src/HOL/BNF/Tools/bnf_wrap.ML
author blanchet
Wed Sep 26 10:01:00 2012 +0200 (2012-09-26)
changeset 49594 55e798614c45
parent 49591 91b228e26348
child 49618 29be73b789f9
permissions -rw-r--r--
tweaked theorem names (in particular, dropped s's)
blanchet@49509
     1
(*  Title:      HOL/BNF/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@49585
    10
  val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
blanchet@49585
    11
  val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
blanchet@49585
    12
blanchet@49203
    13
  val mk_ctr: typ list -> term -> term
blanchet@49484
    14
  val mk_disc_or_sel: typ list -> term -> term
blanchet@49585
    15
blanchet@49437
    16
  val base_name_of_ctr: term -> string
blanchet@49585
    17
blanchet@49199
    18
  val wrap_datatype: ({prems: thm list, context: Proof.context} -> tactic) list list ->
blanchet@49280
    19
    ((bool * term list) * term) *
blanchet@49280
    20
      (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
blanchet@49591
    21
    (term list * term list list * thm * thm list * thm list * thm list * thm list list * thm list *
blanchet@49484
    22
     thm list list) * local_theory
blanchet@49278
    23
  val parse_wrap_options: bool parser
blanchet@49286
    24
  val parse_bound_term: (binding * string) parser
blanchet@49017
    25
end;
blanchet@49017
    26
blanchet@49074
    27
structure BNF_Wrap : BNF_WRAP =
blanchet@49017
    28
struct
blanchet@49017
    29
blanchet@49017
    30
open BNF_Util
blanchet@49074
    31
open BNF_Wrap_Tactics
blanchet@49017
    32
blanchet@49223
    33
val isN = "is_";
blanchet@49223
    34
val unN = "un_";
blanchet@49223
    35
fun mk_unN 1 1 suf = unN ^ suf
blanchet@49223
    36
  | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
blanchet@49046
    37
blanchet@49594
    38
val caseN = "case";
blanchet@49054
    39
val case_congN = "case_cong";
blanchet@49594
    40
val case_convN = "case_conv";
blanchet@49118
    41
val collapseN = "collapse";
blanchet@49122
    42
val disc_excludeN = "disc_exclude";
blanchet@49054
    43
val disc_exhaustN = "disc_exhaust";
blanchet@49054
    44
val discsN = "discs";
blanchet@49054
    45
val distinctN = "distinct";
blanchet@49075
    46
val exhaustN = "exhaust";
blanchet@49486
    47
val expandN = "expand";
blanchet@49075
    48
val injectN = "inject";
blanchet@49075
    49
val nchotomyN = "nchotomy";
blanchet@49054
    50
val selsN = "sels";
blanchet@49054
    51
val splitN = "split";
blanchet@49054
    52
val split_asmN = "split_asm";
blanchet@49054
    53
val weak_case_cong_thmsN = "weak_case_cong";
blanchet@49019
    54
blanchet@49336
    55
val std_binding = @{binding _};
blanchet@49300
    56
blanchet@49300
    57
val induct_simp_attrs = @{attributes [induct_simp]};
blanchet@49300
    58
val cong_attrs = @{attributes [cong]};
blanchet@49300
    59
val iff_attrs = @{attributes [iff]};
blanchet@49300
    60
val safe_elim_attrs = @{attributes [elim!]};
blanchet@49300
    61
val simp_attrs = @{attributes [simp]};
blanchet@49046
    62
blanchet@49056
    63
fun pad_list x n xs = xs @ replicate (n - length xs) x;
blanchet@49056
    64
blanchet@49259
    65
fun unflat_lookup eq ys zs = map (map (fn x => nth zs (find_index (curry eq x) ys)));
blanchet@49258
    66
blanchet@49585
    67
fun mk_half_pairss' _ ([], []) = []
blanchet@49591
    68
  | mk_half_pairss' indent (x :: xs, _ :: ys) =
blanchet@49585
    69
    indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
blanchet@49486
    70
blanchet@49585
    71
fun mk_half_pairss p = mk_half_pairss' [[]] p;
blanchet@49027
    72
blanchet@49486
    73
fun join_halves n half_xss other_half_xss =
blanchet@49486
    74
  let
blanchet@49486
    75
    val xsss =
blanchet@49486
    76
      map2 (map2 append) (Library.chop_groups n half_xss)
blanchet@49486
    77
        (transpose (Library.chop_groups n other_half_xss))
blanchet@49486
    78
    val xs = interleave (flat half_xss) (flat other_half_xss);
blanchet@49585
    79
  in (xs, xsss) end;
blanchet@49027
    80
blanchet@49280
    81
fun mk_undefined T = Const (@{const_name undefined}, T);
blanchet@49055
