single o pair y) ys (mk_half_pairss' ([] :: indent) ys);
blanchet@49027
    51
blanchet@49048
    52
fun mk_half_pairss ys = mk_half_pairss' [[]] ys;
blanchet@49027
    53
blanchet@49055
    54
fun mk_undef T Ts = Const (@{const_name undefined}, Ts ---> T);
blanchet@49055
    55
blanchet@49130
    56
fun eta_expand_case_arg xs f_xs = fold_rev Term.lambda xs f_xs;
blanchet@49032
    57
blanchet@49046
    58
fun name_of_ctr t =
blanchet@49046
    59
  case head_of t of
blanchet@49046
    60
    Const (s, _) => s
blanchet@49046
    61
  | Free (s, _) => s
blanchet@49046
    62
  | _ => error "Cannot extract name of constructor";
blanchet@49046
    63
blanchet@49130
    64
fun prepare_wrap_data prep_term ((raw_ctrs, raw_case), (raw_disc_binders, raw_sel_binderss))
blanchet@49054
    65
  no_defs_lthy =
blanchet@49017
    66
  let
blanchet@49019
    67
    (* TODO: sanity checks on arguments *)
blanchet@49113
    68
    (* TODO: attributes (simp, case_names, etc.) *)
blanchet@49113
    69
    (* TODO: case syntax *)
blanchet@49113
    70
    (* TODO: integration with function package ("size") *)
blanchet@49025
    71
blanchet@49025
    72
    val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
blanchet@49130
    73
    val case0 = prep_term no_defs_lthy raw_case;
blanchet@49017
    74
blanchet@49054
    75
    val n = length ctrs0;
blanchet@49054
    76
    val ks = 1 upto n;
blanchet@49054
    77
blanchet@49121
    78
    val _ = if n > 0 then () else error "No constructors specified";
blanchet@49121
    79
blanchet@49121
    80
    val Type (T_name, As0) = body_type (fastype_of (hd ctrs0));
blanchet@49055
    81
    val b = Binding.qualified_name T_name;
blanchet@49055
    82
blanchet@49055
    83
    val (As, B) =
blanchet@49055
    84
      no_defs_lthy
blanchet@49055
    85
      |> mk_TFrees (length As0)
blanchet@49055
    86
      ||> the_single o fst o mk_TFrees 1;
blanchet@49055
    87
blanchet@49055
    88
    fun mk_ctr Ts ctr =
blanchet@49121
    89
      let val Type (_, Ts0) = body_type (fastype_of ctr) in
blanchet@49055
    90
        Term.subst_atomic_types (Ts0 ~~ Ts) ctr
blanchet@49055
    91
      end;
blanchet@49055
    92
blanchet@49055
    93
    val T = Type (T_name, As);
blanchet@49055
    94
    val ctrs = map (mk_ctr As) ctrs0;
blanchet@49055
    95
    val ctr_Tss = map (binder_types o fastype_of) ctrs;
blanchet@49055
    96
blanchet@49055
    97
    val ms = map length ctr_Tss;
blanchet@49055
    98
blanchet@49129
    99
    val raw_disc_binders' = pad_list no_binder n raw_disc_binders;
blanchet@49120
   100
blanchet@49120
   101
    fun can_rely_on_disc i =
blanchet@49129
   102
      not (Binding.eq_name (nth raw_disc_binders' i, no_binder)) orelse nth ms i = 0;
blanchet@49129
   103
    fun can_omit_disc_binder k m =
blanchet@49120
   104
      n = 1 orelse m = 0 orelse (n = 2 andalso can_rely_on_disc (2 - k))
blanchet@49120
   105
blanchet@49129
   106
    val fallback_disc_binder = Binding.name o prefix is_N o Long_Name.base_name o name_of_ctr;
blanchet@49120
   107
blanchet@49129
   108
    val disc_binders =
blanchet@49129
   109
      raw_disc_binders'
blanchet@49120
   110
      |> map4 (fn k => fn m => fn ctr => fn disc =>
blanchet@49129
   111
        if Binding.eq_name (disc, no_binder) then
blanchet@49129
   112
          if can_omit_disc_binder k m then NONE else SOME (fallback_disc_binder ctr)
blanchet@49129
   113
        else if Binding.eq_name (disc, fallback_binder) then
blanchet@49129
   114
          SOME (fallback_disc_binder ctr)
blanchet@49046
   115
        else
blanchet@49120
   116
          SOME disc) ks ms ctrs0;
blanchet@49056
   117
blanchet@49129
   118
    val no_discs = map is_none disc_binders;
blanchet@49116
   119
blanchet@49129
   120
    fun fallback_sel_binder m l = Binding.name o mk_un_N m l o Long_Name.base_name o name_of_ctr;
blanchet@49120
   121
