src/HOL/BNF/Tools/bnf_fp_def_sugar.ML
author blanchet
Tue Aug 06 15:50:23 2013 +0200 (2013-08-06)
changeset 52869 79f5e137779a
parent 52868 cca9e958da5c
child 52870 47b1c2f3ff24
permissions -rw-r--r--
tuning
blanchet@49636
     1
(*  Title:      HOL/BNF/Tools/bnf_fp_def_sugar.ML
blanchet@49112
     2
    Author:     Jasmin Blanchette, TU Muenchen
blanchet@52349
     3
    Copyright   2012, 2013
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@52356
    15
     nested_bnfs: BNF_Def.bnf list,
blanchet@51850
    16
     fp_res: BNF_FP_Util.fp_result,
blanchet@51906
    17
     ctr_defss: thm list list,
blanchet@51842
    18
     ctr_sugars: BNF_Ctr_Sugar.ctr_sugar list,
blanchet@52336
    19
     co_iterss: term list list,
blanchet@52343
    20
     co_inducts: thm list,
blanchet@52337
    21
     co_iter_thmsss: thm list list list};
blanchet@51823
    22
blanchet@52295
    23
  val of_fp_sugar: (fp_sugar -> 'a list) -> fp_sugar -> 'a
blanchet@51896
    24
  val morph_fp_sugar: morphism -> fp_sugar -> fp_sugar
blanchet@51896
    25
  val fp_sugar_of: Proof.context -> string -> fp_sugar option
blanchet@51852
    26
blanchet@51911
    27
  val tvar_subst: theory -> typ list -> typ list -> ((string * int) * typ) list
blanchet@51860
    28
  val exists_subtype_in: typ list -> typ -> bool
blanchet@52868
    29
  val flat_rec_arg_args: 'a list list -> 'a list
blanchet@52868
    30
  val flat_corec_preds_predsss_gettersss: 'a list -> 'a list list list -> 'a list list list ->
blanchet@52868
    31
    'a list
blanchet@52207
    32
  val mk_co_iter: theory -> BNF_FP_Util.fp_kind -> typ -> typ list -> term -> term
blanchet@51907
    33
  val nesty_bnfs: Proof.context -> typ list list list -> typ list -> BNF_Def.bnf list
blanchet@52347
    34
  val mk_map: int -> typ list -> typ list -> term -> term
blanchet@52347
    35
  val build_map: local_theory -> (typ * typ -> term) -> typ * typ -> term
blanchet@52334
    36
  val mk_co_iters_prelims: BNF_FP_Util.fp_kind -> typ list -> typ list -> int list ->
blanchet@52315
    37
    int list list -> term list list -> Proof.context ->
blanchet@52315
    38
    (term list list
blanchet@52315
    39
     * (typ list list * typ list list list list * term list list
blanchet@52315
    40
        * term list list list list) list option
blanchet@52347
    41
     * (string * term list * term list list
blanchet@52349
    42
        * ((term list list * term list list list) * (typ list * typ list list)) list) option)
blanchet@51903
    43
    * Proof.context
blanchet@51823
    44
blanchet@52215
    45
  val mk_iter_fun_arg_typessss: typ list -> int list -> int list list -> term ->
blanchet@52215
    46
    typ list list list list
blanchet@52320
    47
  val define_iters: string list ->
blanchet@52315
    48
    (typ list list * typ list list list list * term list list * term list list list list) list ->
blanchet@52319
    49
    (string -> binding) -> typ list -> typ list -> term list -> Proof.context ->
blanchet@52320
    50
    (term list * thm list) * Proof.context
blanchet@52347
    51
  val define_coiters: string list -> string * term list * term list list
blanchet@52349
    52
    * ((term list list * term list list list) * (typ list * typ list list)) list ->
blanchet@52319
    53
    (string -> binding) -> typ list -> typ list -> term list -> Proof.context ->
blanchet@52320
    54
    (term list * thm list) * Proof.context
blanchet@52346
    55
  val derive_induct_iters_thms_for_types: BNF_Def.bnf list ->
blanchet@52315
    56
    (typ list list * typ list list list list * term list list * term list list list list) list ->
blanchet@52344
    57
    thm list -> thm list list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list ->
blanchet@52315
    58
    typ list -> typ list list list -> term list list -> thm list list -> term list list ->
blanchet@52315
    59
    thm list list -> local_theory ->
blanchet@52345
    60
    (thm list * thm * Args.src list) * (thm list list * Args.src list)
blanchet@51827
    61
    * (thm list list * Args.src list)
blanchet@52346
    62
  val derive_coinduct_coiters_thms_for_types: BNF_Def.bnf list ->
blanchet@52348
    63
    string * term list * term list list * ((term list list * term list list list)
blanchet@52351
    64
      * (typ list * typ list list)) list ->
blanchet@52344
    65
    thm list -> thm list -> thm list list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list ->
blanchet@52321
    66
    typ list -> typ list -> int list list -> int list list -> int list -> thm list list ->
blanchet@52357
    67
    BNF_Ctr_Sugar.ctr_sugar list -> term list list -> thm list list -> (thm list -> thm list) ->
blanchet@52357
    68
    local_theory ->
blanchet@52345
    69
    ((thm list * thm) list * Args.src list)
blanchet@51839
    70
    * (thm list list * thm list list * Args.src list)
blanchet@51811
    71
    * (thm list list * thm list list) * (thm list list * thm list list * Args.src list)
blanchet@51824
    72
    * (thm list list * thm list list * Args.src list)
blanchet@51824
    73
    * (thm list list * thm list list * Args.src list)
blanchet@51823
    74
blanchet@52207
    75
  val co_datatypes: BNF_FP_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
blanchet@52207
    76
      binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
blanchet@52207
    77
      BNF_Def.bnf list -> local_theory -> BNF_FP_Util.fp_result * local_theory) ->
blanchet@51767
    78
    (bool * bool) * (((((binding * (typ * sort)) list * binding) * (binding * binding)) * mixfix) *
blanchet@51758
    79
      ((((binding * binding) * (binding * typ) list) * (binding * term) list) *
blanchet@51758
    80
        mixfix) list) list ->
blanchet@49297
    81
    local_theory -> local_theory
blanchet@52207
    82
  val parse_co_datatype_cmd: BNF_FP_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
blanchet@51867
    83
      binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
blanchet@51867
    84
      BNF_Def.bnf list -> local_theory -> BNF_FP_Util.fp_result * local_theory) ->
blanchet@49308
    85
    (local_theory -> local_theory) parser
blanchet@49112
    86
end;
blanchet@49112
    87
blanchet@49636
    88
structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR =
blanchet@49112
    89
struct
blanchet@49112
    90
blanchet@49119
    91
open BNF_Util
blanchet@51797
    92
open BNF_Ctr_Sugar
blanchet@49214
    93
open BNF_Def
blanchet@51850
    94
open BNF_FP_Util
blanchet@49636
    95
open BNF_FP_Def_Sugar_Tactics
blanchet@49119
    96
blanchet@51788
    97
val EqN = "Eq_";
blanchet@51777
    98
blanchet@51840
    99
type fp_sugar =
blanchet@51859
   100
  {T: typ,
blanchet@52207
   101
   fp: fp_kind,
blanchet@51838
   102
   index: int,
blanchet@51838
   103
   pre_bnfs: bnf list,
blanchet@52356
   104
   nested_bnfs: bnf list,
blanchet@51823
   105
   fp_res: fp_result,
blanchet@51906
   106
   ctr_defss: thm list list,
blanchet@51842
   107
   ctr_sugars: ctr_sugar list,
blanchet@52336
   108
   co_iterss: term list list,
blanchet@52343
   109
   co_inducts: thm list,
blanchet@52337
   110
   co_iter_thmsss: thm list list list};
blanchet@51823
   111
blanchet@52295
   112
fun of_fp_sugar f (fp_sugar as {index, ...}) = nth (f fp_sugar) index;
blanchet@52295
   113
blanchet@52207
   114
fun eq_fp_sugar ({T = T1, fp = fp1, index = index1, fp_res = fp_res1, ...} : fp_sugar,
blanchet@52207
   115
    {T = T2, fp = fp2, index = index2, fp_res = fp_res2, ...} : fp_sugar) =
blanchet@52207
   116
  T1 = T2 andalso fp1 = fp2 andalso index1 = index2 andalso eq_fp_result (fp_res1, fp_res2);
blanchet@51823
   117
blanchet@52356
   118
fun morph_fp_sugar phi {T, fp, index, pre_bnfs, nested_bnfs, fp_res, ctr_defss, ctr_sugars,
blanchet@52356
   119
    co_iterss, co_inducts, co_iter_thmsss} =
blanchet@52356
   120
  {T = Morphism.typ phi T, fp = fp, index = index, pre_bnfs = map (morph_bnf phi) pre_bnfs,
blanchet@52356
   121
    nested_bnfs = map (morph_bnf phi) nested_bnfs, fp_res = morph_fp_result phi fp_res,
blanchet@52207
   122
   ctr_defss = map (map (Morphism.thm phi)) ctr_defss,
blanchet@52336
   123
   ctr_sugars = map (morph_ctr_sugar phi) ctr_sugars,
blanchet@52343
   124
   co_iterss = map (map (Morphism.term phi)) co_iterss,
blanchet@52343
   125
   co_inducts = map (Morphism.thm phi) co_inducts,
blanchet@52337
   126
   co_iter_thmsss = map (map (map (Morphism.thm phi))) co_iter_thmsss};
blanchet@51823
   127
blanchet@51823
   128
structure Data = Generic_Data
blanchet@51823
   129
(
blanchet@51840
   130
  type T = fp_sugar Symtab.table;
blanchet@51823
   131
  val empty = Symtab.empty;
blanchet@51823
   132
  val extend = I;
blanchet@51840
   133
  val merge = Symtab.merge eq_fp_sugar;
blanchet@51823
   134
);
blanchet@51823
   135
blanchet@51840
   136
val fp_sugar_of = Symtab.lookup o Data.get o Context.Proof;
blanchet@51823
   137
blanchet@51840
   138
fun register_fp_sugar key fp_sugar =
blanchet@51823
   139
  Local_Theory.declaration {syntax = false, pervasive = true}
blanchet@52793
   140
    (fn phi => Data.map (Symtab.default (key, morph_fp_sugar phi fp_sugar)));
blanchet@51823
   141
blanchet@52356
   142
fun register_fp_sugars fp pre_bnfs nested_bnfs (fp_res as {Ts, ...}) ctr_defss ctr_sugars co_iterss
blanchet@52356
   143
    co_inducts co_iter_thmsss lthy =
blanchet@51844
   144
  (0, lthy)
blanchet@51859
   145
  |> fold (fn T as Type (s, _) => fn (kk, lthy) => (kk + 1,
blanchet@52356
   146
    register_fp_sugar s {T = T, fp = fp, index = kk, pre_bnfs = pre_bnfs,
blanchet@52356
   147
        nested_bnfs = nested_bnfs, fp_res = fp_res, ctr_defss = ctr_defss, ctr_sugars = ctr_sugars,
blanchet@52356
   148
        co_iterss = co_iterss, co_inducts = co_inducts, co_iter_thmsss = co_iter_thmsss}
blanchet@52337
   149
      lthy)) Ts
blanchet@51824
   150
  |> snd;
blanchet@51824
   151
blanchet@51777
   152
(* This function could produce clashes in contrived examples (e.g., "x.A", "x.x_A", "y.A"). *)
blanchet@49622
   153
fun quasi_unambiguous_case_names names =
blanchet@49622
   154
  let
blanchet@49622
   155
    val ps = map (`Long_Name.base_name) names;
blanchet@49622
   156
    val dups = Library.duplicates (op =) (map fst ps);
blanchet@49622
   157
    fun underscore s =
blanchet@49622
   158
      let val ss = space_explode Long_Name.separator s in
blanchet@49622
   159
        space_implode "_" (drop (length ss - 2) ss)
blanchet@49622
   160
      end;
blanchet@49622
   161
  in
blanchet@49622
   162
    map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
blanchet@49622
   163
  end;
blanchet@49622
   164
blanchet@52355
   165
val id_def = @{thm id_def};
blanchet@49591
   166
val mp_conj = @{thm mp_conj};
blanchet@49591
   167
blanchet@49300
   168
val simp_attrs = @{attributes [simp]};
blanchet@49585
   169
val code_simp_attrs = Code.add_default_eqn_attrib :: simp_attrs;
blanchet@49300
   170
blanchet@51911
   171
fun tvar_subst thy Ts Us =
blanchet@51911
   172
  Vartab.fold (cons o apsnd snd) (fold (Sign.typ_match thy) (Ts ~~ Us) Vartab.empty) [];
blanchet@51911
   173