    82
blanchet@49500
    83
fun mk_ctr Ts t =
blanchet@49500
    84
  let val Type (_, Ts0) = body_type (fastype_of t) in
blanchet@49500
    85
    Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49203
    86
  end;
blanchet@49203
    87
blanchet@49484
    88
fun mk_disc_or_sel Ts t =
blanchet@49484
    89
  Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
blanchet@49484
    90
blanchet@49536
    91
fun mk_case Ts T t =
blanchet@49536
    92
  let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
blanchet@49536
    93
    Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) t
blanchet@49536
    94
  end;
blanchet@49536
    95
blanchet@49300
    96
fun base_name_of_ctr c =
blanchet@49300
    97
  Long_Name.base_name (case head_of c of
blanchet@49300
    98
      Const (s, _) => s
blanchet@49300
    99
    | Free (s, _) => s
blanchet@49300
   100
    | _ => error "Cannot extract name of constructor");
blanchet@49046
   101
blanchet@49437
   102
fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
blanchet@49437
   103
blanchet@49278
   104
fun prepare_wrap_datatype prep_term (((no_dests, raw_ctrs), raw_case),
blanchet@49336
   105
    (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
blanchet@49017
   106
  let
blanchet@49019
   107
    (* TODO: sanity checks on arguments *)
blanchet@49113
   108
    (* TODO: case syntax *)
blanchet@49025
   109
blanchet@49280
   110
    val n = length raw_ctrs;
blanchet@49054
   111
    val ks = 1 upto n;
blanchet@49054
   112
blanchet@49121
   113
    val _ = if n > 0 then () else error "No constructors specified";
blanchet@49121
   114
blanchet@49280
   115
    val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
blanchet@49280
   116
    val case0 = prep_term no_defs_lthy raw_case;
blanchet@49280
   117
    val sel_defaultss =
blanchet@49280
   118
      pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
blanchet@49280
   119
blanchet@49300
   120
    val Type (dataT_name, As0) = body_type (fastype_of (hd ctrs0));
blanchet@49302
   121
    val data_b = Binding.qualified_name dataT_name;
blanchet@49498
   122
    val data_b_name = Binding.name_of data_b;
blanchet@49055
   123
blanchet@49055
   124
    val (As, B) =
blanchet@49055
   125
      no_defs_lthy
blanchet@49298
   126
      |> mk_TFrees' (map Type.sort_of_atyp As0)
blanchet@49055
   127
      ||> the_single o fst o mk_TFrees 1;
blanchet@49055
   128
blanchet@49300
   129
    val dataT = Type (dataT_name, As);
blanchet@49055
   130
    val ctrs = map (mk_ctr As) ctrs0;
blanchet@49055
   131
    val ctr_Tss = map (binder_types o fastype_of) ctrs;
blanchet@49055
   132
blanchet@49055
   133
    val ms = map length ctr_Tss;
blanchet@49055
   134
traytel@49434
   135
    val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
blanchet@49120
   136
blanchet@49174
   137
    fun can_really_rely_on_disc k =
traytel@49434
   138
      not (Binding.eq_name (nth raw_disc_bindings' (k - 1), Binding.empty)) orelse
traytel@49434
   139
      nth ms (k - 1) = 0;
blanchet@49174
   140
    fun can_rely_on_disc k =
blanchet@49174
   141
      can_really_rely_on_disc k orelse (k = 1 andalso not (can_really_rely_on_disc 2));
blanchet@49336
   142
    fun can_omit_disc_binding k m =
blanchet@49174
   143
      n = 1 orelse m = 0 orelse (n = 2 andalso can_rely_on_disc (3 - k));
blanchet@49120
   144
blanchet@49336
   145
    val std_disc_binding =
blanchet@49498
   146
      Binding.qualify false data_b_name o Binding.name o prefix isN o base_name_of_ctr;
blanchet@49120
   147
blanchet@49336
   148
    val disc_bindings =
blanchet@49336
   149
      raw_disc_bindings'
blanchet@49120
   150
      |> map4 (fn k => fn m => fn ctr => fn disc =>
blanchet@49498
   151
        Option.map (Binding.qualify false data_b_name)
traytel@49434
   152
          (if Binding.eq_name (disc, Binding.empty) then
blanchet@49336
   153
             if can_omit_disc_binding k m then NONE else SOME (std_disc_binding ctr)
blanchet@49336
   154
           else if Binding.eq_name (disc, std_binding) then
blanchet@49336
   155
             SOME (std_disc_binding ctr)