blanchet@49129
   122
    val sel_binderss =
blanchet@49129
   123
      pad_list [] n raw_sel_binderss
blanchet@49056
   124
      |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
blanchet@49129
   125
        if Binding.eq_name (sel, no_binder) orelse Binding.eq_name (sel, fallback_binder) then
blanchet@49129
   126
          fallback_sel_binder m l ctr
blanchet@49056
   127
        else
blanchet@49129
   128
          sel) (1 upto m) o pad_list no_binder m) ctrs0 ms;
blanchet@49020
   129
blanchet@49130
   130
    fun mk_case Ts T =
blanchet@49121
   131
      let
blanchet@49130
   132
        val (binders, body) = strip_type (fastype_of case0)
blanchet@49121
   133
        val Type (_, Ts0) = List.last binders
blanchet@49130
   134
      in Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) case0 end;
blanchet@49022
   135
blanchet@49130
   136
    val caseB = mk_case As B;
blanchet@49130
   137
    val caseB_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
blanchet@49025
   138
blanchet@49130
   139
    fun mk_caseB_term eta_fs = Term.list_comb (caseB, eta_fs);
blanchet@49043
   140
blanchet@49043
   141
    val (((((((xss, yss), fs), gs), (v, v')), w), (p, p')), names_lthy) = no_defs_lthy |>
blanchet@49025
   142
      mk_Freess "x" ctr_Tss
blanchet@49025
   143
      ||>> mk_Freess "y" ctr_Tss
blanchet@49130
   144
      ||>> mk_Frees "f" caseB_Ts
blanchet@49130
   145
      ||>> mk_Frees "g" caseB_Ts
blanchet@49020
   146
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") T
blanchet@49032
   147
      ||>> yield_singleton (mk_Frees "w") T
blanchet@49043
   148
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
blanchet@49043
   149
blanchet@49043
   150
    val q = Free (fst p', B --> HOLogic.boolT);
blanchet@49020
   151
blanchet@49025
   152
    val xctrs = map2 (curry Term.list_comb) ctrs xss;
blanchet@49025
   153
    val yctrs = map2 (curry Term.list_comb) ctrs yss;
blanchet@49032
   154
blanchet@49043
   155
    val xfs = map2 (curry Term.list_comb) fs xss;
blanchet@49043
   156
    val xgs = map2 (curry Term.list_comb) gs xss;
blanchet@49043
   157
blanchet@49130
   158
    val eta_fs = map2 eta_expand_case_arg xss xfs;
blanchet@49130
   159
    val eta_gs = map2 eta_expand_case_arg xss xgs;
blanchet@49043
   160
blanchet@49130
   161
    val caseB_fs = Term.list_comb (caseB, eta_fs);
blanchet@49020
   162
blanchet@49025
   163
    val exist_xs_v_eq_ctrs =
blanchet@49025
   164
      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (v, xctr))) xctrs xss;
blanchet@49022
   165
blanchet@49130
   166
    fun mk_sel_case_args k xs x T =
blanchet@49025
   167
      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
   168
blanchet@49116
   169
    fun disc_free b = Free (Binding.name_of b, T --> HOLogic.boolT);
blanchet@49116
   170
blanchet@49116
   171
    fun disc_spec b exist_xs_v_eq_ctr = mk_Trueprop_eq (disc_free b $ v, exist_xs_v_eq_ctr);
blanchet@49116
   172
blanchet@49116
   173
    fun not_other_disc_lhs i =
blanchet@49116
   174
      HOLogic.mk_not
blanchet@49129
   175
        (case nth disc_binders i of NONE => nth exist_xs_v_eq_ctrs i | SOME b => disc_free b $ v);
blanchet@49116
   176
blanchet@49116
   177
    fun not_other_disc k =
blanchet@49116
   178
      if n = 2 then Term.lambda v (not_other_disc_lhs (2 - k)) else error "Cannot use \"*\" here"
blanchet@49025
   179
blanchet@49028
   180
    fun sel_spec b x xs k =
blanchet@49025
   181
      let val T' = fastype_of x in
blanchet@49032
   182
        mk_Trueprop_eq (Free (Binding.name_of b, T --> T') $ v,
blanchet@49130
   183
          Term.list_comb (mk_case As T', mk_sel_case_args k xs x T') $ v)
blanchet@49022
   184
      end;
blanchet@49022
   185
blanchet@49116
   186
    val missing_disc_def = TrueI; (* marker *)
blanchet@49116
   187
blanchet@49114
   188
