src/HOL/Tools/BNF/bnf_fp_def_sugar.ML
author blanchet
Mon Mar 03 12:48:20 2014 +0100 (2014-03-03)
changeset 55867 79b915f26533
parent 55865 3be27c07e36d
child 55868 37b99986d435
permissions -rw-r--r--
rationalized internals
blanchet@55061
     1
(*  Title:      HOL/Tools/BNF/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@55772
    12
     X: typ,
blanchet@55575
    13
     fp: BNF_Util.fp_kind,
blanchet@55539
    14
     fp_res_index: int,
blanchet@55539
    15
     fp_res: BNF_FP_Util.fp_result,
blanchet@55539
    16
     pre_bnf: BNF_Def.bnf,
traytel@55803
    17
     absT_info: BNF_Comp.absT_info,
blanchet@52356
    18
     nested_bnfs: BNF_Def.bnf list,
traytel@53267
    19
     nesting_bnfs: BNF_Def.bnf list,
blanchet@55772
    20
     ctrXs_Tss: typ list list,
blanchet@55539
    21
     ctr_defs: thm list,
blanchet@55539
    22
     ctr_sugar: Ctr_Sugar.ctr_sugar,
blanchet@55863
    23
     co_rec: term,
blanchet@55539
    24
     maps: thm list,
blanchet@55539
    25
     common_co_inducts: thm list,
blanchet@52343
    26
     co_inducts: thm list,
blanchet@55863
    27
     co_rec_thms: thm list,
blanchet@55863
    28
     disc_co_recs: thm list,
blanchet@55863
    29
     sel_co_recss: thm list list};
blanchet@51823
    30
blanchet@51896
    31
  val morph_fp_sugar: morphism -> fp_sugar -> fp_sugar
blanchet@54256
    32
  val transfer_fp_sugar: Proof.context -> fp_sugar -> fp_sugar
blanchet@51896
    33
  val fp_sugar_of: Proof.context -> string -> fp_sugar option
blanchet@53907
    34
  val fp_sugars_of: Proof.context -> fp_sugar list
blanchet@51852
    35
traytel@53106
    36
  val co_induct_of: 'a list -> 'a
traytel@53106
    37
  val strong_co_induct_of: 'a list -> 'a
traytel@53106
    38
blanchet@52868
    39
  val flat_corec_preds_predsss_gettersss: 'a list -> 'a list list list -> 'a list list list ->
blanchet@52868
    40
    'a list
blanchet@51907
    41
  val nesty_bnfs: Proof.context -> typ list list list -> typ list -> BNF_Def.bnf list
blanchet@53746
    42
blanchet@53746
    43
  type lfp_sugar_thms =
blanchet@55856
    44
    (thm list * thm * Args.src list) * (thm list list * Args.src list)
blanchet@53746
    45
blanchet@54256
    46
  val morph_lfp_sugar_thms: morphism -> lfp_sugar_thms -> lfp_sugar_thms
blanchet@54256
    47
  val transfer_lfp_sugar_thms: Proof.context -> lfp_sugar_thms -> lfp_sugar_thms
blanchet@54256
    48
blanchet@53746
    49
  type gfp_sugar_thms =
blanchet@53746
    50
    ((thm list * thm) list * Args.src list)
blanchet@55856
    51
    * (thm list list * Args.src list)
blanchet@55856
    52
    * (thm list list * Args.src list)
blanchet@55856
    53
    * (thm list list * Args.src list)
blanchet@55856
    54
    * (thm list list list * Args.src list)
blanchet@53746
    55
blanchet@54256
    56
  val morph_gfp_sugar_thms: morphism -> gfp_sugar_thms -> gfp_sugar_thms
blanchet@54256
    57
  val transfer_gfp_sugar_thms: Proof.context -> gfp_sugar_thms -> gfp_sugar_thms
blanchet@54256
    58
blanchet@55867
    59
  val mk_co_recs_prelims: BNF_Util.fp_kind -> typ list list list -> typ list -> typ list ->
blanchet@55867
    60
     typ list -> typ list -> int list -> int list list -> term list -> Proof.context ->
blanchet@55867
    61
     (term list
blanchet@55867
    62
      * (typ list list * typ list list list list * term list list * term list list list list) option
blanchet@55862
    63
      * (string * term list * term list list
blanchet@55867
    64
         * ((term list list * term list list list) * typ list)) option)
blanchet@55862
    65
     * Proof.context
blanchet@55772
    66
  val repair_nullary_single_ctr: typ list list -> typ list list
blanchet@55867
    67
  val mk_corec_p_pred_types: typ list -> int list -> typ list list
blanchet@55867
    68
  val mk_corec_fun_arg_types: typ list list list -> typ list -> typ list -> typ list -> int list ->
traytel@55803
    69
    int list list -> term ->
traytel@55803
    70
    typ list list
traytel@55803
    71
    * (typ list list list list * typ list list list * typ list list list list * typ list)
blanchet@55867
    72
  val define_rec:
blanchet@55862
    73
    (typ list list * typ list list list list * term list list * term list list list list) option ->
blanchet@55862
    74
    (string -> binding) -> typ list -> typ list -> term list -> term -> Proof.context ->
blanchet@55864
    75
    (term * thm) * Proof.context
blanchet@55867
    76
  val define_corec: 'a * term list * term list list
blanchet@55862
    77
      * ((term list list * term list list list) * typ list) -> (string -> binding) -> 'b list ->
blanchet@55864
    78
    typ list -> term list -> term -> Proof.context -> (term * thm) * local_theory
blanchet@55867
    79
  val derive_induct_recs_thms_for_types: BNF_Def.bnf list ->
blanchet@55867
    80
     ('a * typ list list list list * term list list * 'b) option -> thm -> thm list ->
blanchet@55862
    81
     BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list -> typ list ->
blanchet@55862
    82
     typ list list list -> thm list -> thm list -> thm list -> term list list -> thm list list ->
blanchet@55864
    83
     term list -> thm list -> Proof.context -> lfp_sugar_thms
blanchet@55867
    84
  val derive_coinduct_corecs_thms_for_types: BNF_Def.bnf list ->
blanchet@55862
    85
    string * term list * term list list * ((term list list * term list list list) * typ list) ->
blanchet@55867
    86
    thm -> thm list -> thm list -> thm list -> BNF_Def.bnf list -> typ list -> typ list ->
traytel@55803
    87
    typ list -> typ list list list -> int list list -> int list list -> int list -> thm list ->
blanchet@55864
    88
    thm list -> (thm -> thm) -> thm list list -> Ctr_Sugar.ctr_sugar list -> term list ->
blanchet@55864
    89
    thm list -> (thm list -> thm list) -> local_theory -> gfp_sugar_thms
blanchet@55469
    90
blanchet@55469
    91
  type co_datatype_spec =
blanchet@55699
    92
    ((((binding option * (typ * sort)) list * binding) * (binding * binding)) * mixfix)
blanchet@55469
    93
    * ((binding, binding * typ, term) Ctr_Sugar.ctr_spec * mixfix) list
blanchet@55469
    94
blanchet@55575
    95
  val co_datatypes: BNF_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
blanchet@52207
    96
      binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
traytel@55803
    97
      BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory ->
traytel@55803
    98
      BNF_FP_Util.fp_result * local_theory) ->
blanchet@55469
    99
    (bool * bool) * co_datatype_spec list ->
blanchet@49297
   100
    local_theory -> local_theory
blanchet@55575
   101
  val parse_co_datatype_cmd: BNF_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
blanchet@51867
   102
      binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
traytel@55803
   103
      BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory ->
traytel@55803
   104
      BNF_FP_Util.fp_result * local_theory) ->
blanchet@49308
   105
    (local_theory -> local_theory) parser
blanchet@49112
   106
end;
blanchet@49112
   107
blanchet@49636
   108
structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR =
blanchet@49112
   109
struct
blanchet@49112
   110
blanchet@54006
   111
open Ctr_Sugar
blanchet@55571
   112
open BNF_FP_Rec_Sugar_Util
blanchet@49119
   113
open BNF_Util
blanchet@53222
   114
open BNF_Comp
blanchet@49214
   115
open BNF_Def
blanchet@51850
   116
open BNF_FP_Util
blanchet@49636
   117
open BNF_FP_Def_Sugar_Tactics
blanchet@49119
   118
blanchet@51788
   119
val EqN = "Eq_";
blanchet@51777
   120
blanchet@51840
   121
type fp_sugar =
blanchet@51859
   122
  {T: typ,
blanchet@55772
   123
   X: typ,
blanchet@52207
   124
   fp: fp_kind,
blanchet@55539
   125
   fp_res_index: int,
blanchet@55539
   126
   fp_res: fp_result,
blanchet@55539
   127
   pre_bnf: bnf,
traytel@55803
   128
   absT_info: absT_info,
blanchet@52356
   129
   nested_bnfs: bnf list,
traytel@53267
   130
   nesting_bnfs: bnf list,
blanchet@55772
   131
   ctrXs_Tss: typ list list,
blanchet@55539
   132
