src/HOL/Codatatype/Tools/bnf_sugar.ML
author blanchet
Fri Aug 31 15:04:03 2012 +0200 (2012-08-31)
changeset 49046 3c5eba97d93a
parent 49045 7d9631754bba
child 49048 4e0f0f98be02
permissions -rw-r--r--
allow default names for selectors via wildcard (_) + fix wrong index (k)
blanchet@49017
     1
(*  Title:      HOL/Codatatype/Tools/bnf_sugar.ML
blanchet@49017
     2
    Author:     Jasmin Blanchette, TU Muenchen
blanchet@49017
     3
    Copyright   2012
blanchet@49017
     4
blanchet@49017
     5
Sugar on top of a BNF.
blanchet@49017
     6
*)
blanchet@49017
     7
blanchet@49017
     8
signature BNF_SUGAR =
blanchet@49017
     9
sig
blanchet@49017
    10
end;
blanchet@49017
    11
blanchet@49017
    12
structure BNF_Sugar : BNF_SUGAR =
blanchet@49017
    13
struct
blanchet@49017
    14
blanchet@49017
    15
open BNF_Util
blanchet@49019
    16
open BNF_FP_Util
blanchet@49020
    17
open BNF_Sugar_Tactics
blanchet@49017
    18
blanchet@49046
    19
val is_N = "is_";
blanchet@49046
    20
blanchet@49025
    21
val case_congN = "case_cong"
blanchet@49025
    22
val case_discsN = "case_discs"
blanchet@49025
    23
val casesN = "cases"
blanchet@49025
    24
val ctr_selsN = "ctr_sels"
blanchet@49025
    25
val disc_disjointN = "disc_disjoint"
blanchet@49027
    26
val disc_exhaustN = "disc_exhaust"
blanchet@49027
    27
val discsN = "discs"
blanchet@49025
    28
val distinctN = "distinct"
blanchet@49025
    29
val selsN = "sels"
blanchet@49025
    30
val splitN = "split"
blanchet@49025
    31
val split_asmN = "split_asm"
blanchet@49025
    32
val weak_case_cong_thmsN = "weak_case_cong"
blanchet@49019
    33
blanchet@49046
    34
val default_name = @{binding _};
blanchet@49046
    35
blanchet@49028
    36
fun mk_half_pairs [] = []
blanchet@49028
    37
  | mk_half_pairs (x :: xs) = fold_rev (cons o pair x) xs (mk_half_pairs xs);
blanchet@49027
    38
blanchet@49046
    39
fun index_of_half_cell n j k = j * (2 * n - (j + 1)) div 2 + k - (j + 1);
blanchet@49027
    40
blanchet@49032
    41
val mk_Trueprop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq;
blanchet@49032
    42
blanchet@49043
    43
fun eta_expand_caseof_arg xs f_xs = fold_rev Term.lambda xs f_xs;
blanchet@49032
    44
blanchet@49046
    45
fun name_of_ctr t =
blanchet@49046
    46
  case head_of t of
blanchet@49046
    47
    Const (s, _) => s
blanchet@49046
    48
  | Free (s, _) => s
blanchet@49046
    49
  | _ => error "Cannot extract name of constructor";
blanchet@49046
    50
blanchet@49046
    51
fun prepare_sugar prep_term (((raw_ctrs, raw_caseof), raw_disc_names), sel_namess) no_defs_lthy =
blanchet@49017
    52
  let
blanchet@49019
    53
    (* TODO: sanity checks on arguments *)
blanchet@49017
    54
blanchet@49025
    55
    (* TODO: normalize types of constructors w.r.t. each other *)
blanchet@49025
    56
blanchet@49025
    57
    val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
blanchet@49025
    58
    val caseof0 = prep_term no_defs_lthy raw_caseof;
blanchet@49017
    59
blanchet@49046
    60
    val disc_names =
blanchet@49046
    61
      map2 (fn ctr => fn disc =>
blanchet@49046
    62
        if Binding.eq_name (disc, default_name) then
blanchet@49046
    63
          Binding.name (prefix is_N (Long_Name.base_name (name_of_ctr ctr)))
blanchet@49046
    64
        else
blanchet@49046
    65
          disc) ctrs0 raw_disc_names;
blanchet@49046
    66
blanchet@49025
    67
    val n = length ctrs0;
blanchet@49025
    68
    val ks = 1 upto n;
blanchet@49022
    69
blanchet@49025
    70
    val (T_name, As0) = dest_Type (body_type (fastype_of (hd ctrs0)));
blanchet@49020
    71
    val b = Binding.qualified_name T_name;
blanchet@49020
    72
blanchet@49025
    73
    val (As, B) =
blanchet@49025
    74
      no_defs_lthy
blanchet@49025
    75
      |> mk_TFrees (length As0)
blanchet@49025
    76
      ||> the_single o fst o mk_TFrees 1;
blanchet@49025
    77
blanchet@49025
    78