    val (((raw_discs, raw_disc_defs), (raw_selss, raw_sel_defss)), (lthy', lthy)) =
blanchet@49022
   189
      no_defs_lthy
blanchet@49116
   190
      |> apfst split_list o fold_map4 (fn k => fn m => fn exist_xs_v_eq_ctr =>
blanchet@49116
   191
        fn NONE =>
blanchet@49116
   192
           if m = 0 then pair (Term.lambda v exist_xs_v_eq_ctr, refl)
blanchet@49116
   193
           else pair (not_other_disc k, missing_disc_def)
blanchet@49114
   194
         | SOME b => Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49114
   195
             ((Thm.def_binding b, []), disc_spec b exist_xs_v_eq_ctr)) #>> apsnd snd)
blanchet@49129
   196
        ks ms exist_xs_v_eq_ctrs disc_binders
blanchet@49114
   197
      ||>> apfst split_list o fold_map3 (fn bs => fn xs => fn k => apfst split_list o
blanchet@49114
   198
          fold_map2 (fn b => fn x => Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49129
   199
            ((Thm.def_binding b, []), sel_spec b x xs k)) #>> apsnd snd) bs xs) sel_binderss xss ks
blanchet@49022
   200
      ||> `Local_Theory.restore;
blanchet@49022
   201
blanchet@49025
   202
    (*transforms defined frees into consts (and more)*)
blanchet@49025
   203
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49025
   204
blanchet@49028
   205
    val disc_defs = map (Morphism.thm phi) raw_disc_defs;
blanchet@49028
   206
    val sel_defss = map (map (Morphism.thm phi)) raw_sel_defss;
blanchet@49028
   207
blanchet@49028
   208
    val discs0 = map (Morphism.term phi) raw_discs;
blanchet@49028
   209
    val selss0 = map (map (Morphism.term phi)) raw_selss;
blanchet@49025
   210
blanchet@49028
   211
    fun mk_disc_or_sel Ts t =
blanchet@49121
   212
      Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
blanchet@49028
   213
blanchet@49028
   214
    val discs = map (mk_disc_or_sel As) discs0;
blanchet@49028
   215
    val selss = map (map (mk_disc_or_sel As)) selss0;
blanchet@49025
   216
blanchet@49032
   217
    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
blanchet@49029
   218
blanchet@49020
   219
    val goal_exhaust =
blanchet@49032
   220
      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (v, xctr)]) in
blanchet@49121
   221
        fold_rev Logic.all [p, v] (mk_imp_p (map2 mk_prem xctrs xss))
blanchet@49020
   222
      end;
blanchet@49019
   223
blanchet@49034
   224
    val goal_injectss =
blanchet@49017
   225
      let
blanchet@49034
   226
        fun mk_goal _ _ [] [] = []
blanchet@49025
   227
          | mk_goal xctr yctr xs ys =
blanchet@49121
   228
            [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
blanchet@49121
   229
              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
blanchet@49017
   230
      in
blanchet@49034
   231
        map4 mk_goal xctrs yctrs xss yss
blanchet@49017
   232
      end;
blanchet@49017
   233
blanchet@49048
   234
    val goal_half_distinctss =
blanchet@49121
   235
      let
blanchet@49121
   236
        fun mk_goal ((xs, t), (xs', t')) =
blanchet@49121
   237
          fold_rev Logic.all (xs @ xs')
blanchet@49121
   238
            (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (t, t'))));
blanchet@49121
   239
      in
blanchet@49121
   240
        map (map mk_goal) (mk_half_pairss (xss ~~ xctrs))
blanchet@49121
   241
      end;
blanchet@49019
   242
blanchet@49121
   243
    val goal_cases =
blanchet@49121
   244
      map3 (fn xs => fn xctr => fn xf =>
blanchet@49130
   245
        fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (caseB_fs $ xctr, xf))) xss xctrs xfs;
blanchet@49025
   246
blanchet@49121
   247
    val goalss = [goal_exhaust] :: goal_injectss @ goal_half_distinctss @ [goal_cases];
blanchet@49019
   248
blanchet@49019
   249
    fun after_qed thmss lthy =
blanchet@49019
   250
      let
blanchet@49048
   251
        val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) =
blanchet@49048