   ctr_defs: thm list,
blanchet@55539
   133
   ctr_sugar: Ctr_Sugar.ctr_sugar,
blanchet@55863
   134
   co_rec: term,
blanchet@55539
   135
   maps: thm list,
blanchet@55539
   136
   common_co_inducts: thm list,
blanchet@52343
   137
   co_inducts: thm list,
blanchet@55863
   138
   co_rec_thms: thm list,
blanchet@55863
   139
   disc_co_recs: thm list,
blanchet@55863
   140
   sel_co_recss: thm list list};
blanchet@52295
   141
traytel@55803
   142
fun morph_fp_sugar phi ({T, X, fp, fp_res, fp_res_index, pre_bnf, absT_info, nested_bnfs,
blanchet@55863
   143
    nesting_bnfs, ctrXs_Tss, ctr_defs, ctr_sugar, co_rec, maps, common_co_inducts, co_inducts,
blanchet@55863
   144
    co_rec_thms, disc_co_recs, sel_co_recss} : fp_sugar) =
blanchet@55539
   145
  {T = Morphism.typ phi T,
blanchet@55772
   146
   X = Morphism.typ phi X,
blanchet@55539
   147
   fp = fp,
traytel@53267
   148
   fp_res = morph_fp_result phi fp_res,
blanchet@55539
   149
   fp_res_index = fp_res_index,
blanchet@55539
   150
   pre_bnf = morph_bnf phi pre_bnf,
traytel@55803
   151
   absT_info = morph_absT_info phi absT_info,
blanchet@55539
   152
   nested_bnfs = map (morph_bnf phi) nested_bnfs,
blanchet@55539
   153
   nesting_bnfs = map (morph_bnf phi) nesting_bnfs,
blanchet@55772
   154
   ctrXs_Tss = map (map (Morphism.typ phi)) ctrXs_Tss,
blanchet@55539
   155
   ctr_defs = map (Morphism.thm phi) ctr_defs,
blanchet@55539
   156
   ctr_sugar = morph_ctr_sugar phi ctr_sugar,
blanchet@55863
   157
   co_rec = Morphism.term phi co_rec,
blanchet@55539
   158
   maps = map (Morphism.thm phi) maps,
blanchet@55539
   159
   common_co_inducts = map (Morphism.thm phi) common_co_inducts,
blanchet@52343
   160
   co_inducts = map (Morphism.thm phi) co_inducts,
blanchet@55863
   161
   co_rec_thms = map (Morphism.thm phi) co_rec_thms,
blanchet@55863
   162
   disc_co_recs = map (Morphism.thm phi) disc_co_recs,
blanchet@55863
   163
   sel_co_recss = map (map (Morphism.thm phi)) sel_co_recss};
blanchet@51823
   164
blanchet@53907
   165
val transfer_fp_sugar =
wenzelm@54740
   166
  morph_fp_sugar o Morphism.transfer_morphism o Proof_Context.theory_of;
blanchet@53907
   167
blanchet@51823
   168
structure Data = Generic_Data
blanchet@51823
   169
(
blanchet@51840
   170
  type T = fp_sugar Symtab.table;
blanchet@51823
   171
  val empty = Symtab.empty;
blanchet@51823
   172
  val extend = I;
blanchet@55394
   173
  fun merge data : T = Symtab.merge (K true) data;
blanchet@51823
   174
);
blanchet@51823
   175
traytel@53126
   176
fun fp_sugar_of ctxt =
traytel@53126
   177
  Symtab.lookup (Data.get (Context.Proof ctxt))
blanchet@53907
   178
  #> Option.map (transfer_fp_sugar ctxt);
blanchet@53907
   179
blanchet@53907
   180
fun fp_sugars_of ctxt =
blanchet@53907
   181
  Symtab.fold (cons o transfer_fp_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
blanchet@51823
   182
traytel@53106
   183
fun co_induct_of (i :: _) = i;
traytel@53106
   184
fun strong_co_induct_of [_, s] = s;
traytel@53106
   185
blanchet@53259
   186
(* TODO: register "sum" and "prod" as datatypes to enable N2M reduction for them *)
blanchet@53259
   187
blanchet@51840
   188
fun register_fp_sugar key fp_sugar =
blanchet@54285
   189
  Local_Theory.declaration {syntax = false, pervasive = true}
blanchet@55444
   190
    (fn phi => Data.map (Symtab.update (key, morph_fp_sugar phi fp_sugar)));
blanchet@51823
   191
traytel@55803
   192
fun register_fp_sugars Xs fp pre_bnfs absT_infos nested_bnfs nesting_bnfs (fp_res as {Ts, ...})
blanchet@55863
   193
    ctrXs_Tsss ctr_defss ctr_sugars co_recs mapss common_co_inducts co_inductss co_rec_thmss
blanchet@55863
   194
    disc_co_recss sel_co_recsss lthy =
blanchet@51844
   195
  (0, lthy)
blanchet@51859
   196
  |> fold (fn T as Type (s, _) => fn (kk, lthy) => (kk + 1,
blanchet@55772
   197
    register_fp_sugar s {T = T, X = nth Xs kk, fp = fp, fp_res = fp_res, fp_res_index = kk,
traytel@55803
   198
        pre_bnf = nth pre_bnfs kk, absT_info = nth absT_infos kk, nested_bnfs = nested_bnfs,
traytel@55803
   199
        nesting_bnfs = nesting_bnfs, ctrXs_Tss = nth ctrXs_Tsss kk, ctr_defs = nth ctr_defss kk,
blanchet@55863
   200
        ctr_sugar = nth ctr_sugars kk, co_rec = nth co_recs kk, maps = nth mapss kk,
traytel@55803
   201
        common_co_inducts = common_co_inducts, co_inducts = nth co_inductss kk,
blanchet@55863
   202
        co_rec_thms = nth co_rec_thmss kk, disc_co_recs = nth disc_co_recss kk,
blanchet@55863
   203
        sel_co_recss = nth sel_co_recsss kk}
blanchet@52337
   204
      lthy)) Ts
blanchet@51824
   205
  |> snd;
blanchet@51824
   206
blanchet@55342
   207
(* This function could produce (fairly harmless) clashes in contrived examples (e.g., "x.A",
blanchet@55342
   208
   "x.x_A", "y.A"). *)
blanchet@49622
   209
fun quasi_unambiguous_case_names names =
blanchet@49622
   210
  let
blanchet@49622
   211
    val ps = map (`Long_Name.base_name) names;
blanchet@49622
   212
    val dups = Library.duplicates (op =) (map fst ps);
blanchet@49622
   213
    fun underscore s =
blanchet@49622
   214
      let val ss = space_explode Long_Name.separator s in
blanchet@49622
   215
        space_implode "_" (drop (length ss - 2) ss)
blanchet@49622
   216
      end;
blanchet@49622
   217
  in
blanchet@49622
   218
    map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
blanchet@49622
   219
  end;
blanchet@49622
   220
blanchet@52355
   221
val id_def = @{thm id_def};
blanchet@49591
   222
val mp_conj = @{thm mp_conj};
blanchet@49591
   223
blanchet@55397
   224
val fundefcong_attrs = @{attributes [fundef_cong]};
blanchet@54145
   225
val nitpicksimp_attrs = @{attributes [nitpick_simp]};
blanchet@54145
   226
val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
blanchet@49300
   227
val simp_attrs = @{attributes [simp]};
blanchet@49300
   228
blanchet@49297
   229
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
blanchet@49202
   230
blanchet@52868
   231
fun flat_corec_predss_getterss qss fss = maps (op @) (qss ~~ fss);
blanchet@51829
   232
blanchet@52868
   233
fun flat_corec_preds_predsss_gettersss [] [qss] [fss] = flat_corec_predss_getterss qss fss
blanchet@52868
   234
  | flat_corec_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
blanchet@52868
   235
    p :: flat_corec_predss_getterss qss fss @ flat_corec_preds_predsss_gettersss ps qsss fsss;
blanchet@51829
   236
blanchet@49585
   237
fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) =
blanchet@49585
   238
  Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1));
blanchet@49585
   239
blanchet@49585
   240
fun flip_rels lthy n thm =
blanchet@49585
   241
  let
blanchet@49585
   242
    val Rs = Term.add_vars (prop_of thm) [];
blanchet@49585
   243
    val Rs' = rev (drop (length Rs - n) Rs);
blanchet@49585
   244
    val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs';
blanchet@49585
   245
  in
blanchet@49585
   246
    Drule.cterm_instantiate cRs thm
blanchet@49585
   247
  end;
blanchet@49585
   248
blanchet@49536
   249
fun mk_ctor_or_dtor get_T Ts t =
blanchet@49536
   250
  let val Type (_, Ts0) = get_T (fastype_of t) in
blanchet@49536
   251
    Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49536
   252
  end;
blanchet@49536
   253
blanchet@49536
   254
val mk_ctor = mk_ctor_or_dtor range_type;
blanchet@49536
   255
val mk_dtor = mk_ctor_or_dtor domain_type;
blanchet@49536
   256
blanchet@55867
   257
fun mk_xtor_co_recs thy fp fpTs Cs ts0 =
blanchet@51911
   258
  let
blanchet@51911
   259
    val nn = length fpTs;
blanchet@51911
   260
    val (fpTs0, Cs0) =
blanchet@52207
   261
      map ((fp = Greatest_FP ? swap) o dest_funT o snd o strip_typeN nn o fastype_of) ts0
blanchet@51911
   262
      |> split_list;
blanchet@51911
   263
    val rho = tvar_subst thy (fpTs0 @ Cs0) (fpTs @ Cs);
blanchet@51911
   264
  in
blanchet@52170
   265
    map (Term.subst_TVars rho) ts0
blanchet@51911
   266
  end;
blanchet@51827
   267
blanchet@55575
   268
fun unzip_recT (Type (@{type_name prod}, _)) T = [T]
blanchet@55575