    fun mk_undef T Ts = Const (@{const_name undefined}, Ts ---> T);
blanchet@49025
    79
blanchet@49025
    80
    fun mk_ctr Ts ctr =
blanchet@49028
    81
      let val Ts0 = snd (dest_Type (body_type (fastype_of ctr))) in
blanchet@49025
    82
        Term.subst_atomic_types (Ts0 ~~ Ts) ctr
blanchet@49025
    83
      end;
blanchet@49020
    84
blanchet@49028
    85
    fun mk_caseof Ts T =
blanchet@49028
    86
      let val (binders, body) = strip_type (fastype_of caseof0) in
blanchet@49028
    87
        Term.subst_atomic_types ((body, T) :: (snd (dest_Type (List.last binders)) ~~ Ts)) caseof0
blanchet@49022
    88
      end;
blanchet@49022
    89
blanchet@49025
    90
    val T = Type (T_name, As);
blanchet@49025
    91
    val ctrs = map (mk_ctr As) ctrs0;
blanchet@49025
    92
    val ctr_Tss = map (binder_types o fastype_of) ctrs;
blanchet@49025
    93
blanchet@49028
    94
    val ms = map length ctr_Tss;
blanchet@49028
    95
blanchet@49028
    96
    val caseofB = mk_caseof As B;
blanchet@49025
    97
    val caseofB_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
blanchet@49025
    98
blanchet@49043
    99
    fun mk_caseofB_term eta_fs = Term.list_comb (caseofB, eta_fs);
blanchet@49043
   100
blanchet@49043
   101
    val (((((((xss, yss), fs), gs), (v, v')), w), (p, p')), names_lthy) = no_defs_lthy |>
blanchet@49025
   102
      mk_Freess "x" ctr_Tss
blanchet@49025
   103
      ||>> mk_Freess "y" ctr_Tss
blanchet@49025
   104
      ||>> mk_Frees "f" caseofB_Ts
blanchet@49032
   105
      ||>> mk_Frees "g" caseofB_Ts
blanchet@49020
   106
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") T
blanchet@49032
   107
      ||>> yield_singleton (mk_Frees "w") T
blanchet@49043
   108
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
blanchet@49043
   109
blanchet@49043
   110
    val q = Free (fst p', B --> HOLogic.boolT);
blanchet@49020
   111
blanchet@49025
   112
    val xctrs = map2 (curry Term.list_comb) ctrs xss;
blanchet@49025
   113
    val yctrs = map2 (curry Term.list_comb) ctrs yss;
blanchet@49032
   114
blanchet@49043
   115
    val xfs = map2 (curry Term.list_comb) fs xss;
blanchet@49043
   116
    val xgs = map2 (curry Term.list_comb) gs xss;
blanchet@49043
   117
blanchet@49043
   118
    val eta_fs = map2 eta_expand_caseof_arg xss xfs;
blanchet@49043
   119
    val eta_gs = map2 eta_expand_caseof_arg xss xgs;
blanchet@49043
   120
blanchet@49043
   121
    val caseofB_fs = Term.list_comb (caseofB, eta_fs);
blanchet@49020
   122
blanchet@49025
   123
    val exist_xs_v_eq_ctrs =
blanchet@49025
   124
      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (v, xctr))) xctrs xss;
blanchet@49022
   125
blanchet@49032
   126
    fun mk_sel_caseof_args k xs x T =
blanchet@49025
   127
      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
   128
blanchet@49025
   129
    fun disc_spec b exist_xs_v_eq_ctr =
blanchet@49032
   130
      mk_Trueprop_eq (Free (Binding.name_of b, T --> HOLogic.boolT) $ v, exist_xs_v_eq_ctr);
blanchet@49025
   131
blanchet@49028
   132
    fun sel_spec b x xs k =
blanchet@49025
   133
      let val T' = fastype_of x in
blanchet@49032
   134
        mk_Trueprop_eq (Free (Binding.name_of b, T --> T') $ v,
blanchet@49032
   135
          Term.list_comb (mk_caseof As T', mk_sel_caseof_args k xs x T') $ v)
blanchet@49022
   136
      end;
blanchet@49022
   137
blanchet@49028
   138
    val (((raw_discs, (_, raw_disc_defs)), (raw_selss, (_, raw_sel_defss))), (lthy', lthy)) =
blanchet@49022
   139
      no_defs_lthy
blanchet@49025
   140
      |> apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn exist_xs_v_eq_ctr =>
blanchet@49022
   141
        Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49025
   142
          ((Thm.def_binding b, []), disc_spec b exist_xs_v_eq_ctr))) disc_names exist_xs_v_eq_ctrs
blanchet@49028
   143
      ||>> apfst (apsnd split_list o split_list) o fold_map3 (fn bs => fn xs => fn k =>
blanchet@49025
