src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
author blanchet
Fri Jun 07 16:19:52 2013 +0100 (2013-06-07)
changeset 52348 740923a6e530
parent 52347 ead18e3b2c1b
child 52349 07fd21c01e93
permissions -rw-r--r--
killed dead code
blanchet@49636
     1
(*  Title:      HOL/BNF/Tools/bnf_fp_def_sugar.ML
blanchet@49112
     2
    Author:     Jasmin Blanchette, TU Muenchen
blanchet@49112
     3
    Copyright   2012
blanchet@49112
     4
blanchet@49389
     5
Sugared datatype and codatatype constructions.
blanchet@49112
     6
*)
blanchet@49112
     7
blanchet@49636
     8
signature BNF_FP_DEF_SUGAR =
blanchet@49112
     9
sig
blanchet@51840
    10
  type fp_sugar =
blanchet@51859
    11
    {T: typ,
blanchet@52207
    12
     fp: BNF_FP_Util.fp_kind,
blanchet@51838
    13
     index: int,
blanchet@51838
    14
     pre_bnfs: BNF_Def.bnf list,
blanchet@51850
    15
     fp_res: BNF_FP_Util.fp_result,
blanchet@51906
    16
     ctr_defss: thm list list,
blanchet@51842
    17
     ctr_sugars: BNF_Ctr_Sugar.ctr_sugar list,
blanchet@52336
    18
     co_iterss: term list list,
blanchet@52343
    19
     co_inducts: thm list,
blanchet@52337
    20
     co_iter_thmsss: thm list list list};
blanchet@51823
    21
blanchet@52295
    22
  val of_fp_sugar: (fp_sugar -> 'a list) -> fp_sugar -> 'a
blanchet@51896
    23
  val morph_fp_sugar: morphism -> fp_sugar -> fp_sugar
blanchet@51896
    24
  val fp_sugar_of: Proof.context -> string -> fp_sugar option
blanchet@51852
    25
blanchet@51911
    26
  val tvar_subst: theory -> typ list -> typ list -> ((string * int) * typ) list
blanchet@51860
    27
  val exists_subtype_in: typ list -> typ -> bool
blanchet@52301
    28
  val flat_rec: 'a list list -> 'a list
blanchet@52207
    29
  val mk_co_iter: theory -> BNF_FP_Util.fp_kind -> typ -> typ list -> term -> term
blanchet@51907
    30
  val nesty_bnfs: Proof.context -> typ list list list -> typ list -> BNF_Def.bnf list
blanchet@52347
    31
  val mk_map: int -> typ list -> typ list -> term -> term
blanchet@52347
    32
  val build_map: local_theory -> (typ * typ -> term) -> typ * typ -> term
blanchet@52334
    33
  val mk_co_iters_prelims: BNF_FP_Util.fp_kind -> typ list -> typ list -> int list ->
blanchet@52315
    34
    int list list -> term list list -> Proof.context ->
blanchet@52315
    35
    (term list list
blanchet@52315
    36
     * (typ list list * typ list list list list * term list list
blanchet@52315
    37
        * term list list list list) list option
blanchet@52347
    38
     * (string * term list * term list list
blanchet@52347
    39
        * ((term list list * term list list list)
blanchet@52326
    40
           * (typ list * typ list list list * typ list list)) list) option)
blanchet@51903
    41
    * Proof.context
blanchet@51823
    42
blanchet@52215
    43
  val mk_iter_fun_arg_typessss: typ list -> int list -> int list list -> term ->
blanchet@52215
    44
    typ list list list list
blanchet@52320
    45
  val define_iters: string list ->
blanchet@52315
    46
    (typ list list * typ list list list list * term list list * term list list list list) list ->
blanchet@52319
    47
    (string -> binding) -> typ list -> typ list -> term list -> Proof.context ->
blanchet@52320
    48
    (term list * thm list) * Proof.context
blanchet@52347
    49
  val define_coiters: string list -> string * term list * term list list
blanchet@52347
    50
    * ((term list list * term list list list)
blanchet@52326
    51
       * (typ list * typ list list list * typ list list)) list ->
blanchet@52319
    52
    (string -> binding) -> typ list -> typ list -> term list -> Proof.context ->
blanchet@52320
    53
    (term list * thm list) * Proof.context
blanchet@52346
    54
  val derive_induct_iters_thms_for_types: BNF_Def.bnf list ->
blanchet@52315
    55
    (typ list list * typ list list list list * term list list * term list list list list) list ->
blanchet@52344
    56
    thm list -> thm list list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list ->
blanchet@52315
    57
    typ list -> typ list list list -> term list list -> thm list list -> term list list ->
blanchet@52315
    58
    thm list list -> local_theory ->
blanchet@52345
    59
    (thm list * thm * Args.src list) * (thm list list * Args.src list)
blanchet@51827
    60
    * (thm list list * Args.src list)
blanchet@52346
    61
  val derive_coinduct_coiters_thms_for_types: BNF_Def.bnf list ->
blanchet@52348
    62
    string * term list * term list list * ((term list list * term list list list)
blanchet@52348
    63
      * (typ list * typ list list list * typ list list)) list ->
blanchet@52344
    64
    thm list -> thm list -> thm list list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list ->
blanchet@52321
    65
    typ list -> typ list -> int list list -> int list list -> int list -> thm list list ->
blanchet@52321
    66
    BNF_Ctr_Sugar.ctr_sugar list -> term list list -> thm list list -> local_theory ->
blanchet@52345
    67
    ((thm list * thm) list * Args.src list)
blanchet@51839
    68
    * (thm list list * thm list list * Args.src list)
blanchet@51811
    69
    * (thm list list * thm list list) * (thm list list * thm list list * Args.src list)
blanchet@51824
    70
    * (thm list list * thm list list * Args.src list)
blanchet@51824
    71
    * (thm list list * thm list list * Args.src list)
blanchet@51823
    72
blanchet@52207
    73
  val co_datatypes: BNF_FP_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
blanchet@52207
    74
      binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
blanchet@52207
    75
      BNF_Def.bnf list -> local_theory -> BNF_FP_Util.fp_result * local_theory) ->
blanchet@51767
    76
    (bool * bool) * (((((binding * (typ * sort)) list * binding) * (binding * binding)) * mixfix) *
blanchet@51758
    77
      ((((binding * binding) * (binding * typ) list) * (binding * term) list) *
blanchet@51758
    78
        mixfix) list) list ->
blanchet@49297
    79
    local_theory -> local_theory
blanchet@52207
    80
  val parse_co_datatype_cmd: BNF_FP_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
blanchet@51867
    81
      binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
blanchet@51867
    82
      BNF_Def.bnf list -> local_theory -> BNF_FP_Util.fp_result * local_theory) ->
blanchet@49308
    83
    (local_theory -> local_theory) parser
blanchet@49112
    84
end;
blanchet@49112
    85
blanchet@49636
    86
structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR =
blanchet@49112
    87
struct
blanchet@49112
    88
blanchet@49119
    89
open BNF_Util
blanchet@51797
    90
open BNF_Ctr_Sugar
blanchet@49214
    91
open BNF_Def
blanchet@51850
    92
open BNF_FP_Util
blanchet@49636
    93
open BNF_FP_Def_Sugar_Tactics
blanchet@49119
    94
blanchet@51788
    95
val EqN = "Eq_";
blanchet@51777
    96
blanchet@51840
    97
type fp_sugar =
blanchet@51859
    98
  {T: typ,
blanchet@52207
    99
   fp: fp_kind,
blanchet@51838
   100
   index: int,
blanchet@51838
   101
   pre_bnfs: bnf list,
blanchet@51823
   102
   fp_res: fp_result,
blanchet@51906
   103
   ctr_defss: thm list list,
blanchet@51842
   104
   ctr_sugars: ctr_sugar list,
blanchet@52336
   105
   co_iterss: term list list,
blanchet@52343
   106
   co_inducts: thm list,
blanchet@52337
   107
   co_iter_thmsss: thm list list list};
blanchet@51823
   108
blanchet@52295
   109
fun of_fp_sugar f (fp_sugar as {index, ...}) = nth (f fp_sugar) index;
blanchet@52295
   110
blanchet@52207
   111
fun eq_fp_sugar ({T = T1, fp = fp1, index = index1, fp_res = fp_res1, ...} : fp_sugar,
blanchet@52207
   112
    {T = T2, fp = fp2, index = index2, fp_res = fp_res2, ...} : fp_sugar) =
blanchet@52207
   113
  T1 = T2 andalso fp1 = fp2 andalso index1 = index2 andalso eq_fp_result (fp_res1, fp_res2);
blanchet@51823
   114
blanchet@52343
   115
fun morph_fp_sugar phi {T, fp, index, pre_bnfs, fp_res, ctr_defss, ctr_sugars, co_iterss,
blanchet@52343
   116
    co_inducts, co_iter_thmsss} =
blanchet@52299
   117
  {T = Morphism.typ phi T, fp = fp, index = index, pre_bnfs = map (morph_bnf phi)
blanchet@52299
   118
   pre_bnfs, fp_res = morph_fp_result phi fp_res,
blanchet@52207
   119
   ctr_defss = map (map (Morphism.thm phi)) ctr_defss,
blanchet@52336
   120
   ctr_sugars = map (morph_ctr_sugar phi) ctr_sugars,
blanchet@52343
   121
   co_iterss = map (map (Morphism.term phi)) co_iterss,
blanchet@52343
   122
   co_inducts = map (Morphism.thm phi) co_inducts,
blanchet@52337
   123
   co_iter_thmsss = map (map (map (Morphism.thm phi))) co_iter_thmsss};
blanchet@51823
   124
blanchet@51823
   125
structure Data = Generic_Data
blanchet@51823
   126
(
blanchet@51840
   127
  type T = fp_sugar Symtab.table;
blanchet@51823
   128
  val empty = Symtab.empty;
blanchet@51823
   129
  val extend = I;
blanchet@51840
   130
  val merge = Symtab.merge eq_fp_sugar;
blanchet@51823
   131
);
blanchet@51823
   132
blanchet@51840
   133
val fp_sugar_of = Symtab.lookup o Data.get o Context.Proof;
blanchet@51823
   134
blanchet@51840
   135
fun register_fp_sugar key fp_sugar =
blanchet@51823
   136
  Local_Theory.declaration {syntax = false, pervasive = true}
blanchet@51840
   137
    (fn phi => Data.map (Symtab.update_new (key, morph_fp_sugar phi fp_sugar)));
blanchet@51823
   138
blanchet@52343
   139
fun register_fp_sugars fp pre_bnfs (fp_res as {Ts, ...}) ctr_defss ctr_sugars co_iterss co_inducts
blanchet@52343
   140
    co_iter_thmsss lthy =
blanchet@51844
   141
  (0, lthy)
blanchet@51859
   142
  |> fold (fn T as Type (s, _) => fn (kk, lthy) => (kk + 1,
blanchet@52299
   143
    register_fp_sugar s {T = T, fp = fp, index = kk, pre_bnfs = pre_bnfs, fp_res = fp_res,
blanchet@52338
   144
        ctr_defss = ctr_defss, ctr_sugars = ctr_sugars, co_iterss = co_iterss,
blanchet@52343
   145
        co_inducts = co_inducts, co_iter_thmsss = co_iter_thmsss}
blanchet@52337
   146
      lthy)) Ts
blanchet@51824
   147
  |> snd;
blanchet@51824
   148
blanchet@51777
   149
(* This function could produce clashes in contrived examples (e.g., "x.A", "x.x_A", "y.A"). *)
blanchet@49622
   150
fun quasi_unambiguous_case_names names =
blanchet@49622
   151
  let
blanchet@49622
   152
    val ps = map (`Long_Name.base_name) names;
blanchet@49622
   153
    val dups = Library.duplicates (op =) (map fst ps);
blanchet@49622
   154
    fun underscore s =
blanchet@49622
   155
      let val ss = space_explode Long_Name.separator s in
blanchet@49622
   156
        space_implode "_" (drop (length ss - 2) ss)
blanchet@49622
   157
      end;
blanchet@49622
   158
  in
blanchet@49622
   159
    map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
blanchet@49622
   160
  end;
blanchet@49622
   161
blanchet@49591
   162
val mp_conj = @{thm mp_conj};
blanchet@49591
   163
blanchet@49300
   164
val simp_attrs = @{attributes [simp]};
blanchet@49585
   165
val code_simp_attrs = Code.add_default_eqn_attrib :: simp_attrs;
blanchet@49300
   166
blanchet@51911
   167
fun tvar_subst thy Ts Us =
blanchet@51911
   168