   269
  | unzip_recT _ (Type (@{type_name prod}, Ts)) = Ts
blanchet@55575
   270
  | unzip_recT _ T = [T];
blanchet@55575
   271
blanchet@53591
   272
fun unzip_corecT (Type (@{type_name sum}, _)) T = [T]
blanchet@53901
   273
  | unzip_corecT _ (Type (@{type_name sum}, Ts)) = Ts
blanchet@52871
   274
  | unzip_corecT _ T = [T];
blanchet@52871
   275
blanchet@52347
   276
fun liveness_of_fp_bnf n bnf =
blanchet@52347
   277
  (case T_of_bnf bnf of
blanchet@52347
   278
    Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
blanchet@52347
   279
  | _ => replicate n false);
blanchet@52347
   280
blanchet@55700
   281
fun cannot_merge_types fp =
blanchet@55700
   282
  error ("Mutually " ^ co_prefix fp ^ "recursive types must have the same type parameters");
blanchet@52347
   283
blanchet@55700
   284
fun merge_type_arg fp T T' = if T = T' then T else cannot_merge_types fp;
blanchet@52347
   285
blanchet@55700
   286
fun merge_type_args fp (As, As') =
blanchet@55700
   287
  if length As = length As' then map2 (merge_type_arg fp) As As' else cannot_merge_types fp;
blanchet@52347
   288
blanchet@52347
   289
fun reassoc_conjs thm =
blanchet@52347
   290
  reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
blanchet@52347
   291
  handle THM _ => thm;
blanchet@52347
   292
blanchet@55469
   293
type co_datatype_spec =
blanchet@55699
   294
  ((((binding option * (typ * sort)) list * binding) * (binding * binding)) * mixfix)
blanchet@55469
   295
  * ((binding, binding * typ, term) ctr_spec * mixfix) list;
blanchet@52347
   296
blanchet@55469
   297
fun type_args_named_constrained_of_spec ((((ncAs, _), _), _), _) = ncAs;
blanchet@55469
   298
fun type_binding_of_spec ((((_, b), _), _), _) = b;
blanchet@55469
   299
fun map_binding_of_spec (((_, (b, _)), _), _) = b;
blanchet@55469
   300
fun rel_binding_of_spec (((_, (_, b)), _), _) = b;
blanchet@55469
   301
fun mixfix_of_spec ((_, mx), _) = mx;
blanchet@55469
   302
fun mixfixed_ctr_specs_of_spec (_, mx_ctr_specs) = mx_ctr_specs;
blanchet@52347
   303
blanchet@52347
   304
fun add_nesty_bnf_names Us =
blanchet@52347
   305
  let
blanchet@52347
   306
    fun add (Type (s, Ts)) ss =
blanchet@52347
   307
        let val (needs, ss') = fold_map add Ts ss in
blanchet@52347
   308
          if exists I needs then (true, insert (op =) s ss') else (false, ss')
blanchet@52347
   309
        end
blanchet@52347
   310
      | add T ss = (member (op =) Us T, ss);
blanchet@52347
   311
  in snd oo add end;
blanchet@52347
   312
blanchet@52347
   313
fun nesty_bnfs ctxt ctr_Tsss Us =
blanchet@52347
   314
  map_filter (bnf_of ctxt) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_Tsss []);
blanchet@52347
   315
blanchet@54237
   316
fun indexify proj xs f p = f (find_index (curry (op =) (proj p)) xs) p;
blanchet@52347
   317
blanchet@53746
   318
type lfp_sugar_thms =
blanchet@55856
   319
  (thm list * thm * Args.src list) * (thm list list * Args.src list);
blanchet@53746
   320
blanchet@55867
   321
fun morph_lfp_sugar_thms phi ((inducts, induct, induct_attrs), (recss, rec_attrs)) =
blanchet@54256
   322
  ((map (Morphism.thm phi) inducts, Morphism.thm phi induct, induct_attrs),
blanchet@55867
   323
   (map (map (Morphism.thm phi)) recss, rec_attrs))
blanchet@55095
   324
  : lfp_sugar_thms;
blanchet@54256
   325
blanchet@54256
   326
val transfer_lfp_sugar_thms =
wenzelm@54740
   327
  morph_lfp_sugar_thms o Morphism.transfer_morphism o Proof_Context.theory_of;
blanchet@54256
   328
blanchet@53746
   329
type gfp_sugar_thms =
blanchet@53746
   330
  ((thm list * thm) list * Args.src list)
blanchet@55856
   331
  * (thm list list * Args.src list)
blanchet@55856
   332
  * (thm list list * Args.src list)
blanchet@55856
   333
  * (thm list list * Args.src list)
blanchet@55856
   334
  * (thm list list list * Args.src list);
blanchet@53746
   335
blanchet@54256
   336
fun morph_gfp_sugar_thms phi ((coinducts_pairs, coinduct_attrs),
blanchet@55867
   337
    (corecss, corec_attrs), (disc_corecss, disc_rec_attrs),
blanchet@55867
   338
    (disc_corec_iffss, disc_rec_iff_attrs), (sel_corecsss, sel_rec_attrs)) =
blanchet@54256
   339
  ((map (apfst (map (Morphism.thm phi)) o apsnd (Morphism.thm phi)) coinducts_pairs,
blanchet@54256
   340
    coinduct_attrs),
blanchet@55867
   341
   (map (map (Morphism.thm phi)) corecss, corec_attrs),
blanchet@55867
   342
   (map (map (Morphism.thm phi)) disc_corecss, disc_rec_attrs),
blanchet@55867
   343
   (map (map (Morphism.thm phi)) disc_corec_iffss, disc_rec_iff_attrs),
blanchet@55867
   344
   (map (map (map (Morphism.thm phi))) sel_corecsss, sel_rec_attrs)) : gfp_sugar_thms;
blanchet@54256
   345
blanchet@54256
   346
val transfer_gfp_sugar_thms =
wenzelm@54740
   347
  morph_gfp_sugar_thms o Morphism.transfer_morphism o Proof_Context.theory_of;
blanchet@54256
   348
blanchet@55867
   349
fun mk_recs_args_types ctr_Tsss Cs absTs repTs ns mss ctor_rec_fun_Ts lthy =
blanchet@51832
   350
  let
blanchet@52214
   351
    val Css = map2 replicate ns Cs;
blanchet@52214
   352
    val z_Tssss =
blanchet@55867
   353
      map6 (fn absT => fn repT => fn n => fn ms => fn ctr_Tss => fn ctor_rec_fun_T =>
traytel@55803
   354
          map2 (map2 unzip_recT)
blanchet@55867
   355
            ctr_Tss (dest_absumprodT absT repT n ms (domain_type ctor_rec_fun_T)))
blanchet@55867
   356
        absTs repTs ns mss ctr_Tsss ctor_rec_fun_Ts;
blanchet@51832
   357
blanchet@52868
   358
    val z_Tsss' = map (map flat_rec_arg_args) z_Tssss;
blanchet@54237
   359
    val h_Tss = map2 (map2 (curry (op --->))) z_Tsss' Css;
blanchet@51832
   360
blanchet@55867
   361
    val ((hss, zssss), lthy) =
blanchet@52214
   362
      lthy
blanchet@55865
   363
      |> mk_Freess "f" h_Tss
blanchet@55867
   364
      ||>> mk_Freessss "x" z_Tssss;
blanchet@51832
   365
  in
blanchet@55862
   366
    ((h_Tss, z_Tssss, hss, zssss), lthy)
blanchet@51832
   367
  end;
blanchet@51832
   368
blanchet@55867
   369
(*avoid "'a itself" arguments in corecursors*)
blanchet@55772
   370
fun repair_nullary_single_ctr [[]] = [[@{typ unit}]]
blanchet@55772
   371
  | repair_nullary_single_ctr Tss = Tss;
blanchet@55772
   372
blanchet@55867
   373
fun mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss fun_Ts =
blanchet@51829
   374
  let
blanchet@55772
   375
    val ctr_Tsss' = map repair_nullary_single_ctr ctr_Tsss;
traytel@55803
   376
    val f_absTs = map range_type fun_Ts;
traytel@55803
   377
    val f_Tsss = map repair_nullary_single_ctr (map5 dest_absumprodT absTs repTs ns mss f_absTs);
blanchet@54237
   378
    val f_Tssss = map3 (fn C => map2 (map2 (map (curry (op -->) C) oo unzip_corecT)))
blanchet@53591
   379
      Cs ctr_Tsss' f_Tsss;
blanchet@52871
   380
    val q_Tssss = map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) f_Tssss;
blanchet@52870
   381
  in
traytel@55803
   382
    (q_Tssss, f_Tsss, f_Tssss, f_absTs)
blanchet@52870
   383
  end;
blanchet@51829
   384
blanchet@55867
   385
fun mk_corec_p_pred_types Cs ns = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@52898
   386
blanchet@55867
   387
fun mk_corec_fun_arg_types ctr_Tsss Cs absTs repTs ns mss dtor_corec =
blanchet@55867
   388
  (mk_corec_p_pred_types Cs ns,
blanchet@55867
   389
   mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss
blanchet@55867
   390
     (binder_fun_types (fastype_of dtor_corec)));
blanchet@51829
   391
blanchet@55867
   392
fun mk_corecs_args_types ctr_Tsss Cs absTs repTs ns mss dtor_corec_fun_Ts lthy =
blanchet@55867
   393
  let
blanchet@55867
   394
    val p_Tss = mk_corec_p_pred_types Cs ns;
blanchet@51829
   395
blanchet@55867
   396
    val (s_Tssss, h_Tsss, h_Tssss, corec_types) =
blanchet@55867
   397
      mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss dtor_corec_fun_Ts;
blanchet@51831
   398
blanchet@55858
   399
    val (((((Free (z, _), cs), pss), sssss), hssss), lthy) =
blanchet@51829
   400
      lthy
blanchet@52347
   401
      |> yield_singleton (mk_Frees "z") dummyT
blanchet@52347
   402
      ||>> mk_Frees "a" Cs