blanchet@49302
   156
           else
blanchet@49302
   157
             SOME disc)) ks ms ctrs0;
blanchet@49056
   158
blanchet@49336
   159
    val no_discs = map is_none disc_bindings;
blanchet@49137
   160
    val no_discs_at_all = forall I no_discs;
blanchet@49116
   161
blanchet@49336
   162
    fun std_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
blanchet@49120
   163
blanchet@49336
   164
    val sel_bindingss =
blanchet@49336
   165
      pad_list [] n raw_sel_bindingss
blanchet@49056
   166
      |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
blanchet@49498
   167
        Binding.qualify false data_b_name
traytel@49434
   168
          (if Binding.eq_name (sel, Binding.empty) orelse Binding.eq_name (sel, std_binding) then
blanchet@49336
   169
            std_sel_binding m l ctr
blanchet@49302
   170
          else
traytel@49434
   171
            sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
blanchet@49020
   172
blanchet@49536
   173
    val casex = mk_case As B case0;
blanchet@49201
   174
    val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
blanchet@49043
   175
blanchet@49498
   176
    val (((((((xss, xss'), yss), fs), gs), [u', v']), (p, p')), names_lthy) = no_defs_lthy |>
blanchet@49364
   177
      mk_Freess' "x" ctr_Tss
blanchet@49025
   178
      ||>> mk_Freess "y" ctr_Tss
blanchet@49201
   179
      ||>> mk_Frees "f" case_Ts
blanchet@49201
   180
      ||>> mk_Frees "g" case_Ts
blanchet@49498
   181
      ||>> (apfst (map (rpair dataT)) oo Variable.variant_fixes) [data_b_name, data_b_name ^ "'"]
blanchet@49043
   182
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
blanchet@49043
   183
blanchet@49498
   184
    val u = Free u';
blanchet@49498
   185
    val v = Free v';
blanchet@49463
   186
    val q = Free (fst p', mk_pred1T B);
blanchet@49020
   187
blanchet@49025
   188
    val xctrs = map2 (curry Term.list_comb) ctrs xss;
blanchet@49025
   189
    val yctrs = map2 (curry Term.list_comb) ctrs yss;
blanchet@49032
   190
blanchet@49043
   191
    val xfs = map2 (curry Term.list_comb) fs xss;
blanchet@49043
   192
    val xgs = map2 (curry Term.list_comb) gs xss;
blanchet@49043
   193
blanchet@49437
   194
    val eta_fs = map2 eta_expand_arg xss xfs;
blanchet@49437
   195
    val eta_gs = map2 eta_expand_arg xss xgs;
blanchet@49043
   196
blanchet@49201
   197
    val fcase = Term.list_comb (casex, eta_fs);
blanchet@49201
   198
    val gcase = Term.list_comb (casex, eta_gs);
blanchet@49020
   199
blanchet@49486
   200
    val ufcase = fcase $ u;
blanchet@49486
   201
    val vfcase = fcase $ v;
blanchet@49486
   202
    val vgcase = gcase $ v;
blanchet@49486
   203
blanchet@49591
   204
    fun mk_uu_eq () = HOLogic.mk_eq (u, u);
blanchet@49486
   205
blanchet@49591
   206
    val uv_eq = mk_Trueprop_eq (u, v);
blanchet@49486
   207
blanchet@49486
   208
    val exist_xs_u_eq_ctrs =
blanchet@49486
   209
      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
blanchet@49022
   210
blanchet@49278
   211
    val unique_disc_no_def = TrueI; (*arbitrary marker*)
blanchet@49278
   212
    val alternate_disc_no_def = FalseE; (*arbitrary marker*)
blanchet@49116
   213
blanchet@49486
   214
    fun alternate_disc_lhs get_udisc k =
blanchet@49116
   215
      HOLogic.mk_not
blanchet@49336
   216
        (case nth disc_bindings (k - 1) of
blanchet@49486
   217
          NONE => nth exist_xs_u_eq_ctrs (k - 1)
blanchet@49486
   218
        | SOME b => get_udisc b (k - 1));
blanchet@49116
   219
blanchet@49486
   220
    val (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
blanchet@49486
   221
         sel_defss, lthy') =
blanchet@49278
   222
      if no_dests then
blanchet@49486
   223
        (true, [], [], [], [], [], [], [], [], [], no_defs_lthy)
blanchet@49278
   224
      else
blanchet@49278
   225
        let
blanchet@49463
   226
          fun disc_free b = Free (Binding.name_of b, mk_pred1T dataT);
blanchet@49025
   227
blanchet@49486
   228
          fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
blanchet@49278
   229
blanchet@49500
   230
          fun alternate_disc k =
