src/HOL/Codatatype/Tools/bnf_wrap.ML
author blanchet
Fri Sep 21 02:19:44 2012 +0200 (2012-09-21)
changeset 49486 64cc57c0d0fe
parent 49484 0194a18f80cf
child 49498 acc583e14167
permissions -rw-r--r--
generate "expand" property
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@49121
    10
  val mk_half_pairss: 'a list -> ('a * 'a) list list
blanchet@49203
    11
  val mk_ctr: typ list -> term -> term
blanchet@49484
    12
  val mk_disc_or_sel: typ list -> term -> term
blanchet@49437
    13
  val base_name_of_ctr: term -> string
blanchet@49199
    14
  val wrap_datatype: ({prems: thm list, context: Proof.context} -> tactic) list list ->
blanchet@49280
    15
    ((bool * term list) * term) *
blanchet@49280
    16
      (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
blanchet@49484
    17
    (term list * term list list * thm list * thm list * thm list * thm list list * thm list *
blanchet@49484
    18
     thm list list) * local_theory
blanchet@49278
    19
  val parse_wrap_options: bool parser
blanchet@49286
    20
  val parse_bound_term: (binding * string) parser
blanchet@49017
    21
end;
blanchet@49017
    22
blanchet@49074
    23
structure BNF_Wrap : BNF_WRAP =
blanchet@49017
    24
struct
blanchet@49017
    25
blanchet@49017
    26
open BNF_Util
blanchet@49074
    27
open BNF_Wrap_Tactics
blanchet@49017
    28
blanchet@49223
    29
val isN = "is_";
blanchet@49223
    30
val unN = "un_";
blanchet@49223
    31
fun mk_unN 1 1 suf = unN ^ suf
blanchet@49223
    32
  | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
blanchet@49046
    33
blanchet@49054
    34
val case_congN = "case_cong";
blanchet@49116
    35
val case_eqN = "case_eq";
blanchet@49054
    36
val casesN = "cases";
blanchet@49118
    37
val collapseN = "collapse";
blanchet@49122
    38
val disc_excludeN = "disc_exclude";
blanchet@49054
    39
val disc_exhaustN = "disc_exhaust";
blanchet@49054
    40
val discsN = "discs";
blanchet@49054
    41
val distinctN = "distinct";
blanchet@49075
    42
val exhaustN = "exhaust";
blanchet@49486
    43
val expandN = "expand";
blanchet@49075
    44
val injectN = "inject";
blanchet@49075
    45
val nchotomyN = "nchotomy";
blanchet@49054
    46
val selsN = "sels";
blanchet@49054
    47
val splitN = "split";
blanchet@49054
    48
val split_asmN = "split_asm";
blanchet@49054
    49
val weak_case_cong_thmsN = "weak_case_cong";
blanchet@49019
    50
blanchet@49336
    51
val std_binding = @{binding _};
blanchet@49300
    52
blanchet@49300
    53
val induct_simp_attrs = @{attributes [induct_simp]};
blanchet@49300
    54
val cong_attrs = @{attributes [cong]};
blanchet@49300
    55
val iff_attrs = @{attributes [iff]};
blanchet@49300
    56
val safe_elim_attrs = @{attributes [elim!]};
blanchet@49300
    57
val simp_attrs = @{attributes [simp]};
blanchet@49046
    58
blanchet@49056
    59
fun pad_list x n xs = xs @ replicate (n - length xs) x;
blanchet@49056
    60
blanchet@49259
    61
fun unflat_lookup eq ys zs = map (map (fn x => nth zs (find_index (curry eq x) ys)));
blanchet@49258
    62
blanchet@49048
    63
fun mk_half_pairss' _ [] = []
blanchet@49486
    64
  | mk_half_pairss' indent (x :: xs) =
blanchet@49486
    65
    indent @ fold_rev (cons o single o pair x) xs (mk_half_pairss' ([] :: indent) xs);
blanchet@49486
    66
blanchet@49486
    67
fun mk_half_pairss xs = mk_half_pairss' [[]] xs;
blanchet@49027
    68
blanchet@49486
    69
fun join_halves n half_xss other_half_xss =
blanchet@49486
    70
  let
blanchet@49486
    71
    val xsss =
blanchet@49486
    72
      map2 (map2 append) (Library.chop_groups n half_xss)
blanchet@49486
    73
        (transpose (Library.chop_groups n other_half_xss))
blanchet@49486
    74
    val xs = interleave (flat half_xss) (flat other_half_xss);
blanchet@49486
    75
  in (xs, xsss |> `transpose) end;
blanchet@49027
    76
blanchet@49280
    77
fun mk_undefined T = Const (@{const_name undefined}, T);
blanchet@49055
    78
blanchet@49203
    79
fun mk_ctr Ts ctr =
blanchet@49203
    80
  let val Type (_, Ts0) = body_type (fastype_of ctr) in
blanchet@49203
    81
    Term.subst_atomic_types (Ts0 ~~ Ts) ctr
blanchet@49203
    82
  end;
blanchet@49203
    83
blanchet@49484
    84
fun mk_disc_or_sel Ts t =
blanchet@49484
    85
  Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
blanchet@49484
    86
blanchet@49300
    87
fun base_name_of_ctr c =
blanchet@49300
    88
  Long_Name.base_name (case head_of c of
blanchet@49300
    89
      Const (s, _) => s
blanchet@49300
    90
    | Free (s, _) => s
blanchet@49300
    91
    | _ => error "Cannot extract name of constructor");
blanchet@49046
    92
blanchet@49486
    93
fun rap u t = betapply (t, u);
blanchet@49486
    94
blanchet@49437
    95
fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
blanchet@49437
    96
blanchet@49278
    97
fun prepare_wrap_datatype prep_term (((no_dests, raw_ctrs), raw_case),
blanchet@49336
    98
    (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
blanchet@49017
    99
  let
blanchet@49019