blanchet@51829
   403
      ||>> mk_Freess "p" p_Tss
blanchet@55856
   404
      ||>> mk_Freessss "q" s_Tssss
blanchet@55858
   405
      ||>> mk_Freessss "g" h_Tssss;
blanchet@51831
   406
blanchet@51831
   407
    val cpss = map2 (map o rapp) cs pss;
blanchet@51829
   408
blanchet@52347
   409
    fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
blanchet@52347
   410
blanchet@55867
   411
    fun build_dtor_corec_arg _ [] [cf] = cf
blanchet@55867
   412
      | build_dtor_corec_arg T [cq] [cf, cf'] =
blanchet@52347
   413
        mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@52347
   414
          (build_sum_inj Inr_const (fastype_of cf', T) $ cf');
blanchet@52347
   415
blanchet@52349
   416
    fun mk_args qssss fssss f_Tsss =
blanchet@51831
   417
      let
blanchet@52868
   418
        val pfss = map3 flat_corec_preds_predsss_gettersss pss qssss fssss;
blanchet@51831
   419
        val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@51831
   420
        val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@55867
   421
        val cqfsss = map3 (map3 (map3 build_dtor_corec_arg)) f_Tsss cqssss cfssss;
blanchet@52347
   422
      in (pfss, cqfsss) end;
blanchet@51831
   423
blanchet@52349
   424
    val corec_args = mk_args sssss hssss h_Tsss;
blanchet@51831
   425
  in
blanchet@55862
   426
    ((z, cs, cpss, (corec_args, corec_types)), lthy)
blanchet@51831
   427
  end;
blanchet@51829
   428
blanchet@55867
   429
fun mk_co_recs_prelims fp ctr_Tsss fpTs Cs absTs repTs ns mss xtor_co_recs0 lthy =
blanchet@51903
   430
  let
blanchet@52169
   431
    val thy = Proof_Context.theory_of lthy;
blanchet@55862
   432
    val nn = length fpTs;
blanchet@52169
   433
blanchet@55867
   434
    val (xtor_co_rec_fun_Ts, xtor_co_recs) =
blanchet@55867
   435
      mk_xtor_co_recs thy fp fpTs Cs xtor_co_recs0 |> `(binder_fun_types o fastype_of o hd);
blanchet@51903
   436
blanchet@55867
   437
    val ((recs_args_types, corecs_args_types), lthy') =
blanchet@52207
   438
      if fp = Least_FP then
blanchet@55862
   439
        if nn = 1 andalso forall (forall (forall (not o exists_subtype_in fpTs))) ctr_Tsss then
blanchet@55862
   440
          ((NONE, NONE), lthy)
blanchet@55862
   441
        else
blanchet@55867
   442
          mk_recs_args_types ctr_Tsss Cs absTs repTs ns mss xtor_co_rec_fun_Ts lthy
blanchet@55862
   443
          |>> (rpair NONE o SOME)
blanchet@51903
   444
      else
blanchet@55867
   445
        mk_corecs_args_types ctr_Tsss Cs absTs repTs ns mss xtor_co_rec_fun_Ts lthy
traytel@55803
   446
        |>> (pair NONE o SOME);
blanchet@51903
   447
  in
blanchet@55867
   448
    ((xtor_co_recs, recs_args_types, corecs_args_types), lthy')
blanchet@51903
   449
  end;
blanchet@51903
   450
traytel@55803
   451
fun mk_preds_getterss_join c cps absT abs cqfss =
traytel@55803
   452
  let
traytel@55803
   453
    val n = length cqfss;
traytel@55803
   454
    val ts = map2 (mk_absumprod absT abs n) (1 upto n) cqfss;
traytel@55803
   455
  in
traytel@55803
   456
    Term.lambda c (mk_IfN absT cps ts)
blanchet@51900
   457
  end;
blanchet@51886
   458
blanchet@55867
   459
fun define_co_rec fp fpT Cs b rhs lthy0 =
blanchet@51897
   460
  let
blanchet@52170
   461
    val thy = Proof_Context.theory_of lthy0;
blanchet@52170
   462
traytel@53569
   463
    val maybe_conceal_def_binding = Thm.def_binding
traytel@53569
   464
      #> Config.get lthy0 bnf_note_all = false ? Binding.conceal;
traytel@53569
   465
blanchet@55864
   466
    val ((cst, (_, def)), (lthy', lthy)) = lthy0
blanchet@55864
   467
      |> Local_Theory.define ((b, NoSyn), ((maybe_conceal_def_binding b, []), rhs))
blanchet@52327
   468
      ||> `Local_Theory.restore;
blanchet@52327
   469
blanchet@52327
   470
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@52327
   471
blanchet@55864
   472
    val cst' = mk_co_iter thy fp fpT Cs (Morphism.term phi cst);
blanchet@55864
   473
    val def' = Morphism.thm phi def;
blanchet@52327
   474
  in
blanchet@55864
   475
    ((cst', def'), lthy')
blanchet@52327
   476
  end;
blanchet@52327
   477
blanchet@55867
   478
fun define_rec NONE _ _ _ _ _ = pair (Term.dummy, refl)
blanchet@55867
   479
  | define_rec (SOME (_, _, fss, xssss)) mk_binding fpTs Cs reps ctor_rec =
blanchet@55862
   480
    let
blanchet@55862
   481
      val nn = length fpTs;
blanchet@55867
   482
      val (ctor_rec_absTs, fpT) = strip_typeN nn (fastype_of ctor_rec)
blanchet@55862
   483
        |>> map domain_type ||> domain_type;
blanchet@55864
   484
    in
blanchet@55867
   485
      define_co_rec Least_FP fpT Cs (mk_binding recN)
blanchet@55867
   486
        (fold_rev (fold_rev Term.lambda) fss (Term.list_comb (ctor_rec,
blanchet@55867
   487
           map4 (fn ctor_rec_absT => fn rep => fn fs => fn xsss =>
blanchet@55867
   488
               mk_case_absumprod ctor_rec_absT rep fs
traytel@55803
   489
                 (map (HOLogic.mk_tuple o map HOLogic.mk_tuple) xsss) (map flat_rec_arg_args xsss))
blanchet@55867
   490
             ctor_rec_absTs reps fss xssss)))
blanchet@55862
   491
    end;
blanchet@51897
   492
blanchet@55867
   493
fun define_corec (_, cs, cpss, ((pfss, cqfsss), f_absTs)) mk_binding fpTs Cs abss dtor_corec =
blanchet@51897
   494
  let
blanchet@51899
   495
    val nn = length fpTs;
blanchet@55867
   496
    val fpT = range_type (snd (strip_typeN nn (fastype_of dtor_corec)));
blanchet@51897
   497
  in
blanchet@55867
   498
    define_co_rec Greatest_FP fpT Cs (mk_binding corecN)
blanchet@55867
   499
      (fold_rev (fold_rev Term.lambda) pfss (Term.list_comb (dtor_corec,
blanchet@55864
   500
         map5 mk_preds_getterss_join cs cpss f_absTs abss cqfsss)))
blanchet@52320
   501
  end;
blanchet@51897
   502
blanchet@55867
   503
fun derive_induct_recs_thms_for_types pre_bnfs rec_args_typess ctor_induct ctor_rec_thms
blanchet@55856
   504
    nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss fp_abs_inverses fp_type_definitions abs_inverses
blanchet@55864
   505
    ctrss ctr_defss recs rec_defs lthy =
blanchet@51808
   506
  let
blanchet@51827
   507
    val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
blanchet@51827
   508
blanchet@51815
   509
    val nn = length pre_bnfs;
blanchet@51827
   510
    val ns = map length ctr_Tsss;
blanchet@51827
   511
    val mss = map (map length) ctr_Tsss;
blanchet@51815
   512
blanchet@51808
   513
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51808
   514
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@53329
   515
    val nesting_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nesting_bnfs;
blanchet@53329
   516
    val nested_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nested_bnfs;
blanchet@53290
   517
    val nested_set_maps = maps set_map_of_bnf nested_bnfs;
blanchet@51808
   518
blanchet@51816
   519
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   520
blanchet@51832
   521
    val ((((ps, ps'), xsss), us'), names_lthy) =
blanchet@52315
   522
      lthy
blanchet@51808
   523
      |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@51827
   524
      ||>> mk_Freesss "x" ctr_Tsss
blanchet@51816
   525
      ||>> Variable.variant_fixes fp_b_names;
blanchet@51808
   526
blanchet@51808
   527
    val us = map2 (curry Free) us' fpTs;
blanchet@51808
   528
blanchet@51808
   529
    fun mk_sets_nested bnf =
blanchet@51808
   530
      let
blanchet@51808
   531
        val Type (T_name, Us) = T_of_bnf bnf;
blanchet@51808
   532
        val lives = lives_of_bnf bnf;
blanchet@51808
   533
        val sets = sets_of_bnf bnf;
blanchet@51808
   534
        fun mk_set U =
blanchet@54237
   535
          (case find_index (curry (op =) U) lives of
blanchet@51808
   536
            ~1 => Term.dummy
blanchet@51808
   537
          | i => nth sets i);
blanchet@51808
   538
      in
blanchet@51808
   539
        (T_name, map mk_set Us)
blanchet@51808
   540
      end;
blanchet@51808
   541
blanchet@51808
   542
    val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@51808
   543