blanchet@49500
   231
            Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
blanchet@49278
   232
blanchet@49364
   233
          fun mk_default T t =
blanchet@49364
   234
            let
blanchet@49364
   235
              val Ts0 = map TFree (Term.add_tfreesT (fastype_of t) []);
blanchet@49364
   236
              val Ts = map TFree (Term.add_tfreesT T []);
blanchet@49364
   237
            in Term.subst_atomic_types (Ts0 ~~ Ts) t end;
blanchet@49364
   238
blanchet@49280
   239
          fun mk_sel_case_args b proto_sels T =
blanchet@49280
   240
            map2 (fn Ts => fn k =>
blanchet@49280
   241
              (case AList.lookup (op =) proto_sels k of
blanchet@49280
   242
                NONE =>
blanchet@49364
   243
                (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
blanchet@49364
   244
                  NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
blanchet@49364
   245
                | SOME t => mk_default (Ts ---> T) t)
blanchet@49280
   246
              | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
blanchet@49258
   247
blanchet@49278
   248
          fun sel_spec b proto_sels =
blanchet@49278
   249
            let
blanchet@49278
   250
              val _ =
blanchet@49278
   251
                (case duplicates (op =) (map fst proto_sels) of
blanchet@49278
   252
                   k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
blanchet@49278
   253
                     " for constructor " ^
blanchet@49278
   254
                     quote (Syntax.string_of_term no_defs_lthy (nth ctrs (k - 1))))
blanchet@49278
   255
                 | [] => ())
blanchet@49278
   256
              val T =
blanchet@49278
   257
                (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
blanchet@49278
   258
                  [T] => T
blanchet@49278
   259
                | T :: T' :: _ => error ("Inconsistent range type for selector " ^
blanchet@49278
   260
                    quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ no_defs_lthy T) ^
blanchet@49278
   261
                    " vs. " ^ quote (Syntax.string_of_typ no_defs_lthy T')));
blanchet@49278
   262
            in
blanchet@49486
   263
              mk_Trueprop_eq (Free (Binding.name_of b, dataT --> T) $ u,
blanchet@49536
   264
                Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
blanchet@49278
   265
            end;
blanchet@49116
   266
blanchet@49336
   267
          val sel_bindings = flat sel_bindingss;
blanchet@49336
   268
          val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
blanchet@49336
   269
          val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
blanchet@49285
   270
blanchet@49336
   271
          val sel_binding_index =
blanchet@49336
   272
            if all_sels_distinct then 1 upto length sel_bindings
blanchet@49336
   273
            else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
blanchet@49285
   274
blanchet@49285
   275
          val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
blanchet@49300
   276
          val sel_infos =
blanchet@49336
   277
            AList.group (op =) (sel_binding_index ~~ proto_sels)
blanchet@49285
   278
            |> sort (int_ord o pairself fst)
blanchet@49336
   279
            |> map snd |> curry (op ~~) uniq_sel_bindings;
blanchet@49336
   280
          val sel_bindings = map fst sel_infos;
blanchet@49258
   281
blanchet@49336
   282
          fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
blanchet@49258
   283
blanchet@49278
   284
          val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
blanchet@49278
   285
            no_defs_lthy
blanchet@49486
   286
            |> apfst split_list o fold_map4 (fn k => fn m => fn exist_xs_u_eq_ctr =>
blanchet@49278
   287
              fn NONE =>
blanchet@49591
   288
                 if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
blanchet@49486
   289
                 else if m = 0 then pair (Term.lambda u exist_xs_u_eq_ctr, refl)
blanchet@49278
   290
                 else pair (alternate_disc k, alternate_disc_no_def)
blanchet@49278