  Vartab.fold (cons o apsnd snd) (fold (Sign.typ_match thy) (Ts ~~ Us) Vartab.empty) [];
blanchet@51911
   169
blanchet@51860
   170
val exists_subtype_in = Term.exists_subtype o member (op =);
blanchet@51808
   171
blanchet@49342
   172
fun resort_tfree S (TFree (s, _)) = TFree (s, S);
blanchet@49342
   173
blanchet@51845
   174
fun typ_subst_nonatomic inst (T as Type (s, Ts)) =
blanchet@49214
   175
    (case AList.lookup (op =) inst T of
blanchet@51845
   176
      NONE => Type (s, map (typ_subst_nonatomic inst) Ts)
blanchet@49214
   177
    | SOME T' => T')
blanchet@51845
   178
  | typ_subst_nonatomic inst T = the_default T (AList.lookup (op =) inst T);
blanchet@49205
   179
blanchet@49297
   180
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
blanchet@49202
   181
blanchet@52301
   182
fun flat_rec xss =
blanchet@52301
   183
  (* The first line below gives the preferred order. The second line is for compatibility with the
blanchet@52301
   184
     old datatype package: *)
blanchet@52215
   185
(*
blanchet@52301
   186
  flat xss
blanchet@51795
   187
*)
blanchet@52301
   188
  map hd xss @ maps tl xss;
blanchet@51793
   189
blanchet@51829
   190
fun flat_predss_getterss qss fss = maps (op @) (qss ~~ fss);
blanchet@51829
   191
blanchet@51829
   192
fun flat_preds_predsss_gettersss [] [qss] [fss] = flat_predss_getterss qss fss
blanchet@51829
   193
  | flat_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
blanchet@51829
   194
    p :: flat_predss_getterss qss fss @ flat_preds_predsss_gettersss ps qsss fsss;
blanchet@51829
   195
blanchet@52214
   196
fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
blanchet@52214
   197
fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
blanchet@52214
   198
fun mk_uncurried2_fun f xss =
blanchet@52301
   199
  mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat_rec xss);
blanchet@52214
   200
blanchet@49585
   201
fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) =
blanchet@49585
   202
  Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1));
blanchet@49585
   203
blanchet@49585
   204
fun flip_rels lthy n thm =
blanchet@49585
   205
  let
blanchet@49585
   206
    val Rs = Term.add_vars (prop_of thm) [];
blanchet@49585
   207
    val Rs' = rev (drop (length Rs - n) Rs);
blanchet@49585
   208
    val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs';
blanchet@49585
   209
  in
blanchet@49585
   210
    Drule.cterm_instantiate cRs thm
blanchet@49585
   211
  end;
blanchet@49585
   212
blanchet@49536
   213
fun mk_ctor_or_dtor get_T Ts t =
blanchet@49536
   214
  let val Type (_, Ts0) = get_T (fastype_of t) in
blanchet@49536
   215
    Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49536
   216
  end;
blanchet@49536
   217
blanchet@49536
   218
val mk_ctor = mk_ctor_or_dtor range_type;
blanchet@49536
   219
val mk_dtor = mk_ctor_or_dtor domain_type;
blanchet@49536
   220
blanchet@52207
   221
fun mk_co_iter thy fp fpT Cs t =
blanchet@49536
   222
  let
blanchet@52309
   223
    val (binders, body) = strip_type (fastype_of t);
blanchet@52309
   224
    val (f_Cs, prebody) = split_last binders;
blanchet@52207
   225
    val fpT0 = if fp = Least_FP then prebody else body;
blanchet@52207
   226
    val Cs0 = distinct (op =) (map (if fp = Least_FP then body_type else domain_type) f_Cs);
blanchet@52197
   227
    val rho = tvar_subst thy (fpT0 :: Cs0) (fpT :: Cs);
blanchet@49536
   228
  in
blanchet@52170
   229
    Term.subst_TVars rho t
blanchet@49536
   230
  end;
blanchet@49536
   231
blanchet@52207
   232
fun mk_co_iters thy fp fpTs Cs ts0 =
blanchet@51911
   233
  let
blanchet@51911
   234
    val nn = length fpTs;
blanchet@51911
   235
    val (fpTs0, Cs0) =
blanchet@52207
   236
      map ((fp = Greatest_FP ? swap) o dest_funT o snd o strip_typeN nn o fastype_of) ts0
blanchet@51911
   237
      |> split_list;
blanchet@51911
   238
    val rho = tvar_subst thy (fpTs0 @ Cs0) (fpTs @ Cs);
blanchet@51911
   239
  in
blanchet@52170
   240
    map (Term.subst_TVars rho) ts0
blanchet@51911
   241
  end;
blanchet@51827
   242
blanchet@52169
   243
val mk_fp_iter_fun_types = fst o split_last o binder_types o fastype_of;
blanchet@52169
   244
blanchet@52296
   245
fun unzip_recT Cs (T as Type (@{type_name prod}, Ts as [_, U])) =
blanchet@52296
   246
    if member (op =) Cs U then Ts else [T]
blanchet@52216
   247
  | unzip_recT _ T = [T];
blanchet@51827
   248
blanchet@52347
   249
fun mk_map live Ts Us t =
blanchet@52347
   250
  let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last in
blanchet@52347
   251
    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@52347
   252
  end;
blanchet@52347
   253
blanchet@52347
   254
fun mk_rel live Ts Us t =
blanchet@52347
   255
  let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in
blanchet@52347
   256
    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@52347
   257
  end;
blanchet@52347
   258
blanchet@52347
   259
fun build_map lthy build_simple =
blanchet@52347
   260
  let
blanchet@52347
   261
    fun build (TU as (T, U)) =
blanchet@52347
   262
      if T = U then
blanchet@52347
   263
        id_const T
blanchet@52347
   264
      else
blanchet@52347
   265
        (case TU of
blanchet@52347
   266
          (Type (s, Ts), Type (s', Us)) =>
blanchet@52347
   267
          if s = s' then
blanchet@52347
   268
            let
blanchet@52347
   269
              val bnf = the (bnf_of lthy s);
blanchet@52347
   270
              val live = live_of_bnf bnf;
blanchet@52347
   271
              val mapx = mk_map live Ts Us (map_of_bnf bnf);
blanchet@52347
   272
              val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
blanchet@52347
   273
            in Term.list_comb (mapx, map build TUs') end
blanchet@52347
   274
          else
blanchet@52347
   275
            build_simple TU
blanchet@52347
   276
        | _ => build_simple TU);
blanchet@52347
   277
  in build end;
blanchet@52347
   278
blanchet@52347
   279
fun liveness_of_fp_bnf n bnf =
blanchet@52347
   280
  (case T_of_bnf bnf of
blanchet@52347
   281
    Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
blanchet@52347
   282
  | _ => replicate n false);
blanchet@52347
   283
blanchet@52347
   284
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
blanchet@52347
   285
blanchet@52347
   286
fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
blanchet@52347
   287
blanchet@52347
   288
fun merge_type_args (As, As') =
blanchet@52347
   289
  if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
blanchet@52347
   290
blanchet@52347
   291
fun reassoc_conjs thm =
blanchet@52347
   292
  reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
blanchet@52347
   293
  handle THM _ => thm;
blanchet@52347
   294
blanchet@52347
   295
fun type_args_named_constrained_of ((((ncAs, _), _), _), _) = ncAs;
blanchet@52347
   296
fun type_binding_of ((((_, b), _), _), _) = b;
blanchet@52347
   297
fun map_binding_of (((_, (b, _)), _), _) = b;
blanchet@52347
   298
fun rel_binding_of (((_, (_, b)), _), _) = b;
blanchet@52347
   299
fun mixfix_of ((_, mx), _) = mx;
blanchet@52347
   300
fun ctr_specs_of (_, ctr_specs) = ctr_specs;
blanchet@52347
   301
blanchet@52347
   302
fun disc_of ((((disc, _), _), _), _) = disc;
blanchet@52347
   303
fun ctr_of ((((_, ctr), _), _), _) = ctr;
blanchet@52347
   304
fun args_of (((_, args), _), _) = args;
blanchet@52347
   305
fun defaults_of ((_, ds), _) = ds;
blanchet@52347
   306
fun ctr_mixfix_of (_, mx) = mx;
blanchet@52347
   307
blanchet@52347
   308
fun add_nesty_bnf_names Us =
blanchet@52347
   309
  let
blanchet@52347
   310
    fun add (Type (s, Ts)) ss =
blanchet@52347
   311
        let val (needs, ss') = fold_map add Ts ss in
blanchet@52347
   312
          if exists I needs then (true, insert (op =) s ss') else (false, ss')
blanchet@52347
   313
        end
blanchet@52347
   314
      | add T ss = (member (op =) Us T, ss);
blanchet@52347
   315
  in snd oo add end;
blanchet@52347
   316
blanchet@52347
   317
fun nesty_bnfs ctxt ctr_Tsss Us =
blanchet@52347
   318
  map_filter (bnf_of ctxt) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_Tsss []);
blanchet@52347
   319
blanchet@52347
   320
fun indexify proj xs f p = f (find_index (curry (op =) (proj p)) xs) p;
blanchet@52347
   321
blanchet@51846
   322
fun mk_fun_arg_typess n ms = map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type;
blanchet@51846
   323
blanchet@52296
   324
fun mk_iter_fun_arg_typessss Cs ns mss =
blanchet@51885
   325
  mk_fp_iter_fun_types
blanchet@51885
   326
  #> map3 mk_fun_arg_typess ns mss
blanchet@52296
   327
  #> map (map (map (unzip_recT Cs)));
blanchet@51885
   328
blanchet@52335
   329
fun mk_iters_args_types Cs ns mss ctor_iter_fun_Tss lthy =
blanchet@51832
   330
  let
blanchet@52214
   331
    val Css = map2 replicate ns Cs;
blanchet@52335
   332
    val y_Tsss = map3 mk_fun_arg_typess ns mss (map un_fold_of ctor_iter_fun_Tss);
blanchet@52214
   333
    val g_Tss = map2 (fn C => map (fn y_Ts => y_Ts ---> C)) Cs y_Tsss;
blanchet@51832
   334
blanchet@51832
   335
    val ((gss, ysss), lthy) =
blanchet@51832
   336
      lthy
blanchet@51832
   337
      |> mk_Freess "f" g_Tss
blanchet@51832
   338
      ||>> mk_Freesss "x" y_Tsss;
blanchet@52301
   339
blanchet@52301
   340
    val y_Tssss = map (map (map single)) y_Tsss;
blanchet@52214
   341
    val yssss = map (map (map single)) ysss;
blanchet@52214
   342
blanchet@52214
   343
    val z_Tssss =
blanchet@52296
   344
      map3 (fn n => fn ms => map2 (map (unzip_recT Cs) oo dest_tupleT) ms o
blanchet@52335
   345
        dest_sumTN_balanced n o domain_type o co_rec_of) ns mss ctor_iter_fun_Tss;
blanchet@51832
   346
blanchet@52301
   347
    val z_Tsss' = map (map flat_rec) z_Tssss;
blanchet@52215
   348
    val h_Tss = map2 (map2 (curry (op --->))) z_Tsss' Css;
blanchet@51832
   349
blanchet@51832
   350
    val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@52214
   351
    val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
blanchet@52214
   352
    val (zssss_tl, lthy) =
blanchet@52214
   353
      lthy
blanchet@52214
   354
      |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
blanchet@52214
   355
    val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
blanchet@51832
   356
  in
blanchet@52315
   357
    ([(g_Tss, y_Tssss, gss, yssss), (h_Tss, z_Tssss, hss, zssss)], lthy)
blanchet@51832
   358
  end;
blanchet@51832
   359
blanchet@52335
   360
fun mk_coiters_args_types Cs ns mss dtor_coiter_fun_Tss lthy =
blanchet@51829
   361
  let
blanchet@51829
   362
    (*avoid "'a itself" arguments in coiterators and corecursors*)
blanchet@51829
   363
    fun repair_arity [0] = [1]
blanchet@51829
   364
      | repair_arity ms = ms;
blanchet@51829
   365
blanchet@52347
   366
    fun unzip_corecT (T as Type (@{type_name sum}, Ts as [_, U])) =
blanchet@52347
   367
        if member (op =) Cs U then Ts else [T]
blanchet@52347
   368
      | unzip_corecT T = [T];
blanchet@51829
   369
blanchet@51831
   370