blanchet@51808
   544
    val (induct_thms, induct_thm) =
blanchet@51808
   545
      let
blanchet@51808
   546
        fun mk_set Ts t =
blanchet@51808
   547
          let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@51808
   548
            Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@51808
   549
          end;
blanchet@51808
   550
blanchet@52310
   551
        fun mk_raw_prem_prems _ (x as Free (_, Type _)) (X as TFree _) =
blanchet@54237
   552
            [([], (find_index (curry (op =) X) Xs + 1, x))]
blanchet@52310
   553
          | mk_raw_prem_prems names_lthy (x as Free (s, Type (T_name, Ts0))) (Type (_, Xs_Ts0)) =
blanchet@52310
   554
            (case AList.lookup (op =) setss_nested T_name of
blanchet@52310
   555
              NONE => []
blanchet@52310
   556
            | SOME raw_sets0 =>
blanchet@52310
   557
              let
blanchet@52310
   558
                val (Xs_Ts, (Ts, raw_sets)) =
blanchet@52310
   559
                  filter (exists_subtype_in Xs o fst) (Xs_Ts0 ~~ (Ts0 ~~ raw_sets0))
blanchet@52310
   560
                  |> split_list ||> split_list;
blanchet@52310
   561
                val sets = map (mk_set Ts0) raw_sets;
blanchet@52310
   562
                val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@52310
   563
                val xysets = map (pair x) (ys ~~ sets);
blanchet@52310
   564
                val ppremss = map2 (mk_raw_prem_prems names_lthy') ys Xs_Ts;
blanchet@52310
   565
              in
blanchet@52310
   566
                flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@52310
   567
              end)
blanchet@52310
   568
          | mk_raw_prem_prems _ _ _ = [];
blanchet@51808
   569
blanchet@51808
   570
        fun close_prem_prem xs t =
blanchet@51808
   571
          fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@51808
   572
            (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@51808
   573
blanchet@51808
   574
        fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@51808
   575
          close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@51808
   576
              HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@51808
   577
            HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@51808
   578
blanchet@52310
   579
        fun mk_raw_prem phi ctr ctr_Ts ctrXs_Ts =
blanchet@51808
   580
          let
blanchet@51808
   581
            val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@52310
   582
            val pprems = flat (map2 (mk_raw_prem_prems names_lthy') xs ctrXs_Ts);
blanchet@51808
   583
          in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@51808
   584
blanchet@51808
   585
        fun mk_prem (xs, raw_pprems, concl) =
blanchet@51808
   586
          fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@51808
   587
blanchet@52310
   588
        val raw_premss = map4 (map3 o mk_raw_prem) ps ctrss ctr_Tsss ctrXs_Tsss;
blanchet@51808
   589
blanchet@51808
   590
        val goal =
blanchet@51808
   591
          Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@54237
   592
            HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@51808
   593
blanchet@51808
   594
        val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@51808
   595
traytel@55803
   596
        val ctor_induct' = ctor_induct OF (map2 mk_absumprodE fp_type_definitions mss);
blanchet@51808
   597
blanchet@51808
   598
        val thm =
blanchet@51808
   599
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
   600
            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' fp_abs_inverses
traytel@55803
   601
              abs_inverses nested_set_maps pre_set_defss)
blanchet@51808
   602
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@55409
   603
          (* for "datatype_realizer.ML": *)
blanchet@55409
   604
          |> Thm.name_derivation (fst (dest_Type (hd fpTs)) ^ Long_Name.separator ^
blanchet@55409
   605
            (if nn > 1 then space_implode "_" (tl fp_b_names) ^ Long_Name.separator else "") ^
blanchet@55409
   606
            inductN);
blanchet@51808
   607
      in
blanchet@51808
   608
        `(conj_dests nn) thm
blanchet@51808
   609
      end;
blanchet@51808
   610
blanchet@51808
   611
    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@52305
   612
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@51808
   613
blanchet@52305
   614
    val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@52305
   615
blanchet@55867
   616
    fun mk_rec_thmss (_, x_Tssss, fss, _) recs rec_defs ctor_rec_thms =
blanchet@51808
   617
      let
blanchet@55867
   618
        val frecs = map (lists_bmoc fss) recs;
blanchet@51808
   619
blanchet@55867
   620
        fun mk_goal fss frec xctr f xs fxs =
blanchet@51808
   621
          fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@55867
   622
            (mk_Trueprop_eq (frec $ xctr, Term.list_comb (f, fxs)));
blanchet@51808
   623
blanchet@52302
   624
        fun maybe_tick (T, U) u f =
blanchet@52302
   625
          if try (fst o HOLogic.dest_prodT) U = SOME T then
blanchet@52302
   626
            Term.lambda u (HOLogic.mk_prod (u, f $ u))
blanchet@52302
   627
          else
blanchet@52302
   628
            f;
blanchet@51808
   629
blanchet@55867
   630
        fun build_rec (x as Free (_, T)) U =
blanchet@52368
   631
          if T = U then
blanchet@52368
   632
            x
blanchet@52368
   633
          else
blanchet@52303
   634
            build_map lthy (indexify (perhaps (try (snd o HOLogic.dest_prodT)) o snd) Cs
blanchet@55867
   635
              (fn kk => fn TU => maybe_tick TU (nth us kk) (nth frecs kk))) (T, U) $ x;
blanchet@52301
   636
blanchet@55867
   637
        val fxsss = map2 (map2 (flat_rec_arg_args oo map2 (map o build_rec))) xsss x_Tssss;
blanchet@51808
   638
blanchet@55867
   639
        val goalss = map5 (map4 o mk_goal fss) frecs xctrss fss xsss fxsss;
blanchet@51808
   640
blanchet@52305
   641
        val tacss =
blanchet@55867
   642
          map4 (map ooo mk_rec_tac pre_map_defs (nested_map_idents @ nesting_map_idents) rec_defs)
blanchet@55867
   643
            ctor_rec_thms fp_abs_inverses abs_inverses ctr_defss;
blanchet@51808
   644
blanchet@51808
   645
        fun prove goal tac =
blanchet@51808
   646
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51808
   647
          |> Thm.close_derivation;
blanchet@51808
   648
      in
blanchet@52305
   649
        map2 (map2 prove) goalss tacss
blanchet@51808
   650
      end;
blanchet@51808
   651
blanchet@55862
   652
    val rec_thmss =
blanchet@55862
   653
      (case rec_args_typess of
blanchet@55867
   654
        SOME types => mk_rec_thmss types recs rec_defs ctor_rec_thms
blanchet@55862
   655
      | NONE => replicate nn []);
blanchet@51808
   656
  in
blanchet@52345
   657
    ((induct_thms, induct_thm, [induct_case_names_attr]),
blanchet@55856
   658
     (rec_thmss, code_nitpicksimp_attrs @ simp_attrs))
blanchet@51808
   659
  end;
blanchet@51808
   660
blanchet@55867
   661
fun derive_coinduct_corecs_thms_for_types pre_bnfs (z, cs, cpss,
blanchet@55867
   662
      corecs_args_types as ((phss, cshsss), _))
blanchet@55867
   663
    dtor_coinduct dtor_injects dtor_ctors dtor_corec_thms nesting_bnfs fpTs Cs Xs ctrXs_Tsss kss
traytel@55803
   664
    mss ns fp_abs_inverses abs_inverses mk_vimage2p ctr_defss (ctr_sugars : ctr_sugar list)
blanchet@55864
   665
    corecs corec_defs export_args lthy =
blanchet@51810
   666
  let
blanchet@55867
   667
    fun mk_ctor_dtor_corec_thm dtor_inject dtor_ctor corec =
blanchet@55867
   668
      iffD1 OF [dtor_inject, trans OF [corec, dtor_ctor RS sym]];
traytel@53203
   669
blanchet@55867
   670
    val ctor_dtor_corec_thms = map3 mk_ctor_dtor_corec_thm dtor_injects dtor_ctors dtor_corec_thms;
traytel@53203
   671
blanchet@51815
   672
    val nn = length pre_bnfs;
blanchet@51815
   673
blanchet@51810
   674
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51810
   675
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@53329
