src/HOL/Codatatype/Tools/bnf_fp_sugar.ML
author blanchet
Wed Sep 12 23:06:39 2012 +0200 (2012-09-12)
changeset 49342 8ea4bad49ed5
parent 49338 4a922800531d
child 49361 cc1d39529dd1
permissions -rw-r--r--
rough and ready induction
blanchet@49112
     1
(*  Title:      HOL/Codatatype/Tools/bnf_fp_sugar.ML
blanchet@49112
     2
    Author:     Jasmin Blanchette, TU Muenchen
blanchet@49112
     3
    Copyright   2012
blanchet@49112
     4
blanchet@49112
     5
Sugar for constructing LFPs and GFPs.
blanchet@49112
     6
*)
blanchet@49112
     7
blanchet@49112
     8
signature BNF_FP_SUGAR =
blanchet@49112
     9
sig
blanchet@49297
    10
  val datatyp: bool ->
blanchet@49308
    11
    (mixfix list -> (string * sort) list option -> binding list -> typ list * typ list list ->
blanchet@49308
    12
      BNF_Def.BNF list -> local_theory ->
blanchet@49337
    13
      (term list * term list * term list * term list * thm * thm list * thm list * thm list *
blanchet@49337
    14
         thm list * thm list) * local_theory) ->
blanchet@49298
    15
    bool * ((((typ * sort) list * binding) * mixfix) * ((((binding * binding) *
blanchet@49297
    16
      (binding * typ) list) * (binding * term) list) * mixfix) list) list ->
blanchet@49297
    17
    local_theory -> local_theory
blanchet@49308
    18
  val parse_datatype_cmd: bool ->
blanchet@49308
    19
    (mixfix list -> (string * sort) list option -> binding list -> typ list * typ list list ->
blanchet@49308
    20
      BNF_Def.BNF list -> local_theory ->
blanchet@49337
    21
      (term list * term list * term list * term list * thm * thm list * thm list * thm list *
blanchet@49337
    22
         thm list * thm list) * local_theory) ->
blanchet@49308
    23
    (local_theory -> local_theory) parser
blanchet@49112
    24
end;
blanchet@49112
    25
blanchet@49112
    26
structure BNF_FP_Sugar : BNF_FP_SUGAR =
blanchet@49112
    27
struct
blanchet@49112
    28
blanchet@49119
    29
open BNF_Util
blanchet@49119
    30
open BNF_Wrap
blanchet@49214
    31
open BNF_Def
blanchet@49119
    32
open BNF_FP_Util
blanchet@49123
    33
open BNF_FP_Sugar_Tactics
blanchet@49119
    34
blanchet@49300
    35
val simp_attrs = @{attributes [simp]};
blanchet@49300
    36
blanchet@49266
    37
fun split_list11 xs =
blanchet@49266
    38
  (map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs,
blanchet@49266
    39
   map #9 xs, map #10 xs, map #11 xs);
blanchet@49214
    40
blanchet@49217
    41
fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' |>> cons T
blanchet@49217
    42
  | strip_map_type T = ([], T);
blanchet@49217
    43
blanchet@49342
    44
fun resort_tfree S (TFree (s, _)) = TFree (s, S);
blanchet@49342
    45
blanchet@49214
    46
fun typ_subst inst (T as Type (s, Ts)) =
blanchet@49214
    47
    (case AList.lookup (op =) inst T of
blanchet@49214
    48
      NONE => Type (s, map (typ_subst inst) Ts)
blanchet@49214
    49
    | SOME T' => T')
blanchet@49214
    50
  | typ_subst inst T = the_default T (AList.lookup (op =) inst T);
blanchet@49205
    51
blanchet@49297
    52
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
blanchet@49202
    53
blanchet@49234
    54
fun mk_id T = Const (@{const_name id}, T --> T);
blanchet@49342
    55
fun mk_id_fun T = Abs (Name.uu, T, Bound 0);
blanchet@49234
    56
blanchet@49200
    57
fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
blanchet@49200
    58
fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
blanchet@49202
    59
fun mk_uncurried2_fun f xss =
blanchet@49200
    60
  mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss);
blanchet@49200
    61
blanchet@49233
    62
fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v));
blanchet@49233
    63
blanchet@49233
    64
fun tack z_name (c, v) f =
blanchet@49273
    65
  let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in
blanchet@49273
    66
    Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z)
blanchet@49273
    67
  end;
blanchet@49214
    68
blanchet@49342
    69
fun fold_def_rule n thm = funpow n (fn thm => thm RS fun_cong) (thm RS meta_eq_to_obj_eq) RS sym;
blanchet@49342
    70
blanchet@49124
    71
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
blanchet@49119
    72
blanchet@49298
    73
fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
blanchet@49119
    74
blanchet@49298
    75
fun merge_type_args (As, As') =
blanchet@49298
    76
  if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
blanchet@49119
    77
blanchet@49121
    78
fun type_args_constrained_of (((cAs, _), _), _) = cAs;
blanchet@49336
    79
fun type_binding_of (((_, b), _), _) = b;
blanchet@49181
    80
fun mixfix_of ((_, mx), _) = mx;
blanchet@49121
    81
fun ctr_specs_of (_, ctr_specs) = ctr_specs;
blanchet@49119
    82
blanchet@49286
    83
fun disc_of ((((disc, _), _), _), _) = disc;
blanchet@49286
    84
fun ctr_of ((((_, ctr), _), _), _) = ctr;
blanchet@49286
    85
fun args_of (((_, args), _), _) = args;
blanchet@49286
    86
fun defaults_of ((_, ds), _) = ds;
blanchet@49181
    87
fun ctr_mixfix_of (_, mx) = mx;
blanchet@49119
    88
blanchet@49308
    89
fun define_datatype prepare_constraint prepare_typ prepare_term lfp construct (no_dests, specs)
blanchet@49298
    90
    no_defs_lthy0 =
blanchet@49112
    91
  let
blanchet@49298
    92
    (* TODO: sanity checks on arguments *)
blanchet@49298
    93
blanchet@49286
    94
    val _ = if not lfp andalso no_dests then error "Cannot define destructor-less codatatypes"
blanchet@49278
    95
      else ();
blanchet@49278
    96
blanchet@49298
    97
    val N = length specs;
blanchet@49298
    98
blanchet@49298
    99
    fun prepare_type_arg (ty, c) =
blanchet@49298
   100
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
   101