   100
    (* TODO: sanity checks on arguments *)
blanchet@49113
   101
    (* TODO: case syntax *)
blanchet@49025
   102
blanchet@49280
   103
    val n = length raw_ctrs;
blanchet@49054
   104
    val ks = 1 upto n;
blanchet@49054
   105
blanchet@49121
   106
    val _ = if n > 0 then () else error "No constructors specified";
blanchet@49121
   107
blanchet@49280
   108
    val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
blanchet@49280
   109
    val case0 = prep_term no_defs_lthy raw_case;
blanchet@49280
   110
    val sel_defaultss =
blanchet@49280
   111
      pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
blanchet@49280
   112
blanchet@49300
   113
    val Type (dataT_name, As0) = body_type (fastype_of (hd ctrs0));
blanchet@49302
   114
    val data_b = Binding.qualified_name dataT_name;
blanchet@49055
   115
blanchet@49055
   116
    val (As, B) =
blanchet@49055
   117
      no_defs_lthy
blanchet@49298
   118
      |> mk_TFrees' (map Type.sort_of_atyp As0)
blanchet@49055
   119
      ||> the_single o fst o mk_TFrees 1;
blanchet@49055
   120
blanchet@49300
   121
    val dataT = Type (dataT_name, As);
blanchet@49055
   122
    val ctrs = map (mk_ctr As) ctrs0;
blanchet@49055
   123
    val ctr_Tss = map (binder_types o fastype_of) ctrs;
blanchet@49055
   124
blanchet@49055
   125
    val ms = map length ctr_Tss;
blanchet@49055
   126
traytel@49434
   127
    val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
blanchet@49120
   128
blanchet@49174
   129
    fun can_really_rely_on_disc k =
traytel@49434
   130
      not (Binding.eq_name (nth raw_disc_bindings' (k - 1), Binding.empty)) orelse
traytel@49434
   131
      nth ms (k - 1) = 0;
blanchet@49174
   132
    fun can_rely_on_disc k =
blanchet@49174
   133
      can_really_rely_on_disc k orelse (k = 1 andalso not (can_really_rely_on_disc 2));
blanchet@49336
   134
    fun can_omit_disc_binding k m =
blanchet@49174
   135
      n = 1 orelse m = 0 orelse (n = 2 andalso can_rely_on_disc (3 - k));
blanchet@49120
   136
blanchet@49336
   137
    val std_disc_binding =
blanchet@49302
   138
      Binding.qualify false (Binding.name_of data_b) o Binding.name o prefix isN o base_name_of_ctr;
blanchet@49120
   139
blanchet@49336
   140
    val disc_bindings =
blanchet@49336
   141
      raw_disc_bindings'
blanchet@49120
   142
      |> map4 (fn k => fn m => fn ctr => fn disc =>
blanchet@49302
   143
        Option.map (Binding.qualify false (Binding.name_of data_b))
traytel@49434
   144
          (if Binding.eq_name (disc, Binding.empty) then
blanchet@49336
   145
             if can_omit_disc_binding k m then NONE else SOME (std_disc_binding ctr)
blanchet@49336
   146
           else if Binding.eq_name (disc, std_binding) then
blanchet@49336
   147
             SOME (std_disc_binding ctr)
blanchet@49302
   148
           else
blanchet@49302
   149
             SOME disc)) ks ms ctrs0;
blanchet@49056
   150
blanchet@49336
   151
    val no_discs = map is_none disc_bindings;
blanchet@49137
   152
    val no_discs_at_all = forall I no_discs;
blanchet@49116
   153
blanchet@49336
   154
    fun std_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
blanchet@49120
   155
blanchet@49336
   156
    val sel_bindingss =
blanchet@49336
   157
      pad_list [] n raw_sel_bindingss
blanchet@49056
   158
      |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
blanchet@49302
   159
        Binding.qualify false (Binding.name_of data_b)
traytel@49434
   160
          (if Binding.eq_name (sel, Binding.empty) orelse Binding.eq_name (sel, std_binding) then
blanchet@49336
   161
            std_sel_binding m l ctr
blanchet@49302
   162
          else
traytel@49434
   163
            sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
blanchet@49020
   164
blanchet@49130
   165
    fun mk_case Ts T =
blanchet@49121
   166
      let
blanchet@49336
   167
        val (bindings, body) = strip_type (fastype_of case0)
blanchet@49336
   168
        val Type (_, Ts0) = List.last bindings
blanchet@49130
   169
      in Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) case0 end;
blanchet@49022
   170
blanchet@49201
   171
    val casex = mk_case As B;
blanchet@49201
   172
    val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
blanchet@49043
   173
blanchet@49486
   174
    val ((((((((xss, xss'), yss), fs), gs), (u, u')), v), (p, p')), names_lthy) = no_defs_lthy |>
blanchet@49364
   175
      mk_Freess' "x" ctr_Tss
blanchet@49025
   176
      ||>> mk_Freess "y" ctr_Tss
blanchet@49201
   177
      ||>> mk_Frees "f" case_Ts
blanchet@49201
   178
      ||>> mk_Frees "g" case_Ts
blanchet@49486
   179
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "u") dataT
blanchet@49486
   180
      ||>> yield_singleton (mk_Frees "v") dataT
blanchet@49043
   181
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
blanchet@49043
   182
blanchet@49463
   183
    val q = Free (fst p', mk_pred1T B);
blanchet@49020
   184
blanchet@49025
   185
    val xctrs = map2 (curry Term.list_comb) ctrs xss;