   676
    val nesting_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nesting_bnfs;
blanchet@51830
   677
    val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@51810
   678
blanchet@51816
   679
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   680
blanchet@53210
   681
    val ctrss = map #ctrs ctr_sugars;
blanchet@53210
   682
    val discss = map #discs ctr_sugars;
blanchet@53210
   683
    val selsss = map #selss ctr_sugars;
blanchet@51840
   684
    val exhausts = map #exhaust ctr_sugars;
blanchet@51840
   685
    val disc_thmsss = map #disc_thmss ctr_sugars;
blanchet@51840
   686
    val discIss = map #discIs ctr_sugars;
blanchet@51840
   687
    val sel_thmsss = map #sel_thmss ctr_sugars;
blanchet@51810
   688
blanchet@51810
   689
    val (((rs, us'), vs'), names_lthy) =
blanchet@52341
   690
      lthy
blanchet@51810
   691
      |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@51816
   692
      ||>> Variable.variant_fixes fp_b_names
blanchet@51816
   693
      ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@51810
   694
blanchet@51810
   695
    val us = map2 (curry Free) us' fpTs;
blanchet@51810
   696
    val udiscss = map2 (map o rapp) us discss;
blanchet@51810
   697
    val uselsss = map2 (map o map o rapp) us selsss;
blanchet@51810
   698
blanchet@51810
   699
    val vs = map2 (curry Free) vs' fpTs;
blanchet@51810
   700
    val vdiscss = map2 (map o rapp) vs discss;
blanchet@51810
   701
    val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@51810
   702
blanchet@52345
   703
    val coinduct_thms_pairs =
blanchet@51810
   704
      let
blanchet@51810
   705
        val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@51810
   706
        val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@51810
   707
        val strong_rs =
blanchet@51810
   708
          map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@51810
   709
            fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@51810
   710
blanchet@54237
   711
        fun build_the_rel rs' T Xs_T =
blanchet@54237
   712
          build_rel lthy (fn (_, X) => nth rs' (find_index (curry (op =) X) Xs)) (T, Xs_T)
blanchet@54237
   713
          |> Term.subst_atomic_types (Xs ~~ fpTs);
blanchet@51810
   714
blanchet@54237
   715
        fun build_rel_app rs' usel vsel Xs_T =
blanchet@54237
   716
          fold rapp [usel, vsel] (build_the_rel rs' (fastype_of usel) Xs_T);
blanchet@51810
   717
blanchet@54237
   718
        fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels ctrXs_Ts =
blanchet@51810
   719
          (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@51810
   720
          (if null usels then
blanchet@51810
   721
             []
blanchet@51810
   722
           else
blanchet@51810
   723
             [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@54237
   724
                Library.foldr1 HOLogic.mk_conj (map3 (build_rel_app rs') usels vsels ctrXs_Ts))]);
blanchet@51810
   725
blanchet@54237
   726
        fun mk_prem_concl rs' n udiscs uselss vdiscs vselss ctrXs_Tss =
blanchet@54237
   727
          Library.foldr1 HOLogic.mk_conj (flat (map6 (mk_prem_ctr_concls rs' n)
blanchet@54237
   728
            (1 upto n) udiscs uselss vdiscs vselss ctrXs_Tss))
blanchet@51810
   729
          handle List.Empty => @{term True};
blanchet@51810
   730
blanchet@54237
   731
        fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss ctrXs_Tss =
blanchet@51810
   732
          fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@54237
   733
            HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss ctrXs_Tss)));
blanchet@51810
   734
blanchet@51810
   735
        val concl =
blanchet@51810
   736
          HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@51810
   737
            (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@51810
   738
               uvrs us vs));
blanchet@51810
   739
blanchet@51810
   740
        fun mk_goal rs' =
blanchet@54237
   741
          Logic.list_implies (map9 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss
blanchet@54237
   742
            ctrXs_Tsss, concl);
blanchet@51810
   743
blanchet@52345
   744
        val goals = map mk_goal [rs, strong_rs];
blanchet@51810
   745
blanchet@51810
   746
        fun prove dtor_coinduct' goal =
blanchet@51810
   747
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
   748
            mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs fp_abs_inverses
traytel@55803
   749
              abs_inverses dtor_ctors exhausts ctr_defss disc_thmsss sel_thmsss)
blanchet@51810
   750
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   751
          |> Thm.close_derivation;
blanchet@51810
   752
blanchet@51810
   753
        fun postproc nn thm =
blanchet@51810
   754
          Thm.permute_prems 0 nn
blanchet@51828
   755
            (if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@51810
   756
          |> Drule.zero_var_indexes
blanchet@51810
   757
          |> `(conj_dests nn);
traytel@53106
   758
traytel@53106
   759
        val rel_eqs = map rel_eq_of_bnf pre_bnfs;
traytel@53106
   760
        val rel_monos = map rel_mono_of_bnf pre_bnfs;
traytel@53106
   761
        val dtor_coinducts =
traytel@55803
   762
          [dtor_coinduct, mk_strong_coinduct_thm dtor_coinduct rel_eqs rel_monos mk_vimage2p lthy]
blanchet@51810
   763
      in
blanchet@52345
   764
        map2 (postproc nn oo prove) dtor_coinducts goals
blanchet@51810
   765
      end;
blanchet@51810
   766
blanchet@51810
   767
    fun mk_coinduct_concls ms discs ctrs =
blanchet@51810
   768
      let
blanchet@51810
   769
        fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51810
   770
        fun mk_ctr_concl 0 _ = []
blanchet@51810
   771
          | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51810
   772
        val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51810
   773
        val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51810
   774
      in
blanchet@51810
   775
        flat (map2 append disc_concls ctr_concls)
blanchet@51810
   776
      end;
blanchet@51810
   777
blanchet@51816
   778
    val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51810
   779
    val coinduct_conclss =
blanchet@51810
   780
      map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51810
   781
blanchet@51810
   782
    fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@51810
   783
blanchet@55867
   784
    val fcorecss' as [hcorecs] =
blanchet@55867
   785
      map2 (fn (pfss, _) => map (lists_bmoc pfss)) [fst corecs_args_types] [corecs];
blanchet@51810
   786
blanchet@55856
   787
    val corec_thmss =
blanchet@51810
   788
      let
blanchet@55867
   789
        fun mk_goal pfss c cps fcorec n k ctr m cfs' =
blanchet@51810
   790
          fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@51810
   791
            (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@55867
   792
               mk_Trueprop_eq (fcorec $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@51810
   793
blanchet@52347
   794
        fun mk_U maybe_mk_sumT =
blanchet@52347
   795
          typ_subst_nonatomic (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@52347
   796
blanchet@52347
   797
        fun tack z_name (c, u) f =
blanchet@52347
   798
          let val z = Free (z_name, mk_sumT (fastype_of u, fastype_of c)) in
blanchet@55414
   799
            Term.lambda z (mk_case_sum (Term.lambda u u, Term.lambda c (f $ c)) $ z)
blanchet@52347
   800
          end;
blanchet@51810
   801
blanchet@55867
   802
        fun build_corec fcorecs maybe_mk_sumT maybe_tack cqf =
blanchet@52347
   803
          let val T = fastype_of cqf in
blanchet@52347
   804
            if exists_subtype_in Cs T then
blanchet@52368
   805
              let val U = mk_U maybe_mk_sumT T in
blanchet@55483
   806
                build_map lthy (indexify fst (map2 maybe_mk_sumT fpTs Cs) (fn kk => fn _ =>
blanchet@55867
   807