    val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@51829
   371
blanchet@52335
   372
    fun mk_types maybe_unzipT get_Ts =
blanchet@51829
   373
      let
blanchet@52335
   374
        val fun_Ts = map get_Ts dtor_coiter_fun_Tss;
blanchet@51829
   375
        val f_sum_prod_Ts = map range_type fun_Ts;
blanchet@51829
   376
        val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
blanchet@51829
   377
        val f_Tsss = map2 (map2 dest_tupleT o repair_arity) mss f_prod_Tss;
blanchet@51889
   378
        val f_Tssss = map2 (fn C => map (map (map (curry (op -->) C) o maybe_unzipT))) Cs f_Tsss;
blanchet@51829
   379
        val q_Tssss =
blanchet@52213
   380
          map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) f_Tssss;
blanchet@51829
   381
        val pf_Tss = map3 flat_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
blanchet@51889
   382
      in (q_Tssss, f_Tssss, (f_sum_prod_Ts, f_Tsss, pf_Tss)) end;
blanchet@51829
   383
blanchet@52335
   384
    val (r_Tssss, g_Tssss, unfold_types) = mk_types single un_fold_of;
blanchet@52335
   385
    val (s_Tssss, h_Tssss, corec_types) = mk_types unzip_corecT co_rec_of;
blanchet@51831
   386
blanchet@52347
   387
    val ((((Free (z, _), cs), pss), gssss), lthy) =
blanchet@51829
   388
      lthy
blanchet@52347
   389
      |> yield_singleton (mk_Frees "z") dummyT
blanchet@52347
   390
      ||>> mk_Frees "a" Cs
blanchet@51829
   391
      ||>> mk_Freess "p" p_Tss
blanchet@51829
   392
      ||>> mk_Freessss "g" g_Tssss;
blanchet@51829
   393
    val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@51829
   394
blanchet@51829
   395
    val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@51829
   396
    val ((sssss, hssss_tl), lthy) =
blanchet@51829
   397
      lthy
blanchet@51829
   398
      |> mk_Freessss "q" s_Tssss
blanchet@51829
   399
      ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@51829
   400
    val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@51831
   401
blanchet@51831
   402
    val cpss = map2 (map o rapp) cs pss;
blanchet@51829
   403
blanchet@52347
   404
    fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
blanchet@52347
   405
blanchet@52347
   406
    fun build_dtor_coiter_arg _ [] [cf] = cf
blanchet@52347
   407
      | build_dtor_coiter_arg T [cq] [cf, cf'] =
blanchet@52347
   408
        mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@52347
   409
          (build_sum_inj Inr_const (fastype_of cf', T) $ cf');
blanchet@52347
   410
blanchet@52347
   411
    fun mk_args qssss fssss (_, f_Tsss, _) =
blanchet@51831
   412
      let
blanchet@51831
   413
        val pfss = map3 flat_preds_predsss_gettersss pss qssss fssss;
blanchet@51831
   414
        val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@51831
   415
        val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@52347
   416
        val cqfsss = map3 (map3 (map3 build_dtor_coiter_arg)) f_Tsss cqssss cfssss;
blanchet@52347
   417
      in (pfss, cqfsss) end;
blanchet@51831
   418
blanchet@52347
   419
    val unfold_args = mk_args rssss gssss unfold_types;
blanchet@52347
   420
    val corec_args = mk_args sssss hssss corec_types;
blanchet@51831
   421
  in
blanchet@52347
   422
    ((z, cs, cpss, [(unfold_args, unfold_types), (corec_args, corec_types)]), lthy)
blanchet@51831
   423
  end;
blanchet@51829
   424
blanchet@52334
   425
fun mk_co_iters_prelims fp fpTs Cs ns mss xtor_co_iterss0 lthy =
blanchet@51903
   426
  let
blanchet@52169
   427
    val thy = Proof_Context.theory_of lthy;
blanchet@52169
   428
blanchet@52335
   429
    val (xtor_co_iter_fun_Tss, xtor_co_iterss) =
blanchet@52329
   430
      map (mk_co_iters thy fp fpTs Cs #> `(mk_fp_iter_fun_types o hd)) (transpose xtor_co_iterss0)
blanchet@52335
   431
      |> apsnd transpose o apfst transpose o split_list;
blanchet@51903
   432
blanchet@52329
   433
    val ((iters_args_types, coiters_args_types), lthy') =
blanchet@52207
   434
      if fp = Least_FP then
blanchet@52335
   435
        mk_iters_args_types Cs ns mss xtor_co_iter_fun_Tss lthy |>> (rpair NONE o SOME)
blanchet@51903
   436
      else
blanchet@52335
   437
        mk_coiters_args_types Cs ns mss xtor_co_iter_fun_Tss lthy |>> (pair NONE o SOME)
blanchet@51903
   438
  in
blanchet@52335
   439
    ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy')
blanchet@51903
   440
  end;
blanchet@51903
   441
blanchet@52298
   442
fun mk_iter_body ctor_iter fss xssss =
blanchet@52298
   443
  Term.list_comb (ctor_iter, map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss);
blanchet@51884
   444
blanchet@51900
   445
fun mk_preds_getterss_join c cps sum_prod_T cqfss =
blanchet@51900
   446
  let val n = length cqfss in
blanchet@51900
   447
    Term.lambda c (mk_IfN sum_prod_T cps
blanchet@51900
   448
      (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)))
blanchet@51900
   449
  end;
blanchet@51886
   450
blanchet@52348
   451
fun mk_coiter_body cs cpss f_sum_prod_Ts cqfsss dtor_coiter =
blanchet@52347
   452
  Term.list_comb (dtor_coiter, map4 mk_preds_getterss_join cs cpss f_sum_prod_Ts cqfsss);
blanchet@51886
   453
blanchet@52327
   454
fun define_co_iters fp fpT Cs binding_specs lthy0 =
blanchet@51897
   455
  let
blanchet@52170
   456
    val thy = Proof_Context.theory_of lthy0;
blanchet@52170
   457
blanchet@52327
   458
    val ((csts, defs), (lthy', lthy)) = lthy0
blanchet@52327
   459
      |> apfst split_list o fold_map (fn (b, spec) =>
blanchet@52327
   460
        Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@52327
   461
        #>> apsnd snd) binding_specs
blanchet@52327
   462
      ||> `Local_Theory.restore;
blanchet@52327
   463
blanchet@52327
   464
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@52327
   465
blanchet@52327
   466
    val csts' = map (mk_co_iter thy fp fpT Cs o Morphism.term phi) csts;
blanchet@52327
   467
    val defs' = map (Morphism.thm phi) defs;
blanchet@52327
   468
  in
blanchet@52327
   469
    ((csts', defs'), lthy')
blanchet@52327
   470
  end;
blanchet@52327
   471
blanchet@52327
   472
fun define_iters iterNs iter_args_typess' mk_binding fpTs Cs ctor_iters lthy =
blanchet@52327
   473
  let
blanchet@51899
   474
    val nn = length fpTs;
blanchet@51899
   475
blanchet@52320
   476
    val fpT_to_C as Type (_, [fpT, _]) = snd (strip_typeN nn (fastype_of (hd ctor_iters)));
blanchet@51897
   477
blanchet@52320
   478
    fun generate_iter suf (f_Tss, _, fss, xssss) ctor_iter =
blanchet@51897
   479
      let
blanchet@51899
   480
        val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@52309
   481
        val b = mk_binding suf;
blanchet@51897
   482
        val spec =
blanchet@52309
   483
          mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of b, res_T)),
blanchet@52298
   484
            mk_iter_body ctor_iter fss xssss);
blanchet@52309
   485
      in (b, spec) end;
blanchet@51897
   486
  in
blanchet@52327
   487
    define_co_iters Least_FP fpT Cs (map3 generate_iter iterNs iter_args_typess' ctor_iters) lthy
blanchet@51897
   488
  end;
blanchet@51897
   489
blanchet@52347
   490
fun define_coiters coiterNs (_, cs, cpss, coiter_args_typess') mk_binding fpTs Cs dtor_coiters
blanchet@52347
   491
    lthy =
blanchet@51897
   492
  let
blanchet@51899
   493
    val nn = length fpTs;
blanchet@51899
   494
blanchet@52326
   495
    val C_to_fpT as Type (_, [_, fpT]) = snd (strip_typeN nn (fastype_of (hd dtor_coiters)));
blanchet@51897
   496
blanchet@52348
   497
    fun generate_coiter suf ((pfss, cqfsss), (f_sum_prod_Ts, _, pf_Tss)) dtor_coiter =
blanchet@51897
   498
      let
blanchet@51899
   499
        val res_T = fold_rev (curry (op --->)) pf_Tss C_to_fpT;
blanchet@52309
   500
        val b = mk_binding suf;
blanchet@51897
   501
        val spec =
blanchet@52309
   502
          mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of b, res_T)),
blanchet@52348
   503
            mk_coiter_body cs cpss f_sum_prod_Ts cqfsss dtor_coiter);
blanchet@52309
   504
      in (b, spec) end;
blanchet@51897
   505
  in
blanchet@52327
   506
    define_co_iters Greatest_FP fpT Cs
blanchet@52327
   507
      (map3 generate_coiter coiterNs coiter_args_typess' dtor_coiters) lthy
blanchet@52320
   508
  end;
blanchet@51897
   509
blanchet@52346
   510
fun derive_induct_iters_thms_for_types pre_bnfs [fold_args_types, rec_args_types] [ctor_induct]
blanchet@52346
   511
    ctor_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss iterss iter_defss
blanchet@52346
   512
    lthy =
blanchet@51808
   513
  let
blanchet@52340
   514
    val iterss' = transpose iterss;
blanchet@52340
   515
    val iter_defss' = transpose iter_defss;
blanchet@52340
   516
blanchet@52340
   517
    val [folds, recs] = iterss';
blanchet@52340
   518
    val [fold_defs, rec_defs] = iter_defss';
blanchet@52340
   519
blanchet@51827
   520
    val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
blanchet@51827
   521
blanchet@51815
   522
    val nn = length pre_bnfs;
blanchet@51827
   523
    val ns = map length ctr_Tsss;
blanchet@51827
   524
    val mss = map (map length) ctr_Tsss;
blanchet@51815
   525
blanchet@51808
   526
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51808
   527
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@51830
   528
    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
blanchet@51808
   529
    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
blanchet@51810
   530
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@51808
   531
blanchet@51816
   532
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   533
blanchet@51832
   534
    val ((((ps, ps'), xsss), us'), names_lthy) =
blanchet@52315
   535
      lthy
blanchet@51808
   536
      |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@51827
   537
      ||>> mk_Freesss "x" ctr_Tsss
blanchet@51816
   538
      ||>> Variable.variant_fixes fp_b_names;
blanchet@51808
   539
blanchet@51808
   540
    val us = map2 (curry Free) us' fpTs;
blanchet@51808
   541
blanchet@51808
   542
    fun mk_sets_nested bnf =
blanchet@51808
   543
      let
blanchet@51808
   544
        val Type (T_name, Us) = T_of_bnf bnf;
blanchet@51808
   545
        val lives = lives_of_bnf bnf;
blanchet@51808
   546
        val sets = sets_of_bnf bnf;
blanchet@51808
   547
        fun mk_set U =
blanchet@51808
   548
          (case find_index (curry (op =) U) lives of
blanchet@51808
   549
            ~1 => Term.dummy
blanchet@51808
   550
          | i => nth sets i);
blanchet@51808
   551
      in
blanchet@51808
   552
        (T_name, map mk_set Us)
blanchet@51808
   553
      end;
blanchet@51808
   554
blanchet@51808
   555
    val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@51808
   556
blanchet@51808
   557
    val (induct_thms, induct_thm) =
blanchet@51808
   558
      let
blanchet@51808
   559
        fun mk_set Ts t =
blanchet@51808
   560
          let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@51808
   561
            Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@51808