blanchet@51860
   174
val exists_subtype_in = Term.exists_subtype o member (op =);
blanchet@51808
   175
blanchet@49342
   176
fun resort_tfree S (TFree (s, _)) = TFree (s, S);
blanchet@49342
   177
blanchet@51845
   178
fun typ_subst_nonatomic inst (T as Type (s, Ts)) =
blanchet@49214
   179
    (case AList.lookup (op =) inst T of
blanchet@51845
   180
      NONE => Type (s, map (typ_subst_nonatomic inst) Ts)
blanchet@49214
   181
    | SOME T' => T')
blanchet@51845
   182
  | typ_subst_nonatomic inst T = the_default T (AList.lookup (op =) inst T);
blanchet@49205
   183
blanchet@49297
   184
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
blanchet@49202
   185
blanchet@52868
   186
fun flat_rec_arg_args xss =
blanchet@52868
   187
  (* FIXME (once the old datatype package is phased out): The first line below gives the preferred
blanchet@52868
   188
     order. The second line is for compatibility with the old datatype package. *)
blanchet@52215
   189
(*
blanchet@52301
   190
  flat xss
blanchet@51795
   191
*)
blanchet@52301
   192
  map hd xss @ maps tl xss;
blanchet@51793
   193
blanchet@52868
   194
fun flat_corec_predss_getterss qss fss = maps (op @) (qss ~~ fss);
blanchet@51829
   195
blanchet@52868
   196
fun flat_corec_preds_predsss_gettersss [] [qss] [fss] = flat_corec_predss_getterss qss fss
blanchet@52868
   197
  | flat_corec_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
blanchet@52868
   198
    p :: flat_corec_predss_getterss qss fss @ flat_corec_preds_predsss_gettersss ps qsss fsss;
blanchet@51829
   199
blanchet@52214
   200
fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs));
blanchet@52214
   201
fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs;
blanchet@52214
   202
fun mk_uncurried2_fun f xss =
blanchet@52868
   203
  mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat_rec_arg_args xss);
blanchet@52214
   204
blanchet@49585
   205
fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) =
blanchet@49585
   206
  Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1));
blanchet@49585
   207
blanchet@49585
   208
fun flip_rels lthy n thm =
blanchet@49585
   209
  let
blanchet@49585
   210
    val Rs = Term.add_vars (prop_of thm) [];
blanchet@49585
   211
    val Rs' = rev (drop (length Rs - n) Rs);
blanchet@49585
   212
    val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs';
blanchet@49585
   213
  in
blanchet@49585
   214
    Drule.cterm_instantiate cRs thm
blanchet@49585
   215
  end;
blanchet@49585
   216
blanchet@49536
   217
fun mk_ctor_or_dtor get_T Ts t =
blanchet@49536
   218
  let val Type (_, Ts0) = get_T (fastype_of t) in
blanchet@49536
   219
    Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49536
   220
  end;
blanchet@49536
   221
blanchet@49536
   222
val mk_ctor = mk_ctor_or_dtor range_type;
blanchet@49536
   223
val mk_dtor = mk_ctor_or_dtor domain_type;
blanchet@49536
   224
blanchet@52207
   225
fun mk_co_iter thy fp fpT Cs t =
blanchet@49536
   226
  let
blanchet@52309
   227
    val (binders, body) = strip_type (fastype_of t);
blanchet@52309
   228
    val (f_Cs, prebody) = split_last binders;
blanchet@52207
   229
    val fpT0 = if fp = Least_FP then prebody else body;
blanchet@52207
   230
    val Cs0 = distinct (op =) (map (if fp = Least_FP then body_type else domain_type) f_Cs);
blanchet@52197
   231
    val rho = tvar_subst thy (fpT0 :: Cs0) (fpT :: Cs);
blanchet@49536
   232
  in
blanchet@52170
   233
    Term.subst_TVars rho t
blanchet@49536
   234
  end;
blanchet@49536
   235
blanchet@52207
   236
fun mk_co_iters thy fp fpTs Cs ts0 =
blanchet@51911
   237
  let
blanchet@51911
   238
    val nn = length fpTs;
blanchet@51911
   239
    val (fpTs0, Cs0) =
blanchet@52207
   240
      map ((fp = Greatest_FP ? swap) o dest_funT o snd o strip_typeN nn o fastype_of) ts0
blanchet@51911
   241
      |> split_list;
blanchet@51911
   242
    val rho = tvar_subst thy (fpTs0 @ Cs0) (fpTs @ Cs);
blanchet@51911
   243
  in
blanchet@52170
   244
    map (Term.subst_TVars rho) ts0
blanchet@51911
   245
  end;
blanchet@51827
   246
blanchet@52169
   247
val mk_fp_iter_fun_types = fst o split_last o binder_types o fastype_of;
blanchet@52169
   248
blanchet@52296
   249
fun unzip_recT Cs (T as Type (@{type_name prod}, Ts as [_, U])) =
blanchet@52296
   250
    if member (op =) Cs U then Ts else [T]
blanchet@52216
   251
  | unzip_recT _ T = [T];
blanchet@51827
   252
blanchet@52347
   253
fun mk_map live Ts Us t =
blanchet@52347
   254
  let val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) |>> List.last in
blanchet@52347
   255
    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@52347
   256
  end;
blanchet@52347
   257
blanchet@52347
   258
fun mk_rel live Ts Us t =
blanchet@52347
   259
  let val [Type (_, Ts0), Type (_, Us0)] = binder_types (snd (strip_typeN live (fastype_of t))) in
blanchet@52347
   260
    Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@52347
   261
  end;
blanchet@52347
   262
blanchet@52347
   263
fun build_map lthy build_simple =
blanchet@52347
   264
  let
blanchet@52347
   265
    fun build (TU as (T, U)) =
blanchet@52347
   266
      if T = U then
blanchet@52347
   267
        id_const T
blanchet@52347
   268
      else
blanchet@52347
   269
        (case TU of
blanchet@52347
   270
          (Type (s, Ts), Type (s', Us)) =>
blanchet@52347
   271
          if s = s' then
blanchet@52347
   272
            let
blanchet@52347
   273
              val bnf = the (bnf_of lthy s);
blanchet@52347
   274
              val live = live_of_bnf bnf;
blanchet@52347
   275
              val mapx = mk_map live Ts Us (map_of_bnf bnf);
blanchet@52347
   276
              val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
blanchet@52347
   277
            in Term.list_comb (mapx, map build TUs') end
blanchet@52347
   278
          else
blanchet@52347
   279
            build_simple TU
blanchet@52347
   280
        | _ => build_simple TU);
blanchet@52347
   281
  in build end;
blanchet@52347
   282
blanchet@52347
   283
fun liveness_of_fp_bnf n bnf =
blanchet@52347
   284
  (case T_of_bnf bnf of
blanchet@52347
   285
    Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
blanchet@52347
   286
  | _ => replicate n false);
blanchet@52347
   287
blanchet@52347
   288
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
blanchet@52347
   289
blanchet@52347
   290
fun merge_type_arg T T' = if T = T' then T else cannot_merge_types ();
blanchet@52347
   291
blanchet@52347
   292
fun merge_type_args (As, As') =
blanchet@52347
   293
  if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types ();
blanchet@52347
   294
blanchet@52347
   295
fun reassoc_conjs thm =
blanchet@52347
   296
  reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
blanchet@52347
   297
  handle THM _ => thm;
blanchet@52347
   298
blanchet@52347
   299
fun type_args_named_constrained_of ((((ncAs, _), _), _), _) = ncAs;
blanchet@52347
   300
fun type_binding_of ((((_, b), _), _), _) = b;
blanchet@52347
   301
fun map_binding_of (((_, (b, _)), _), _) = b;
blanchet@52347
   302
fun rel_binding_of (((_, (_, b)), _), _) = b;
blanchet@52347
   303
fun mixfix_of ((_, mx), _) = mx;
blanchet@52347
   304
fun ctr_specs_of (_, ctr_specs) = ctr_specs;
blanchet@52347
   305
blanchet@52347
   306
fun disc_of ((((disc, _), _), _), _) = disc;
blanchet@52347
   307
fun ctr_of ((((_, ctr), _), _), _) = ctr;
blanchet@52347
   308
fun args_of (((_, args), _), _) = args;
blanchet@52347
   309
fun defaults_of ((_, ds), _) = ds;
blanchet@52347
   310
fun ctr_mixfix_of (_, mx) = mx;
blanchet@52347
   311
blanchet@52347
   312
fun add_nesty_bnf_names Us =
blanchet@52347
   313
  let
blanchet@52347
   314
    fun add (Type (s, Ts)) ss =
blanchet@52347
   315
        let val (needs, ss') = fold_map add Ts ss in
blanchet@52347
   316
          if exists I needs then (true, insert (op =) s ss') else (false, ss')
blanchet@52347
   317
        end
blanchet@52347
   318
      | add T ss = (member (op =) Us T, ss);
blanchet@52347
   319
  in snd oo add end;
blanchet@52347
   320
blanchet@52347
   321
fun nesty_bnfs ctxt ctr_Tsss Us =
blanchet@52347
   322
  map_filter (bnf_of ctxt) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_Tsss []);
blanchet@52347
   323
blanchet@52347
   324
fun indexify proj xs f p = f (find_index (curry (op =) (proj p)) xs) p;
blanchet@52347
   325
blanchet@51846
   326
fun mk_fun_arg_typess n ms = map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type;
blanchet@51846
   327
blanchet@52296
   328
fun mk_iter_fun_arg_typessss Cs ns mss =
blanchet@51885
   329
  mk_fp_iter_fun_types
blanchet@51885
   330
  #> map3 mk_fun_arg_typess ns mss
blanchet@52296
   331
  #> map (map (map (unzip_recT Cs)));
blanchet@51885
   332
blanchet@52335
   333
fun mk_iters_args_types Cs ns mss ctor_iter_fun_Tss lthy =
blanchet@51832
   334
  let
blanchet@52214
   335
    val Css = map2 replicate ns Cs;
blanchet@52335
   336
    val y_Tsss = map3 mk_fun_arg_typess ns mss (map un_fold_of ctor_iter_fun_Tss);
blanchet@52214
   337
    val g_Tss = map2 (fn C => map (fn y_Ts => y_Ts ---> C)) Cs y_Tsss;
blanchet@51832
   338
blanchet@51832
   339
    val ((gss, ysss), lthy) =
blanchet@51832
   340
      lthy
blanchet@51832
   341
      |> mk_Freess "f" g_Tss
blanchet@51832
   342
      ||>> mk_Freesss "x" y_Tsss;
blanchet@52301
   343
blanchet@52301
   344
    val y_Tssss = map (map (map single)) y_Tsss;
blanchet@52214
   345
    val yssss = map (map (map single)) ysss;
blanchet@52214
   346
blanchet@52214
   347
    val z_Tssss =
blanchet@52296
   348
      map3 (fn n => fn ms => map2 (map (unzip_recT Cs) oo dest_tupleT) ms o
blanchet@52335
   349
        dest_sumTN_balanced n o domain_type o co_rec_of) ns mss ctor_iter_fun_Tss;
blanchet@51832
   350
blanchet@52868
   351
    val z_Tsss' = map (map flat_rec_arg_args) z_Tssss;
blanchet@52215
   352
    val h_Tss = map2 (map2 (curry (op --->))) z_Tsss' Css;
blanchet@51832
   353
blanchet@51832
   354
    val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@52214
   355
    val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
blanchet@52214
   356
    val (zssss_tl, lthy) =
blanchet@52214
   357
      lthy
blanchet@52214
   358
      |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
blanchet@52214
   359
    val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
blanchet@51832
   360
  in
blanchet@52315
   361
    ([(g_Tss, y_Tssss, gss, yssss), (h_Tss, z_Tssss, hss, zssss)], lthy)
blanchet@51832
   362
  end;
blanchet@51832
   363
blanchet@52335
   364
fun mk_coiters_args_types Cs ns mss dtor_coiter_fun_Tss lthy =
blanchet@51829
   365
  let
blanchet@51829
   366
    (*avoid "'a itself" arguments in coiterators and corecursors*)
blanchet@51829
   367
    fun repair_arity [0] = [1]
blanchet@51829
   368
      | repair_arity ms = ms;
blanchet@51829
   369
blanchet@52347
   370
    fun unzip_corecT (T as Type (@{type_name sum}, Ts as [_, U])) =
blanchet@52347
   371
        if member (op =) Cs U then Ts else [T]
blanchet@52347
   372
      | unzip_corecT T = [T];