blanchet@49025
   186
    val yctrs = map2 (curry Term.list_comb) ctrs yss;
blanchet@49032
   187
blanchet@49043
   188
    val xfs = map2 (curry Term.list_comb) fs xss;
blanchet@49043
   189
    val xgs = map2 (curry Term.list_comb) gs xss;
blanchet@49043
   190
blanchet@49437
   191
    val eta_fs = map2 eta_expand_arg xss xfs;
blanchet@49437
   192
    val eta_gs = map2 eta_expand_arg xss xgs;
blanchet@49043
   193
blanchet@49201
   194
    val fcase = Term.list_comb (casex, eta_fs);
blanchet@49201
   195
    val gcase = Term.list_comb (casex, eta_gs);
blanchet@49020
   196
blanchet@49486
   197
    val ufcase = fcase $ u;
blanchet@49486
   198
    val vfcase = fcase $ v;
blanchet@49486
   199
    val vgcase = gcase $ v;
blanchet@49486
   200
blanchet@49486
   201
    fun mk_u_eq_u () = HOLogic.mk_eq (u, u);
blanchet@49486
   202
blanchet@49486
   203
    val u_eq_v = mk_Trueprop_eq (u, v);
blanchet@49486
   204
blanchet@49486
   205
    val exist_xs_u_eq_ctrs =
blanchet@49486
   206
      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
blanchet@49022
   207
blanchet@49278
   208
    val unique_disc_no_def = TrueI; (*arbitrary marker*)
blanchet@49278
   209
    val alternate_disc_no_def = FalseE; (*arbitrary marker*)
blanchet@49116
   210
blanchet@49486
   211
    fun alternate_disc_lhs get_udisc k =
blanchet@49116
   212
      HOLogic.mk_not
blanchet@49336
   213
        (case nth disc_bindings (k - 1) of
blanchet@49486
   214
          NONE => nth exist_xs_u_eq_ctrs (k - 1)
blanchet@49486
   215
        | SOME b => get_udisc b (k - 1));
blanchet@49116
   216
blanchet@49486
   217
    val (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
blanchet@49486
   218
         sel_defss, lthy') =
blanchet@49278
   219
      if no_dests then
blanchet@49486
   220
        (true, [], [], [], [], [], [], [], [], [], no_defs_lthy)
blanchet@49278
   221
      else
blanchet@49278
   222
        let
blanchet@49463
   223
          fun disc_free b = Free (Binding.name_of b, mk_pred1T dataT);
blanchet@49025
   224
blanchet@49486
   225
          fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
blanchet@49278
   226
blanchet@49486
   227
          fun alternate_disc k = Term.lambda u (alternate_disc_lhs (K o rap u o disc_free) (3 - k));
blanchet@49278
   228
blanchet@49364
   229
          fun mk_default T t =
blanchet@49364
   230
            let
blanchet@49364
   231
              val Ts0 = map TFree (Term.add_tfreesT (fastype_of t) []);
blanchet@49364
   232
              val Ts = map TFree (Term.add_tfreesT T []);
blanchet@49364
   233
            in Term.subst_atomic_types (Ts0 ~~ Ts) t end;
blanchet@49364
   234
blanchet@49280
   235
          fun mk_sel_case_args b proto_sels T =
blanchet@49280
   236
            map2 (fn Ts => fn k =>
blanchet@49280
   237
              (case AList.lookup (op =) proto_sels k of
blanchet@49280
   238
                NONE =>
blanchet@49364
   239
                (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
blanchet@49364
   240
                  NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
blanchet@49364
   241
                | SOME t => mk_default (Ts ---> T) t)
blanchet@49280
   242
              | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
blanchet@49258
   243
blanchet@49278
   244
          fun sel_spec b proto_sels =
blanchet@49278
   245
            let
blanchet@49278
   246
              val _ =
blanchet@49278
   247
                (case duplicates (op =) (map fst proto_sels) of
blanchet@49278
   248
                   k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
blanchet@49278
   249
                     " for constructor " ^
blanchet@49278
   250
                     quote (Syntax.string_of_term no_defs_lthy (nth ctrs (k - 1))))
blanchet@49278
   251
                 | [] => ())
blanchet@49278
   252
              val T =
blanchet@49278
   253
                (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
blanchet@49278
   254
                  [T] => T
blanchet@49278
   255
                | T :: T' :: _ => error ("Inconsistent range type for selector " ^
blanchet@49278
   256
                    quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ no_defs_lthy T) ^
blanchet@49278
   257
                    " vs. " ^ quote (Syntax.string_of_typ no_defs_lthy T')));
blanchet@49278
   258
            in
blanchet@49486
   259
              mk_Trueprop_eq (Free (Binding.name_of b, dataT --> T) $ u,
blanchet@49486
   260
                Term.list_comb (mk_case As T, mk_sel_case_args b proto_sels T) $ u)
blanchet@49278
   261
            end;
blanchet@49116
   262
blanchet@49336
   263
          val sel_bindings = flat sel_bindingss;
blanchet@49336
   264
          val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
blanchet@49336
   265
          val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
blanchet@49285
   266
blanchet@49336
   267
          val sel_binding_index =
blanchet@49336
   268