   252
          (hd thmss, apsnd (chop (n * n)) (chop n (tl thmss)));
blanchet@49019
   253
blanchet@49032
   254
        val exhaust_thm' =
blanchet@49032
   255
          let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in
blanchet@49032
   256
            Drule.instantiate' [] [SOME (certify lthy v)]
blanchet@49032
   257
              (Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm))
blanchet@49032
   258
          end;
blanchet@49032
   259
blanchet@49048
   260
        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
blanchet@49048
   261
blanchet@49052
   262
        val (distinct_thmsss', distinct_thmsss) =
blanchet@49048
   263
          map2 (map2 append) (Library.chop_groups n half_distinct_thmss)
blanchet@49052
   264
            (transpose (Library.chop_groups n other_half_distinct_thmss))
blanchet@49052
   265
          |> `transpose;
blanchet@49048
   266
        val distinct_thms = interleave (flat half_distinct_thmss) (flat other_half_distinct_thmss);
blanchet@49019
   267
blanchet@49020
   268
        val nchotomy_thm =
blanchet@49020
   269
          let
blanchet@49020
   270
            val goal =
blanchet@49022
   271
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v',
blanchet@49029
   272
                Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs));
blanchet@49020
   273
          in
blanchet@49020
   274
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
blanchet@49020
   275
          end;
blanchet@49020
   276
blanchet@49030
   277
        val sel_thmss =
blanchet@49025
   278
          let
blanchet@49028
   279
            fun mk_thm k xs goal_case case_thm x sel_def =
blanchet@49025
   280
              let
blanchet@49025
   281
                val T = fastype_of x;
blanchet@49025
   282
                val cTs =
blanchet@49025
   283
                  map ((fn T' => certifyT lthy (if T' = B then T else T')) o TFree)
blanchet@49025
   284
                    (rev (Term.add_tfrees goal_case []));
blanchet@49130
   285
                val cxs = map (certify lthy) (mk_sel_case_args k xs x T);
blanchet@49025
   286
              in
blanchet@49025
   287
                Local_Defs.fold lthy [sel_def]
blanchet@49025
   288
                  (Drule.instantiate' (map SOME cTs) (map SOME cxs) case_thm)
blanchet@49025
   289
              end;
blanchet@49028
   290
            fun mk_thms k xs goal_case case_thm sel_defs =
blanchet@49028
   291
              map2 (mk_thm k xs goal_case case_thm) xs sel_defs;
blanchet@49025
   292
          in
blanchet@49030
   293
            map5 mk_thms ks xss goal_cases case_thms sel_defss
blanchet@49025
   294
          end;
blanchet@49025
   295
blanchet@49116
   296
        fun not_other_disc_def k =
blanchet@49116
   297
          let
blanchet@49116
   298
            val goal =
blanchet@49116
   299
              mk_Trueprop_eq (Morphism.term phi (not_other_disc_lhs (2 - k)),
blanchet@49116
   300
                nth exist_xs_v_eq_ctrs (k - 1));
blanchet@49116
   301
          in
blanchet@49116
   302
            Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49116
   303
              mk_not_other_disc_def_tac ctxt (nth disc_defs (2 - k)) (nth distinct_thms (2 - k))
blanchet@49116
   304
                exhaust_thm')
blanchet@49116
   305
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49125
   306
            |> Thm.close_derivation
blanchet@49116
   307
          end;
blanchet@49116
   308
blanchet@49116
   309
        val has_not_other_disc_def =
blanchet@49116
   310
          exists (fn def => Thm.eq_thm_prop (def, missing_disc_def)) disc_defs;
blanchet@49116
   311
blanchet@49116
   312
        val disc_defs' =
blanchet@49116
   313
          map2 (fn k => fn def =>
blanchet@49116
   314
            if Thm.eq_thm_prop (def, missing_disc_def) then not_other_disc_def k else def)
blanchet@49116
   315