blanchet@51829
   373
blanchet@51831
   374
    val p_Tss = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@51829
   375
blanchet@52335
   376
    fun mk_types maybe_unzipT get_Ts =
blanchet@51829
   377
      let
blanchet@52335
   378
        val fun_Ts = map get_Ts dtor_coiter_fun_Tss;
blanchet@51829
   379
        val f_sum_prod_Ts = map range_type fun_Ts;
blanchet@51829
   380
        val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts;
blanchet@51829
   381
        val f_Tsss = map2 (map2 dest_tupleT o repair_arity) mss f_prod_Tss;
blanchet@51889
   382
        val f_Tssss = map2 (fn C => map (map (map (curry (op -->) C) o maybe_unzipT))) Cs f_Tsss;
blanchet@51829
   383
        val q_Tssss =
blanchet@52213
   384
          map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) f_Tssss;
blanchet@52868
   385
        val pf_Tss = map3 flat_corec_preds_predsss_gettersss p_Tss q_Tssss f_Tssss;
blanchet@52349
   386
      in (q_Tssss, f_Tsss, f_Tssss, (f_sum_prod_Ts, pf_Tss)) end;
blanchet@51829
   387
blanchet@52349
   388
    val (r_Tssss, g_Tsss, g_Tssss, unfold_types) = mk_types single un_fold_of;
blanchet@52349
   389
    val (s_Tssss, h_Tsss, h_Tssss, corec_types) = mk_types unzip_corecT co_rec_of;
blanchet@51831
   390
blanchet@52347
   391
    val ((((Free (z, _), cs), pss), gssss), lthy) =
blanchet@51829
   392
      lthy
blanchet@52347
   393
      |> yield_singleton (mk_Frees "z") dummyT
blanchet@52347
   394
      ||>> mk_Frees "a" Cs
blanchet@51829
   395
      ||>> mk_Freess "p" p_Tss
blanchet@51829
   396
      ||>> mk_Freessss "g" g_Tssss;
blanchet@51829
   397
    val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@51829
   398
blanchet@51829
   399
    val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@51829
   400
    val ((sssss, hssss_tl), lthy) =
blanchet@51829
   401
      lthy
blanchet@51829
   402
      |> mk_Freessss "q" s_Tssss
blanchet@51829
   403
      ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@51829
   404
    val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@51831
   405
blanchet@51831
   406
    val cpss = map2 (map o rapp) cs pss;
blanchet@51829
   407
blanchet@52347
   408
    fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
blanchet@52347
   409
blanchet@52347
   410
    fun build_dtor_coiter_arg _ [] [cf] = cf
blanchet@52347
   411
      | build_dtor_coiter_arg T [cq] [cf, cf'] =
blanchet@52347
   412
        mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@52347
   413
          (build_sum_inj Inr_const (fastype_of cf', T) $ cf');
blanchet@52347
   414
blanchet@52349
   415
    fun mk_args qssss fssss f_Tsss =
blanchet@51831
   416
      let
blanchet@52868
   417
        val pfss = map3 flat_corec_preds_predsss_gettersss pss qssss fssss;
blanchet@51831
   418
        val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@51831
   419
        val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@52347
   420
        val cqfsss = map3 (map3 (map3 build_dtor_coiter_arg)) f_Tsss cqssss cfssss;
blanchet@52347
   421
      in (pfss, cqfsss) end;
blanchet@51831
   422
blanchet@52349
   423
    val unfold_args = mk_args rssss gssss g_Tsss;
blanchet@52349
   424
    val corec_args = mk_args sssss hssss h_Tsss;
blanchet@51831
   425
  in
blanchet@52347
   426
    ((z, cs, cpss, [(unfold_args, unfold_types), (corec_args, corec_types)]), lthy)
blanchet@51831
   427
  end;
blanchet@51829
   428
blanchet@52334
   429
fun mk_co_iters_prelims fp fpTs Cs ns mss xtor_co_iterss0 lthy =
blanchet@51903
   430
  let
blanchet@52169
   431
    val thy = Proof_Context.theory_of lthy;
blanchet@52169
   432
blanchet@52335
   433
    val (xtor_co_iter_fun_Tss, xtor_co_iterss) =
blanchet@52329
   434
      map (mk_co_iters thy fp fpTs Cs #> `(mk_fp_iter_fun_types o hd)) (transpose xtor_co_iterss0)
blanchet@52335
   435
      |> apsnd transpose o apfst transpose o split_list;
blanchet@51903
   436
blanchet@52329
   437
    val ((iters_args_types, coiters_args_types), lthy') =
blanchet@52207
   438
      if fp = Least_FP then
blanchet@52335
   439
        mk_iters_args_types Cs ns mss xtor_co_iter_fun_Tss lthy |>> (rpair NONE o SOME)
blanchet@51903
   440
      else
blanchet@52335
   441
        mk_coiters_args_types Cs ns mss xtor_co_iter_fun_Tss lthy |>> (pair NONE o SOME)
blanchet@51903
   442
  in
blanchet@52335
   443
    ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy')
blanchet@51903
   444
  end;
blanchet@51903
   445
blanchet@52298
   446
fun mk_iter_body ctor_iter fss xssss =
blanchet@52298
   447
  Term.list_comb (ctor_iter, map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss);
blanchet@51884
   448
blanchet@51900
   449
fun mk_preds_getterss_join c cps sum_prod_T cqfss =
blanchet@51900
   450
  let val n = length cqfss in
blanchet@51900
   451
    Term.lambda c (mk_IfN sum_prod_T cps
blanchet@51900
   452
      (map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n)))
blanchet@51900
   453
  end;
blanchet@51886
   454
blanchet@52348
   455
fun mk_coiter_body cs cpss f_sum_prod_Ts cqfsss dtor_coiter =
blanchet@52347
   456
  Term.list_comb (dtor_coiter, map4 mk_preds_getterss_join cs cpss f_sum_prod_Ts cqfsss);
blanchet@51886
   457
blanchet@52327
   458
fun define_co_iters fp fpT Cs binding_specs lthy0 =
blanchet@51897
   459
  let
blanchet@52170
   460
    val thy = Proof_Context.theory_of lthy0;
blanchet@52170
   461
blanchet@52327
   462
    val ((csts, defs), (lthy', lthy)) = lthy0
blanchet@52327
   463
      |> apfst split_list o fold_map (fn (b, spec) =>
blanchet@52327
   464
        Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec))
blanchet@52327
   465
        #>> apsnd snd) binding_specs
blanchet@52327
   466
      ||> `Local_Theory.restore;
blanchet@52327
   467
blanchet@52327
   468
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@52327
   469
blanchet@52327
   470
    val csts' = map (mk_co_iter thy fp fpT Cs o Morphism.term phi) csts;
blanchet@52327
   471
    val defs' = map (Morphism.thm phi) defs;
blanchet@52327
   472
  in
blanchet@52327
   473
    ((csts', defs'), lthy')
blanchet@52327
   474
  end;
blanchet@52327
   475
blanchet@52327
   476
fun define_iters iterNs iter_args_typess' mk_binding fpTs Cs ctor_iters lthy =
blanchet@52327
   477
  let
blanchet@51899
   478
    val nn = length fpTs;
blanchet@51899
   479
blanchet@52320
   480
    val fpT_to_C as Type (_, [fpT, _]) = snd (strip_typeN nn (fastype_of (hd ctor_iters)));
blanchet@51897
   481
blanchet@52320
   482
    fun generate_iter suf (f_Tss, _, fss, xssss) ctor_iter =
blanchet@51897
   483
      let
blanchet@51899
   484
        val res_T = fold_rev (curry (op --->)) f_Tss fpT_to_C;
blanchet@52309
   485
        val b = mk_binding suf;
blanchet@51897
   486
        val spec =
blanchet@52309
   487
          mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of b, res_T)),
blanchet@52298
   488
            mk_iter_body ctor_iter fss xssss);
blanchet@52309
   489
      in (b, spec) end;
blanchet@51897
   490
  in
blanchet@52327
   491
    define_co_iters Least_FP fpT Cs (map3 generate_iter iterNs iter_args_typess' ctor_iters) lthy
blanchet@51897
   492
  end;
blanchet@51897
   493
blanchet@52347
   494
fun define_coiters coiterNs (_, cs, cpss, coiter_args_typess') mk_binding fpTs Cs dtor_coiters
blanchet@52347
   495
    lthy =
blanchet@51897
   496
  let
blanchet@51899
   497
    val nn = length fpTs;
blanchet@51899
   498
blanchet@52326
   499
    val C_to_fpT as Type (_, [_, fpT]) = snd (strip_typeN nn (fastype_of (hd dtor_coiters)));
blanchet@51897
   500
blanchet@52349
   501
    fun generate_coiter suf ((pfss, cqfsss), (f_sum_prod_Ts, pf_Tss)) dtor_coiter =
blanchet@51897
   502
      let
blanchet@51899
   503
        val res_T = fold_rev (curry (op --->)) pf_Tss C_to_fpT;
blanchet@52309
   504
        val b = mk_binding suf;
blanchet@51897
   505
        val spec =
blanchet@52309
   506
          mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of b, res_T)),
blanchet@52348
   507
            mk_coiter_body cs cpss f_sum_prod_Ts cqfsss dtor_coiter);
blanchet@52309
   508
      in (b, spec) end;
blanchet@51897
   509
  in
blanchet@52327
   510
    define_co_iters Greatest_FP fpT Cs
blanchet@52327
   511
      (map3 generate_coiter coiterNs coiter_args_typess' dtor_coiters) lthy
blanchet@52320
   512
  end;
blanchet@51897
   513
blanchet@52346
   514
fun derive_induct_iters_thms_for_types pre_bnfs [fold_args_types, rec_args_types] [ctor_induct]
blanchet@52346
   515
    ctor_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss iterss iter_defss
blanchet@52346
   516
    lthy =
blanchet@51808
   517
  let
blanchet@52340
   518
    val iterss' = transpose iterss;
blanchet@52340
   519
    val iter_defss' = transpose iter_defss;
blanchet@52340
   520
blanchet@52340
   521
    val [folds, recs] = iterss';
blanchet@52340
   522
    val [fold_defs, rec_defs] = iter_defss';
blanchet@52340
   523
blanchet@51827
   524
    val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
blanchet@51827
   525
blanchet@51815
   526
    val nn = length pre_bnfs;
blanchet@51827
   527
    val ns = map length ctr_Tsss;
blanchet@51827
   528
    val mss = map (map length) ctr_Tsss;
blanchet@51815
   529
blanchet@51808
   530
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51808
   531
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@52355
   532
    val nesting_map_ids'' = map (unfold_thms lthy [id_def] o map_id_of_bnf) nesting_bnfs;
blanchet@52355
   533
    val nested_map_ids'' = map (unfold_thms lthy [id_def] o map_id_of_bnf) nested_bnfs;
blanchet@51810
   534
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@51808
   535
blanchet@51816
   536
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   537
blanchet@51832
   538
    val ((((ps, ps'), xsss), us'), names_lthy) =
blanchet@52315
   539
      lthy
blanchet@51808
   540
      |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@51827
   541
      ||>> mk_Freesss "x" ctr_Tsss
blanchet@51816
   542
      ||>> Variable.variant_fixes fp_b_names;
blanchet@51808
   543
blanchet@51808
   544
    val us = map2 (curry Free) us' fpTs;
blanchet@51808
   545
blanchet@51808
   546
    fun mk_sets_nested bnf =
blanchet@51808
   547
      let
blanchet@51808
   548
        val Type (T_name, Us) = T_of_bnf bnf;
blanchet@51808
   549
        val lives = lives_of_bnf bnf;
blanchet@51808
   550
        val sets = sets_of_bnf bnf;
blanchet@51808
   551
        fun mk_set U =
blanchet@51808
   552
          (case find_index (curry (op =) U) lives of
blanchet@51808
   553
            ~1 => Term.dummy
blanchet@51808
   554
          | i => nth sets i);
blanchet@51808
   555
      in
blanchet@51808
   556
        (T_name, map mk_set Us)
blanchet@51808
   557
      end;
blanchet@51808
   558
blanchet@51808
   559
    val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@51808
   560
blanchet@51808
   561
    val (induct_thms, induct_thm) =
blanchet@51808
   562
      let
blanchet@51808
   563
        fun mk_set Ts t =
blanchet@51808
   564