                  maybe_tack (nth cs kk, nth us kk) (nth fcorecs kk))) (T, U) $ cqf
blanchet@52368
   808
              end
blanchet@52347
   809
            else
blanchet@52347
   810
              cqf
blanchet@52347
   811
          end;
blanchet@51810
   812
blanchet@55867
   813
        val cshsss' = map (map (map (build_corec (co_rec_of fcorecss') (curry mk_sumT) (tack z))))
blanchet@52351
   814
          cshsss;
blanchet@51810
   815
blanchet@55856
   816
        val goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss';
blanchet@51810
   817
blanchet@55856
   818
        val tacss =
blanchet@55867
   819
          map4 (map ooo mk_corec_tac corec_defs nesting_map_idents)
blanchet@55867
   820
            ctor_dtor_corec_thms pre_map_defs abs_inverses ctr_defss;
blanchet@51810
   821
blanchet@51810
   822
        fun prove goal tac =
blanchet@51815
   823
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51815
   824
          |> Thm.close_derivation;
blanchet@51810
   825
      in
blanchet@55856
   826
        map2 (map2 prove) goalss tacss
blanchet@55856
   827
        |> map (map (unfold_thms lthy @{thms case_sum_if}))
blanchet@51810
   828
      end;
blanchet@51810
   829
blanchet@55856
   830
    val disc_corec_iff_thmss =
blanchet@51810
   831
      let
blanchet@55867
   832
        fun mk_goal c cps fcorec n k disc =
blanchet@55867
   833
          mk_Trueprop_eq (disc $ (fcorec $ c),
blanchet@51810
   834
            if n = 1 then @{const True}
blanchet@51810
   835
            else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@51810
   836
blanchet@55856
   837
        val goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@51810
   838
blanchet@51828
   839
        fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@51810
   840
blanchet@51810
   841
        val case_splitss' = map (map mk_case_split') cpss;
blanchet@51810
   842
blanchet@55867
   843
        val tacss = map3 (map oo mk_disc_corec_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@51810
   844
blanchet@51810
   845
        fun prove goal tac =
blanchet@51810
   846
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@52357
   847
          |> singleton export_args
blanchet@51829
   848
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   849
          |> Thm.close_derivation;
blanchet@51810
   850
blanchet@51810
   851
        fun proves [_] [_] = []
blanchet@51810
   852
          | proves goals tacs = map2 prove goals tacs;
blanchet@51810
   853
      in
blanchet@55856
   854
        map2 proves goalss tacss
blanchet@51810
   855
      end;
blanchet@51810
   856
blanchet@55867
   857
    fun mk_disc_corec_thms corecs discIs = map (op RS) (corecs ~~ discIs);
blanchet@51810
   858
blanchet@55867
   859
    val disc_corec_thmss = map2 mk_disc_corec_thms corec_thmss discIss;
blanchet@51810
   860
blanchet@55867
   861
    fun mk_sel_corec_thm corec_thm sel sel_thm =
blanchet@51810
   862
      let
blanchet@51810
   863
        val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@51810
   864
        val arg_cong' =
blanchet@51810
   865
          Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@51810
   866
            [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@51810
   867
          |> Thm.varifyT_global;
blanchet@51810
   868
        val sel_thm' = sel_thm RSN (2, trans);
blanchet@51810
   869
      in
blanchet@55867
   870
        corec_thm RS arg_cong' RS sel_thm'
blanchet@51810
   871
      end;
blanchet@51810
   872
blanchet@55867
   873
    fun mk_sel_corec_thms corec_thmss =
blanchet@55867
   874
      map3 (map3 (map2 o mk_sel_corec_thm)) corec_thmss selsss sel_thmsss;
blanchet@51810
   875
blanchet@55867
   876
    val sel_corec_thmsss = mk_sel_corec_thms corec_thmss;
blanchet@51810
   877
blanchet@51810
   878
    val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51810
   879
    val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51810
   880
    val coinduct_case_concl_attrs =
blanchet@51810
   881
      map2 (fn casex => fn concls =>
blanchet@51810
   882
          Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51810
   883
        coinduct_cases coinduct_conclss;
blanchet@51810
   884
    val coinduct_case_attrs =
blanchet@51810
   885
      coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51810
   886
  in
blanchet@52345
   887
    ((coinduct_thms_pairs, coinduct_case_attrs),
blanchet@55856
   888
     (corec_thmss, code_nitpicksimp_attrs),
blanchet@55856
   889
     (disc_corec_thmss, []),
blanchet@55856
   890
     (disc_corec_iff_thmss, simp_attrs),
blanchet@55856
   891
     (sel_corec_thmsss, simp_attrs))
blanchet@51810
   892
  end;
blanchet@51810
   893
blanchet@52207
   894
fun define_co_datatypes prepare_constraint prepare_typ prepare_term fp construct_fp
blanchet@55410
   895
    (wrap_opts as (no_discs_sels, _), specs) no_defs_lthy0 =
blanchet@49112
   896
  let
blanchet@49298
   897
    (* TODO: sanity checks on arguments *)
blanchet@49298
   898
blanchet@52969
   899
    val _ = if fp = Greatest_FP andalso no_discs_sels then
blanchet@52969
   900
        error "Cannot define codatatypes without discriminators and selectors"
blanchet@52207
   901
      else
blanchet@52207
   902
        ();
blanchet@49278
   903
blanchet@49367
   904
    val nn = length specs;
blanchet@55469
   905
    val fp_bs = map type_binding_of_spec specs;
blanchet@49498
   906
    val fp_b_names = map Binding.name_of fp_bs;
blanchet@49498
   907
    val fp_common_name = mk_common_name fp_b_names;
blanchet@55469
   908
    val map_bs = map map_binding_of_spec specs;
blanchet@55469
   909
    val rel_bs = map rel_binding_of_spec specs;
blanchet@49298
   910
blanchet@51758
   911
    fun prepare_type_arg (_, (ty, c)) =
blanchet@49298
   912
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
   913
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
   914
      end;
blanchet@49298
   915
blanchet@55469
   916
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of_spec) specs;
blanchet@49298
   917
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@55700
   918
    val unsorted_As = Library.foldr1 (merge_type_args fp) unsorted_Ass0;
blanchet@53266
   919
    val num_As = length unsorted_As;
blanchet@55699
   920
blanchet@55699
   921
    val set_boss = map (map fst o type_args_named_constrained_of_spec) specs;
blanchet@55699
   922
    val set_bss = map (map (the_default Binding.empty)) set_boss;
blanchet@49119
   923
blanchet@49585
   924
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
   925
      no_defs_lthy0
blanchet@49298
   926
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@53266
   927
      |> mk_TFrees num_As
blanchet@49585
   928
      ||>> mk_TFrees nn
blanchet@51858
   929
      ||>> variant_tfrees fp_b_names;
blanchet@49119
   930
blanchet@55469
   931
    fun add_fake_type spec =
blanchet@55469
   932
      Typedecl.basic_typedecl (type_binding_of_spec spec, num_As, mixfix_of_spec spec);
blanchet@51768
   933
blanchet@53268
   934
    val (fake_T_names, fake_lthy) = fold_map add_fake_type specs no_defs_lthy0;
blanchet@49119
   935
blanchet@53262
   936
    val qsoty = quote o Syntax.string_of_typ fake_lthy;
blanchet@53262
   937
blanchet@54253
   938
    val _ = (case Library.duplicates (op =) unsorted_As of [] => ()
blanchet@53262
   939
      | A :: _ => error ("Duplicate type parameter " ^ qsoty A ^ " in " ^ co_prefix fp ^
blanchet@53262
   940
          "datatype specification"));
blanchet@53262
   941
blanchet@53262
   942
    val bad_args =
blanchet@53262
   943
      map (Logic.type_map (singleton (Variable.polymorphic no_defs_lthy0))) unsorted_As
blanchet@53262
   944
      |> filter_out Term.is_TVar;
blanchet@53262
   945
    val _ = null bad_args orelse
blanchet@53262
   946
      error ("Locally fixed type argument " ^ qsoty (hd bad_args) ^ " in " ^ co_prefix fp ^
blanchet@53262
   947
        "datatype specification");
blanchet@53262
   948
blanchet@55469
   949
    val mixfixes = map mixfix_of_spec specs;
blanchet@49119
   950
blanchet@54253
   951