            if all_sels_distinct then 1 upto length sel_bindings
blanchet@49336
   269
            else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
blanchet@49285
   270
blanchet@49285
   271
          val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
blanchet@49300
   272
          val sel_infos =
blanchet@49336
   273
            AList.group (op =) (sel_binding_index ~~ proto_sels)
blanchet@49285
   274
            |> sort (int_ord o pairself fst)
blanchet@49336
   275
            |> map snd |> curry (op ~~) uniq_sel_bindings;
blanchet@49336
   276
          val sel_bindings = map fst sel_infos;
blanchet@49258
   277
blanchet@49336
   278
          fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
blanchet@49258
   279
blanchet@49278
   280
          val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
blanchet@49278
   281
            no_defs_lthy
blanchet@49486
   282
            |> apfst split_list o fold_map4 (fn k => fn m => fn exist_xs_u_eq_ctr =>
blanchet@49278
   283
              fn NONE =>
blanchet@49486
   284
                 if n = 1 then pair (Term.lambda u (mk_u_eq_u ()), unique_disc_no_def)
blanchet@49486
   285
                 else if m = 0 then pair (Term.lambda u exist_xs_u_eq_ctr, refl)
blanchet@49278
   286
                 else pair (alternate_disc k, alternate_disc_no_def)
blanchet@49278
   287
               | SOME b => Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49486
   288
                   ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
blanchet@49486
   289
              ks ms exist_xs_u_eq_ctrs disc_bindings
blanchet@49278
   290
            ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
blanchet@49278
   291
              Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49300
   292
                ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
blanchet@49278
   293
            ||> `Local_Theory.restore;
blanchet@49022
   294
blanchet@49278
   295
          val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49025
   296
blanchet@49278
   297
          val disc_defs = map (Morphism.thm phi) raw_disc_defs;
blanchet@49281
   298
          val sel_defs = map (Morphism.thm phi) raw_sel_defs;
blanchet@49281
   299
          val sel_defss = unflat_selss sel_defs;
blanchet@49278
   300
blanchet@49278
   301
          val discs0 = map (Morphism.term phi) raw_discs;
blanchet@49278
   302
          val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
blanchet@49028
   303
blanchet@49278
   304
          val discs = map (mk_disc_or_sel As) discs0;
blanchet@49278
   305
          val selss = map (map (mk_disc_or_sel As)) selss0;
blanchet@49486
   306
blanchet@49486
   307
          val udiscs = map (rap u) discs;
blanchet@49486
   308
          val uselss = map (map (rap u)) selss;
blanchet@49486
   309
blanchet@49486
   310
          val vdiscs = map (rap v) discs;
blanchet@49486
   311
          val vselss = map (map (rap v)) selss;
blanchet@49278
   312
        in
blanchet@49486
   313
          (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
blanchet@49486
   314
           sel_defss, lthy')
blanchet@49278
   315
        end;
blanchet@49025
   316
blanchet@49032
   317
    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
blanchet@49029
   318
blanchet@49458
   319
    val exhaust_goal =
blanchet@49486
   320
      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (u, xctr)]) in
blanchet@49486
   321
        fold_rev Logic.all [p, u] (mk_imp_p (map2 mk_prem xctrs xss))
blanchet@49020
   322
      end;
blanchet@49019
   323
blanchet@49484
   324
    val inject_goalss =
blanchet@49017
   325
      let
blanchet@49034
   326
        fun mk_goal _ _ [] [] = []
blanchet@49025
   327
          | mk_goal xctr yctr xs ys =
blanchet@49121
   328
            [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
blanchet@49121
   329
              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
blanchet@49017
   330
      in
blanchet@49034
   331
        map4 mk_goal xctrs yctrs xss yss
blanchet@49017
   332
      end;
blanchet@49017
   333
blanchet@49484
   334
    val half_distinct_goalss =
blanchet@49121
   335
      let
blanchet@49203
   336
        fun mk_goal ((xs, xc), (xs', xc')) =
blanchet@49121
   337
          fold_rev Logic.all (xs @ xs')
blanchet@49203
   338
            (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
blanchet@49121
   339
      in
blanchet@49121
   340
        map (map mk_goal) (mk_half_pairss (xss ~~ xctrs))
blanchet@49121
   341
      end;
blanchet@49019
   342
blanchet@49458
   343
    val cases_goal =
blanchet@49121
   344
      map3 (fn xs => fn xctr => fn xf =>
blanchet@49201
   345
        fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xss xctrs xfs;
blanchet@49025
   346
blanchet@49484
   347
    val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss @ [cases_goal];
blanchet@49019
   348
blanchet@49019
   349
    fun after_qed thmss lthy =
blanchet@49019
   350
      let
blanchet@49048
   351