   562
          end;
blanchet@51808
   563
blanchet@52310
   564
        fun mk_raw_prem_prems _ (x as Free (_, Type _)) (X as TFree _) =
blanchet@52310
   565
            [([], (find_index (curry (op =) X) Xs + 1, x))]
blanchet@52310
   566
          | mk_raw_prem_prems names_lthy (x as Free (s, Type (T_name, Ts0))) (Type (_, Xs_Ts0)) =
blanchet@52310
   567
            (case AList.lookup (op =) setss_nested T_name of
blanchet@52310
   568
              NONE => []
blanchet@52310
   569
            | SOME raw_sets0 =>
blanchet@52310
   570
              let
blanchet@52310
   571
                val (Xs_Ts, (Ts, raw_sets)) =
blanchet@52310
   572
                  filter (exists_subtype_in Xs o fst) (Xs_Ts0 ~~ (Ts0 ~~ raw_sets0))
blanchet@52310
   573
                  |> split_list ||> split_list;
blanchet@52310
   574
                val sets = map (mk_set Ts0) raw_sets;
blanchet@52310
   575
                val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@52310
   576
                val xysets = map (pair x) (ys ~~ sets);
blanchet@52310
   577
                val ppremss = map2 (mk_raw_prem_prems names_lthy') ys Xs_Ts;
blanchet@52310
   578
              in
blanchet@52310
   579
                flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@52310
   580
              end)
blanchet@52310
   581
          | mk_raw_prem_prems _ _ _ = [];
blanchet@51808
   582
blanchet@51808
   583
        fun close_prem_prem xs t =
blanchet@51808
   584
          fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@51808
   585
            (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@51808
   586
blanchet@51808
   587
        fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@51808
   588
          close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@51808
   589
              HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@51808
   590
            HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@51808
   591
blanchet@52310
   592
        fun mk_raw_prem phi ctr ctr_Ts ctrXs_Ts =
blanchet@51808
   593
          let
blanchet@51808
   594
            val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@52310
   595
            val pprems = flat (map2 (mk_raw_prem_prems names_lthy') xs ctrXs_Ts);
blanchet@51808
   596
          in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@51808
   597
blanchet@51808
   598
        fun mk_prem (xs, raw_pprems, concl) =
blanchet@51808
   599
          fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@51808
   600
blanchet@52310
   601
        val raw_premss = map4 (map3 o mk_raw_prem) ps ctrss ctr_Tsss ctrXs_Tsss;
blanchet@51808
   602
blanchet@51808
   603
        val goal =
blanchet@51808
   604
          Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@51808
   605
            HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@51808
   606
blanchet@51808
   607
        val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@51808
   608
blanchet@51814
   609
        val ctor_induct' = ctor_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@51808
   610
blanchet@51808
   611
        val thm =
blanchet@51808
   612
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51808
   613
            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
blanchet@51808
   614
              pre_set_defss)
blanchet@51808
   615
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51808
   616
          |> Thm.close_derivation;
blanchet@51808
   617
      in
blanchet@51808
   618
        `(conj_dests nn) thm
blanchet@51808
   619
      end;
blanchet@51808
   620
blanchet@51808
   621
    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@52305
   622
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@51808
   623
blanchet@52305
   624
    val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@52305
   625
blanchet@52306
   626
    fun mk_iter_thmss (_, x_Tssss, fss, _) iters iter_defs ctor_iter_thms =
blanchet@51808
   627
      let
blanchet@52305
   628
        val fiters = map (lists_bmoc fss) iters;
blanchet@51808
   629
blanchet@51843
   630
        fun mk_goal fss fiter xctr f xs fxs =
blanchet@51808
   631
          fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@51843
   632
            (mk_Trueprop_eq (fiter $ xctr, Term.list_comb (f, fxs)));
blanchet@51808
   633
blanchet@52302
   634
        fun maybe_tick (T, U) u f =
blanchet@52302
   635
          if try (fst o HOLogic.dest_prodT) U = SOME T then
blanchet@52302
   636
            Term.lambda u (HOLogic.mk_prod (u, f $ u))
blanchet@52302
   637
          else
blanchet@52302
   638
            f;
blanchet@51808
   639
blanchet@52305
   640
        fun unzip_iters (x as Free (_, T)) =
blanchet@52301
   641
          map (fn U => if U = T then x else
blanchet@52303
   642
            build_map lthy (indexify (perhaps (try (snd o HOLogic.dest_prodT)) o snd) Cs
blanchet@52305
   643
              (fn kk => fn TU => maybe_tick TU (nth us kk) (nth fiters kk))) (T, U) $ x);
blanchet@52301
   644
blanchet@52305
   645
        val fxsss = map2 (map2 (flat_rec oo map2 unzip_iters)) xsss x_Tssss;
blanchet@51808
   646
blanchet@52306
   647
        val goalss = map5 (map4 o mk_goal fss) fiters xctrss fss xsss fxsss;
blanchet@51808
   648
blanchet@52305
   649
        val tacss =
blanchet@52305
   650
          map2 (map o mk_iter_tac pre_map_defs (nested_map_ids'' @ nesting_map_ids'') iter_defs)
blanchet@52305
   651
            ctor_iter_thms ctr_defss;
blanchet@51808
   652
blanchet@51808
   653
        fun prove goal tac =
blanchet@51808
   654
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51808
   655
          |> Thm.close_derivation;
blanchet@51808
   656
      in
blanchet@52305
   657
        map2 (map2 prove) goalss tacss
blanchet@51808
   658
      end;
blanchet@51808
   659
blanchet@52340
   660
    val fold_thmss = mk_iter_thmss fold_args_types folds fold_defs (map un_fold_of ctor_iter_thmss);
blanchet@52340
   661
    val rec_thmss = mk_iter_thmss rec_args_types recs rec_defs (map co_rec_of ctor_iter_thmss);
blanchet@51808
   662
  in
blanchet@52345
   663
    ((induct_thms, induct_thm, [induct_case_names_attr]),
blanchet@51808
   664
     (fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
blanchet@51808
   665
  end;
blanchet@51808
   666
blanchet@52347
   667
fun derive_coinduct_coiters_thms_for_types pre_bnfs (z, cs, cpss,
blanchet@52347
   668
      [(unfold_args as (pgss, crgsss), _), (corec_args as (phss, cshsss), _)])
blanchet@52344
   669
    dtor_coinducts dtor_ctors dtor_coiter_thmss nesting_bnfs nested_bnfs fpTs Cs As kss mss ns
blanchet@52344
   670
    ctr_defss ctr_sugars coiterss coiter_defss lthy =
blanchet@51810
   671
  let
blanchet@52339
   672
    val coiterss' = transpose coiterss;
blanchet@52339
   673
    val coiter_defss' = transpose coiter_defss;
blanchet@52339
   674
blanchet@52339
   675
    val [unfold_defs, corec_defs] = coiter_defss';
blanchet@52338
   676
blanchet@51815
   677
    val nn = length pre_bnfs;
blanchet@51815
   678
blanchet@51810
   679
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51810
   680
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@51830
   681
    val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
blanchet@51830
   682
    val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@51810
   683
    val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
blanchet@51810
   684
    val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
blanchet@51810
   685
blanchet@51816
   686
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   687
blanchet@51840
   688
    val ctrss = map (map (mk_ctr As) o #ctrs) ctr_sugars;
blanchet@51840
   689
    val discss = map (map (mk_disc_or_sel As) o #discs) ctr_sugars;
blanchet@51840
   690
    val selsss = map (map (map (mk_disc_or_sel As)) o #selss) ctr_sugars;
blanchet@51840
   691
    val exhausts = map #exhaust ctr_sugars;
blanchet@51840
   692
    val disc_thmsss = map #disc_thmss ctr_sugars;
blanchet@51840
   693
    val discIss = map #discIs ctr_sugars;
blanchet@51840
   694
    val sel_thmsss = map #sel_thmss ctr_sugars;
blanchet@51810
   695
blanchet@51810
   696
    val (((rs, us'), vs'), names_lthy) =
blanchet@52341
   697
      lthy
blanchet@51810
   698
      |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@51816
   699
      ||>> Variable.variant_fixes fp_b_names
blanchet@51816
   700
      ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@51810
   701
blanchet@51810
   702
    val us = map2 (curry Free) us' fpTs;
blanchet@51810
   703
    val udiscss = map2 (map o rapp) us discss;
blanchet@51810
   704
    val uselsss = map2 (map o map o rapp) us selsss;
blanchet@51810
   705
blanchet@51810
   706
    val vs = map2 (curry Free) vs' fpTs;
blanchet@51810
   707
    val vdiscss = map2 (map o rapp) vs discss;
blanchet@51810
   708
    val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@51810
   709
blanchet@52345
   710
    val coinduct_thms_pairs =
blanchet@51810
   711
      let
blanchet@51810
   712
        val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@51810
   713
        val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@51810
   714
        val strong_rs =
blanchet@51810
   715
          map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@51810
   716
            fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@51810
   717
blanchet@52347
   718
        (* TODO: generalize (cf. "build_map") *)
blanchet@51810
   719
        fun build_rel rs' T =
blanchet@51810
   720
          (case find_index (curry (op =) T) fpTs of
blanchet@51810
   721
            ~1 =>
blanchet@51856
   722
            if exists_subtype_in fpTs T then
blanchet@51856
   723
              let
blanchet@51856
   724
                val Type (s, Ts) = T
blanchet@51856
   725
                val bnf = the (bnf_of lthy s);
blanchet@51856
   726
                val live = live_of_bnf bnf;
blanchet@51856
   727
                val rel = mk_rel live Ts Ts (rel_of_bnf bnf);
blanchet@51856
   728
                val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel)));
blanchet@51856
   729
              in Term.list_comb (rel, map (build_rel rs') Ts') end
blanchet@51856
   730
            else
blanchet@51856
   731
              HOLogic.eq_const T
blanchet@51810
   732
          | kk => nth rs' kk);
blanchet@51810
   733
blanchet@51856
   734
        fun build_rel_app rs' usel vsel = fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
blanchet@51810
   735
blanchet@51810
   736
        fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
blanchet@51810
   737
          (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@51810
   738
          (if null usels then
blanchet@51810
   739
             []
blanchet@51810
   740
           else
blanchet@51810
   741
             [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@51810
   742
                Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
blanchet@51810
   743