   144
        apfst (apsnd split_list o split_list) o fold_map2 (fn b => fn x =>
blanchet@49022
   145
          Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49028
   146
            ((Thm.def_binding b, []), sel_spec b x xs k))) bs xs) sel_namess xss ks
blanchet@49022
   147
      ||> `Local_Theory.restore;
blanchet@49022
   148
blanchet@49025
   149
    (*transforms defined frees into consts (and more)*)
blanchet@49025
   150
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49025
   151
blanchet@49028
   152
    val disc_defs = map (Morphism.thm phi) raw_disc_defs;
blanchet@49028
   153
    val sel_defss = map (map (Morphism.thm phi)) raw_sel_defss;
blanchet@49028
   154
blanchet@49028
   155
    val discs0 = map (Morphism.term phi) raw_discs;
blanchet@49028
   156
    val selss0 = map (map (Morphism.term phi)) raw_selss;
blanchet@49025
   157
blanchet@49028
   158
    fun mk_disc_or_sel Ts t =
blanchet@49028
   159
      Term.subst_atomic_types (snd (dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
blanchet@49028
   160
blanchet@49028
   161
    val discs = map (mk_disc_or_sel As) discs0;
blanchet@49028
   162
    val selss = map (map (mk_disc_or_sel As)) selss0;
blanchet@49025
   163
blanchet@49032
   164
    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
blanchet@49029
   165
blanchet@49020
   166
    val goal_exhaust =
blanchet@49032
   167
      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (v, xctr)]) in
blanchet@49025
   168
        mk_imp_p (map2 mk_prem xctrs xss)
blanchet@49020
   169
      end;
blanchet@49019
   170
blanchet@49034
   171
    val goal_injectss =
blanchet@49017
   172
      let
blanchet@49034
   173
        fun mk_goal _ _ [] [] = []
blanchet@49025
   174
          | mk_goal xctr yctr xs ys =
blanchet@49034
   175
            [mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
blanchet@49034
   176
              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys))];
blanchet@49017
   177
      in
blanchet@49034
   178
        map4 mk_goal xctrs yctrs xss yss
blanchet@49017
   179
      end;
blanchet@49017
   180
blanchet@49019
   181
    val goal_half_distincts =
blanchet@49028
   182
      map (HOLogic.mk_Trueprop o HOLogic.mk_not o HOLogic.mk_eq) (mk_half_pairs xctrs);
blanchet@49019
   183
blanchet@49043
   184
    val goal_cases = map2 (fn xctr => fn xf => mk_Trueprop_eq (caseofB_fs $ xctr, xf)) xctrs xfs;
blanchet@49025
   185
blanchet@49034
   186
    val goals = [goal_exhaust] :: goal_injectss @ [goal_half_distincts, goal_cases];
blanchet@49019
   187
blanchet@49019
   188
    fun after_qed thmss lthy =
blanchet@49019
   189
      let
blanchet@49034
   190
        val ([exhaust_thm], (inject_thmss, [half_distinct_thms, case_thms])) =
blanchet@49034
   191
          (hd thmss, chop n (tl thmss));
blanchet@49019
   192
blanchet@49043
   193
        val inject_thms = flat inject_thmss;
blanchet@49043
   194
blanchet@49032
   195
        val exhaust_thm' =
blanchet@49032
   196
          let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in
blanchet@49032
   197
            Drule.instantiate' [] [SOME (certify lthy v)]
blanchet@49032
   198
              (Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm))
blanchet@49032
   199
          end;
blanchet@49032
   200
blanchet@49019
   201
        val other_half_distinct_thms = map (fn thm => thm RS not_sym) half_distinct_thms;
blanchet@49045
   202
        val distinct_thms = interleave half_distinct_thms other_half_distinct_thms;
blanchet@49019
   203
blanchet@49020
   204
        val nchotomy_thm =
blanchet@49020
   205
          let
blanchet@49020
   206
            val goal =
blanchet@49022
   207
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v',
blanchet@49029
   208
                Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs));
blanchet@49020
   209
          in
blanchet@49020
   210
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