   291
               | SOME b => Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49486
   292
                   ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
blanchet@49486
   293
              ks ms exist_xs_u_eq_ctrs disc_bindings
blanchet@49278
   294
            ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
blanchet@49278
   295
              Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49300
   296
                ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
blanchet@49278
   297
            ||> `Local_Theory.restore;
blanchet@49022
   298
blanchet@49278
   299
          val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49025
   300
blanchet@49278
   301
          val disc_defs = map (Morphism.thm phi) raw_disc_defs;
blanchet@49281
   302
          val sel_defs = map (Morphism.thm phi) raw_sel_defs;
blanchet@49281
   303
          val sel_defss = unflat_selss sel_defs;
blanchet@49278
   304
blanchet@49278
   305
          val discs0 = map (Morphism.term phi) raw_discs;
blanchet@49278
   306
          val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
blanchet@49028
   307
blanchet@49278
   308
          val discs = map (mk_disc_or_sel As) discs0;
blanchet@49278
   309
          val selss = map (map (mk_disc_or_sel As)) selss0;
blanchet@49486
   310
blanchet@49500
   311
          val udiscs = map (rapp u) discs;
blanchet@49500
   312
          val uselss = map (map (rapp u)) selss;
blanchet@49486
   313
blanchet@49500
   314
          val vdiscs = map (rapp v) discs;
blanchet@49500
   315
          val vselss = map (map (rapp v)) selss;
blanchet@49278
   316
        in
blanchet@49486
   317
          (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
blanchet@49486
   318
           sel_defss, lthy')
blanchet@49278
   319
        end;
blanchet@49025
   320
blanchet@49032
   321
    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
blanchet@49029
   322
blanchet@49458
   323
    val exhaust_goal =
blanchet@49486
   324
      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (u, xctr)]) in
blanchet@49486
   325
        fold_rev Logic.all [p, u] (mk_imp_p (map2 mk_prem xctrs xss))
blanchet@49020
   326
      end;
blanchet@49019
   327
blanchet@49484
   328
    val inject_goalss =
blanchet@49017
   329
      let
blanchet@49034
   330
        fun mk_goal _ _ [] [] = []
blanchet@49025
   331
          | mk_goal xctr yctr xs ys =
blanchet@49121
   332
            [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
blanchet@49121
   333
              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
blanchet@49017
   334
      in
blanchet@49034
   335
        map4 mk_goal xctrs yctrs xss yss
blanchet@49017
   336
      end;
blanchet@49017
   337
blanchet@49484
   338
    val half_distinct_goalss =
blanchet@49121
   339
      let
blanchet@49203
   340
        fun mk_goal ((xs, xc), (xs', xc')) =
blanchet@49121
   341
          fold_rev Logic.all (xs @ xs')
blanchet@49203
   342
            (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
blanchet@49121
   343
      in
blanchet@49585
   344
        map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
blanchet@49121
   345
      end;
blanchet@49019
   346
blanchet@49458
   347
    val cases_goal =
blanchet@49121
   348
      map3 (fn xs => fn xctr => fn xf =>
blanchet@49201
   349
        fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xss xctrs xfs;
blanchet@49025
   350
blanchet@49484
   351
    val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss @ [cases_goal];
blanchet@49019
   352
blanchet@49019
   353
    fun after_qed thmss lthy =
blanchet@49019
   354
      let
blanchet@49048
   355
        val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) =
blanchet@49048
   356
          (hd thmss, apsnd (chop (n * n)) (chop n (tl thmss)));
blanchet@49019
   357
blanchet@49438
   358
        val inject_thms = flat inject_thmss;
blanchet@49438
   359
blanchet@49486
   360
        val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
blanchet@49486
   361
blanchet@49486
   362
        fun inst_thm t thm =
blanchet@49486