        val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) =
blanchet@49048
   352
          (hd thmss, apsnd (chop (n * n)) (chop n (tl thmss)));
blanchet@49019
   353
blanchet@49438
   354
        val inject_thms = flat inject_thmss;
blanchet@49438
   355
blanchet@49486
   356
        val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
blanchet@49486
   357
blanchet@49486
   358
        fun inst_thm t thm =
blanchet@49486
   359
          Drule.instantiate' [] [SOME (certify lthy t)]
blanchet@49486
   360
            (Thm.instantiate (Tinst, []) (Drule.zero_var_indexes thm));
blanchet@49486
   361
blanchet@49486
   362
        val uexhaust_thm = inst_thm u exhaust_thm;
blanchet@49032
   363
blanchet@49300
   364
        val exhaust_cases = map base_name_of_ctr ctrs;
blanchet@49300
   365
blanchet@49048
   366
        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
blanchet@49048
   367
blanchet@49486
   368
        val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
blanchet@49486
   369
          join_halves n half_distinct_thmss other_half_distinct_thmss;
blanchet@49019
   370
blanchet@49020
   371
        val nchotomy_thm =
blanchet@49020
   372
          let
blanchet@49020
   373
            val goal =
blanchet@49486
   374
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
blanchet@49486
   375
                Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
blanchet@49020
   376
          in
blanchet@49020
   377
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
blanchet@49020
   378
          end;
blanchet@49020
   379
blanchet@49484
   380
        val (all_sel_thms, sel_thmss, disc_thmss, disc_thms, discI_thms, disc_exclude_thms,
blanchet@49486
   381
             disc_exhaust_thms, collapse_thms, expand_thms, case_eq_thms) =
blanchet@49278
   382
          if no_dests then
blanchet@49486
   383
            ([], [], [], [], [], [], [], [], [], [])
blanchet@49116
   384
          else
blanchet@49116
   385
            let
blanchet@49364
   386
              fun make_sel_thm xs' case_thm sel_def =
blanchet@49364
   387
                zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
blanchet@49364
   388
                    (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
blanchet@49281
   389
blanchet@49281
   390
              fun has_undefined_rhs thm =
blanchet@49281
   391
                (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
blanchet@49281
   392
                  Const (@{const_name undefined}, _) => true
blanchet@49281
   393
                | _ => false);
blanchet@49281
   394
blanchet@49364
   395
              val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
blanchet@49281
   396
blanchet@49281
   397
              val all_sel_thms =
blanchet@49285
   398
                (if all_sels_distinct andalso forall null sel_defaultss then
blanchet@49285
   399
                   flat sel_thmss
blanchet@49285
   400
                 else
blanchet@49364
   401
                   map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
blanchet@49364
   402
                     (xss' ~~ case_thms))
blanchet@49285
   403
                |> filter_out has_undefined_rhs;
blanchet@49278
   404
blanchet@49278
   405
              fun mk_unique_disc_def () =
blanchet@49278
   406
                let
blanchet@49278
   407
                  val m = the_single ms;
blanchet@49486
   408
                  val goal = mk_Trueprop_eq (mk_u_eq_u (), the_single exist_xs_u_eq_ctrs);
blanchet@49278
   409
                in
blanchet@49486
   410
                  Skip_Proof.prove lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
blanchet@49278
   411
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   412
                  |> Thm.close_derivation
blanchet@49278
   413
                end;
blanchet@49278
   414
blanchet@49278
   415
              fun mk_alternate_disc_def k =
blanchet@49278
   416
                let
blanchet@49278
   417
                  val goal =
blanchet@49486
   418
                    mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
blanchet@49486
   419
                      nth exist_xs_u_eq_ctrs (k - 1));
blanchet@49278
   420
                in
blanchet@49278
   421
                  Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49278
   422
                    mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
blanchet@49486
   423
                      (nth distinct_thms (2 - k)) uexhaust_thm)
blanchet@49278
   424
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   425
                  |> Thm.close_derivation
blanchet@49278
   426
                end;
blanchet@49028
   427
blanchet@49278
   428
              val has_alternate_disc_def =
blanchet@49278
   429
                exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
blanchet@49278
   430
blanchet@49278
   431
              val disc_defs' =
blanchet@49278
   432
                map2 (fn k => fn def =>
blanchet@49278
   433