blanchet@49020
   211
          end;
blanchet@49020
   212
blanchet@49030
   213
        val sel_thmss =
blanchet@49025
   214
          let
blanchet@49028
   215
            fun mk_thm k xs goal_case case_thm x sel_def =
blanchet@49025
   216
              let
blanchet@49025
   217
                val T = fastype_of x;
blanchet@49025
   218
                val cTs =
blanchet@49025
   219
                  map ((fn T' => certifyT lthy (if T' = B then T else T')) o TFree)
blanchet@49025
   220
                    (rev (Term.add_tfrees goal_case []));
blanchet@49032
   221
                val cxs = map (certify lthy) (mk_sel_caseof_args k xs x T);
blanchet@49025
   222
              in
blanchet@49025
   223
                Local_Defs.fold lthy [sel_def]
blanchet@49025
   224
                  (Drule.instantiate' (map SOME cTs) (map SOME cxs) case_thm)
blanchet@49025
   225
              end;
blanchet@49028
   226
            fun mk_thms k xs goal_case case_thm sel_defs =
blanchet@49028
   227
              map2 (mk_thm k xs goal_case case_thm) xs sel_defs;
blanchet@49025
   228
          in
blanchet@49030
   229
            map5 mk_thms ks xss goal_cases case_thms sel_defss
blanchet@49025
   230
          end;
blanchet@49025
   231
blanchet@49030
   232
        val discD_thms = map (fn def => def RS iffD1) disc_defs;
blanchet@49028
   233
        val discI_thms =
blanchet@49030
   234
          map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms disc_defs;
blanchet@49028
   235
        val not_disc_thms =
blanchet@49030
   236
          map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49030
   237
                  (Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49028
   238
            ms disc_defs;
blanchet@49028
   239
blanchet@49027
   240
        val disc_thms =
blanchet@49027
   241
          let
blanchet@49027
   242
            fun get_distinct_thm k k' =
blanchet@49028
   243
              if k > k' then nth half_distinct_thms (index_of_half_cell n (k' - 1) (k - 1))
blanchet@49046
   244
              else nth other_half_distinct_thms (index_of_half_cell n (k - 1) (k' - 1))
blanchet@49028
   245
            fun mk_thm ((k, discI), not_disc) k' =
blanchet@49028
   246
              if k = k' then refl RS discI else get_distinct_thm k k' RS not_disc;
blanchet@49027
   247
          in
blanchet@49028
   248
            map_product mk_thm (ks ~~ discI_thms ~~ not_disc_thms) ks
blanchet@49027
   249
          end;
blanchet@49025
   250
blanchet@49028
   251
        val disc_disjoint_thms =
blanchet@49028
   252
          let
blanchet@49028
   253
            fun get_disc_thm k k' = nth disc_thms ((k' - 1) * n + (k - 1));
blanchet@49028
   254
            fun mk_goal ((_, disc), (_, disc')) =
blanchet@49029
   255
              Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v),
blanchet@49029
   256
                HOLogic.mk_Trueprop (HOLogic.mk_not (disc' $ v))));
blanchet@49028
   257
            fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);
blanchet@49028
   258
blanchet@49030
   259
            val bundles = ks ~~ ms ~~ discD_thms ~~ discs;
blanchet@49028
   260
            val half_pairs = mk_half_pairs bundles;
blanchet@49028
   261
blanchet@49028
   262
            val goal_halves = map mk_goal half_pairs;
blanchet@49028
   263
            val half_thms =
blanchet@49030
   264
              map2 (fn ((((k, m), discD), _), (((k', _), _), _)) =>
blanchet@49030
   265
                prove (mk_half_disc_disjoint_tac m discD (get_disc_thm k k')))
blanchet@49028
   266
              half_pairs goal_halves;
blanchet@49028
   267
blanchet@49028
   268
            val goal_other_halves = map (mk_goal o swap) half_pairs;
blanchet@49028
   269
            val other_half_thms =
blanchet@49028
   270
              map2 (prove o mk_other_half_disc_disjoint_tac) half_thms goal_other_halves;
blanchet@49028
   271
          in
blanchet@49045