   363
          Drule.instantiate' [] [SOME (certify lthy t)]
blanchet@49486
   364
            (Thm.instantiate (Tinst, []) (Drule.zero_var_indexes thm));
blanchet@49486
   365
blanchet@49486
   366
        val uexhaust_thm = inst_thm u exhaust_thm;
blanchet@49032
   367
blanchet@49300
   368
        val exhaust_cases = map base_name_of_ctr ctrs;
blanchet@49300
   369
blanchet@49048
   370
        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
blanchet@49048
   371
blanchet@49486
   372
        val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
blanchet@49585
   373
          join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
blanchet@49019
   374
blanchet@49020
   375
        val nchotomy_thm =
blanchet@49020
   376
          let
blanchet@49020
   377
            val goal =
blanchet@49486
   378
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
blanchet@49486
   379
                Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
blanchet@49020
   380
          in
blanchet@49020
   381
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
blanchet@49020
   382
          end;
blanchet@49020
   383
blanchet@49484
   384
        val (all_sel_thms, sel_thmss, disc_thmss, disc_thms, discI_thms, disc_exclude_thms,
blanchet@49594
   385
             disc_exhaust_thms, collapse_thms, expand_thms, case_conv_thms) =
blanchet@49278
   386
          if no_dests then
blanchet@49486
   387
            ([], [], [], [], [], [], [], [], [], [])
blanchet@49116
   388
          else
blanchet@49116
   389
            let
blanchet@49364
   390
              fun make_sel_thm xs' case_thm sel_def =
blanchet@49364
   391
                zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
blanchet@49364
   392
                    (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
blanchet@49281
   393
blanchet@49281
   394
              fun has_undefined_rhs thm =
blanchet@49281
   395
                (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
blanchet@49281
   396
                  Const (@{const_name undefined}, _) => true
blanchet@49281
   397
                | _ => false);
blanchet@49281
   398
blanchet@49364
   399
              val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
blanchet@49281
   400
blanchet@49281
   401
              val all_sel_thms =
blanchet@49285
   402
                (if all_sels_distinct andalso forall null sel_defaultss then
blanchet@49285
   403
                   flat sel_thmss
blanchet@49285
   404
                 else
blanchet@49364
   405
                   map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
blanchet@49364
   406
                     (xss' ~~ case_thms))
blanchet@49285
   407
                |> filter_out has_undefined_rhs;
blanchet@49278
   408
blanchet@49278
   409
              fun mk_unique_disc_def () =
blanchet@49278
   410
                let
blanchet@49278
   411
                  val m = the_single ms;
blanchet@49591
   412
                  val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
blanchet@49278
   413
                in
blanchet@49486
   414
                  Skip_Proof.prove lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
blanchet@49278
   415
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   416
                  |> Thm.close_derivation
blanchet@49278
   417
                end;
blanchet@49278
   418
blanchet@49278
   419
              fun mk_alternate_disc_def k =
blanchet@49278
   420
                let
blanchet@49278
   421
                  val goal =
blanchet@49486
   422
                    mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
blanchet@49486
   423
                      nth exist_xs_u_eq_ctrs (k - 1));
blanchet@49278
   424
                in
blanchet@49278
   425
                  Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49278
   426
                    mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
blanchet@49486
   427
                      (nth distinct_thms (2 - k)) uexhaust_thm)
blanchet@49278
   428
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   429