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
   102
      end;
blanchet@49298
   103
blanchet@49298
   104
    val Ass0 = map (map prepare_type_arg o type_args_constrained_of) specs;
blanchet@49298
   105
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@49298
   106
    val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
blanchet@49119
   107
blanchet@49298
   108
    val ((Bs, Cs), no_defs_lthy) =
blanchet@49298
   109
      no_defs_lthy0
blanchet@49298
   110
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@49298
   111
      |> mk_TFrees N
blanchet@49298
   112
      ||>> mk_TFrees N;
blanchet@49119
   113
blanchet@49298
   114
    (* TODO: cleaner handling of fake contexts, without "background_theory" *)
blanchet@49298
   115
    (*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a
blanchet@49298
   116
      locale and shadows an existing global type*)
blanchet@49298
   117
    val fake_thy =
blanchet@49298
   118
      Theory.copy #> fold (fn spec => perhaps (try (Sign.add_type no_defs_lthy
blanchet@49336
   119
        (type_binding_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs;
blanchet@49298
   120
    val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
blanchet@49119
   121
blanchet@49182
   122
    fun mk_fake_T b =
blanchet@49121
   123
      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
blanchet@49298
   124
        unsorted_As);
blanchet@49121
   125
blanchet@49336
   126
    val fp_bs = map type_binding_of specs;
blanchet@49337
   127
    val fp_common_name = mk_common_name fp_bs;
blanchet@49337
   128
blanchet@49302
   129
    val fake_Ts = map mk_fake_T fp_bs;
blanchet@49121
   130
blanchet@49181
   131
    val mixfixes = map mixfix_of specs;
blanchet@49119
   132
blanchet@49302
   133
    val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
   134
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
   135
blanchet@49121
   136
    val ctr_specss = map ctr_specs_of specs;
blanchet@49119
   137
blanchet@49336
   138
    val disc_bindingss = map (map disc_of) ctr_specss;
blanchet@49336
   139
    val ctr_bindingss =
blanchet@49302
   140
      map2 (fn fp_b => map (Binding.qualify false (Binding.name_of fp_b) o ctr_of))
blanchet@49302
   141
        fp_bs ctr_specss;
blanchet@49121
   142
    val ctr_argsss = map (map args_of) ctr_specss;
blanchet@49181
   143
    val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
blanchet@49119
   144
blanchet@49336
   145
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
   146
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@49286
   147
    val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
blanchet@49286
   148
blanchet@49308
   149
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
   150
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@49298
   151
blanchet@49298
   152
    val _ = (case duplicates (op =) unsorted_As of [] => ()
blanchet@49298
   153
      | A :: _ => error ("Duplicate type parameter " ^
blanchet@49298
   154
          quote (Syntax.string_of_typ no_defs_lthy A)));
blanchet@49298
   155
blanchet@49183
   156
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@49298
   157
    val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
blanchet@49165
   158
        [] => ()
blanchet@49342
   159
      | A' :: _ => error ("Extra type variable on right-hand side: " ^
blanchet@49204
   160
          quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
blanchet@49165
   161
blanchet@49204
   162
    fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) =
blanchet@49146
   163
        s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
blanchet@49146
   164
          quote (Syntax.string_of_typ fake_lthy T)))
blanchet@49204
   165
      | eq_fpT _ _ = false;
blanchet@49146
   166
blanchet@49204
   167
    fun freeze_fp (T as Type (s, Us)) =
blanchet@49298
   168
        (case find_index (eq_fpT T) fake_Ts of ~1 => Type (s, map freeze_fp Us) | j => nth Bs j)
blanchet@49204
   169
      | freeze_fp T = T;
blanchet@49121
   170
blanchet@49297
   171
    val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss;
blanchet@49297
   172
    val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs;
blanchet@49119
   173
blanchet@49298
   174
    val fp_eqs =
blanchet@49298
   175
      map dest_TFree Bs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsBs;
blanchet@49121
   176
blanchet@49337
   177
    val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, fp_induct, unf_flds, fld_unfs, fld_injects,
blanchet@49207
   178
        fp_iter_thms, fp_rec_thms), lthy)) =
blanchet@49308
   179
      fp_bnf construct fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0;
blanchet@49121
   180
blanchet@49226
   181
    val add_nested_bnf_names =
blanchet@49226
   182
      let
blanchet@49226
   183
        fun add (Type (s, Ts)) ss =
blanchet@49226
   184
            let val (needs, ss') = fold_map add Ts ss in
blanchet@49226
   185
              if exists I needs then (true, insert (op =) s ss') else (false, ss')
blanchet@49226
   186
            end
blanchet@49226
   187
          | add T ss = (member (op =) As T, ss);
blanchet@49226
   188
      in snd oo add end;
blanchet@49226
   189
blanchet@49226
   190
    val nested_bnfs =
blanchet@49297
   191
      map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssBs []);
blanchet@49226
   192
blanchet@49167
   193
    val timer = time (Timer.startRealTimer ());
blanchet@49167
   194
blanchet@49176
   195
    fun mk_unf_or_fld get_T Ts t =
blanchet@49176
   196
      let val Type (_, Ts0) = get_T (fastype_of t) in
blanchet@49124
   197
        Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49121
   198
      end;
blanchet@49119
   199
blanchet@49126