   272
            interleave half_thms other_half_thms
blanchet@49028
   273
          end;
blanchet@49025
   274
blanchet@49029
   275
        val disc_exhaust_thm =
blanchet@49029
   276
          let
blanchet@49029
   277
            fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (disc $ v)];
blanchet@49029
   278
            val goal = fold Logic.all [p, v] (mk_imp_p (map mk_prem discs));
blanchet@49029
   279
          in
blanchet@49029
   280
            Skip_Proof.prove lthy [] [] goal (fn _ => mk_disc_exhaust_tac n exhaust_thm discI_thms)
blanchet@49029
   281
          end;
blanchet@49025
   282
blanchet@49030
   283
        val ctr_sel_thms =
blanchet@49030
   284
          let
blanchet@49030
   285
            fun mk_goal ctr disc sels =
blanchet@49030
   286
              Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (disc $ v),
blanchet@49032
   287
                mk_Trueprop_eq ((null sels ? swap)
blanchet@49032
   288
                  (Term.list_comb (ctr, map (fn sel => sel $ v) sels), v))));
blanchet@49030
   289
            val goals = map3 mk_goal ctrs discs selss;
blanchet@49030
   290
          in
blanchet@49030
   291
            map4 (fn goal => fn m => fn discD => fn sel_thms =>
blanchet@49030
   292
              Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49030
   293
                mk_ctr_sel_tac ctxt m discD sel_thms))
blanchet@49030
   294
              goals ms discD_thms sel_thmss
blanchet@49030
   295
          end;
blanchet@49025
   296
blanchet@49031
   297
        val case_disc_thm =
blanchet@49031
   298
          let
blanchet@49031
   299
            fun mk_core f sels = Term.list_comb (f, map (fn sel => sel $ v) sels);
blanchet@49031
   300
            fun mk_rhs _ [f] [sels] = mk_core f sels
blanchet@49031
   301
              | mk_rhs (disc :: discs) (f :: fs) (sels :: selss) =
blanchet@49031
   302
                Const (@{const_name If}, HOLogic.boolT --> B --> B --> B) $
blanchet@49031
   303
                  (disc $ v) $ mk_core f sels $ mk_rhs discs fs selss;
blanchet@49043
   304
            val goal = mk_Trueprop_eq (caseofB_fs $ v, mk_rhs discs fs selss);
blanchet@49031
   305
          in
blanchet@49031
   306
            Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49031
   307
              mk_case_disc_tac ctxt exhaust_thm' case_thms disc_thms sel_thmss)
blanchet@49031
   308
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49031
   309
          end;
blanchet@49025
   310
blanchet@49033
   311
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   312
          let
blanchet@49032
   313
            fun mk_prem xctr xs f g =
blanchet@49045
   314
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr),
blanchet@49032
   315
                mk_Trueprop_eq (f, g)));
blanchet@49033
   316
blanchet@49033
   317
            val v_eq_w = mk_Trueprop_eq (v, w);
blanchet@49043
   318
            val caseof_fs = mk_caseofB_term eta_fs;
blanchet@49043
   319
            val caseof_gs = mk_caseofB_term eta_gs;
blanchet@49032
   320
blanchet@49032
   321
            val goal =
blanchet@49033
   322
              Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs,
blanchet@49033
   323
                 mk_Trueprop_eq (caseof_fs $ v, caseof_gs $ w));
blanchet@49033
   324
            val goal_weak =
blanchet@49033
   325
              Logic.mk_implies (v_eq_w, mk_Trueprop_eq (caseof_fs $ v, caseof_fs $ w));
blanchet@49032
   326
          in
blanchet@49033
   327
            (Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49033
   328
               mk_case_cong_tac ctxt exhaust_thm' case_thms),
blanchet@49033
   329
             Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1)))
blanchet@49033
   330
            |> pairself (singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   331
          end;
blanchet@49025
   332
blanchet@49044
   333
        val (split_thm, split_asm_thm) =