                  |> Thm.close_derivation
blanchet@49278
   430
                end;
blanchet@49028
   431
blanchet@49278
   432
              val has_alternate_disc_def =
blanchet@49278
   433
                exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
blanchet@49278
   434
blanchet@49278
   435
              val disc_defs' =
blanchet@49278
   436
                map2 (fn k => fn def =>
blanchet@49278
   437
                  if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
blanchet@49278
   438
                  else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
blanchet@49278
   439
                  else def) ks disc_defs;
blanchet@49278
   440
blanchet@49278
   441
              val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49278
   442
              val discI_thms =
blanchet@49278
   443
                map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
blanchet@49278
   444
                  disc_defs';
blanchet@49278
   445
              val not_discI_thms =
blanchet@49278
   446
                map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49504
   447
                    (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49278
   448
                  ms disc_defs';
blanchet@49278
   449
blanchet@49278
   450
              val (disc_thmss', disc_thmss) =
blanchet@49278
   451
                let
blanchet@49278
   452
                  fun mk_thm discI _ [] = refl RS discI
blanchet@49278
   453
                    | mk_thm _ not_discI [distinct] = distinct RS not_discI;
blanchet@49278
   454
                  fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
blanchet@49278
   455
                in
blanchet@49278
   456
                  map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
blanchet@49278
   457
                end;
blanchet@49278
   458
blanchet@49278
   459
              val disc_thms = flat (map2 (fn true => K [] | false => I) no_discs disc_thmss);
blanchet@49028
   460
blanchet@49486
   461
              val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
blanchet@49486
   462
                let
blanchet@49486
   463
                  fun mk_goal [] = []
blanchet@49486
   464
                    | mk_goal [((_, udisc), (_, udisc'))] =
blanchet@49486
   465
                      [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
blanchet@49486
   466
                         HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
blanchet@49486
   467
blanchet@49486
   468
                  fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);
blanchet@49486
   469
blanchet@49585
   470
                  val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
blanchet@49486
   471
blanchet@49486
   472
                  val half_goalss = map mk_goal half_pairss;
blanchet@49486
   473
                  val half_thmss =
blanchet@49486
   474
                    map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
blanchet@49486
   475
                        fn disc_thm => [prove (mk_half_disc_exclude_tac m discD disc_thm) goal])
blanchet@49486
   476
                      half_goalss half_pairss (flat disc_thmss');
blanchet@49278
   477
blanchet@49486
   478
                  val other_half_goalss = map (mk_goal o map swap) half_pairss;
blanchet@49486
   479
                  val other_half_thmss =
blanchet@49486
   480
                    map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
blanchet@49486
   481
                      other_half_goalss;
blanchet@49486
   482
                in
blanchet@49585
   483
                  join_halves n half_thmss other_half_thmss ||> `transpose
blanchet@49486
   484
                  |>> has_alternate_disc_def ? K []
blanchet@49486
   485
                end;
blanchet@49278
   486
blanchet@49486
   487
              val disc_exhaust_thm =
blanchet@49486
   488
                let
blanchet@49486
   489
                  fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
blanchet@49486
   490
                  val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
blanchet@49486
   491
                in