   200
    val mk_unf = mk_unf_or_fld domain_type;
blanchet@49126
   201
    val mk_fld = mk_unf_or_fld range_type;
blanchet@49121
   202
blanchet@49203
   203
    val unfs = map (mk_unf As) unfs0;
blanchet@49203
   204
    val flds = map (mk_fld As) flds0;
blanchet@49124
   205
blanchet@49201
   206
    val fpTs = map (domain_type o fastype_of) unfs;
blanchet@49204
   207
blanchet@49297
   208
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs;
blanchet@49203
   209
    val ns = map length ctr_Tsss;
blanchet@49212
   210
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
   211
    val mss = map (map length) ctr_Tsss;
blanchet@49203
   212
    val Css = map2 replicate ns Cs;
blanchet@49203
   213
blanchet@49214
   214
    fun mk_iter_like Ts Us t =
blanchet@49121
   215
      let
blanchet@49336
   216
        val (bindings, body) = strip_type (fastype_of t);
blanchet@49336
   217
        val (f_Us, prebody) = split_last bindings;
blanchet@49210
   218
        val Type (_, Ts0) = if lfp then prebody else body;
blanchet@49210
   219
        val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us);
blanchet@49176
   220
      in
blanchet@49214
   221
        Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49176
   222
      end;
blanchet@49176
   223
blanchet@49210
   224
    val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0;
blanchet@49210
   225
    val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0;
blanchet@49210
   226
blanchet@49212
   227
    val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1)));
blanchet@49212
   228
    val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1)));
blanchet@49204
   229
blanchet@49256
   230
    val ((iter_only as (gss, _, _), rec_only as (hss, _, _)),
blanchet@49276
   231
         (zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) =
blanchet@49208
   232
      if lfp then
blanchet@49208
   233
        let
blanchet@49208
   234
          val y_Tsss =
blanchet@49255
   235
            map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
blanchet@49212
   236
              ns mss fp_iter_fun_Ts;
blanchet@49208
   237
          val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
blanchet@49208
   238
blanchet@49208
   239
          val ((gss, ysss), _) =
blanchet@49208
   240
            lthy
blanchet@49208
   241
            |> mk_Freess "f" g_Tss
blanchet@49208
   242
            ||>> mk_Freesss "x" y_Tsss;
blanchet@49274
   243
          val yssss = map (map (map single)) ysss;
blanchet@49274
   244
blanchet@49274
   245
          fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) =
blanchet@49274
   246
              if member (op =) Cs U then Us else [T]
blanchet@49274
   247
            | dest_rec_prodT T = [T];
blanchet@49204
   248
blanchet@49208
   249
          val z_Tssss =
blanchet@49274
   250
            map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o
blanchet@49255
   251
              dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts;
blanchet@49208
   252
          val h_Tss = map2 (map2 (fold_rev (curry (op --->)))) z_Tssss Css;
blanchet@49204
   253
blanchet@49298
   254
          val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@49298
   255
          val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
blanchet@49274
   256
          val (zssss_tl, _) =
blanchet@49208
   257
            lthy
blanchet@49274
   258
            |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
blanchet@49274
   259
          val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
blanchet@49210
   260
        in
blanchet@49274
   261
          (((gss, g_Tss, yssss), (hss, h_Tss, zssss)),
blanchet@49276
   262
           ([], [], [], (([], []), ([], [])), (([], []), ([], []))))
blanchet@49210
   263
        end
blanchet@49208
   264
      else
blanchet@49210
   265
        let
blanchet@49221
   266
          (*avoid "'a itself" arguments in coiterators and corecursors*)
blanchet@49221
   267
          val mss' =  map (fn [0] => [1] | ms => ms) mss;
blanchet@49221
   268
blanchet@49275
   269
          val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_predT) ns Cs;
blanchet@49275
   270
blanchet@49276
   271
          fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss);
blanchet@49211
   272
blanchet@49276
   273
          fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss
blanchet@49276
   274
            | zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
blanchet@49276
   275
              p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss;
blanchet@49274
   276
blanchet@49274
   277
          fun mk_types maybe_dest_sumT fun_Ts =
blanchet@49212
   278
            let
blanchet@49212
   279
              val f_sum_prod_Ts = map range_type fun_Ts;
blanchet@49255
   280
              val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
blanchet@49275
   281
              val f_Tssss =
blanchet@49275
   282
                map3 (fn C => map2 (map (map (curry (op -->) C) o maybe_dest_sumT) oo dest_tupleT))
blanchet@49275
   283
                  Cs mss' f_prod_Tss;
blanchet@49275
   284
              val q_Tssss =
blanchet@49275
   285
                map (map (map (fn [_] => [] | [_, C] => [mk_predT (domain_type C)]))) f_Tssss;
blanchet@49276
   286
              val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
blanchet@49275
   287
            in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end;
blanchet@49176
   288
blanchet@49275
   289
          val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts;
blanchet@49211
   290
blanchet@49275
   291
          val ((((Free (z, _), cs), pss), gssss), _) =
blanchet@49210
   292
            lthy
blanchet@49233
   293