blanchet@51810
   744
        fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
blanchet@51810
   745
          Library.foldr1 HOLogic.mk_conj
blanchet@51810
   746
            (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
blanchet@51810
   747
          handle List.Empty => @{term True};
blanchet@51810
   748
blanchet@51810
   749
        fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
blanchet@51810
   750
          fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@51810
   751
            HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
blanchet@51810
   752
blanchet@51810
   753
        val concl =
blanchet@51810
   754
          HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@51810
   755
            (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@51810
   756
               uvrs us vs));
blanchet@51810
   757
blanchet@51810
   758
        fun mk_goal rs' =
blanchet@51810
   759
          Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
blanchet@51810
   760
            concl);
blanchet@51810
   761
blanchet@52345
   762
        val goals = map mk_goal [rs, strong_rs];
blanchet@51810
   763
blanchet@51810
   764
        fun prove dtor_coinduct' goal =
blanchet@51810
   765
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51810
   766
            mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
blanchet@51819
   767
              exhausts ctr_defss disc_thmsss sel_thmsss)
blanchet@51810
   768
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   769
          |> Thm.close_derivation;
blanchet@51810
   770
blanchet@51810
   771
        fun postproc nn thm =
blanchet@51810
   772
          Thm.permute_prems 0 nn
blanchet@51828
   773
            (if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@51810
   774
          |> Drule.zero_var_indexes
blanchet@51810
   775
          |> `(conj_dests nn);
blanchet@51810
   776
      in
blanchet@52345
   777
        map2 (postproc nn oo prove) dtor_coinducts goals
blanchet@51810
   778
      end;
blanchet@51810
   779
blanchet@51810
   780
    fun mk_coinduct_concls ms discs ctrs =
blanchet@51810
   781
      let
blanchet@51810
   782
        fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51810
   783
        fun mk_ctr_concl 0 _ = []
blanchet@51810
   784
          | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51810
   785
        val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51810
   786
        val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51810
   787
      in
blanchet@51810
   788
        flat (map2 append disc_concls ctr_concls)
blanchet@51810
   789
      end;
blanchet@51810
   790
blanchet@51816
   791
    val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51810
   792
    val coinduct_conclss =
blanchet@51810
   793
      map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51810
   794
blanchet@51810
   795
    fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@51810
   796
blanchet@52339
   797
    val fcoiterss' as [gunfolds, hcorecs] =
blanchet@52347
   798
      map2 (fn (pfss, _) => map (lists_bmoc pfss)) [unfold_args, corec_args] coiterss';
blanchet@51810
   799
blanchet@51810
   800
    val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@51810
   801
      let
blanchet@51843
   802
        fun mk_goal pfss c cps fcoiter n k ctr m cfs' =
blanchet@51810
   803
          fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@51810
   804
            (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@51843
   805
               mk_Trueprop_eq (fcoiter $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@51810
   806
blanchet@52347
   807
        fun build_coiter fcoiters maybe_tack (T, U) =
blanchet@52347
   808
          if T = U then
blanchet@52347
   809
             id_const T
blanchet@52347
   810
          else
blanchet@52347
   811
            (case find_index (curry (op =) U) fpTs of
blanchet@52347
   812
              ~1 => build_map lthy (build_coiter fcoiters maybe_tack) (T, U)
blanchet@52347
   813
            | kk => maybe_tack (nth cs kk, nth us kk) (nth fcoiters kk));
blanchet@52347
   814
 
blanchet@52347
   815
        fun mk_U maybe_mk_sumT =
blanchet@52347
   816
          typ_subst_nonatomic (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@52347
   817
blanchet@52347
   818
        fun tack z_name (c, u) f =
blanchet@52347
   819
          let val z = Free (z_name, mk_sumT (fastype_of u, fastype_of c)) in
blanchet@52347
   820
            Term.lambda z (mk_sum_case (Term.lambda u u, Term.lambda c (f $ c)) $ z)
blanchet@52347
   821
          end;
blanchet@51810
   822
blanchet@52347
   823
        fun intr_coiters fcoiters maybe_mk_sumT maybe_tack cqf =
blanchet@52347
   824
          let val T = fastype_of cqf in
blanchet@52347
   825
            if exists_subtype_in Cs T then
blanchet@52347
   826
              build_coiter fcoiters maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf
blanchet@52347
   827
            else
blanchet@52347
   828
              cqf
blanchet@52347
   829
          end;
blanchet@51810
   830
blanchet@52347
   831
        val crgsss' =
blanchet@52347
   832
          (fn fcoiters => fn (_, cqfsss) =>
blanchet@52347
   833
              map (map (map (intr_coiters fcoiters (K I) (K I)))) cqfsss)
blanchet@52347
   834
            (un_fold_of fcoiterss') unfold_args;
blanchet@52347
   835
        val cshsss' =
blanchet@52347
   836
          (fn fcoiters => fn (_, cqfsss) =>
blanchet@52347
   837
              map (map (map (intr_coiters fcoiters (curry mk_sumT) (tack z)))) cqfsss)
blanchet@52347
   838
            (co_rec_of fcoiterss') corec_args;
blanchet@52347
   839
blanchet@52347
   840
(*###
blanchet@52347
   841
        val [crgsss', cshsss'] =
blanchet@52339
   842
          map2 (fn fcoiters => fn (_, cqssss, cfssss) =>
blanchet@52339
   843
              map2 (map2 (map2 (intr_coiters fcoiters))) cqssss cfssss)
blanchet@52339
   844
            fcoiterss' [unfold_args, corec_args];
blanchet@52347
   845
*)
blanchet@51810
   846
blanchet@52347
   847
        val unfold_goalss = map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss';
blanchet@52347
   848
        val corec_goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss';
blanchet@51810
   849
blanchet@51810
   850
        fun mk_map_if_distrib bnf =
blanchet@51810
   851
          let
blanchet@51810
   852
            val mapx = map_of_bnf bnf;
blanchet@51810
   853
            val live = live_of_bnf bnf;
blanchet@51810
   854
            val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
blanchet@51810
   855
            val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
blanchet@51810
   856
            val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
blanchet@51810
   857
          in
blanchet@51810
   858
            Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
blanchet@51810
   859
              @{thm if_distrib}
blanchet@51810
   860
          end;
blanchet@51810
   861
blanchet@51810
   862
        val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
blanchet@51810
   863
blanchet@51810
   864
        val unfold_tacss =
blanchet@52347
   865
          map3 (map oo mk_coiter_tac unfold_defs [] nesting_map_ids'' [])
blanchet@52340
   866
            (map un_fold_of dtor_coiter_thmss) pre_map_defs ctr_defss;
blanchet@51810
   867
        val corec_tacss =
blanchet@52347
   868
          map3 (map oo mk_coiter_tac corec_defs nested_map_comp's
blanchet@51810
   869
              (nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs)
blanchet@52340
   870
            (map co_rec_of dtor_coiter_thmss) pre_map_defs ctr_defss;
blanchet@51810
   871
blanchet@51810
   872
        fun prove goal tac =
blanchet@51815
   873
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51815
   874
          |> Thm.close_derivation;
blanchet@51810
   875
blanchet@51810
   876
        val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@52347
   877
        val corec_thmss =
blanchet@52347
   878
          map2 (map2 prove) corec_goalss corec_tacss
blanchet@52347
   879
          |> map (map (unfold_thms lthy @{thms sum_case_if}));
blanchet@52347
   880
blanchet@52347
   881
        val unfold_safesss = map2 (map2 (map2 (curry (op =)))) crgsss' crgsss;
blanchet@52347
   882
        val corec_safesss = map2 (map2 (map2 (curry (op =)))) cshsss' cshsss;
blanchet@52347
   883
blanchet@51810
   884
        val filter_safesss =
blanchet@51810
   885
          map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@52347
   886
            curry (op ~~));
blanchet@51810
   887
blanchet@52347
   888
        val safe_unfold_thmss = filter_safesss unfold_safesss unfold_thmss;
blanchet@52347
   889
        val safe_corec_thmss = filter_safesss corec_safesss corec_thmss;
blanchet@51810
   890
      in
blanchet@51810
   891
        (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@51810
   892
      end;
blanchet@51810
   893
blanchet@51810
   894
    val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@51810
   895
      let
blanchet@51843
   896
        fun mk_goal c cps fcoiter n k disc =
blanchet@51843
   897
          mk_Trueprop_eq (disc $ (fcoiter $ c),
blanchet@51810
   898
            if n = 1 then @{const True}
blanchet@51810
   899
            else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@51810
   900
blanchet@51810
   901
        val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@51810
   902
        val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@51810
   903
blanchet@51828
   904
        fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@51810
   905
blanchet@51810
   906
        val case_splitss' = map (map mk_case_split') cpss;
blanchet@51810
   907
blanchet@51810
   908
        val unfold_tacss =
blanchet@51843
   909
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@51810
   910
        val corec_tacss =
blanchet@51843
   911
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@51810
   912
blanchet@51810
   913
        fun prove goal tac =
blanchet@51810
   914
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51829
   915
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   916
          |> Thm.close_derivation;
blanchet@51810
   917
blanchet@51810
   918
        fun proves [_] [_] = []
blanchet@51810
   919
          | proves goals tacs = map2 prove goals tacs;
blanchet@51810
   920
      in
blanchet@51828
   921
        (map2 proves unfold_goalss unfold_tacss, map2 proves corec_goalss corec_tacss)
blanchet@51810
   922
      end;
blanchet@51810
   923
blanchet@51810
   924
    val is_triv_discI = is_triv_implies orf is_concl_refl;
blanchet@51810
   925
blanchet@51843
   926
    fun mk_disc_coiter_thms coiters discIs =
blanchet@51843
   927
      map (op RS) (filter_out (is_triv_discI o snd) (coiters ~~ discIs));
blanchet@51810
   928
blanchet@51843
   929
    val disc_unfold_thmss = map2 mk_disc_coiter_thms unfold_thmss discIss;
blanchet@51843
   930