                  if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
blanchet@49278
   434
                  else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
blanchet@49278
   435
                  else def) ks disc_defs;
blanchet@49278
   436
blanchet@49278
   437
              val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49278
   438
              val discI_thms =
blanchet@49278
   439
                map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
blanchet@49278
   440
                  disc_defs';
blanchet@49278
   441
              val not_discI_thms =
blanchet@49278
   442
                map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49463
   443
                    (unfold_defs lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49278
   444
                  ms disc_defs';
blanchet@49278
   445
blanchet@49278
   446
              val (disc_thmss', disc_thmss) =
blanchet@49278
   447
                let
blanchet@49278
   448
                  fun mk_thm discI _ [] = refl RS discI
blanchet@49278
   449
                    | mk_thm _ not_discI [distinct] = distinct RS not_discI;
blanchet@49278
   450
                  fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
blanchet@49278
   451
                in
blanchet@49278
   452
                  map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
blanchet@49278
   453
                end;
blanchet@49278
   454
blanchet@49278
   455
              val disc_thms = flat (map2 (fn true => K [] | false => I) no_discs disc_thmss);
blanchet@49028
   456
blanchet@49486
   457
              val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
blanchet@49486
   458
                let
blanchet@49486
   459
                  fun mk_goal [] = []
blanchet@49486
   460
                    | mk_goal [((_, udisc), (_, udisc'))] =
blanchet@49486
   461
                      [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
blanchet@49486
   462
                         HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
blanchet@49486
   463
blanchet@49486
   464
                  fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);
blanchet@49486
   465
blanchet@49486
   466
                  val infos = ms ~~ discD_thms ~~ udiscs;
blanchet@49486
   467
                  val half_pairss = mk_half_pairss infos;
blanchet@49486
   468
blanchet@49486
   469
                  val half_goalss = map mk_goal half_pairss;
blanchet@49486
   470
                  val half_thmss =
blanchet@49486
   471
                    map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
blanchet@49486
   472
                        fn disc_thm => [prove (mk_half_disc_exclude_tac m discD disc_thm) goal])
blanchet@49486
   473
                      half_goalss half_pairss (flat disc_thmss');
blanchet@49278
   474
blanchet@49486
   475
                  val other_half_goalss = map (mk_goal o map swap) half_pairss;
blanchet@49486
   476
                  val other_half_thmss =
blanchet@49486
   477
                    map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
blanchet@49486
   478
                      other_half_goalss;
blanchet@49486
   479
                in
blanchet@49486
   480
                  join_halves n half_thmss other_half_thmss
blanchet@49486
   481
                  |>> has_alternate_disc_def ? K []
blanchet@49486
   482
                end;
blanchet@49278
   483
blanchet@49486
   484
              val disc_exhaust_thm =
blanchet@49486
   485
                let
blanchet@49486
   486
                  fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
blanchet@49486
   487
                  val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
blanchet@49486
   488
                in
blanchet@49486
   489
                  Skip_Proof.prove lthy [] [] goal (fn _ =>
blanchet@49486
   490
                    mk_disc_exhaust_tac n exhaust_thm discI_thms)
blanchet@49486
   491
                end;
blanchet@49028
   492
blanchet@49278
   493
              val disc_exhaust_thms =
blanchet@49486
   494
                if has_alternate_disc_def orelse no_discs_at_all then [] else [disc_exhaust_thm];
blanchet@49486
   495
blanchet@49486
   496
              val (collapse_thms, collapse_thm_opts) =
blanchet@49486
   497
                let
blanchet@49486
   498
                  fun mk_goal ctr udisc usels =
blanchet@49486
   499
                    let
blanchet@49486
   500
                      val prem = HOLogic.mk_Trueprop udisc;
blanchet@49486
   501
                      val concl =
blanchet@49486
   502
                        mk_Trueprop_eq ((null usels ? swap) (Term.list_comb (ctr, usels), u));
blanchet@49486
   503
                    in
blanchet@49486
   504
                      if prem aconv concl then NONE
blanchet@49486
   505
                      else SOME (Logic.all u (Logic.mk_implies (prem, concl)))
blanchet@49486
   506
                    end;
blanchet@49486
   507
                  val goals = map3 mk_goal ctrs udiscs uselss;