            |> yield_singleton (mk_Frees "z") dummyT
blanchet@49233
   294
            ||>> mk_Frees "a" Cs
blanchet@49211
   295
            ||>> mk_Freess "p" p_Tss
blanchet@49275
   296
            ||>> mk_Freessss "g" g_Tssss;
blanchet@49275
   297
          val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@49274
   298
blanchet@49274
   299
          fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) =
blanchet@49274
   300
              if member (op =) Cs U then Us else [T]
blanchet@49274
   301
            | dest_corec_sumT T = [T];
blanchet@49274
   302
blanchet@49275
   303
          val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts;
blanchet@49210
   304
blanchet@49298
   305
          val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@49275
   306
          val ((sssss, hssss_tl), _) =
blanchet@49275
   307
            lthy
blanchet@49275
   308
            |> mk_Freessss "q" s_Tssss
blanchet@49275
   309
            ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@49275
   310
          val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@49211
   311
blanchet@49212
   312
          val cpss = map2 (fn c => map (fn p => p $ c)) cs pss;
blanchet@49212
   313
blanchet@49276
   314
          fun mk_preds_getters_join [] [cf] = cf
blanchet@49276
   315
            | mk_preds_getters_join [cq] [cf, cf'] =
blanchet@49276
   316
              mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf');
blanchet@49276
   317
blanchet@49275
   318
          fun mk_terms qssss fssss =
blanchet@49212
   319
            let
blanchet@49276
   320
              val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss;
blanchet@49275
   321
              val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss;
blanchet@49274
   322
              val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss;
blanchet@49276
   323
              val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss;
blanchet@49276
   324
            in (pfss, cqfsss) end;
blanchet@49210
   325
        in
blanchet@49212
   326
          ((([], [], []), ([], [], [])),
blanchet@49275
   327
           ([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)),
blanchet@49275
   328
            (mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss))))
blanchet@49210
   329
        end;
blanchet@49210
   330
blanchet@49302
   331
    fun define_ctrs_case_for_type ((((((((((((((((((fp_b, fpT), C), fld), unf), fp_iter), fp_rec),
blanchet@49336
   332
          fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_bindings), ctr_mixfixes), ctr_Tss),
blanchet@49336
   333
        disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
   334
      let
blanchet@49201
   335
        val unfT = domain_type (fastype_of fld);
blanchet@49210
   336
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
   337
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
   338
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   339
blanchet@49176
   340
        val ((((u, v), fs), xss), _) =
blanchet@49204
   341
          no_defs_lthy
blanchet@49201
   342
          |> yield_singleton (mk_Frees "u") unfT
blanchet@49201
   343
          ||>> yield_singleton (mk_Frees "v") fpT
blanchet@49176
   344
          ||>> mk_Frees "f" case_Ts
blanchet@49124
   345
          ||>> mk_Freess "x" ctr_Tss;
blanchet@49121
   346
blanchet@49129
   347
        val ctr_rhss =
blanchet@49256
   348
          map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $
blanchet@49256
   349
            mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss;
blanchet@49121
   350
blanchet@49336
   351
        val case_binding = Binding.suffix_name ("_" ^ caseN) fp_b;
blanchet@49129
   352
blanchet@49134
   353
        val case_rhs =
blanchet@49255
   354
          fold_rev Term.lambda (fs @ [v])
blanchet@49255
   355
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v));
blanchet@49129
   356
blanchet@49201
   357
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   358
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
   359
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
   360
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
   361
          ||> `Local_Theory.restore;
blanchet@49121
   362
blanchet@49121
   363
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   364
blanchet@49121
   365
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49130
   366
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   367
blanchet@49203
   368
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
   369
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
   370
blanchet@49203
   371
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
   372
blanchet@49135
   373
        fun exhaust_tac {context = ctxt, ...} =
blanchet@49123
   374
          let
blanchet@49135
   375
            val fld_iff_unf_thm =
blanchet@49135
   376
              let
blanchet@49135
   377
                val goal =
blanchet@49135
   378
                  fold_rev Logic.all [u, v]
blanchet@49135
   379
                    (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
blanchet@49135
   380
              in
blanchet@49135
   381
                Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49201
   382
                  mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT])
blanchet@49176
   383
                    (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
blanchet@49135
   384
                |> Thm.close_derivation
blanchet@49135
   385
                |> Morphism.thm phi
blanchet@49135
   386
              end;
blanchet@49135
   387
blanchet@49135
   388
            val sumEN_thm' =
blanchet@49135
   389
              Local_Defs.unfold lthy @{thms all_unit_eq}