    val disc_corec_thmss = map2 mk_disc_coiter_thms corec_thmss discIss;
blanchet@51810
   931
blanchet@51843
   932
    fun mk_sel_coiter_thm coiter_thm sel sel_thm =
blanchet@51810
   933
      let
blanchet@51810
   934
        val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@51810
   935
        val arg_cong' =
blanchet@51810
   936
          Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@51810
   937
            [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@51810
   938
          |> Thm.varifyT_global;
blanchet@51810
   939
        val sel_thm' = sel_thm RSN (2, trans);
blanchet@51810
   940
      in
blanchet@51843
   941
        coiter_thm RS arg_cong' RS sel_thm'
blanchet@51810
   942
      end;
blanchet@51810
   943
blanchet@52321
   944
    fun mk_sel_coiter_thms coiter_thmss =
blanchet@52321
   945
      map3 (map3 (map2 o mk_sel_coiter_thm)) coiter_thmss selsss sel_thmsss |> map flat;
blanchet@51810
   946
blanchet@51843
   947
    val sel_unfold_thmss = mk_sel_coiter_thms unfold_thmss;
blanchet@51843
   948
    val sel_corec_thmss = mk_sel_coiter_thms corec_thmss;
blanchet@51810
   949
blanchet@51810
   950
    val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51810
   951
    val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51810
   952
    val coinduct_case_concl_attrs =
blanchet@51810
   953
      map2 (fn casex => fn concls =>
blanchet@51810
   954
          Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51810
   955
        coinduct_cases coinduct_conclss;
blanchet@51810
   956
    val coinduct_case_attrs =
blanchet@51810
   957
      coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51810
   958
  in
blanchet@52345
   959
    ((coinduct_thms_pairs, coinduct_case_attrs),
blanchet@51810
   960
     (unfold_thmss, corec_thmss, []),
blanchet@51810
   961
     (safe_unfold_thmss, safe_corec_thmss),
blanchet@51810
   962
     (disc_unfold_thmss, disc_corec_thmss, simp_attrs),
blanchet@51810
   963
     (disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs),
blanchet@51810
   964
     (sel_unfold_thmss, sel_corec_thmss, simp_attrs))
blanchet@51810
   965
  end;
blanchet@51810
   966
blanchet@52207
   967
fun define_co_datatypes prepare_constraint prepare_typ prepare_term fp construct_fp
blanchet@49633
   968
    (wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 =
blanchet@49112
   969
  let
blanchet@49298
   970
    (* TODO: sanity checks on arguments *)
blanchet@49298
   971
blanchet@52207
   972
    val _ = if fp = Greatest_FP andalso no_dests then
blanchet@52207
   973
        error "Cannot define destructor-less codatatypes"
blanchet@52207
   974
      else
blanchet@52207
   975
        ();
blanchet@49278
   976
blanchet@49633
   977
    fun qualify mandatory fp_b_name =
blanchet@49633
   978
      Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
blanchet@49633
   979
blanchet@49367
   980
    val nn = length specs;
blanchet@49361
   981
    val fp_bs = map type_binding_of specs;
blanchet@49498
   982
    val fp_b_names = map Binding.name_of fp_bs;
blanchet@49498
   983
    val fp_common_name = mk_common_name fp_b_names;
blanchet@51758
   984
    val map_bs = map map_binding_of specs;
blanchet@51767
   985
    val rel_bs = map rel_binding_of specs;
blanchet@49298
   986
blanchet@51758
   987
    fun prepare_type_arg (_, (ty, c)) =
blanchet@49298
   988
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
   989
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
   990
      end;
blanchet@49298
   991
blanchet@51758
   992
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of) specs;
blanchet@49298
   993
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@49298
   994
    val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
blanchet@51758
   995
    val set_bss = map (map fst o type_args_named_constrained_of) specs;
blanchet@49119
   996
blanchet@49585
   997
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
   998
      no_defs_lthy0
blanchet@49298
   999
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@49585
  1000
      |> mk_TFrees (length unsorted_As)
blanchet@49585
  1001
      ||>> mk_TFrees nn
blanchet@51858
  1002
      ||>> variant_tfrees fp_b_names;
blanchet@49119
  1003
blanchet@52195
  1004
    (* TODO: Cleaner handling of fake contexts, without "background_theory". The case where the new
blanchet@52195
  1005
       type is defined in a locale and shadows an existing global type is currently not handled. *)
blanchet@51768
  1006
blanchet@51769
  1007
    fun add_fake_type spec =
blanchet@51768
  1008
      Sign.add_type no_defs_lthy (type_binding_of spec,
blanchet@51769
  1009
        length (type_args_named_constrained_of spec), mixfix_of spec);
blanchet@51768
  1010
blanchet@51769
  1011
    val fake_thy = Theory.copy #> fold add_fake_type specs;
blanchet@49298
  1012
    val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
blanchet@49119
  1013
blanchet@49182
  1014
    fun mk_fake_T b =
blanchet@49121
  1015
      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
blanchet@49298
  1016
        unsorted_As);
blanchet@49121
  1017
blanchet@49302
  1018
    val fake_Ts = map mk_fake_T fp_bs;
blanchet@49121
  1019
blanchet@49181
  1020
    val mixfixes = map mixfix_of specs;
blanchet@49119
  1021
blanchet@49302
  1022
    val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
  1023
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
  1024
blanchet@49121
  1025
    val ctr_specss = map ctr_specs_of specs;
blanchet@49119
  1026
blanchet@49336
  1027
    val disc_bindingss = map (map disc_of) ctr_specss;
blanchet@49336
  1028
    val ctr_bindingss =
blanchet@49633
  1029
      map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss;
blanchet@49121
  1030
    val ctr_argsss = map (map args_of) ctr_specss;
blanchet@49181
  1031
    val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
blanchet@49119
  1032
blanchet@49336
  1033
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
  1034
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@49286
  1035
    val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
blanchet@49286
  1036
blanchet@49308
  1037
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
  1038
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@49298
  1039
blanchet@49298
  1040
    val _ = (case duplicates (op =) unsorted_As of [] => ()
blanchet@49298
  1041
      | A :: _ => error ("Duplicate type parameter " ^
blanchet@49298
  1042
          quote (Syntax.string_of_typ no_defs_lthy A)));
blanchet@49298
  1043
blanchet@49183
  1044
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@49298
  1045
    val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
blanchet@49165
  1046
        [] => ()
blanchet@49342
  1047
      | A' :: _ => error ("Extra type variable on right-hand side: " ^
blanchet@49204
  1048
          quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
blanchet@49165
  1049
blanchet@49591
  1050
    fun eq_fpT_check (T as Type (s, Us)) (Type (s', Us')) =
blanchet@49146
  1051
        s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
blanchet@49146
  1052
          quote (Syntax.string_of_typ fake_lthy T)))
blanchet@49591
  1053
      | eq_fpT_check _ _ = false;
blanchet@49146
  1054
blanchet@49204
  1055
    fun freeze_fp (T as Type (s, Us)) =
blanchet@49591
  1056
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@49591
  1057
          ~1 => Type (s, map freeze_fp Us)
blanchet@49591
  1058
        | kk => nth Xs kk)
blanchet@49204
  1059
      | freeze_fp T = T;
blanchet@49121
  1060
blanchet@52310
  1061
    val ctrXs_Tsss = map (map (map freeze_fp)) fake_ctr_Tsss;
blanchet@52310
  1062
    val ctrXs_sum_prod_Ts = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctrXs_Tsss;
blanchet@49119
  1063
blanchet@49298
  1064
    val fp_eqs =
blanchet@52310
  1065
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctrXs_sum_prod_Ts;
blanchet@49121
  1066
blanchet@51839
  1067
    val (pre_bnfs, (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0, dtors = dtors0,
blanchet@52344
  1068
           xtor_co_iterss = xtor_co_iterss0, xtor_co_inducts, dtor_ctors, ctor_dtors, ctor_injects,
blanchet@52344
  1069
           xtor_map_thms, xtor_set_thmss, xtor_rel_thms, xtor_co_iter_thmss, ...}, lthy)) =
blanchet@51868
  1070
      fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As) fp_eqs
blanchet@51868
  1071
        no_defs_lthy0;
blanchet@49585
  1072
blanchet@49585
  1073
    val timer = time (Timer.startRealTimer ());
blanchet@49121
  1074
blanchet@52310
  1075
    val nesting_bnfs = nesty_bnfs lthy ctrXs_Tsss As;
blanchet@52310
  1076
    val nested_bnfs = nesty_bnfs lthy ctrXs_Tsss Xs;
blanchet@49226
  1077
blanchet@49585
  1078
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
  1079
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
  1080
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@51830
  1081
    val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
blanchet@51766
  1082
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@49585
  1083
blanchet@49585
  1084
    val live = live_of_bnf any_fp_bnf;
blanchet@49585
  1085
blanchet@49585
  1086
    val Bs =
blanchet@49585
  1087
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@49585
  1088
        (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
blanchet@49585
  1089
blanchet@49585
  1090
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
  1091
blanchet@49501
  1092
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
  1093
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
  1094
blanchet@49501
  1095
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
  1096
blanchet@51780
  1097
    fun massage_simple_notes base =
blanchet@51780
  1098
      filter_out (null o #2)
blanchet@51780
  1099
      #> map (fn (thmN, thms, attrs) =>
blanchet@51780
  1100
        ((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
  1101
blanchet@51780
  1102
    val massage_multi_notes =
blanchet@51780
  1103
      maps (fn (thmN, thmss, attrs) =>
blanchet@51780
  1104
        if forall null thmss then
blanchet@51780
  1105
          []
blanchet@51780
  1106
        else
blanchet@51780
  1107
          map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@52311
  1108
              ((qualify true fp_b_name (Binding.name thmN), attrs T_name), [(thms, [])]))
blanchet@52311
  1109
            fp_b_names fpTs thmss);
blanchet@51780
  1110
blanchet@52310
  1111
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctrXs_Tsss;
blanchet@49203
  1112
    val ns = map length ctr_Tsss;
blanchet@49212
  1113
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
  1114
    val mss = map (map length) ctr_Tsss;
blanchet@49203
  1115
blanchet@52334
  1116
    val ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy) =
blanchet@52334
  1117
      mk_co_iters_prelims fp fpTs Cs ns mss xtor_co_iterss0 lthy;
blanchet@49210
  1118
blanchet@52328
  1119
    fun define_ctrs_case_for_type ((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor),