blanchet@49043
   334
          let
blanchet@49044
   335
            fun mk_conjunct xctr xs f_xs =
blanchet@49043
   336
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs));
blanchet@49044
   337
            fun mk_disjunct xctr xs f_xs =
blanchet@49044
   338
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr),
blanchet@49044
   339
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   340
blanchet@49044
   341
            val lhs = q $ (mk_caseofB_term eta_fs $ v);
blanchet@49044
   342
blanchet@49043
   343
            val goal =
blanchet@49044
   344
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49044
   345
            val goal_asm =
blanchet@49044
   346
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   347
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   348
blanchet@49044
   349
            val split_thm =
blanchet@49044
   350
              Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49044
   351
                mk_split_tac ctxt exhaust_thm' case_thms inject_thms distinct_thms)
blanchet@49044
   352
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49044
   353
            val split_asm_thm =
blanchet@49044
   354
              Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} =>
blanchet@49044
   355
                mk_split_asm_tac ctxt split_thm)
blanchet@49044
   356
              |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49043
   357
          in
blanchet@49044
   358
            (split_thm, split_asm_thm)
blanchet@49043
   359
          end;
blanchet@49025
   360
blanchet@49043
   361
        (* TODO: case syntax *)
blanchet@49043
   362
        (* TODO: attributes (simp, case_names, etc.) *)
blanchet@49025
   363
blanchet@49019
   364
        fun note thmN thms =
blanchet@49019
   365
          snd o Local_Theory.note
blanchet@49019
   366
            ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), thms);
blanchet@49019
   367
      in
blanchet@49019
   368
        lthy
blanchet@49025
   369
        |> note case_congN [case_cong_thm]
blanchet@49031
   370
        |> note case_discsN [case_disc_thm]
blanchet@49025
   371
        |> note casesN case_thms
blanchet@49025
   372
        |> note ctr_selsN ctr_sel_thms
blanchet@49027
   373
        |> note discsN disc_thms
blanchet@49025
   374
        |> note disc_disjointN disc_disjoint_thms
blanchet@49029
   375
        |> note disc_exhaustN [disc_exhaust_thm]
blanchet@49043
   376
        |> note distinctN distinct_thms
blanchet@49020
   377
        |> note exhaustN [exhaust_thm]
blanchet@49043
   378
        |> note injectN inject_thms
blanchet@49020
   379
        |> note nchotomyN [nchotomy_thm]
blanchet@49030
   380
        |> note selsN (flat sel_thmss)
blanchet@49043
   381
        |> note splitN [split_thm]
blanchet@49043
   382
        |> note split_asmN [split_asm_thm]
blanchet@49033
   383
        |> note weak_case_cong_thmsN [weak_case_cong_thm]
blanchet@49019
   384
      end;
blanchet@49017
   385
  in
blanchet@49025
   386
    (goals, after_qed, lthy')
blanchet@49017
   387
  end;
blanchet@49017
   388
blanchet@49017
   389
val parse_binding_list = Parse.$$$ "[" |--  Parse.list Parse.binding --| Parse.$$$ "]";
blanchet@49017
   390
blanchet@49019
   391
val bnf_sugar_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49019
   392
  Proof.theorem NONE after_qed (map (map (rpair [])) goalss) lthy) oo
blanchet@49020
   393
  prepare_sugar Syntax.read_term;
blanchet@49017
   394
blanchet@49017
   395
val _ =
blanchet@49017
   396
  Outer_Syntax.local_theory_to_proof @{command_spec "bnf_sugar"} "adds sugar on top of a BNF"
blanchet@49023
   397
    (((Parse.$$$ "[" |-- Parse.list Parse.term --| Parse.$$$ "]") -- Parse.term --
blanchet@49023
   398
      parse_binding_list -- (Parse.$$$ "[" |-- Parse.list parse_binding_list --| Parse.$$$ "]"))
blanchet@49023
   399
      >> bnf_sugar_cmd);
blanchet@49017
   400
blanchet@49017
   401
end;