blanchet@49255
   390
                (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49255
   391
                   (mk_sumEN_balanced n))
blanchet@49135
   392
              |> Morphism.thm phi;
blanchet@49123
   393
          in
blanchet@49161
   394
            mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
blanchet@49123
   395
          end;
blanchet@49121
   396
blanchet@49126
   397
        val inject_tacss =
blanchet@49205
   398
          map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49205
   399
              mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs;
blanchet@49126
   400
blanchet@49127
   401
        val half_distinct_tacss =
blanchet@49127
   402
          map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49127
   403
            mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
blanchet@49127
   404
blanchet@49130
   405
        val case_tacs =
blanchet@49130
   406
          map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49130
   407
            mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
blanchet@49121
   408
blanchet@49121
   409
        val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49134
   410
blanchet@49287
   411
        fun define_iter_rec ((selss0, discIs, sel_thmss), no_defs_lthy) =
blanchet@49134
   412
          let
blanchet@49208
   413
            val fpT_to_C = fpT --> C;
blanchet@49199
   414
blanchet@49215
   415
            fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) =
blanchet@49215
   416
              let
blanchet@49215
   417
                val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@49336
   418
                val binding = Binding.suffix_name ("_" ^ suf) fp_b;
blanchet@49215
   419
                val spec =
blanchet@49336
   420
                  mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)),
blanchet@49215
   421
                    Term.list_comb (fp_iter_like,
blanchet@49255
   422
                      map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss));
blanchet@49336
   423
              in (binding, spec) end;
blanchet@49199
   424
blanchet@49300
   425
            val iter_like_infos =
blanchet@49215
   426
              [(iterN, fp_iter, iter_only),
blanchet@49215
   427
               (recN, fp_rec, rec_only)];
blanchet@49215
   428
blanchet@49336
   429
            val (bindings, specs) = map generate_iter_like iter_like_infos |> split_list;
blanchet@49215
   430
blanchet@49215
   431
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49201
   432
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49199
   433
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   434
                #>> apsnd snd) bindings specs
blanchet@49199
   435
              ||> `Local_Theory.restore;
blanchet@49201
   436
blanchet@49201
   437
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49201
   438
blanchet@49215
   439
            val [iter_def, rec_def] = map (Morphism.thm phi) defs;
blanchet@49201
   440
blanchet@49215
   441
            val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49134
   442
          in
blanchet@49267
   443
            ((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def),
blanchet@49266
   444
             lthy)
blanchet@49134
   445
          end;
blanchet@49134
   446
blanchet@49287
   447
        fun define_coiter_corec ((selss0, discIs, sel_thmss), no_defs_lthy) =
blanchet@49210
   448
          let
blanchet@49210
   449
            val B_to_fpT = C --> fpT;
blanchet@49211
   450
blanchet@49276
   451
            fun mk_preds_getterss_join c n cps sum_prod_T cqfss =
blanchet@49276
   452
              Term.lambda c (mk_IfN sum_prod_T cps
blanchet@49276
   453
                (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)));
blanchet@49275
   454
blanchet@49276
   455
            fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts,
blanchet@49274
   456
                pf_Tss))) =
blanchet@49211
   457
              let
blanchet@49211
   458
                val res_T = fold_rev (curry (op --->)) pf_Tss B_to_fpT;
blanchet@49336
   459
                val binding = Binding.suffix_name ("_" ^ suf) fp_b;
blanchet@49211
   460
                val spec =
blanchet@49336
   461
                  mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)),
blanchet@49211
   462
                    Term.list_comb (fp_iter_like,
blanchet@49276
   463
                      map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss));
blanchet@49336
   464
              in (binding, spec) end;
blanchet@49210
   465
blanchet@49300
   466
            val coiter_like_infos =
blanchet@49215
   467
              [(coiterN, fp_iter, coiter_only),
blanchet@49215
   468
               (corecN, fp_rec, corec_only)];
blanchet@49212
   469
blanchet@49336
   470
            val (bindings, specs) = map generate_coiter_like coiter_like_infos |> split_list;
blanchet@49211
   471
blanchet@49211
   472
            val ((csts, defs), (lthy', lthy)) = no_defs_lthy
blanchet@49210
   473
              |> apfst split_list o fold_map2 (fn b => fn spec =>
blanchet@49210
   474
                Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@49336
   475
                #>> apsnd snd) bindings specs
blanchet@49210
   476
              ||> `Local_Theory.restore;
blanchet@49210
   477
blanchet@49210
   478
            val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49210
   479
blanchet@49211
   480
            val [coiter_def, corec_def] = map (Morphism.thm phi) defs;
blanchet@49210
   481
blanchet@49211
   482
            val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts;
blanchet@49210
   483
          in
blanchet@49267
   484