          let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@51808
   565
            Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@51808
   566
          end;
blanchet@51808
   567
blanchet@52310
   568
        fun mk_raw_prem_prems _ (x as Free (_, Type _)) (X as TFree _) =
blanchet@52310
   569
            [([], (find_index (curry (op =) X) Xs + 1, x))]
blanchet@52310
   570
          | mk_raw_prem_prems names_lthy (x as Free (s, Type (T_name, Ts0))) (Type (_, Xs_Ts0)) =
blanchet@52310
   571
            (case AList.lookup (op =) setss_nested T_name of
blanchet@52310
   572
              NONE => []
blanchet@52310
   573
            | SOME raw_sets0 =>
blanchet@52310
   574
              let
blanchet@52310
   575
                val (Xs_Ts, (Ts, raw_sets)) =
blanchet@52310
   576
                  filter (exists_subtype_in Xs o fst) (Xs_Ts0 ~~ (Ts0 ~~ raw_sets0))
blanchet@52310
   577
                  |> split_list ||> split_list;
blanchet@52310
   578
                val sets = map (mk_set Ts0) raw_sets;
blanchet@52310
   579
                val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@52310
   580
                val xysets = map (pair x) (ys ~~ sets);
blanchet@52310
   581
                val ppremss = map2 (mk_raw_prem_prems names_lthy') ys Xs_Ts;
blanchet@52310
   582
              in
blanchet@52310
   583
                flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@52310
   584
              end)
blanchet@52310
   585
          | mk_raw_prem_prems _ _ _ = [];
blanchet@51808
   586
blanchet@51808
   587
        fun close_prem_prem xs t =
blanchet@51808
   588
          fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@51808
   589
            (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@51808
   590
blanchet@51808
   591
        fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@51808
   592
          close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@51808
   593
              HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@51808
   594
            HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@51808
   595
blanchet@52310
   596
        fun mk_raw_prem phi ctr ctr_Ts ctrXs_Ts =
blanchet@51808
   597
          let
blanchet@51808
   598
            val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@52310
   599
            val pprems = flat (map2 (mk_raw_prem_prems names_lthy') xs ctrXs_Ts);
blanchet@51808
   600
          in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@51808
   601
blanchet@51808
   602
        fun mk_prem (xs, raw_pprems, concl) =
blanchet@51808
   603
          fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@51808
   604
blanchet@52310
   605
        val raw_premss = map4 (map3 o mk_raw_prem) ps ctrss ctr_Tsss ctrXs_Tsss;
blanchet@51808
   606
blanchet@51808
   607
        val goal =
blanchet@51808
   608
          Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@51808
   609
            HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@51808
   610
blanchet@51808
   611
        val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@51808
   612
blanchet@51814
   613
        val ctor_induct' = ctor_induct OF (map mk_sumEN_tupled_balanced mss);
blanchet@51808
   614
blanchet@51808
   615
        val thm =
blanchet@51808
   616
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51808
   617
            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
blanchet@51808
   618
              pre_set_defss)
blanchet@51808
   619
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51808
   620
          |> Thm.close_derivation;
blanchet@51808
   621
      in
blanchet@51808
   622
        `(conj_dests nn) thm
blanchet@51808
   623
      end;
blanchet@51808
   624
blanchet@51808
   625
    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@52305
   626
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@51808
   627
blanchet@52305
   628
    val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@52305
   629
blanchet@52306
   630
    fun mk_iter_thmss (_, x_Tssss, fss, _) iters iter_defs ctor_iter_thms =
blanchet@51808
   631
      let
blanchet@52305
   632
        val fiters = map (lists_bmoc fss) iters;
blanchet@51808
   633
blanchet@51843
   634
        fun mk_goal fss fiter xctr f xs fxs =
blanchet@51808
   635
          fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@51843
   636
            (mk_Trueprop_eq (fiter $ xctr, Term.list_comb (f, fxs)));
blanchet@51808
   637
blanchet@52302
   638
        fun maybe_tick (T, U) u f =
blanchet@52302
   639
          if try (fst o HOLogic.dest_prodT) U = SOME T then
blanchet@52302
   640
            Term.lambda u (HOLogic.mk_prod (u, f $ u))
blanchet@52302
   641
          else
blanchet@52302
   642
            f;
blanchet@51808
   643
blanchet@52368
   644
        fun build_iter (x as Free (_, T)) U =
blanchet@52368
   645
          if T = U then
blanchet@52368
   646
            x
blanchet@52368
   647
          else
blanchet@52303
   648
            build_map lthy (indexify (perhaps (try (snd o HOLogic.dest_prodT)) o snd) Cs
blanchet@52368
   649
              (fn kk => fn TU => maybe_tick TU (nth us kk) (nth fiters kk))) (T, U) $ x;
blanchet@52301
   650
blanchet@52868
   651
        val fxsss = map2 (map2 (flat_rec_arg_args oo map2 (map o build_iter))) xsss x_Tssss;
blanchet@51808
   652
blanchet@52306
   653
        val goalss = map5 (map4 o mk_goal fss) fiters xctrss fss xsss fxsss;
blanchet@51808
   654
blanchet@52305
   655
        val tacss =
blanchet@52305
   656
          map2 (map o mk_iter_tac pre_map_defs (nested_map_ids'' @ nesting_map_ids'') iter_defs)
blanchet@52305
   657
            ctor_iter_thms ctr_defss;
blanchet@51808
   658
blanchet@51808
   659
        fun prove goal tac =
blanchet@51808
   660
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51808
   661
          |> Thm.close_derivation;
blanchet@51808
   662
      in
blanchet@52305
   663
        map2 (map2 prove) goalss tacss
blanchet@51808
   664
      end;
blanchet@51808
   665
blanchet@52340
   666
    val fold_thmss = mk_iter_thmss fold_args_types folds fold_defs (map un_fold_of ctor_iter_thmss);
blanchet@52340
   667
    val rec_thmss = mk_iter_thmss rec_args_types recs rec_defs (map co_rec_of ctor_iter_thmss);
blanchet@51808
   668
  in
blanchet@52345
   669
    ((induct_thms, induct_thm, [induct_case_names_attr]),
blanchet@51808
   670
     (fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
blanchet@51808
   671
  end;
blanchet@51808
   672
blanchet@52347
   673
fun derive_coinduct_coiters_thms_for_types pre_bnfs (z, cs, cpss,
blanchet@52869
   674
      coiters_args_types as [((pgss, crgsss), _), ((phss, cshsss), _)])
blanchet@52344
   675
    dtor_coinducts dtor_ctors dtor_coiter_thmss nesting_bnfs nested_bnfs fpTs Cs As kss mss ns
blanchet@52357
   676
    ctr_defss ctr_sugars coiterss coiter_defss export_args lthy =
blanchet@51810
   677
  let
blanchet@52339
   678
    val coiterss' = transpose coiterss;
blanchet@52339
   679
    val coiter_defss' = transpose coiter_defss;
blanchet@52339
   680
blanchet@52339
   681
    val [unfold_defs, corec_defs] = coiter_defss';
blanchet@52338
   682
blanchet@51815
   683
    val nn = length pre_bnfs;
blanchet@51815
   684
blanchet@51810
   685
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51810
   686
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@52355
   687
    val nesting_map_ids'' = map (unfold_thms lthy [id_def] o map_id_of_bnf) nesting_bnfs;
blanchet@51830
   688
    val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@51810
   689
    val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
blanchet@52355
   690
    val nested_map_ids'' = map (unfold_thms lthy [id_def] o map_id_of_bnf) nested_bnfs;
blanchet@51810
   691
blanchet@51816
   692
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   693
blanchet@51840
   694
    val ctrss = map (map (mk_ctr As) o #ctrs) ctr_sugars;
blanchet@51840
   695
    val discss = map (map (mk_disc_or_sel As) o #discs) ctr_sugars;
blanchet@51840
   696
    val selsss = map (map (map (mk_disc_or_sel As)) o #selss) ctr_sugars;
blanchet@51840
   697
    val exhausts = map #exhaust ctr_sugars;
blanchet@51840
   698
    val disc_thmsss = map #disc_thmss ctr_sugars;
blanchet@51840
   699
    val discIss = map #discIs ctr_sugars;
blanchet@51840
   700
    val sel_thmsss = map #sel_thmss ctr_sugars;
blanchet@51810
   701
blanchet@51810
   702
    val (((rs, us'), vs'), names_lthy) =
blanchet@52341
   703
      lthy
blanchet@51810
   704
      |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@51816
   705
      ||>> Variable.variant_fixes fp_b_names
blanchet@51816
   706
      ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@51810
   707
blanchet@51810
   708
    val us = map2 (curry Free) us' fpTs;
blanchet@51810
   709
    val udiscss = map2 (map o rapp) us discss;
blanchet@51810
   710
    val uselsss = map2 (map o map o rapp) us selsss;
blanchet@51810
   711
blanchet@51810
   712
    val vs = map2 (curry Free) vs' fpTs;
blanchet@51810
   713
    val vdiscss = map2 (map o rapp) vs discss;
blanchet@51810
   714
    val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@51810
   715
blanchet@52345
   716
    val coinduct_thms_pairs =
blanchet@51810
   717
      let
blanchet@51810
   718
        val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@51810
   719
        val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@51810
   720
        val strong_rs =
blanchet@51810
   721
          map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@51810
   722
            fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@51810
   723
blanchet@52347
   724
        (* TODO: generalize (cf. "build_map") *)
blanchet@51810
   725
        fun build_rel rs' T =
blanchet@51810
   726
          (case find_index (curry (op =) T) fpTs of
blanchet@51810
   727
            ~1 =>
blanchet@51856
   728
            if exists_subtype_in fpTs T then
blanchet@51856
   729
              let
blanchet@51856
   730
                val Type (s, Ts) = T
blanchet@51856
   731
                val bnf = the (bnf_of lthy s);
blanchet@51856
   732
                val live = live_of_bnf bnf;
blanchet@51856
   733
                val rel = mk_rel live Ts Ts (rel_of_bnf bnf);
blanchet@51856
   734
                val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel)));
blanchet@51856
   735
              in Term.list_comb (rel, map (build_rel rs') Ts') end
blanchet@51856
   736
            else
blanchet@51856
   737
              HOLogic.eq_const T
blanchet@51810
   738
          | kk => nth rs' kk);
blanchet@51810
   739
blanchet@51856
   740
        fun build_rel_app rs' usel vsel = fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
blanchet@51810
   741
blanchet@51810
   742
        fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
blanchet@51810
   743
          (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@51810
   744
          (if null usels then
blanchet@51810
   745
             []