blanchet@49486
   492
                  Skip_Proof.prove lthy [] [] goal (fn _ =>
blanchet@49486
   493
                    mk_disc_exhaust_tac n exhaust_thm discI_thms)
blanchet@49486
   494
                end;
blanchet@49028
   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@49591
   528
                  val goal =
blanchet@49591
   529
                    Library.foldr Logic.list_implies
blanchet@49591
   530
                      (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
blanchet@49591
   531
blanchet@49486
   532
                  val uncollapse_thms =
blanchet@49486
   533
                    map (fn NONE => Drule.dummy_thm | SOME thm => thm RS sym) collapse_thm_opts;
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@49594
   542
              val case_conv_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@49594
   548
                     mk_case_conv_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@49594
   553
               [disc_exhaust_thm], collapse_thms, expand_thms, case_conv_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@49591
   563
              Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss fs gs,
blanchet@49486
   564
                 mk_Trueprop_eq (ufcase, vgcase));
blanchet@49591
   565
            val weak_goal = Logic.mk_implies (uv_eq, 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@49594
   604
          [(caseN, case_thms, simp_attrs),
blanchet@49594
   605
           (case_congN, [case_cong_thm], []),
blanchet@49594
   606
           (case_convN, case_conv_thms, []),
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@49498
   622
            ((Binding.qualify true data_b_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49300
   623
blanchet@49300
   624
        val notes' =
blanchet@49300
   625
          [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs)]
blanchet@49300
   626
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49019
   627
      in
blanchet@49591
   628
        ((discs, selss, exhaust_thm, inject_thms, distinct_thms, case_thms, disc_thmss, discI_thms,
blanchet@49591
   629
          sel_thmss), lthy |> Local_Theory.notes (notes' @ notes) |> snd)
blanchet@49019
   630
      end;
blanchet@49017
   631
  in
blanchet@49121
   632
    (goalss, after_qed, lthy')
blanchet@49017
   633
  end;
blanchet@49017
   634
blanchet@49199
   635
fun wrap_datatype tacss = (fn (goalss, after_qed, lthy) =>
blanchet@49111
   636
  map2 (map2 (Skip_Proof.prove lthy [] [])) goalss tacss
blanchet@49280
   637
  |> (fn thms => after_qed thms lthy)) oo prepare_wrap_datatype (K I);
blanchet@49280
   638
blanchet@49297
   639
val wrap_datatype_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49297
   640
  Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
blanchet@49297
   641
  prepare_wrap_datatype Syntax.read_term;
blanchet@49297
   642
blanchet@49280
   643
fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
blanchet@49111
   644
blanchet@49280
   645
val parse_bindings = parse_bracket_list Parse.binding;
blanchet@49280
   646
val parse_bindingss = parse_bracket_list parse_bindings;
blanchet@49280
   647
blanchet@49280
   648
val parse_bound_term = (Parse.binding --| @{keyword ":"}) -- Parse.term;
blanchet@49280
   649
val parse_bound_terms = parse_bracket_list parse_bound_term;
blanchet@49280
   650
val parse_bound_termss = parse_bracket_list parse_bound_terms;
blanchet@49017
   651
blanchet@49278
   652
val parse_wrap_options =
blanchet@49278
   653
  Scan.optional (@{keyword "("} |-- (@{keyword "no_dests"} >> K true) --| @{keyword ")"}) false;
blanchet@49278
   654
blanchet@49017
   655
val _ =
blanchet@49074
   656
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype"
blanchet@49278
   657
    ((parse_wrap_options -- (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) --
blanchet@49280
   658
      Parse.term -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
blanchet@49280
   659
        Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
blanchet@49199
   660
     >> wrap_datatype_cmd);
blanchet@49017
   661
blanchet@49017
   662
end;