          ks disc_defs;
blanchet@49116
   316
blanchet@49116
   317
        val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49028
   318
        val discI_thms =
blanchet@49116
   319
          map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms disc_defs';
blanchet@49028
   320
        val not_disc_thms =
blanchet@49030
   321
          map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49116
   322
            (Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49116
   323
          ms disc_defs';
blanchet@49028
   324
blanchet@49050
   325
        val (disc_thmss', disc_thmss) =
blanchet@49027
   326
          let
blanchet@49048
   327
            fun mk_thm discI _ [] = refl RS discI
blanchet@49048
   328
              | mk_thm _ not_disc [distinct] = distinct RS not_disc;
blanchet@49048
   329
            fun mk_thms discI not_disc distinctss = map (mk_thm discI not_disc) distinctss;
blanchet@49027
   330
          in
blanchet@49114
   331
            map3 mk_thms discI_thms not_disc_thms distinct_thmsss' |> `transpose
blanchet@49027
   332
          end;
blanchet@49025
   333
blanchet@49116
   334
        val disc_thms = flat (map2 (fn true => K [] | false => I) no_discs disc_thmss);
blanchet@49116
   335
blanchet@49122
   336
        val disc_exclude_thms =
blanchet@49116
   337
          if has_not_other_disc_def then
blanchet@49116
   338
            []
blanchet@49116
   339
          else
blanchet@49116
   340
            let
blanchet@49116
   341
              fun mk_goal [] = []
blanchet@49116
   342
                | mk_goal [((_, true), (_, true))] = []
blanchet@49116
   343
                | mk_goal [(((_, disc), _), ((_, disc'), _))] =
blanchet@49116
   344
                  [Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (betapply (disc, v)),
blanchet@49116
   345
                     HOLogic.mk_Trueprop (HOLogic.mk_not (betapply (disc', v)))))];
blanchet@49116
   346
              fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);
blanchet@49028
   347
blanchet@49116
   348
              val bundles = ms ~~ discD_thms ~~ discs ~~ no_discs;
blanchet@49116
   349
              val half_pairss = mk_half_pairss bundles;
blanchet@49028
   350
blanchet@49116
   351
              val goal_halvess = map mk_goal half_pairss;
blanchet@49116
   352
              val half_thmss =
blanchet@49116
   353
                map3 (fn [] => K (K []) | [goal] => fn [((((m, discD), _), _), _)] => fn disc_thm =>
blanchet@49122
   354
                  [prove (mk_half_disc_exclude_tac m discD disc_thm) goal])
blanchet@49116
   355
                goal_halvess half_pairss (flat disc_thmss');
blanchet@49028
   356
blanchet@49116
   357
              val goal_other_halvess = map (mk_goal o map swap) half_pairss;
blanchet@49116
   358
              val other_half_thmss =
blanchet@49122
   359
                map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss goal_other_halvess;
blanchet@49116
   360
            in
blanchet@49116
   361
              interleave (flat half_thmss) (flat other_half_thmss)
blanchet@49116
   362
            end;
blanchet@49025
   363
blanchet@49116
   364
        val disc_exhaust_thms =
blanchet@49116
   365
          if has_not_other_disc_def orelse forall I no_discs then
blanchet@49116
   366
            []
blanchet@49116
   367
          else
blanchet@49116
   368
            let
blanchet@49116
   369
              fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (betapply (disc, v))];
blanchet@49121
   370
              val goal = fold_rev Logic.all [p, v] (mk_imp_p (map mk_prem discs));
blanchet@49116
   371
            in
blanchet@49116
   372
              [Skip_Proof.prove lthy [] [] goal (fn _ =>
blanchet@49116
   373
                 mk_disc_exhaust_tac n exhaust_thm discI_thms)]
blanchet@49116
   374
            end;
blanchet@49025
   375