            ((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def,
blanchet@49266
   485
              corec_def), lthy)
blanchet@49210
   486
          end;
blanchet@49286
   487
blanchet@49287
   488
        fun wrap lthy =
blanchet@49287
   489
          let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in
blanchet@49336
   490
            wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_bindings, (sel_bindingss,
blanchet@49287
   491
              sel_defaultss))) lthy
blanchet@49287
   492
          end;
blanchet@49287
   493
blanchet@49287
   494
        val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec;
blanchet@49119
   495
      in
blanchet@49287
   496
        ((wrap, define_iter_likes), lthy')
blanchet@49119
   497
      end;
blanchet@49167
   498
blanchet@49226
   499
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49342
   500
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49229
   501
    val map_ids = map map_id_of_bnf nested_bnfs;
blanchet@49226
   502
blanchet@49214
   503
    fun mk_map Ts Us t =
blanchet@49217
   504
      let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) |>> List.last in
blanchet@49214
   505
        Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49214
   506
      end;
blanchet@49214
   507
blanchet@49234
   508
    fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
blanchet@49234
   509
      let
traytel@49236
   510
        val map0 = map_of_bnf (the (bnf_of lthy s));
blanchet@49234
   511
        val mapx = mk_map Ts Us map0;
blanchet@49234
   512
        val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx)))));
blanchet@49234
   513
        val args = map build_arg TUs;
blanchet@49234
   514
      in Term.list_comb (mapx, args) end;
blanchet@49234
   515
blanchet@49337
   516
    fun derive_induct_iter_rec_thms_for_types ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _,
blanchet@49337
   517
        iter_defs, rec_defs), lthy) =
blanchet@49202
   518
      let
blanchet@49337
   519
        val (induct_thms, induct_thm) =
blanchet@49337
   520
          let
blanchet@49342
   521
            val sym_ctr_defss = map2 (map2 fold_def_rule) mss ctr_defss;
blanchet@49342
   522
blanchet@49342
   523
            val ss = @{simpset} |> fold Simplifier.add_simp
blanchet@49342
   524
              @{thms collect_def[abs_def] sum_setl_def[abs_def] sum_setr_def[abs_def]
blanchet@49342
   525
                 fsts_def[abs_def] snds_def[abs_def] False_imp_eq all_point_1};
blanchet@49342
   526
blanchet@49342
   527
            val induct_thm0 = fp_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@49342
   528
blanchet@49342
   529
            val spurious_fs =
blanchet@49342
   530
              Term.add_vars (prop_of induct_thm0) []
blanchet@49342
   531
              |> filter (fn (_, Type (@{type_name fun}, [_, T'])) => T' <> HOLogic.boolT
blanchet@49342
   532
                | _ => false);
blanchet@49342
   533
blanchet@49342
   534
            val cxs =
blanchet@49342
   535
              map (fn s as (_, T) =>
blanchet@49342
   536
                (certify lthy (Var s), certify lthy (mk_id_fun (domain_type T)))) spurious_fs;
blanchet@49342
   537
blanchet@49342
   538
            val induct_thm =
blanchet@49342
   539
              Drule.cterm_instantiate cxs induct_thm0
blanchet@49342
   540
              |> Tactic.rule_by_tactic lthy (ALLGOALS (REPEAT_DETERM o bound_hyp_subst_tac))
blanchet@49342
   541
              |> Local_Defs.unfold lthy
blanchet@49342
   542
                (@{thm triv_forall_equality} :: flat sym_ctr_defss @ flat pre_set_defss)
blanchet@49342
   543
              |> Simplifier.full_simplify ss;
blanchet@49337
   544
          in
blanchet@49337
   545
            `(conj_dests N) induct_thm
blanchet@49337
   546
          end;
blanchet@49201
   547
blanchet@49202
   548
        val (iter_thmss, rec_thmss) =
blanchet@49207
   549
          let
blanchet@49337
   550
            val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@49337
   551
            val giters = map (lists_bmoc gss) iters;
blanchet@49337
   552
            val hrecs = map (lists_bmoc hss) recs;
blanchet@49337
   553
blanchet@49212
   554
            fun mk_goal_iter_like fss fiter_like xctr f xs fxs =
blanchet@49207
   555
              fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@49212
   556
                (mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs)));
blanchet@49204
   557
blanchet@49234
   558
            fun build_call fiter_likes maybe_tick (T, U) =
blanchet@49234
   559
              if T = U then
blanchet@49234
   560
                mk_id T
blanchet@49234
   561
              else
blanchet@49234
   562
                (case find_index (curry (op =) T) fpTs of
blanchet@49234
   563
                  ~1 => build_map (build_call fiter_likes maybe_tick) T U
blanchet@49234
   564
                | j => maybe_tick (nth vs j) (nth fiter_likes j));
blanchet@49233
   565
blanchet@49274
   566
            fun mk_U maybe_mk_prodT =
blanchet@49274
   567
              typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs);
blanchet@49214
   568
blanchet@49342
   569
            fun intr_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) =
blanchet@49214
   570
              if member (op =) fpTs T then
blanchet@49233
   571
                maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x]
blanchet@49214
   572
              else if exists_subtype (member (op =) fpTs) T then
blanchet@49274
   573
                [build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x]
blanchet@49214
   574
              else
blanchet@49214
   575
                [x];
blanchet@49214
   576
blanchet@49342
   577