blanchet@51810
   746
           else
blanchet@51810
   747
             [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@51810
   748
                Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
blanchet@51810
   749
blanchet@51810
   750
        fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
blanchet@51810
   751
          Library.foldr1 HOLogic.mk_conj
blanchet@51810
   752
            (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
blanchet@51810
   753
          handle List.Empty => @{term True};
blanchet@51810
   754
blanchet@51810
   755
        fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
blanchet@51810
   756
          fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@51810
   757
            HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
blanchet@51810
   758
blanchet@51810
   759
        val concl =
blanchet@51810
   760
          HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@51810
   761
            (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@51810
   762
               uvrs us vs));
blanchet@51810
   763
blanchet@51810
   764
        fun mk_goal rs' =
blanchet@51810
   765
          Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
blanchet@51810
   766
            concl);
blanchet@51810
   767
blanchet@52345
   768
        val goals = map mk_goal [rs, strong_rs];
blanchet@51810
   769
blanchet@51810
   770
        fun prove dtor_coinduct' goal =
blanchet@51810
   771
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@51810
   772
            mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
blanchet@51819
   773
              exhausts ctr_defss disc_thmsss sel_thmsss)
blanchet@51810
   774
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   775
          |> Thm.close_derivation;
blanchet@51810
   776
blanchet@51810
   777
        fun postproc nn thm =
blanchet@51810
   778
          Thm.permute_prems 0 nn
blanchet@51828
   779
            (if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@51810
   780
          |> Drule.zero_var_indexes
blanchet@51810
   781
          |> `(conj_dests nn);
blanchet@51810
   782
      in
blanchet@52345
   783
        map2 (postproc nn oo prove) dtor_coinducts goals
blanchet@51810
   784
      end;
blanchet@51810
   785
blanchet@51810
   786
    fun mk_coinduct_concls ms discs ctrs =
blanchet@51810
   787
      let
blanchet@51810
   788
        fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51810
   789
        fun mk_ctr_concl 0 _ = []
blanchet@51810
   790
          | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51810
   791
        val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51810
   792
        val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51810
   793
      in
blanchet@51810
   794
        flat (map2 append disc_concls ctr_concls)
blanchet@51810
   795
      end;
blanchet@51810
   796
blanchet@51816
   797
    val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51810
   798
    val coinduct_conclss =
blanchet@51810
   799
      map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51810
   800
blanchet@51810
   801
    fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@51810
   802
blanchet@52339
   803
    val fcoiterss' as [gunfolds, hcorecs] =
blanchet@52869
   804
      map2 (fn (pfss, _) => map (lists_bmoc pfss)) (map fst coiters_args_types) coiterss';
blanchet@51810
   805
blanchet@51810
   806
    val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
blanchet@51810
   807
      let
blanchet@51843
   808
        fun mk_goal pfss c cps fcoiter n k ctr m cfs' =
blanchet@51810
   809
          fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@51810
   810
            (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@51843
   811
               mk_Trueprop_eq (fcoiter $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@51810
   812
blanchet@52347
   813
        fun mk_U maybe_mk_sumT =
blanchet@52347
   814
          typ_subst_nonatomic (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@52347
   815
blanchet@52347
   816
        fun tack z_name (c, u) f =
blanchet@52347
   817
          let val z = Free (z_name, mk_sumT (fastype_of u, fastype_of c)) in
blanchet@52347
   818
            Term.lambda z (mk_sum_case (Term.lambda u u, Term.lambda c (f $ c)) $ z)
blanchet@52347
   819
          end;
blanchet@51810
   820
blanchet@52368
   821
        fun build_coiter fcoiters maybe_mk_sumT maybe_tack cqf =
blanchet@52347
   822
          let val T = fastype_of cqf in
blanchet@52347
   823
            if exists_subtype_in Cs T then
blanchet@52368
   824
              let val U = mk_U maybe_mk_sumT T in
blanchet@52368
   825
                build_map lthy (indexify snd fpTs (fn kk => fn TU =>
blanchet@52368
   826
                  maybe_tack (nth cs kk, nth us kk) (nth fcoiters kk))) (T, U) $ cqf
blanchet@52368
   827
              end
blanchet@52347
   828
            else
blanchet@52347
   829
              cqf
blanchet@52347
   830
          end;
blanchet@51810
   831
blanchet@52368
   832
        val crgsss' = map (map (map (build_coiter (un_fold_of fcoiterss') (K I) (K I)))) crgsss;
blanchet@52368
   833
        val cshsss' = map (map (map (build_coiter (co_rec_of fcoiterss') (curry mk_sumT) (tack z))))
blanchet@52351
   834
          cshsss;
blanchet@51810
   835
blanchet@52347
   836
        val unfold_goalss = map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss';
blanchet@52347
   837
        val corec_goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss';
blanchet@51810
   838
blanchet@51810
   839
        fun mk_map_if_distrib bnf =
blanchet@51810
   840
          let
blanchet@51810
   841
            val mapx = map_of_bnf bnf;
blanchet@51810
   842
            val live = live_of_bnf bnf;
blanchet@51810
   843
            val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
blanchet@51810
   844
            val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
blanchet@51810
   845
            val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
blanchet@51810
   846
          in
blanchet@51810
   847
            Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
blanchet@51810
   848
              @{thm if_distrib}
blanchet@51810
   849
          end;
blanchet@51810
   850
blanchet@51810
   851
        val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
blanchet@51810
   852
blanchet@51810
   853
        val unfold_tacss =
blanchet@52349
   854
          map3 (map oo mk_coiter_tac unfold_defs nesting_map_ids'')
blanchet@52340
   855
            (map un_fold_of dtor_coiter_thmss) pre_map_defs ctr_defss;
blanchet@51810
   856
        val corec_tacss =
blanchet@52349
   857
          map3 (map oo mk_coiter_tac corec_defs nesting_map_ids'')
blanchet@52340
   858
            (map co_rec_of dtor_coiter_thmss) pre_map_defs ctr_defss;
blanchet@51810
   859
blanchet@51810
   860
        fun prove goal tac =
blanchet@51815
   861
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51815
   862
          |> Thm.close_derivation;
blanchet@51810
   863
blanchet@51810
   864
        val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@52347
   865
        val corec_thmss =
blanchet@52347
   866
          map2 (map2 prove) corec_goalss corec_tacss
blanchet@52347
   867
          |> map (map (unfold_thms lthy @{thms sum_case_if}));
blanchet@52347
   868
blanchet@52347
   869
        val unfold_safesss = map2 (map2 (map2 (curry (op =)))) crgsss' crgsss;
blanchet@52347
   870
        val corec_safesss = map2 (map2 (map2 (curry (op =)))) cshsss' cshsss;
blanchet@52347
   871
blanchet@51810
   872
        val filter_safesss =
blanchet@51810
   873
          map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
blanchet@52347
   874
            curry (op ~~));
blanchet@51810
   875
blanchet@52347
   876
        val safe_unfold_thmss = filter_safesss unfold_safesss unfold_thmss;
blanchet@52347
   877
        val safe_corec_thmss = filter_safesss corec_safesss corec_thmss;
blanchet@51810
   878
      in
blanchet@51810
   879
        (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
blanchet@51810
   880
      end;
blanchet@51810
   881
blanchet@51810
   882
    val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@51810
   883
      let
blanchet@51843
   884
        fun mk_goal c cps fcoiter n k disc =
blanchet@51843
   885
          mk_Trueprop_eq (disc $ (fcoiter $ c),
blanchet@51810
   886
            if n = 1 then @{const True}
blanchet@51810
   887
            else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@51810
   888
blanchet@51810
   889
        val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@51810
   890
        val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@51810
   891
blanchet@51828
   892
        fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@51810
   893
blanchet@51810
   894
        val case_splitss' = map (map mk_case_split') cpss;
blanchet@51810
   895
blanchet@51810
   896
        val unfold_tacss =
blanchet@51843
   897
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@51810
   898
        val corec_tacss =
blanchet@51843
   899
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@51810
   900
blanchet@51810
   901
        fun prove goal tac =
blanchet@51810
   902
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@52357
   903
          |> singleton export_args
blanchet@51829
   904
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   905
          |> Thm.close_derivation;
blanchet@51810
   906
blanchet@51810
   907
        fun proves [_] [_] = []
blanchet@51810
   908
          | proves goals tacs = map2 prove goals tacs;
blanchet@51810
   909
      in
blanchet@51828
   910
        (map2 proves unfold_goalss unfold_tacss, map2 proves corec_goalss corec_tacss)
blanchet@51810
   911
      end;
blanchet@51810
   912
blanchet@51810
   913
    val is_triv_discI = is_triv_implies orf is_concl_refl;
blanchet@51810
   914
blanchet@51843
   915
    fun mk_disc_coiter_thms coiters discIs =
blanchet@51843
   916
      map (op RS) (filter_out (is_triv_discI o snd) (coiters ~~ discIs));
blanchet@51810
   917
blanchet@51843
   918
    val disc_unfold_thmss = map2 mk_disc_coiter_thms unfold_thmss discIss;
blanchet@51843
   919
    val disc_corec_thmss = map2 mk_disc_coiter_thms corec_thmss discIss;
blanchet@51810
   920
blanchet@51843
   921
    fun mk_sel_coiter_thm coiter_thm sel sel_thm =
blanchet@51810
   922
      let
blanchet@51810
   923
        val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@51810
   924
        val arg_cong' =
blanchet@51810
   925
          Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@51810
   926
            [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@51810
   927
          |> Thm.varifyT_global;
blanchet@51810
   928
        val sel_thm' = sel_thm RSN (2, trans);
blanchet@51810
   929
      in
blanchet@51843
   930
        coiter_thm RS arg_cong' RS sel_thm'
blanchet@51810
   931
      end;
blanchet@51810
   932
blanchet@52321
   933