blanchet@49118
   376
        val collapse_thms =
blanchet@49030
   377
          let
blanchet@49030
   378
            fun mk_goal ctr disc sels =
blanchet@49114
   379
              let
blanchet@49114
   380
                val prem = HOLogic.mk_Trueprop (betapply (disc, v));
blanchet@49114
   381
                val concl =
blanchet@49114
   382
                  mk_Trueprop_eq ((null sels ? swap)
blanchet@49114
   383
                    (Term.list_comb (ctr, map (fn sel => sel $ v) sels), v));
blanchet@49114
   384
              in
blanchet@49114
   385
                if prem aconv concl then NONE
blanchet@49114
   386
                else SOME (Logic.all v (Logic.mk_implies (prem, concl)))
blanchet@49114
   387
              end;
blanchet@49030
   388
            val goals = map3 mk_goal ctrs discs selss;
blanchet@49030
   389
          in
blanchet@49114
   390
            map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>
blanchet@49030
   391
              Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49118
   392
                mk_collapse_tac ctxt m discD sel_thms))) ms discD_thms sel_thmss goals
blanchet@49114
   393
            |> map_filter I
blanchet@49030
   394
          end;
blanchet@49025
   395
blanchet@49116
   396
        val case_eq_thm =
blanchet@49031
   397
          let
blanchet@49031
   398
            fun mk_core f sels = Term.list_comb (f, map (fn sel => sel $ v) sels);
blanchet@49031
   399
            fun mk_rhs _ [f] [sels] = mk_core f sels
blanchet@49031
   400
              | mk_rhs (disc :: discs) (f :: fs) (sels :: selss) =
blanchet@49031
   401
                Const (@{const_name If}, HOLogic.boolT --> B --> B --> B) $
blanchet@49114
   402
                  betapply (disc, v) $ mk_core f sels $ mk_rhs discs fs selss;
blanchet@49130
   403
            val goal = mk_Trueprop_eq (caseB_fs $ v, mk_rhs discs fs selss);
blanchet@49031
   404
          in
blanchet@49031
   405
            Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49116
   406
              mk_case_eq_tac ctxt exhaust_thm' case_thms disc_thmss' sel_thmss)
blanchet@49031
   407
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49031
   408
          end;
blanchet@49025
   409
blanchet@49033
   410
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   411
          let
blanchet@49032
   412
            fun mk_prem xctr xs f g =
blanchet@49045
   413
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr),
blanchet@49032
   414
                mk_Trueprop_eq (f, g)));
blanchet@49033
   415
blanchet@49033
   416
            val v_eq_w = mk_Trueprop_eq (v, w);
blanchet@49130
   417
            val case_fs = mk_caseB_term eta_fs;
blanchet@49130
   418
            val case_gs = mk_caseB_term eta_gs;
blanchet@49032
   419
blanchet@49032
   420
            val goal =
blanchet@49033
   421
              Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs,
blanchet@49130
   422
                 mk_Trueprop_eq (case_fs $ v, case_gs $ w));
blanchet@49130
   423
            val goal_weak = Logic.mk_implies (v_eq_w, mk_Trueprop_eq (case_fs $ v, case_fs $ w));
blanchet@49032
   424
          in
blanchet@49049
   425
            (Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms),
blanchet@49033
   426
             Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1)))
blanchet@49033
   427
            |> pairself (singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   428
          end;
blanchet@49025
   429
blanchet@49044
   430
        val (split_thm, split_asm_thm) =
blanchet@49043
   431
          let
blanchet@49044
   432
            fun mk_conjunct xctr xs f_xs =
blanchet@49043
   433
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs));
blanchet@49044
   434
            fun mk_disjunct xctr xs f_xs =
blanchet@49044
   435
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr),