blanchet@49486
   508
                in
blanchet@49486
   509
                  map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>
blanchet@49486
   510
                    Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49486
   511
                      mk_collapse_tac ctxt m discD sel_thms)
blanchet@49486
   512
                    |> perhaps (try (fn thm => refl RS thm)))) ms discD_thms sel_thmss goals
blanchet@49486
   513
                  |> `(map_filter I)
blanchet@49486
   514
                end;
blanchet@49025
   515
blanchet@49486
   516
              val expand_thms =
blanchet@49486
   517
                let
blanchet@49486
   518
                  fun mk_prems k udisc usels vdisc vsels =
blanchet@49486
   519
                    (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
blanchet@49486
   520
                    (if null usels then
blanchet@49486
   521
                       []
blanchet@49486
   522
                     else
blanchet@49486
   523
                       [Logic.list_implies
blanchet@49486
   524
                          (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
blanchet@49486
   525
                             HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49486
   526
                               (map2 (curry HOLogic.mk_eq) usels vsels)))]);
blanchet@49486
   527
blanchet@49486
   528
                  val uncollapse_thms =
blanchet@49486
   529
                    map (fn NONE => Drule.dummy_thm | SOME thm => thm RS sym) collapse_thm_opts;
blanchet@49486
   530
blanchet@49486
   531
                  val goal =
blanchet@49486
   532
                    Library.foldr Logic.list_implies
blanchet@49486
   533
                      (map5 mk_prems ks udiscs uselss vdiscs vselss, u_eq_v);
blanchet@49486
   534
                in
blanchet@49486
   535
                  [Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49486
   536
                     mk_expand_tac ctxt n ms (inst_thm u disc_exhaust_thm)
blanchet@49486
   537
                       (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
blanchet@49486
   538
                       disc_exclude_thmsss')]
blanchet@49486
   539
                  |> Proof_Context.export names_lthy lthy
blanchet@49486
   540
                end;
blanchet@49278
   541
blanchet@49278
   542
              val case_eq_thms =
blanchet@49486
   543
                let
blanchet@49486
   544
                  fun mk_body f usels = Term.list_comb (f, usels);
blanchet@49486
   545
                  val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs (map2 mk_body fs uselss));
blanchet@49486
   546
                in
blanchet@49486
   547
                  [Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49486
   548
                     mk_case_eq_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)]
blanchet@49486
   549
                  |> Proof_Context.export names_lthy lthy
blanchet@49486
   550
                end;
blanchet@49116
   551
            in
blanchet@49484
   552
              (all_sel_thms, sel_thmss, disc_thmss, disc_thms, discI_thms, disc_exclude_thms,
blanchet@49486
   553
               disc_exhaust_thms, collapse_thms, expand_thms, case_eq_thms)
blanchet@49116
   554
            end;
blanchet@49025
   555
blanchet@49033
   556
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   557
          let
blanchet@49032
   558
            fun mk_prem xctr xs f g =
blanchet@49486
   559
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
blanchet@49032
   560
                mk_Trueprop_eq (f, g)));
blanchet@49033
   561
blanchet@49032
   562
            val goal =
blanchet@49486
   563
              Logic.list_implies (u_eq_v :: map4 mk_prem xctrs xss fs gs,
blanchet@49486
   564
                 mk_Trueprop_eq (ufcase, vgcase));
blanchet@49486
   565
            val weak_goal = Logic.mk_implies (u_eq_v, mk_Trueprop_eq (ufcase, vfcase));
blanchet@49032
   566
          in
blanchet@49486
   567
            (Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac uexhaust_thm case_thms),
blanchet@49458
   568
             Skip_Proof.prove lthy [] [] weak_goal (K (etac arg_cong 1)))
blanchet@49033
   569
            |> pairself (singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   570
          end;
blanchet@49025
   571
blanchet@49044
   572
        val (split_thm, split_asm_thm) =
blanchet@49043
   573
          let
blanchet@49044
   574
            fun mk_conjunct xctr xs f_xs =
blanchet@49486
   575
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
blanchet@49044
   576
            fun mk_disjunct xctr xs f_xs =
blanchet@49486
   577
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
blanchet@49044
   578
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   579
blanchet@49486
   580
            val lhs = q $ ufcase;
blanchet@49044
   581
blanchet@49043
   582
            val goal =
blanchet@49044
   583
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49458
   584