blanchet@52345
  1120
            xtor_co_iters), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
blanchet@52345
  1121
          pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings),
blanchet@52345
  1122
        ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
  1123
      let
blanchet@49498
  1124
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
  1125
blanchet@49501
  1126
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
  1127
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
  1128
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
  1129
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
  1130
blanchet@49593
  1131
        val (((((w, fs), xss), yss), u'), names_lthy) =
blanchet@49204
  1132
          no_defs_lthy
blanchet@49501
  1133
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49176
  1134
          ||>> mk_Frees "f" case_Ts
blanchet@49370
  1135
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
  1136
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
  1137
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
  1138
blanchet@49498
  1139
        val u = Free (u', fpT);
blanchet@49121
  1140
blanchet@49585
  1141
        val tuple_xs = map HOLogic.mk_tuple xss;
blanchet@49585
  1142
        val tuple_ys = map HOLogic.mk_tuple yss;
blanchet@49585
  1143
blanchet@49129
  1144
        val ctr_rhss =
blanchet@49585
  1145
          map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
blanchet@49585
  1146
            mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
blanchet@49121
  1147
blanchet@49633
  1148
        val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b);
blanchet@49129
  1149
blanchet@49134
  1150
        val case_rhs =
blanchet@49498
  1151
          fold_rev Term.lambda (fs @ [u])
blanchet@49501
  1152
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
blanchet@49129
  1153
blanchet@49201
  1154
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
  1155
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
  1156
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
  1157
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
  1158
          ||> `Local_Theory.restore;
blanchet@49121
  1159
blanchet@49121
  1160
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
  1161
blanchet@49121
  1162
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
  1163
        val ctr_defs' =
blanchet@49585
  1164
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
  1165
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
  1166
blanchet@49203
  1167
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
  1168
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
  1169
blanchet@49203
  1170
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
  1171
blanchet@51897
  1172
        fun wrap_ctrs lthy =
blanchet@49123
  1173
          let
traytel@50170
  1174
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
  1175
              let
blanchet@49585
  1176
                val ctor_iff_dtor_thm =
blanchet@49585
  1177
                  let
blanchet@49585
  1178
                    val goal =
blanchet@49585
  1179
                      fold_rev Logic.all [w, u]
blanchet@49585
  1180
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
  1181
                  in
wenzelm@51551
  1182
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49585
  1183
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49585
  1184
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49585
  1185
                    |> Thm.close_derivation
blanchet@49585
  1186
                    |> Morphism.thm phi
blanchet@49585
  1187
                  end;
blanchet@49585
  1188
blanchet@49585
  1189
                val sumEN_thm' =
blanchet@49585
  1190
                  unfold_thms lthy @{thms all_unit_eq}
blanchet@49585
  1191
                    (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49585
  1192
                       (mk_sumEN_balanced n))
blanchet@49585
  1193
                  |> Morphism.thm phi;
blanchet@49135
  1194
              in
blanchet@49585
  1195
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
  1196
              end;
blanchet@49135
  1197
blanchet@49585
  1198
            val inject_tacss =
blanchet@49585
  1199
              map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49585
  1200
                  mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49585
  1201
blanchet@49585
  1202
            val half_distinct_tacss =
blanchet@49585
  1203
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49585
  1204
                mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
blanchet@49585
  1205
blanchet@49585
  1206
            val case_tacs =
blanchet@49585
  1207
              map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49585
  1208
                mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs;
blanchet@49585
  1209
blanchet@49585
  1210
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49585
  1211
blanchet@49585
  1212
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@49123
  1213
          in
blanchet@51781
  1214
            wrap_free_constructors tacss (((wrap_opts, ctrs0), casex0), (disc_bindings,
blanchet@51781
  1215
              (sel_bindingss, sel_defaultss))) lthy
blanchet@49123
  1216
          end;
blanchet@49121
  1217
blanchet@51840
  1218
        fun derive_maps_sets_rels (ctr_sugar, lthy) =
blanchet@51835
  1219
          if live = 0 then
blanchet@51840
  1220
            ((([], [], [], []), ctr_sugar), lthy)
blanchet@51835
  1221
          else
blanchet@51835
  1222
            let
blanchet@51835
  1223
              val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@51835
  1224
              val nones = replicate live NONE;
blanchet@49585
  1225
blanchet@51835
  1226
              val ctor_cong =
blanchet@52207
  1227
                if fp = Least_FP then
blanchet@51835
  1228
                  Drule.dummy_thm
blanchet@51835
  1229
                else
blanchet@51835
  1230
                  let val ctor' = mk_ctor Bs ctor in
blanchet@51835
  1231
                    cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51835
  1232
                  end;
blanchet@49585
  1233
blanchet@51835
  1234
              fun mk_cIn ify =
blanchet@52207
  1235
                certify lthy o (fp = Greatest_FP ? curry (op $) (map_types ify ctor)) oo
blanchet@51835
  1236
                mk_InN_balanced (ify ctr_sum_prod_T) n;
blanchet@49585
  1237
blanchet@51835
  1238
              val cxIns = map2 (mk_cIn I) tuple_xs ks;
blanchet@51835
  1239
              val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
blanchet@49585
  1240
blanchet@51835
  1241
              fun mk_map_thm ctr_def' cxIn =
blanchet@51835
  1242
                fold_thms lthy [ctr_def']
blanchet@51835
  1243
                  (unfold_thms lthy (pre_map_def ::
blanchet@52207
  1244
                       (if fp = Least_FP then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
blanchet@51835
  1245
                     (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@52207
  1246
                        (if fp = Least_FP then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@51835
  1247
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1248
blanchet@51835
  1249
              fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@51835
  1250
                fold_thms lthy [ctr_def']
blanchet@51835
  1251
                  (unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
blanchet@52207
  1252
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_set)
blanchet@51835
  1253
                     (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@51835
  1254
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1255
blanchet@51835
  1256
              fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49127
  1257
blanchet@51835
  1258
              val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@51835
  1259
              val set_thmss = map mk_set_thms fp_set_thms;
blanchet@51835
  1260
blanchet@51835
  1261
              val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
  1262
blanchet@51835
  1263
              fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@51835
  1264
                fold_thms lthy ctr_defs'
blanchet@51835
  1265
                   (unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
blanchet@52207
  1266
                        (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_rel)
blanchet@51835
  1267
                      (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@51835
  1268
                |> postproc
blanchet@51835
  1269
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1270
blanchet@51835
  1271
              fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@51835
  1272
                mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
  1273
blanchet@51835
  1274
              val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
  1275
blanchet@51835
  1276
              fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@51835
  1277
                mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@51835
  1278
                  cxIn cyIn;
blanchet@49121
  1279
blanchet@51835
  1280
              fun mk_other_half_rel_distinct_thm thm =
blanchet@51835
  1281
                flip_rels lthy live thm
blanchet@51835
  1282
                RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
  1283
blanchet@51835
  1284
              val half_rel_distinct_thmss =
blanchet@51835
  1285
                map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@51835
  1286
              val other_half_rel_distinct_thmss =
blanchet@51835
  1287
                map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@51835
  1288
              val (rel_distinct_thms, _) =
blanchet@51835
  1289
                join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
  1290
blanchet@51835
  1291
              val notes =
blanchet@51835
  1292
                [(mapN, map_thms, code_simp_attrs),
blanchet@51835
  1293
                 (rel_distinctN, rel_distinct_thms, code_simp_attrs),
blanchet@51835
  1294
                 (rel_injectN, rel_inject_thms, code_simp_attrs),
blanchet@51835
  1295
                 (setsN, flat set_thmss, code_simp_attrs)]
blanchet@51835
  1296
                |> massage_simple_notes fp_b_name;
blanchet@51835
  1297
            in
blanchet@51840
  1298
              (((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
blanchet@51835
  1299
               lthy |> Local_Theory.notes notes |> snd)
blanchet@51835
  1300
            end;
blanchet@49585
  1301
blanchet@51897
  1302
        fun mk_binding suf = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49287
  1303
blanchet@51883
  1304
        fun massage_res (((maps_sets_rels, ctr_sugar), co_iter_res), lthy) =
blanchet@51883
  1305
          (((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), co_iter_res), lthy);