blanchet@49044
   436
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   437
blanchet@49130
   438
            val lhs = q $ (mk_caseB_term eta_fs $ v);
blanchet@49044
   439
blanchet@49043
   440
            val goal =
blanchet@49044
   441
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49044
   442
            val goal_asm =
blanchet@49044
   443
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   444
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   445
blanchet@49044
   446
            val split_thm =
blanchet@49049
   447
              Skip_Proof.prove lthy [] [] goal
blanchet@49052
   448
                (fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss)
blanchet@49044
   449
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49044
   450
            val split_asm_thm =
blanchet@49044
   451
              Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} =>
blanchet@49044
   452
                mk_split_asm_tac ctxt split_thm)
blanchet@49044
   453
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49043
   454
          in
blanchet@49044
   455
            (split_thm, split_asm_thm)
blanchet@49043
   456
          end;
blanchet@49025
   457
blanchet@49052
   458
        val notes =
blanchet@49052
   459
          [(case_congN, [case_cong_thm]),
blanchet@49116
   460
           (case_eqN, [case_eq_thm]),
blanchet@49052
   461
           (casesN, case_thms),
blanchet@49118
   462
           (collapseN, collapse_thms),
blanchet@49116
   463
           (discsN, disc_thms),
blanchet@49122
   464
           (disc_excludeN, disc_exclude_thms),
blanchet@49116
   465
           (disc_exhaustN, disc_exhaust_thms),
blanchet@49052
   466
           (distinctN, distinct_thms),
blanchet@49052
   467
           (exhaustN, [exhaust_thm]),
blanchet@49121
   468
           (injectN, flat inject_thmss),
blanchet@49052
   469
           (nchotomyN, [nchotomy_thm]),
blanchet@49121
   470
           (selsN, flat sel_thmss),
blanchet@49052
   471
           (splitN, [split_thm]),
blanchet@49052
   472
           (split_asmN, [split_asm_thm]),
blanchet@49052
   473
           (weak_case_cong_thmsN, [weak_case_cong_thm])]
blanchet@49116
   474
          |> filter_out (null o snd)
blanchet@49052
   475
          |> map (fn (thmN, thms) =>
blanchet@49052
   476
            ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])]));
blanchet@49019
   477
      in
blanchet@49052
   478
        lthy |> Local_Theory.notes notes |> snd
blanchet@49019
   479
      end;
blanchet@49017
   480
  in
blanchet@49121
   481
    (goalss, after_qed, lthy')
blanchet@49017
   482
  end;
blanchet@49017
   483
blanchet@49121
   484
fun wrap_data tacss = (fn (goalss, after_qed, lthy) =>
blanchet@49111
   485
  map2 (map2 (Skip_Proof.prove lthy [] [])) goalss tacss
blanchet@49111
   486
  |> (fn thms => after_qed thms lthy)) oo
blanchet@49121
   487
  prepare_wrap_data (K I) (* FIXME? (singleton o Type_Infer_Context.infer_types) *)
blanchet@49111
   488
blanchet@49114
   489
val parse_bindings = Parse.$$$ "[" |-- Parse.list Parse.binding --| Parse.$$$ "]";
blanchet@49057
   490
val parse_bindingss = Parse.$$$ "[" |-- Parse.list parse_bindings --| Parse.$$$ "]";
blanchet@49017
   491
blanchet@49074
   492
val wrap_data_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49019
   493
  Proof.theorem NONE after_qed (map (map (rpair [])) goalss) lthy) oo
blanchet@49121
   494
  prepare_wrap_data Syntax.read_term;
blanchet@49017
   495
blanchet@49017
   496
val _ =
blanchet@49074
   497
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype"
blanchet@49023
   498
    (((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term --
blanchet@49057
   499
      Scan.optional (parse_bindings -- Scan.optional parse_bindingss []) ([], []))
blanchet@49074
   500
     >> wrap_data_cmd);
blanchet@49017
   501
blanchet@49017
   502
end;