    fun mk_sel_coiter_thms coiter_thmss =
blanchet@52321
   934
      map3 (map3 (map2 o mk_sel_coiter_thm)) coiter_thmss selsss sel_thmsss |> map flat;
blanchet@51810
   935
blanchet@51843
   936
    val sel_unfold_thmss = mk_sel_coiter_thms unfold_thmss;
blanchet@51843
   937
    val sel_corec_thmss = mk_sel_coiter_thms corec_thmss;
blanchet@51810
   938
blanchet@51810
   939
    val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51810
   940
    val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51810
   941
    val coinduct_case_concl_attrs =
blanchet@51810
   942
      map2 (fn casex => fn concls =>
blanchet@51810
   943
          Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51810
   944
        coinduct_cases coinduct_conclss;
blanchet@51810
   945
    val coinduct_case_attrs =
blanchet@51810
   946
      coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51810
   947
  in
blanchet@52345
   948
    ((coinduct_thms_pairs, coinduct_case_attrs),
blanchet@51810
   949
     (unfold_thmss, corec_thmss, []),
blanchet@51810
   950
     (safe_unfold_thmss, safe_corec_thmss),
blanchet@51810
   951
     (disc_unfold_thmss, disc_corec_thmss, simp_attrs),
blanchet@51810
   952
     (disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs),
blanchet@51810
   953
     (sel_unfold_thmss, sel_corec_thmss, simp_attrs))
blanchet@51810
   954
  end;
blanchet@51810
   955
blanchet@52207
   956
fun define_co_datatypes prepare_constraint prepare_typ prepare_term fp construct_fp
blanchet@49633
   957
    (wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 =
blanchet@49112
   958
  let
blanchet@49298
   959
    (* TODO: sanity checks on arguments *)
blanchet@49298
   960
blanchet@52207
   961
    val _ = if fp = Greatest_FP andalso no_dests then
blanchet@52207
   962
        error "Cannot define destructor-less codatatypes"
blanchet@52207
   963
      else
blanchet@52207
   964
        ();
blanchet@49278
   965
blanchet@49633
   966
    fun qualify mandatory fp_b_name =
blanchet@49633
   967
      Binding.qualify mandatory fp_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
blanchet@49633
   968
blanchet@49367
   969
    val nn = length specs;
blanchet@49361
   970
    val fp_bs = map type_binding_of specs;
blanchet@49498
   971
    val fp_b_names = map Binding.name_of fp_bs;
blanchet@49498
   972
    val fp_common_name = mk_common_name fp_b_names;
blanchet@51758
   973
    val map_bs = map map_binding_of specs;
blanchet@51767
   974
    val rel_bs = map rel_binding_of specs;
blanchet@49298
   975
blanchet@51758
   976
    fun prepare_type_arg (_, (ty, c)) =
blanchet@49298
   977
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
   978
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
   979
      end;
blanchet@49298
   980
blanchet@51758
   981
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of) specs;
blanchet@49298
   982
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@49298
   983
    val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0;
blanchet@51758
   984
    val set_bss = map (map fst o type_args_named_constrained_of) specs;
blanchet@49119
   985
blanchet@49585
   986
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
   987
      no_defs_lthy0
blanchet@49298
   988
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@49585
   989
      |> mk_TFrees (length unsorted_As)
blanchet@49585
   990
      ||>> mk_TFrees nn
blanchet@51858
   991
      ||>> variant_tfrees fp_b_names;
blanchet@49119
   992
blanchet@52195
   993
    (* TODO: Cleaner handling of fake contexts, without "background_theory". The case where the new
blanchet@52195
   994
       type is defined in a locale and shadows an existing global type is currently not handled. *)
blanchet@51768
   995
blanchet@51769
   996
    fun add_fake_type spec =
blanchet@51768
   997
      Sign.add_type no_defs_lthy (type_binding_of spec,
blanchet@51769
   998
        length (type_args_named_constrained_of spec), mixfix_of spec);
blanchet@51768
   999
wenzelm@52788
  1000
    val fake_thy = fold add_fake_type specs;
blanchet@49298
  1001
    val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy;
blanchet@49119
  1002
blanchet@49182
  1003
    fun mk_fake_T b =
blanchet@49121
  1004
      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
blanchet@49298
  1005
        unsorted_As);
blanchet@49121
  1006
blanchet@49302
  1007
    val fake_Ts = map mk_fake_T fp_bs;
blanchet@49121
  1008
blanchet@49181
  1009
    val mixfixes = map mixfix_of specs;
blanchet@49119
  1010
blanchet@49302
  1011
    val _ = (case duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
  1012
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
  1013
blanchet@49121
  1014
    val ctr_specss = map ctr_specs_of specs;
blanchet@49119
  1015
blanchet@49336
  1016
    val disc_bindingss = map (map disc_of) ctr_specss;
blanchet@49336
  1017
    val ctr_bindingss =
blanchet@49633
  1018
      map2 (fn fp_b_name => map (qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss;
blanchet@49121
  1019
    val ctr_argsss = map (map args_of) ctr_specss;
blanchet@49181
  1020
    val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss;
blanchet@49119
  1021
blanchet@49336
  1022
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
  1023
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@49286
  1024
    val raw_sel_defaultsss = map (map defaults_of) ctr_specss;
blanchet@49286
  1025
blanchet@49308
  1026
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
  1027
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@49298
  1028
blanchet@49298
  1029
    val _ = (case duplicates (op =) unsorted_As of [] => ()
blanchet@49298
  1030
      | A :: _ => error ("Duplicate type parameter " ^
blanchet@49298
  1031
          quote (Syntax.string_of_typ no_defs_lthy A)));
blanchet@49298
  1032
blanchet@49183
  1033
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@49298
  1034
    val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of
blanchet@49165
  1035
        [] => ()
blanchet@49342
  1036
      | A' :: _ => error ("Extra type variable on right-hand side: " ^
blanchet@49204
  1037
          quote (Syntax.string_of_typ no_defs_lthy (TFree A'))));
blanchet@49165
  1038
blanchet@49591
  1039
    fun eq_fpT_check (T as Type (s, Us)) (Type (s', Us')) =
blanchet@49146
  1040
        s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
blanchet@49146
  1041
          quote (Syntax.string_of_typ fake_lthy T)))
blanchet@49591
  1042
      | eq_fpT_check _ _ = false;
blanchet@49146
  1043
blanchet@49204
  1044
    fun freeze_fp (T as Type (s, Us)) =
blanchet@49591
  1045
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@49591
  1046
          ~1 => Type (s, map freeze_fp Us)
blanchet@49591
  1047
        | kk => nth Xs kk)
blanchet@49204
  1048
      | freeze_fp T = T;
blanchet@49121
  1049
blanchet@52310
  1050
    val ctrXs_Tsss = map (map (map freeze_fp)) fake_ctr_Tsss;
blanchet@52310
  1051
    val ctrXs_sum_prod_Ts = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctrXs_Tsss;
blanchet@49119
  1052
blanchet@49298
  1053
    val fp_eqs =
blanchet@52310
  1054
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctrXs_sum_prod_Ts;
blanchet@49121
  1055
blanchet@51839
  1056
    val (pre_bnfs, (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0, dtors = dtors0,
blanchet@52344
  1057
           xtor_co_iterss = xtor_co_iterss0, xtor_co_inducts, dtor_ctors, ctor_dtors, ctor_injects,
blanchet@52344
  1058
           xtor_map_thms, xtor_set_thmss, xtor_rel_thms, xtor_co_iter_thmss, ...}, lthy)) =
blanchet@51868
  1059
      fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As) fp_eqs
blanchet@51868
  1060
        no_defs_lthy0;
blanchet@49585
  1061
blanchet@49585
  1062
    val timer = time (Timer.startRealTimer ());
blanchet@49121
  1063
blanchet@52310
  1064
    val nesting_bnfs = nesty_bnfs lthy ctrXs_Tsss As;
blanchet@52310
  1065
    val nested_bnfs = nesty_bnfs lthy ctrXs_Tsss Xs;
blanchet@49226
  1066
blanchet@49585
  1067
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
  1068
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
  1069
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@51830
  1070
    val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
blanchet@51766
  1071
    val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
blanchet@49585
  1072
blanchet@49585
  1073
    val live = live_of_bnf any_fp_bnf;
blanchet@49585
  1074
blanchet@49585
  1075
    val Bs =
blanchet@49585
  1076
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@49585
  1077
        (liveness_of_fp_bnf (length As) any_fp_bnf) As Bs0;
blanchet@49585
  1078
blanchet@49585
  1079
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
  1080
blanchet@49501
  1081
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
  1082
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
  1083
blanchet@49501
  1084
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
  1085
blanchet@51780
  1086
    fun massage_simple_notes base =
blanchet@51780
  1087
      filter_out (null o #2)
blanchet@51780
  1088
      #> map (fn (thmN, thms, attrs) =>
blanchet@51780
  1089
        ((qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
  1090
blanchet@51780
  1091
    val massage_multi_notes =
blanchet@51780
  1092
      maps (fn (thmN, thmss, attrs) =>
blanchet@51780
  1093
        if forall null thmss then
blanchet@51780
  1094
          []
blanchet@51780
  1095
        else
blanchet@51780
  1096
          map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@52311
  1097
              ((qualify true fp_b_name (Binding.name thmN), attrs T_name), [(thms, [])]))
blanchet@52311
  1098
            fp_b_names fpTs thmss);
blanchet@51780
  1099
blanchet@52310
  1100
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctrXs_Tsss;
blanchet@49203
  1101
    val ns = map length ctr_Tsss;
blanchet@49212
  1102
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
  1103
    val mss = map (map length) ctr_Tsss;
blanchet@49203
  1104
blanchet@52367
  1105
    val ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy') =
blanchet@52334
  1106
      mk_co_iters_prelims fp fpTs Cs ns mss xtor_co_iterss0 lthy;
blanchet@49210
  1107
blanchet@52328
  1108
    fun define_ctrs_case_for_type ((((((((((((((((((((((((fp_bnf, fp_b), fpT), C), ctor), dtor),
blanchet@52345
  1109
            xtor_co_iters), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
blanchet@52345
  1110
          pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), ctr_bindings),
blanchet@52345
  1111
        ctr_mixfixes), ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
  1112
      let
blanchet@49498
  1113
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
  1114
blanchet@49501
  1115
        val dtorT = domain_type (fastype_of ctor);
blanchet@49210
  1116
        val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49255
  1117
        val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts;
blanchet@49134
  1118
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