            val asm_goal =
blanchet@49044
   585
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   586
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   587
blanchet@49044
   588
            val split_thm =
blanchet@49049
   589
              Skip_Proof.prove lthy [] [] goal
blanchet@49486
   590
                (fn _ => mk_split_tac uexhaust_thm case_thms inject_thmss distinct_thmsss)
blanchet@49044
   591
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49044
   592
            val split_asm_thm =
blanchet@49458
   593
              Skip_Proof.prove lthy [] [] asm_goal (fn {context = ctxt, ...} =>
blanchet@49044
   594
                mk_split_asm_tac ctxt split_thm)
blanchet@49044
   595
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49043
   596
          in
blanchet@49044
   597
            (split_thm, split_asm_thm)
blanchet@49043
   598
          end;
blanchet@49025
   599
blanchet@49437
   600
        val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
blanchet@49300
   601
        val cases_type_attr = Attrib.internal (K (Induct.cases_type dataT_name));
blanchet@49300
   602
blanchet@49052
   603
        val notes =
blanchet@49300
   604
          [(case_congN, [case_cong_thm], []),
blanchet@49300
   605
           (case_eqN, case_eq_thms, []),
blanchet@49300
   606
           (casesN, case_thms, simp_attrs),
blanchet@49300
   607
           (collapseN, collapse_thms, simp_attrs),
blanchet@49300
   608
           (discsN, disc_thms, simp_attrs),
blanchet@49300
   609
           (disc_excludeN, disc_exclude_thms, []),
blanchet@49300
   610
           (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
blanchet@49300
   611
           (distinctN, distinct_thms, simp_attrs @ induct_simp_attrs),
blanchet@49300
   612
           (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
blanchet@49486
   613
           (expandN, expand_thms, []),
blanchet@49438
   614
           (injectN, inject_thms, iff_attrs @ induct_simp_attrs),
blanchet@49300
   615
           (nchotomyN, [nchotomy_thm], []),
blanchet@49300
   616
           (selsN, all_sel_thms, simp_attrs),
blanchet@49300
   617
           (splitN, [split_thm], []),
blanchet@49300
   618
           (split_asmN, [split_asm_thm], []),
blanchet@49300
   619
           (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
blanchet@49300
   620
          |> filter_out (null o #2)
blanchet@49300
   621
          |> map (fn (thmN, thms, attrs) =>
blanchet@49302
   622
            ((Binding.qualify true (Binding.name_of data_b) (Binding.name thmN), attrs),
blanchet@49302
   623
             [(thms, [])]));
blanchet@49300
   624
blanchet@49300
   625
        val notes' =
blanchet@49300
   626
          [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs)]
blanchet@49300
   627
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49019
   628
      in
blanchet@49484
   629
        ((discs, selss, inject_thms, distinct_thms, case_thms, disc_thmss, discI_thms, sel_thmss),
blanchet@49438
   630
         lthy |> Local_Theory.notes (notes' @ notes) |> snd)
blanchet@49019
   631
      end;
blanchet@49017
   632
  in
blanchet@49121
   633
    (goalss, after_qed, lthy')
blanchet@49017
   634
  end;
blanchet@49017
   635
blanchet@49199
   636
fun wrap_datatype tacss = (fn (goalss, after_qed, lthy) =>
blanchet@49111
   637
  map2 (map2 (Skip_Proof.prove lthy [] [])) goalss tacss
blanchet@49280
   638
  |> (fn thms => after_qed thms lthy)) oo prepare_wrap_datatype (K I);
blanchet@49280
   639
blanchet@49297
   640
val wrap_datatype_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49297
   641
  Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
blanchet@49297
   642
  prepare_wrap_datatype Syntax.read_term;
blanchet@49297
   643
blanchet@49280
   644
fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
blanchet@49111
   645
blanchet@49280
   646
val parse_bindings = parse_bracket_list Parse.binding;
blanchet@49280
   647
val parse_bindingss = parse_bracket_list parse_bindings;
blanchet@49280
   648
blanchet@49280
   649
val parse_bound_term = (Parse.binding --| @{keyword ":"}) -- Parse.term;
blanchet@49280
   650
val parse_bound_terms = parse_bracket_list parse_bound_term;
blanchet@49280
   651
val parse_bound_termss = parse_bracket_list parse_bound_terms;
blanchet@49017
   652
blanchet@49278
   653
val parse_wrap_options =
blanchet@49278
   654
  Scan.optional (@{keyword "("} |-- (@{keyword "no_dests"} >> K true) --| @{keyword ")"}) false;
blanchet@49278
   655
blanchet@49017
   656
val _ =
blanchet@49074
   657
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype"
blanchet@49278
   658
    ((parse_wrap_options -- (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) --
blanchet@49280
   659
      Parse.term -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
blanchet@49280
   660
        Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
blanchet@49199
   661
     >> wrap_datatype_cmd);
blanchet@49017
   662
blanchet@49017
   663
end;