blanchet@49119
  1306
      in
blanchet@51897
  1307
        (wrap_ctrs
blanchet@51835
  1308
         #> derive_maps_sets_rels
blanchet@52313
  1309
         ##>>
blanchet@52329
  1310
           (if fp = Least_FP then define_iters [foldN, recN] (the iters_args_types)
blanchet@52329
  1311
            else define_coiters [unfoldN, corecN] (the coiters_args_types))
blanchet@52328
  1312
             mk_binding fpTs Cs xtor_co_iters
blanchet@51835
  1313
         #> massage_res, lthy')
blanchet@49119
  1314
      end;
blanchet@49167
  1315
blanchet@51835
  1316
    fun wrap_types_etc (wrap_types_etcs, lthy) =
blanchet@51835
  1317
      fold_map I wrap_types_etcs lthy
blanchet@52342
  1318
      |>> apsnd split_list o apfst (apsnd split_list4 o apfst split_list4 o split_list)
blanchet@52342
  1319
        o split_list;
blanchet@49226
  1320
blanchet@49479
  1321
    val mk_simp_thmss =
blanchet@51857
  1322
      map7 (fn {injects, distincts, case_thms, ...} => fn un_folds => fn co_recs =>
blanchet@51835
  1323
        fn mapsx => fn rel_injects => fn rel_distincts => fn setss =>
blanchet@51857
  1324
          injects @ distincts @ case_thms @ co_recs @ un_folds @ mapsx @ rel_injects
blanchet@51835
  1325
          @ rel_distincts @ flat setss);
blanchet@49479
  1326
blanchet@52329
  1327
    fun derive_and_note_induct_iters_thms_for_types
blanchet@51840
  1328
        ((((mapsx, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
blanchet@52342
  1329
          (iterss, iter_defss)), lthy) =
blanchet@49202
  1330
      let
blanchet@52345
  1331
        val ((induct_thms, induct_thm, induct_attrs), (fold_thmss, fold_attrs),
blanchet@51808
  1332
             (rec_thmss, rec_attrs)) =
blanchet@52346
  1333
          derive_induct_iters_thms_for_types pre_bnfs (the iters_args_types) xtor_co_inducts
blanchet@52346
  1334
            xtor_co_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss iterss
blanchet@52346
  1335
            iter_defss lthy;
blanchet@49201
  1336
blanchet@51830
  1337
        val induct_type_attr = Attrib.internal o K o Induct.induct_type;
blanchet@51810
  1338
blanchet@51835
  1339
        val simp_thmss =
blanchet@51843
  1340
          mk_simp_thmss ctr_sugars fold_thmss rec_thmss mapsx rel_injects rel_distincts setss;
blanchet@49438
  1341
blanchet@49337
  1342
        val common_notes =
blanchet@51808
  1343
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
  1344
          |> massage_simple_notes fp_common_name;
blanchet@49337
  1345
blanchet@49226
  1346
        val notes =
blanchet@51808
  1347
          [(foldN, fold_thmss, K fold_attrs),
blanchet@51810
  1348
           (inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
blanchet@51808
  1349
           (recN, rec_thmss, K rec_attrs),
blanchet@49585
  1350
           (simpsN, simp_thmss, K [])]
blanchet@51780
  1351
          |> massage_multi_notes;
blanchet@49202
  1352
      in
blanchet@51824
  1353
        lthy
blanchet@51824
  1354
        |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@52343
  1355
        |> register_fp_sugars Least_FP pre_bnfs fp_res ctr_defss ctr_sugars iterss [induct_thm]
blanchet@52343
  1356
          (transpose [fold_thmss, rec_thmss])
blanchet@49202
  1357
      end;
blanchet@49202
  1358
blanchet@52329
  1359
    fun derive_and_note_coinduct_coiters_thms_for_types
blanchet@51859
  1360
        ((((mapsx, rel_injects, rel_distincts, setss), (_, _, ctr_defss, ctr_sugars)),
blanchet@52342
  1361
          (coiterss, coiter_defss)), lthy) =
blanchet@49212
  1362
      let
blanchet@52345
  1363
        val (([(coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)],
blanchet@51810
  1364
              coinduct_attrs),
blanchet@51843
  1365
             (unfold_thmss, corec_thmss, coiter_attrs),
blanchet@51810
  1366
             (safe_unfold_thmss, safe_corec_thmss),
blanchet@51843
  1367
             (disc_unfold_thmss, disc_corec_thmss, disc_coiter_attrs),
blanchet@51843
  1368
             (disc_unfold_iff_thmss, disc_corec_iff_thmss, disc_coiter_iff_attrs),
blanchet@51843
  1369
             (sel_unfold_thmss, sel_corec_thmss, sel_coiter_attrs)) =
blanchet@52346
  1370
          derive_coinduct_coiters_thms_for_types pre_bnfs (the coiters_args_types) xtor_co_inducts
blanchet@52346
  1371
            dtor_ctors xtor_co_iter_thmss nesting_bnfs nested_bnfs fpTs Cs As kss mss ns ctr_defss
blanchet@52346
  1372
            ctr_sugars coiterss coiter_defss lthy;
blanchet@49212
  1373
blanchet@51830
  1374
        val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
blanchet@49479
  1375
blanchet@51843
  1376
        fun flat_coiter_thms coiters disc_coiters sel_coiters =
blanchet@51843
  1377
          coiters @ disc_coiters @ sel_coiters;
blanchet@49479
  1378
blanchet@49479
  1379
        val simp_thmss =
blanchet@51840
  1380
          mk_simp_thmss ctr_sugars
blanchet@51843
  1381
            (map3 flat_coiter_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss)
blanchet@51843
  1382
            (map3 flat_coiter_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@51835
  1383
            mapsx rel_injects rel_distincts setss;
blanchet@49479
  1384
blanchet@49479
  1385
        val anonymous_notes =
blanchet@49504
  1386
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
  1387
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
  1388
blanchet@49342
  1389
        val common_notes =
blanchet@49591
  1390
          (if nn > 1 then
blanchet@51810
  1391
             [(coinductN, [coinduct_thm], coinduct_attrs),
blanchet@51810
  1392
              (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
blanchet@49591
  1393
           else
blanchet@49591
  1394
             [])
blanchet@51780
  1395
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1396
blanchet@49212
  1397
        val notes =
blanchet@51780
  1398
          [(coinductN, map single coinduct_thms,
blanchet@51810
  1399
            fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
blanchet@51843
  1400
           (corecN, corec_thmss, K coiter_attrs),
blanchet@51843
  1401
           (disc_corecN, disc_corec_thmss, K disc_coiter_attrs),
blanchet@51843
  1402
           (disc_corec_iffN, disc_corec_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1403
           (disc_unfoldN, disc_unfold_thmss, K disc_coiter_attrs),
blanchet@51843
  1404
           (disc_unfold_iffN, disc_unfold_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1405
           (sel_corecN, sel_corec_thmss, K sel_coiter_attrs),
blanchet@51843
  1406
           (sel_unfoldN, sel_unfold_thmss, K sel_coiter_attrs),
blanchet@51780
  1407
           (simpsN, simp_thmss, K []),
blanchet@51810
  1408
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs),
blanchet@51843
  1409
           (unfoldN, unfold_thmss, K coiter_attrs)]
blanchet@51780
  1410
          |> massage_multi_notes;
blanchet@49212
  1411
      in
blanchet@51824
  1412
        lthy
blanchet@51824
  1413
        |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@52343
  1414
        |> register_fp_sugars Greatest_FP pre_bnfs fp_res ctr_defss ctr_sugars coiterss
blanchet@52343
  1415
          [coinduct_thm, strong_coinduct_thm] (transpose [unfold_thmss, corec_thmss])
blanchet@49212
  1416
      end;
blanchet@49212
  1417
blanchet@49204
  1418
    val lthy' = lthy
blanchet@49585
  1419
      |> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~
blanchet@52330
  1420
        xtor_co_iterss ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@52314
  1421
        pre_set_defss ~~ pre_rel_defs ~~ xtor_map_thms ~~ xtor_set_thmss ~~ xtor_rel_thms ~~ ns ~~
blanchet@52314
  1422
        kss ~~ mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~
blanchet@52314
  1423
        sel_bindingsss ~~ raw_sel_defaultsss)
blanchet@51835
  1424
      |> wrap_types_etc
blanchet@52329
  1425
      |> (if fp = Least_FP then derive_and_note_induct_iters_thms_for_types
blanchet@52329
  1426
          else derive_and_note_coinduct_coiters_thms_for_types);
blanchet@49167
  1427
blanchet@49167
  1428
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@52207
  1429
      datatype_word fp));
blanchet@49112
  1430
  in
blanchet@49308
  1431
    timer; lthy'
blanchet@49112
  1432
  end;
blanchet@49112
  1433
blanchet@51863
  1434
val co_datatypes = define_co_datatypes (K I) (K I) (K I);
blanchet@49297
  1435
blanchet@51863
  1436
val co_datatype_cmd =
blanchet@51863
  1437
  define_co_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term;
blanchet@49119
  1438
blanchet@49112
  1439
val parse_ctr_arg =
blanchet@49329
  1440
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
  1441
  (Parse.typ >> pair Binding.empty);
blanchet@49112
  1442
blanchet@49286
  1443
val parse_defaults =
blanchet@49286
  1444
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
  1445
blanchet@51758
  1446
val parse_type_arg_constrained =
blanchet@51790
  1447
  Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
blanchet@51758
  1448
blanchet@51790
  1449
val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
blanchet@51758
  1450
blanchet@51758
  1451
val parse_type_args_named_constrained =
blanchet@51758
  1452
  parse_type_arg_constrained >> (single o pair Binding.empty) ||
blanchet@51758
  1453
  @{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
blanchet@51756
  1454
  Scan.succeed [];
blanchet@51756
  1455
blanchet@51790
  1456
val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
blanchet@51767
  1457
blanchet@51767
  1458
val no_map_rel = (Binding.empty, Binding.empty);
blanchet@51767
  1459
blanchet@51767
  1460
(* "map" and "rel" are purposedly not registered as keywords, because they are short and nice names
blanchet@51833
  1461
   that we don't want them to be highlighted everywhere. *)
blanchet@51767
  1462
fun extract_map_rel ("map", b) = apfst (K b)
blanchet@51767
  1463
  | extract_map_rel ("rel", b) = apsnd (K b)
blanchet@51767
  1464
  | extract_map_rel (s, _) = error ("Expected \"map\" or \"rel\" instead of " ^ quote s);
blanchet@49112
  1465
blanchet@51767
  1466
val parse_map_rel_bindings =
blanchet@51767
  1467
  @{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
blanchet@51767
  1468
    >> (fn ps => fold extract_map_rel ps no_map_rel) ||
blanchet@51767
  1469
  Scan.succeed no_map_rel;
blanchet@51767
  1470
blanchet@51767
  1471
val parse_ctr_spec =
blanchet@51790
  1472
  parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
blanchet@51767
  1473
  Scan.optional parse_defaults [] -- Parse.opt_mixfix;
blanchet@51767
  1474
blanchet@51767
  1475
val parse_spec =
blanchet@51790
  1476
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@51767
  1477
  Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
blanchet@51767
  1478
blanchet@51863
  1479
val parse_co_datatype = parse_wrap_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1480
blanchet@52207
  1481
fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp;
blanchet@49112
  1482
blanchet@49112
  1483
end;