  1119
blanchet@49593
  1120
        val (((((w, fs), xss), yss), u'), names_lthy) =
blanchet@49204
  1121
          no_defs_lthy
blanchet@49501
  1122
          |> yield_singleton (mk_Frees "w") dtorT
blanchet@49176
  1123
          ||>> mk_Frees "f" case_Ts
blanchet@49370
  1124
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
  1125
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
  1126
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
  1127
blanchet@49498
  1128
        val u = Free (u', fpT);
blanchet@49121
  1129
blanchet@49585
  1130
        val tuple_xs = map HOLogic.mk_tuple xss;
blanchet@49585
  1131
        val tuple_ys = map HOLogic.mk_tuple yss;
blanchet@49585
  1132
blanchet@49129
  1133
        val ctr_rhss =
blanchet@49585
  1134
          map3 (fn k => fn xs => fn tuple_x => fold_rev Term.lambda xs (ctor $
blanchet@49585
  1135
            mk_InN_balanced ctr_sum_prod_T n tuple_x k)) ks xss tuple_xs;
blanchet@49121
  1136
blanchet@49633
  1137
        val case_binding = qualify false fp_b_name (Binding.suffix_name ("_" ^ caseN) fp_b);
blanchet@49129
  1138
blanchet@49134
  1139
        val case_rhs =
blanchet@49498
  1140
          fold_rev Term.lambda (fs @ [u])
blanchet@49501
  1141
            (mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u));
blanchet@49129
  1142
blanchet@49201
  1143
        val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
  1144
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49302
  1145
              Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49336
  1146
            (case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss)
blanchet@49121
  1147
          ||> `Local_Theory.restore;
blanchet@49121
  1148
blanchet@49121
  1149
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
  1150
blanchet@49121
  1151
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
  1152
        val ctr_defs' =
blanchet@49585
  1153
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
  1154
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
  1155
blanchet@49203
  1156
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
  1157
        val casex0 = Morphism.term phi raw_case;
blanchet@49203
  1158
blanchet@49203
  1159
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
  1160
blanchet@51897
  1161
        fun wrap_ctrs lthy =
blanchet@49123
  1162
          let
traytel@50170
  1163
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
  1164
              let
blanchet@49585
  1165
                val ctor_iff_dtor_thm =
blanchet@49585
  1166
                  let
blanchet@49585
  1167
                    val goal =
blanchet@49585
  1168
                      fold_rev Logic.all [w, u]
blanchet@49585
  1169
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
  1170
                  in
wenzelm@51551
  1171
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49585
  1172
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT])
blanchet@49585
  1173
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@49585
  1174
                    |> Thm.close_derivation
blanchet@49585
  1175
                    |> Morphism.thm phi
blanchet@49585
  1176
                  end;
blanchet@49585
  1177
blanchet@49585
  1178
                val sumEN_thm' =
traytel@52659
  1179
                  unfold_thms lthy @{thms unit_all_eq1}
blanchet@49585
  1180
                    (Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) []
blanchet@49585
  1181
                       (mk_sumEN_balanced n))
blanchet@49585
  1182
                  |> Morphism.thm phi;
blanchet@49135
  1183
              in
blanchet@49585
  1184
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
  1185
              end;
blanchet@49135
  1186
blanchet@49585
  1187
            val inject_tacss =
blanchet@49585
  1188
              map2 (fn 0 => K [] | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49585
  1189
                  mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs;
blanchet@49585
  1190
blanchet@49585
  1191
            val half_distinct_tacss =
blanchet@49585
  1192
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49585
  1193
                mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss (`I ctr_defs));
blanchet@49585
  1194
blanchet@49585
  1195
            val case_tacs =
blanchet@49585
  1196
              map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49585
  1197
                mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs;
blanchet@49585
  1198
blanchet@49585
  1199
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49585
  1200
blanchet@49585
  1201
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@49123
  1202
          in
blanchet@51781
  1203
            wrap_free_constructors tacss (((wrap_opts, ctrs0), casex0), (disc_bindings,
blanchet@51781
  1204
              (sel_bindingss, sel_defaultss))) lthy
blanchet@49123
  1205
          end;
blanchet@49121
  1206
blanchet@51840
  1207
        fun derive_maps_sets_rels (ctr_sugar, lthy) =
blanchet@51835
  1208
          if live = 0 then
blanchet@51840
  1209
            ((([], [], [], []), ctr_sugar), lthy)
blanchet@51835
  1210
          else
blanchet@51835
  1211
            let
blanchet@51835
  1212
              val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@51835
  1213
              val nones = replicate live NONE;
blanchet@49585
  1214
blanchet@51835
  1215
              val ctor_cong =
blanchet@52207
  1216
                if fp = Least_FP then
blanchet@51835
  1217
                  Drule.dummy_thm
blanchet@51835
  1218
                else
blanchet@51835
  1219
                  let val ctor' = mk_ctor Bs ctor in
blanchet@51835
  1220
                    cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51835
  1221
                  end;
blanchet@49585
  1222
blanchet@51835
  1223
              fun mk_cIn ify =
blanchet@52207
  1224
                certify lthy o (fp = Greatest_FP ? curry (op $) (map_types ify ctor)) oo
blanchet@51835
  1225
                mk_InN_balanced (ify ctr_sum_prod_T) n;
blanchet@49585
  1226
blanchet@51835
  1227
              val cxIns = map2 (mk_cIn I) tuple_xs ks;
blanchet@51835
  1228
              val cyIns = map2 (mk_cIn B_ify) tuple_ys ks;
blanchet@49585
  1229
blanchet@51835
  1230
              fun mk_map_thm ctr_def' cxIn =
blanchet@51835
  1231
                fold_thms lthy [ctr_def']
blanchet@51835
  1232
                  (unfold_thms lthy (pre_map_def ::
blanchet@52207
  1233
                       (if fp = Least_FP then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map)
blanchet@51835
  1234
                     (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@52207
  1235
                        (if fp = Least_FP then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@51835
  1236
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1237
blanchet@51835
  1238
              fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@51835
  1239
                fold_thms lthy [ctr_def']
blanchet@51835
  1240
                  (unfold_thms lthy (pre_set_defs @ nested_set_map's @ nesting_set_map's @
blanchet@52207
  1241
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_set)
blanchet@51835
  1242
                     (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@51835
  1243
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1244
blanchet@51835
  1245
              fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49127
  1246
blanchet@51835
  1247
              val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@51835
  1248
              val set_thmss = map mk_set_thms fp_set_thms;
blanchet@51835
  1249
blanchet@51835
  1250
              val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
  1251
blanchet@51835
  1252
              fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@51835
  1253
                fold_thms lthy ctr_defs'
blanchet@51835
  1254
                   (unfold_thms lthy (@{thm Inl_Inr_False} :: pre_rel_def ::
blanchet@52207
  1255
                        (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_rel)
blanchet@51835
  1256
                      (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@51835
  1257
                |> postproc
blanchet@51835
  1258
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1259
blanchet@51835
  1260
              fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@51835
  1261
                mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
  1262
blanchet@51835
  1263
              val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
  1264
blanchet@51835
  1265
              fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@51835
  1266
                mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@51835
  1267
                  cxIn cyIn;
blanchet@49121
  1268
blanchet@51835
  1269
              fun mk_other_half_rel_distinct_thm thm =
blanchet@51835
  1270
                flip_rels lthy live thm
blanchet@51835
  1271
                RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
  1272
blanchet@51835
  1273
              val half_rel_distinct_thmss =
blanchet@51835
  1274
                map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@51835
  1275
              val other_half_rel_distinct_thmss =
blanchet@51835
  1276
                map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@51835
  1277
              val (rel_distinct_thms, _) =
blanchet@51835
  1278
                join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
  1279
blanchet@51835
  1280
              val notes =
blanchet@51835
  1281
                [(mapN, map_thms, code_simp_attrs),
blanchet@51835
  1282
                 (rel_distinctN, rel_distinct_thms, code_simp_attrs),
blanchet@51835
  1283
                 (rel_injectN, rel_inject_thms, code_simp_attrs),
blanchet@51835
  1284
                 (setsN, flat set_thmss, code_simp_attrs)]
blanchet@51835
  1285
                |> massage_simple_notes fp_b_name;
blanchet@51835
  1286
            in
blanchet@51840
  1287
              (((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
blanchet@51835
  1288
               lthy |> Local_Theory.notes notes |> snd)
blanchet@51835
  1289
            end;
blanchet@49585
  1290
blanchet@51897
  1291
        fun mk_binding suf = qualify false fp_b_name (Binding.suffix_name ("_" ^ suf) fp_b);
blanchet@49287
  1292
blanchet@51883
  1293
        fun massage_res (((maps_sets_rels, ctr_sugar), co_iter_res), lthy) =
blanchet@51883
  1294
          (((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), co_iter_res), lthy);
blanchet@49119
  1295
      in
blanchet@51897
  1296
        (wrap_ctrs
blanchet@51835
  1297
         #> derive_maps_sets_rels
blanchet@52313
  1298
         ##>>
blanchet@52329
  1299
           (if fp = Least_FP then define_iters [foldN, recN] (the iters_args_types)
blanchet@52329
  1300
            else define_coiters [unfoldN, corecN] (the coiters_args_types))
blanchet@52328
  1301