            val gxsss = map (map (maps (intr_calls giters (K I) (K I) (K I)))) xsss;
blanchet@49342
   578
            val hxsss = map (map (maps (intr_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss;
blanchet@49204
   579
blanchet@49212
   580
            val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss;
blanchet@49212
   581
            val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss;
blanchet@49204
   582
blanchet@49203
   583
            val iter_tacss =
blanchet@49229
   584
              map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss;
blanchet@49203
   585
            val rec_tacss =
blanchet@49229
   586
              map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss;
blanchet@49202
   587
          in
blanchet@49276
   588
            (map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49205
   589
               goal_iterss iter_tacss,
blanchet@49276
   590
             map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context)))
blanchet@49205
   591
               goal_recss rec_tacss)
blanchet@49202
   592
          end;
blanchet@49201
   593
blanchet@49337
   594
        val common_notes =
blanchet@49342
   595
          (if N > 1 then [(inductN, [induct_thm], [])] (* FIXME: attribs *) else [])
blanchet@49337
   596
          |> map (fn (thmN, thms, attrs) =>
blanchet@49337
   597
              ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49337
   598
blanchet@49226
   599
        val notes =
blanchet@49342
   600
          [(inductN, map single induct_thms, []), (* FIXME: attribs *)
blanchet@49342
   601
           (itersN, iter_thmss, simp_attrs),
blanchet@49300
   602
           (recsN, rec_thmss, Code.add_default_eqn_attrib :: simp_attrs)]
blanchet@49300
   603
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@49202
   604
            map2 (fn b => fn thms =>
blanchet@49300
   605
              ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
blanchet@49302
   606
                [(thms, [])])) fp_bs thmss);
blanchet@49202
   607
      in
blanchet@49337
   608
        lthy |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@49202
   609
      end;
blanchet@49202
   610
blanchet@49337
   611
    fun derive_coinduct_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, vs, _,
blanchet@49337
   612
        ctr_defss, discIss, sel_thmsss, coiter_defs, corec_defs), lthy) =
blanchet@49212
   613
      let
blanchet@49337
   614
        val (coinduct_thms, coinduct_thm) =
blanchet@49337
   615
          let
blanchet@49337
   616
            val coinduct_thm = fp_induct;
blanchet@49337
   617
          in
blanchet@49337
   618
            `(conj_dests N) coinduct_thm
blanchet@49337
   619
          end;
blanchet@49212
   620
blanchet@49212
   621
        val (coiter_thmss, corec_thmss) =
blanchet@49212
   622
          let
blanchet@49337
   623
            val z = the_single zs;
blanchet@49337
   624
            val gcoiters = map (lists_bmoc pgss) coiters;
blanchet@49337
   625
            val hcorecs = map (lists_bmoc phss) corecs;
blanchet@49337
   626
blanchet@49232
   627
            fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not);
blanchet@49212
   628
blanchet@49276
   629
            fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' =
blanchet@49212
   630
              fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@49232
   631
                (Logic.list_implies (seq_conds mk_goal_cond n k cps,
blanchet@49276
   632
                   mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@49212
   633
blanchet@49234
   634
            fun build_call fiter_likes maybe_tack (T, U) =
blanchet@49234
   635
              if T = U then
blanchet@49234
   636
                mk_id T
blanchet@49234
   637
              else
blanchet@49234
   638
                (case find_index (curry (op =) U) fpTs of
blanchet@49234
   639
                  ~1 => build_map (build_call fiter_likes maybe_tack) T U
blanchet@49234
   640
                | j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j));
blanchet@49233
   641
blanchet@49274
   642
            fun mk_U maybe_mk_sumT =
blanchet@49274
   643
              typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@49212
   644
blanchet@49342
   645
            fun intr_calls fiter_likes maybe_mk_sumT maybe_tack cqf =
blanchet@49276
   646
              let val T = fastype_of cqf in
blanchet@49276
   647
                if exists_subtype (member (op =) Cs) T then
blanchet@49276
   648
                  build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
blanchet@49276
   649
                else
blanchet@49276
   650
                  cqf
blanchet@49276
   651
              end;
blanchet@49232
   652
blanchet@49342
   653
            val crgsss' = map (map (map (intr_calls gcoiters (K I) (K I)))) crgsss;
blanchet@49342
   654
            val cshsss' = map (map (map (intr_calls hcorecs (curry mk_sumT) (tack z)))) cshsss;
blanchet@49212
   655
blanchet@49212
   656
            val goal_coiterss =
blanchet@49276
   657
              map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss';
blanchet@49233
   658
            val goal_corecss =
blanchet@49276
   659
              map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss';
blanchet@49213
   660
blanchet@49213
   661
            val coiter_tacss =
blanchet@49229
   662
              map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs
blanchet@49226
   663
                ctr_defss;
blanchet@49233
   664
            val corec_tacss =
blanchet@49233
   665
              map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs
blanchet@49233
   666
                ctr_defss;
blanchet@49212
   667
          in
blanchet@49276
   668
            (map2 (map2 (fn goal => fn tac =>
blanchet@49276
   669
                 Skip_Proof.prove lthy [] [] goal (tac o #context) |> Thm.close_derivation))
blanchet@49213
   670
               goal_coiterss coiter_tacss,
blanchet@49276
   671
             map2 (map2 (fn goal => fn tac =>
blanchet@49276
   672
                 Skip_Proof.prove lthy [] [] goal (tac o #context)
blanchet@49276
   673
                 |> Local_Defs.unfold lthy @{thms sum_case_if} |> Thm.close_derivation))
blanchet@49233
   674
               goal_corecss corec_tacss)
blanchet@49212
   675
          end;
blanchet@49212
   676
blanchet@49266
   677
        fun mk_disc_coiter_like_thms [_] = K []
blanchet@49266
   678
          | mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms;
blanchet@49266
   679
blanchet@49266
   680
        val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss;
blanchet@49266
   681
        val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss;
blanchet@49266
   682
blanchet@49267
   683
        fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm =
blanchet@49266
   684
          let
blanchet@49267
   685
            val (domT, ranT) = dest_funT (fastype_of sel0);
blanchet@49266
   686
            val arg_cong' =
blanchet@49266
   687
              Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@49267
   688
                [NONE, NONE, SOME (certify lthy sel0)] arg_cong
blanchet@49267
   689
              |> Thm.varifyT_global;
blanchet@49266
   690
            val sel_thm' = sel_thm RSN (2, trans);
blanchet@49266
   691
          in
blanchet@49267
   692
            coiter_like_thm RS arg_cong' RS sel_thm'
blanchet@49266
   693
          end;
blanchet@49266
   694
blanchet@49266
   695
        val sel_coiter_thmsss =
blanchet@49266
   696
          map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss;
blanchet@49266
   697
        val sel_corec_thmsss =
blanchet@49267
   698
          map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss;
blanchet@49266
   699
blanchet@49342
   700
        val common_notes =
blanchet@49342
   701
          (if N > 1 then [(coinductN, [coinduct_thm], [])] (* FIXME: attribs *) else [])
blanchet@49342
   702
          |> map (fn (thmN, thms, attrs) =>
blanchet@49342
   703
              ((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49342
   704
blanchet@49212
   705
        val notes =
blanchet@49342
   706
          [(coinductN, map single coinduct_thms, []), (* FIXME: attribs *)
blanchet@49342
   707
           (coitersN, coiter_thmss, []),
blanchet@49300
   708
           (disc_coitersN, disc_coiter_thmss, []),
blanchet@49300
   709
           (sel_coitersN, map flat sel_coiter_thmsss, []),
blanchet@49300
   710
           (corecsN, corec_thmss, []),
blanchet@49300
   711
           (disc_corecsN, disc_corec_thmss, []),
blanchet@49300
   712
           (sel_corecsN, map flat sel_corec_thmsss, [])]
blanchet@49300
   713
          |> maps (fn (thmN, thmss, attrs) =>
blanchet@49266
   714
            map_filter (fn (_, []) => NONE | (b, thms) =>
blanchet@49300
   715
              SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs),
blanchet@49302
   716
                [(thms, [])])) (fp_bs ~~ thmss));
blanchet@49212
   717
      in
blanchet@49230
   718
        lthy |> Local_Theory.notes notes |> snd
blanchet@49212
   719
      end;
blanchet@49212
   720
blanchet@49287
   721
    fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) =
blanchet@49287
   722
      fold_map2 (curry (op o)) define_iter_likess wraps lthy |>> split_list11
blanchet@49287
   723
blanchet@49204
   724
    val lthy' = lthy
blanchet@49302
   725
      |> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~
blanchet@49336
   726
        fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_bindingss ~~
blanchet@49336
   727
        ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ raw_sel_defaultsss)
blanchet@49287
   728
      |>> split_list |> wrap_types_and_define_iter_likes
blanchet@49337
   729
      |> (if lfp then derive_induct_iter_rec_thms_for_types
blanchet@49337
   730
          else derive_coinduct_coiter_corec_thms_for_types);
blanchet@49167
   731
blanchet@49167
   732
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49208
   733
      (if lfp then "" else "co") ^ "datatype"));
blanchet@49112
   734
  in
blanchet@49308
   735
    timer; lthy'
blanchet@49112
   736
  end;
blanchet@49112
   737
blanchet@49298
   738
val datatyp = define_datatype (K I) (K I) (K I);
blanchet@49297
   739
blanchet@49298
   740
val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term;
blanchet@49119
   741
blanchet@49329
   742
val parse_binding_colon = Parse.binding --| @{keyword ":"};
blanchet@49336
   743
val parse_opt_binding_colon = Scan.optional parse_binding_colon no_binding;
blanchet@49119
   744
blanchet@49112
   745
val parse_ctr_arg =
blanchet@49329
   746
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
blanchet@49336
   747
  (Parse.typ >> pair no_binding);
blanchet@49112
   748
blanchet@49286
   749
val parse_defaults =
blanchet@49286
   750
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
   751
blanchet@49112
   752
val parse_single_spec =
blanchet@49112
   753
  Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
blanchet@49119
   754
  (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
blanchet@49286
   755
    Scan.repeat parse_ctr_arg -- Scan.optional parse_defaults [] -- Parse.opt_mixfix));
blanchet@49112
   756
blanchet@49278
   757
val parse_datatype = parse_wrap_options -- Parse.and_list1 parse_single_spec;
blanchet@49278
   758
blanchet@49308
   759
fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct;
blanchet@49112
   760
blanchet@49112
   761
end;