             mk_binding fpTs Cs xtor_co_iters
blanchet@51835
  1302
         #> massage_res, lthy')
blanchet@49119
  1303
      end;
blanchet@49167
  1304
blanchet@51835
  1305
    fun wrap_types_etc (wrap_types_etcs, lthy) =
blanchet@51835
  1306
      fold_map I wrap_types_etcs lthy
blanchet@52342
  1307
      |>> apsnd split_list o apfst (apsnd split_list4 o apfst split_list4 o split_list)
blanchet@52342
  1308
        o split_list;
blanchet@49226
  1309
blanchet@49479
  1310
    val mk_simp_thmss =
blanchet@51857
  1311
      map7 (fn {injects, distincts, case_thms, ...} => fn un_folds => fn co_recs =>
blanchet@51835
  1312
        fn mapsx => fn rel_injects => fn rel_distincts => fn setss =>
blanchet@51857
  1313
          injects @ distincts @ case_thms @ co_recs @ un_folds @ mapsx @ rel_injects
blanchet@51835
  1314
          @ rel_distincts @ flat setss);
blanchet@49479
  1315
blanchet@52329
  1316
    fun derive_and_note_induct_iters_thms_for_types
blanchet@51840
  1317
        ((((mapsx, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
blanchet@52342
  1318
          (iterss, iter_defss)), lthy) =
blanchet@49202
  1319
      let
blanchet@52345
  1320
        val ((induct_thms, induct_thm, induct_attrs), (fold_thmss, fold_attrs),
blanchet@51808
  1321
             (rec_thmss, rec_attrs)) =
blanchet@52346
  1322
          derive_induct_iters_thms_for_types pre_bnfs (the iters_args_types) xtor_co_inducts
blanchet@52346
  1323
            xtor_co_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss iterss
blanchet@52346
  1324
            iter_defss lthy;
blanchet@49201
  1325
blanchet@51830
  1326
        val induct_type_attr = Attrib.internal o K o Induct.induct_type;
blanchet@51810
  1327
blanchet@51835
  1328
        val simp_thmss =
blanchet@51843
  1329
          mk_simp_thmss ctr_sugars fold_thmss rec_thmss mapsx rel_injects rel_distincts setss;
blanchet@49438
  1330
blanchet@49337
  1331
        val common_notes =
blanchet@51808
  1332
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
  1333
          |> massage_simple_notes fp_common_name;
blanchet@49337
  1334
blanchet@49226
  1335
        val notes =
blanchet@51808
  1336
          [(foldN, fold_thmss, K fold_attrs),
blanchet@51810
  1337
           (inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
blanchet@51808
  1338
           (recN, rec_thmss, K rec_attrs),
blanchet@49585
  1339
           (simpsN, simp_thmss, K [])]
blanchet@51780
  1340
          |> massage_multi_notes;
blanchet@49202
  1341
      in
blanchet@51824
  1342
        lthy
blanchet@51824
  1343
        |> Local_Theory.notes (common_notes @ notes) |> snd
blanchet@52356
  1344
        |> register_fp_sugars Least_FP pre_bnfs nested_bnfs fp_res ctr_defss ctr_sugars iterss
blanchet@52356
  1345
          [induct_thm] (transpose [fold_thmss, rec_thmss])
blanchet@49202
  1346
      end;
blanchet@49202
  1347
blanchet@52329
  1348
    fun derive_and_note_coinduct_coiters_thms_for_types
blanchet@51859
  1349
        ((((mapsx, rel_injects, rel_distincts, setss), (_, _, ctr_defss, ctr_sugars)),
blanchet@52342
  1350
          (coiterss, coiter_defss)), lthy) =
blanchet@49212
  1351
      let
blanchet@52345
  1352
        val (([(coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)],
blanchet@51810
  1353
              coinduct_attrs),
blanchet@51843
  1354
             (unfold_thmss, corec_thmss, coiter_attrs),
blanchet@51810
  1355
             (safe_unfold_thmss, safe_corec_thmss),
blanchet@51843
  1356
             (disc_unfold_thmss, disc_corec_thmss, disc_coiter_attrs),
blanchet@51843
  1357
             (disc_unfold_iff_thmss, disc_corec_iff_thmss, disc_coiter_iff_attrs),
blanchet@51843
  1358
             (sel_unfold_thmss, sel_corec_thmss, sel_coiter_attrs)) =
blanchet@52346
  1359
          derive_coinduct_coiters_thms_for_types pre_bnfs (the coiters_args_types) xtor_co_inducts
blanchet@52346
  1360
            dtor_ctors xtor_co_iter_thmss nesting_bnfs nested_bnfs fpTs Cs As kss mss ns ctr_defss
blanchet@52367
  1361
            ctr_sugars coiterss coiter_defss (Proof_Context.export lthy' no_defs_lthy)
blanchet@52367
  1362
            lthy;
blanchet@49212
  1363
blanchet@51830
  1364
        val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
blanchet@49479
  1365
blanchet@51843
  1366
        fun flat_coiter_thms coiters disc_coiters sel_coiters =
blanchet@51843
  1367
          coiters @ disc_coiters @ sel_coiters;
blanchet@49479
  1368
blanchet@49479
  1369
        val simp_thmss =
blanchet@51840
  1370
          mk_simp_thmss ctr_sugars
blanchet@51843
  1371
            (map3 flat_coiter_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss)
blanchet@51843
  1372
            (map3 flat_coiter_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
blanchet@51835
  1373
            mapsx rel_injects rel_distincts setss;
blanchet@49479
  1374
blanchet@49479
  1375
        val anonymous_notes =
blanchet@49504
  1376
          [(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
blanchet@49479
  1377
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49266
  1378
blanchet@49342
  1379
        val common_notes =
blanchet@49591
  1380
          (if nn > 1 then
blanchet@51810
  1381
             [(coinductN, [coinduct_thm], coinduct_attrs),
blanchet@51810
  1382
              (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
blanchet@49591
  1383
           else
blanchet@49591
  1384
             [])
blanchet@51780
  1385
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1386
blanchet@49212
  1387
        val notes =
blanchet@51780
  1388
          [(coinductN, map single coinduct_thms,
blanchet@51810
  1389
            fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
blanchet@51843
  1390
           (corecN, corec_thmss, K coiter_attrs),
blanchet@51843
  1391
           (disc_corecN, disc_corec_thmss, K disc_coiter_attrs),
blanchet@51843
  1392
           (disc_corec_iffN, disc_corec_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1393
           (disc_unfoldN, disc_unfold_thmss, K disc_coiter_attrs),
blanchet@51843
  1394
           (disc_unfold_iffN, disc_unfold_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1395
           (sel_corecN, sel_corec_thmss, K sel_coiter_attrs),
blanchet@51843
  1396
           (sel_unfoldN, sel_unfold_thmss, K sel_coiter_attrs),
blanchet@51780
  1397
           (simpsN, simp_thmss, K []),
blanchet@51810
  1398
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs),
blanchet@51843
  1399
           (unfoldN, unfold_thmss, K coiter_attrs)]
blanchet@51780
  1400
          |> massage_multi_notes;
blanchet@49212
  1401
      in
blanchet@51824
  1402
        lthy
blanchet@51824
  1403
        |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
blanchet@52356
  1404
        |> register_fp_sugars Greatest_FP pre_bnfs nested_bnfs fp_res ctr_defss ctr_sugars coiterss
blanchet@52343
  1405
          [coinduct_thm, strong_coinduct_thm] (transpose [unfold_thmss, corec_thmss])
blanchet@49212
  1406
      end;
blanchet@49212
  1407
blanchet@52367
  1408
    val lthy'' = lthy'
blanchet@49585
  1409
      |> fold_map define_ctrs_case_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~
blanchet@52330
  1410
        xtor_co_iterss ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@52314
  1411
        pre_set_defss ~~ pre_rel_defs ~~ xtor_map_thms ~~ xtor_set_thmss ~~ xtor_rel_thms ~~ ns ~~
blanchet@52314
  1412
        kss ~~ mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~
blanchet@52314
  1413
        sel_bindingsss ~~ raw_sel_defaultsss)
blanchet@51835
  1414
      |> wrap_types_etc
blanchet@52329
  1415
      |> (if fp = Least_FP then derive_and_note_induct_iters_thms_for_types
blanchet@52329
  1416
          else derive_and_note_coinduct_coiters_thms_for_types);
blanchet@49167
  1417
blanchet@49167
  1418
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@52207
  1419
      datatype_word fp));
blanchet@49112
  1420
  in
blanchet@52367
  1421
    timer; lthy''
blanchet@49112
  1422
  end;
blanchet@49112
  1423
blanchet@51863
  1424
val co_datatypes = define_co_datatypes (K I) (K I) (K I);
blanchet@49297
  1425
blanchet@51863
  1426
val co_datatype_cmd =
blanchet@51863
  1427
  define_co_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term;
blanchet@49119
  1428
blanchet@49112
  1429
val parse_ctr_arg =
blanchet@49329
  1430
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
traytel@49434
  1431
  (Parse.typ >> pair Binding.empty);
blanchet@49112
  1432
blanchet@49286
  1433
val parse_defaults =
blanchet@49286
  1434
  @{keyword "("} |-- @{keyword "defaults"} |-- Scan.repeat parse_bound_term --| @{keyword ")"};
blanchet@49286
  1435
blanchet@51758
  1436
val parse_type_arg_constrained =
blanchet@51790
  1437
  Parse.type_ident -- Scan.option (@{keyword "::"} |-- Parse.!!! Parse.sort);
blanchet@51758
  1438
blanchet@51790
  1439
val parse_type_arg_named_constrained = parse_opt_binding_colon -- parse_type_arg_constrained;
blanchet@51758
  1440
blanchet@51758
  1441
val parse_type_args_named_constrained =
blanchet@51758
  1442
  parse_type_arg_constrained >> (single o pair Binding.empty) ||
blanchet@51758
  1443
  @{keyword "("} |-- Parse.!!! (Parse.list1 parse_type_arg_named_constrained --| @{keyword ")"}) ||
blanchet@51756
  1444
  Scan.succeed [];
blanchet@51756
  1445
blanchet@51790
  1446
val parse_map_rel_binding = Parse.short_ident --| @{keyword ":"} -- parse_binding;
blanchet@51767
  1447
blanchet@51767
  1448
val no_map_rel = (Binding.empty, Binding.empty);
blanchet@51767
  1449
blanchet@51767
  1450
(* "map" and "rel" are purposedly not registered as keywords, because they are short and nice names
blanchet@51833
  1451
   that we don't want them to be highlighted everywhere. *)
blanchet@51767
  1452
fun extract_map_rel ("map", b) = apfst (K b)
blanchet@51767
  1453
  | extract_map_rel ("rel", b) = apsnd (K b)
blanchet@51767
  1454
  | extract_map_rel (s, _) = error ("Expected \"map\" or \"rel\" instead of " ^ quote s);
blanchet@49112
  1455
blanchet@51767
  1456
val parse_map_rel_bindings =
blanchet@51767
  1457
  @{keyword "("} |-- Scan.repeat parse_map_rel_binding --| @{keyword ")"}
blanchet@51767
  1458
    >> (fn ps => fold extract_map_rel ps no_map_rel) ||
blanchet@51767
  1459
  Scan.succeed no_map_rel;
blanchet@51767
  1460
blanchet@51767
  1461
val parse_ctr_spec =
blanchet@51790
  1462
  parse_opt_binding_colon -- parse_binding -- Scan.repeat parse_ctr_arg --
blanchet@51767
  1463
  Scan.optional parse_defaults [] -- Parse.opt_mixfix;
blanchet@51767
  1464
blanchet@51767
  1465
val parse_spec =
blanchet@51790
  1466
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@51767
  1467
  Parse.opt_mixfix -- (@{keyword "="} |-- Parse.enum1 "|" parse_ctr_spec);
blanchet@51767
  1468
blanchet@52823
  1469
val parse_co_datatype = parse_wrap_free_constructors_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1470
blanchet@52207
  1471
fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp;
blanchet@49112
  1472
blanchet@49112
  1473
end;