    val _ = (case Library.duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
   952
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
   953
blanchet@55469
   954
    val mx_ctr_specss = map mixfixed_ctr_specs_of_spec specs;
blanchet@55469
   955
    val ctr_specss = map (map fst) mx_ctr_specss;
blanchet@55469
   956
    val ctr_mixfixess = map (map snd) mx_ctr_specss;
blanchet@49119
   957
blanchet@55469
   958
    val disc_bindingss = map (map disc_of_ctr_spec) ctr_specss;
blanchet@49336
   959
    val ctr_bindingss =
blanchet@55469
   960
      map2 (fn fp_b_name => map (Binding.qualify false fp_b_name o ctr_of_ctr_spec)) fp_b_names
blanchet@55469
   961
        ctr_specss;
blanchet@55469
   962
    val ctr_argsss = map (map args_of_ctr_spec) ctr_specss;
blanchet@49119
   963
blanchet@49336
   964
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
   965
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@55469
   966
    val raw_sel_defaultsss = map (map sel_defaults_of_ctr_spec) ctr_specss;
blanchet@49286
   967
blanchet@49308
   968
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
   969
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@53262
   970
    val As' = map dest_TFree As;
blanchet@49298
   971
blanchet@49183
   972
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@53262
   973
    val _ = (case subtract (op =) As' rhs_As' of [] => ()
blanchet@53262
   974
      | extras => error ("Extra type variables on right-hand side: " ^
blanchet@53262
   975
          commas (map (qsoty o TFree) extras)));
blanchet@49165
   976
blanchet@53268
   977
    val fake_Ts = map (fn s => Type (s, As)) fake_T_names;
blanchet@53268
   978
blanchet@53262
   979
    fun eq_fpT_check (T as Type (s, Ts)) (T' as Type (s', Ts')) =
blanchet@53262
   980
        s = s' andalso (Ts = Ts' orelse
blanchet@53262
   981
          error ("Wrong type arguments in " ^ co_prefix fp ^ "recursive type " ^ qsoty T ^
blanchet@53262
   982
            " (expected " ^ qsoty T' ^ ")"))
blanchet@49591
   983
      | eq_fpT_check _ _ = false;
blanchet@49146
   984
blanchet@53222
   985
    fun freeze_fp (T as Type (s, Ts)) =
blanchet@49591
   986
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@53222
   987
          ~1 => Type (s, map freeze_fp Ts)
blanchet@49591
   988
        | kk => nth Xs kk)
blanchet@49204
   989
      | freeze_fp T = T;
blanchet@49121
   990
blanchet@53222
   991
    val unfreeze_fp = Term.typ_subst_atomic (Xs ~~ fake_Ts);
blanchet@53222
   992
blanchet@52310
   993
    val ctrXs_Tsss = map (map (map freeze_fp)) fake_ctr_Tsss;
traytel@55803
   994
    val ctrXs_repTs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctrXs_Tsss;
blanchet@49119
   995
blanchet@49298
   996
    val fp_eqs =
traytel@55803
   997
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctrXs_repTs;
blanchet@49121
   998
blanchet@53262
   999
    val rhsXs_As' = fold (fold (fold Term.add_tfreesT)) ctrXs_Tsss [];
blanchet@53262
  1000
    val _ = (case subtract (op =) rhsXs_As' As' of [] => ()
blanchet@53266
  1001
      | extras => List.app (fn extra => warning ("Unused type variable on right-hand side of " ^
blanchet@53266
  1002
          co_prefix fp ^ "datatype definition: " ^ qsoty (TFree extra))) extras);
blanchet@53262
  1003
blanchet@55701
  1004
    val killed_As =
blanchet@55701
  1005
      map_filter (fn (A, set_bos) => if exists is_none set_bos then SOME A else NONE)
blanchet@55701
  1006
        (unsorted_As ~~ transpose set_boss);
blanchet@55701
  1007
traytel@55803
  1008
    val ((pre_bnfs, absT_infos), (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0,
traytel@55803
  1009
             dtors = dtors0, xtor_co_iterss = xtor_co_iterss0, xtor_co_induct, dtor_ctors,
traytel@55803
  1010
             ctor_dtors, ctor_injects, dtor_injects, xtor_map_thms, xtor_set_thmss, xtor_rel_thms,
traytel@55803
  1011
             xtor_co_iter_thmss, ...},
traytel@53203
  1012
           lthy)) =
blanchet@55701
  1013
      fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As)
blanchet@55701
  1014
        (map dest_TFree killed_As) fp_eqs no_defs_lthy0
blanchet@53222
  1015
      handle BAD_DEAD (X, X_backdrop) =>
blanchet@53222
  1016
        (case X_backdrop of
blanchet@53222
  1017
          Type (bad_tc, _) =>
blanchet@53222
  1018
          let
blanchet@53222
  1019
            val fake_T = qsoty (unfreeze_fp X);
blanchet@53222
  1020
            val fake_T_backdrop = qsoty (unfreeze_fp X_backdrop);
blanchet@53222
  1021
            fun register_hint () =
blanchet@53222
  1022
              "\nUse the " ^ quote (fst (fst @{command_spec "bnf"})) ^ " command to register " ^
blanchet@53222
  1023
              quote bad_tc ^ " as a bounded natural functor to allow nested (co)recursion through \
blanchet@53222
  1024
              \it";
blanchet@53222
  1025
          in
blanchet@53222
  1026
            if is_some (bnf_of no_defs_lthy bad_tc) orelse
blanchet@53222
  1027
               is_some (fp_sugar_of no_defs_lthy bad_tc) then
blanchet@53256
  1028
              error ("Inadmissible " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53256
  1029
                " in type expression " ^ fake_T_backdrop)
blanchet@53222
  1030
            else if is_some (Datatype_Data.get_info (Proof_Context.theory_of no_defs_lthy)
blanchet@53222
  1031
                bad_tc) then
blanchet@53222
  1032
              error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53222
  1033
                " via the old-style datatype " ^ quote bad_tc ^ " in type expression " ^
blanchet@53222
  1034
                fake_T_backdrop ^ register_hint ())
blanchet@53222
  1035
            else
blanchet@53222
  1036
              error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53222
  1037
                " via type constructor " ^ quote bad_tc ^ " in type expression " ^ fake_T_backdrop ^
blanchet@53222
  1038
                register_hint ())
blanchet@53222
  1039
          end);
blanchet@49585
  1040
traytel@55803
  1041
    val abss = map #abs absT_infos;
traytel@55803
  1042
    val reps = map #rep absT_infos;
traytel@55803
  1043
    val absTs = map #absT absT_infos;
traytel@55803
  1044
    val repTs = map #repT absT_infos;
traytel@55803
  1045
    val abs_injects = map #abs_inject absT_infos;
traytel@55803
  1046
    val abs_inverses = map #abs_inverse absT_infos;
traytel@55803
  1047
    val type_definitions = map #type_definition absT_infos;
traytel@55803
  1048
traytel@53143
  1049
    val time = time lthy;
blanchet@49585
  1050
    val timer = time (Timer.startRealTimer ());
blanchet@49121
  1051
blanchet@52310
  1052
    val nesting_bnfs = nesty_bnfs lthy ctrXs_Tsss As;
blanchet@52310
  1053
    val nested_bnfs = nesty_bnfs lthy ctrXs_Tsss Xs;
blanchet@49226
  1054
blanchet@49585
  1055
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
  1056
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
  1057
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@53290
  1058
    val nesting_set_maps = maps set_map_of_bnf nesting_bnfs;
blanchet@53290
  1059
    val nested_set_maps = maps set_map_of_bnf nested_bnfs;
blanchet@49585
  1060
blanchet@49585
  1061
    val live = live_of_bnf any_fp_bnf;
blanchet@52961
  1062
    val _ =
blanchet@52961
  1063
      if live = 0 andalso exists (not o Binding.is_empty) (map_bs @ rel_bs) then
blanchet@53266
  1064
        warning "Map function and relator names ignored"
blanchet@52961
  1065
      else
blanchet@52961
  1066
        ();
blanchet@49585
  1067
blanchet@49585
  1068
    val Bs =
blanchet@49585
  1069
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@53266
  1070
        (liveness_of_fp_bnf num_As any_fp_bnf) As Bs0;
blanchet@49585
  1071
blanchet@49585
  1072
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
  1073
blanchet@49501
  1074
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
  1075
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
  1076
blanchet@49501
  1077
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
  1078
blanchet@51780
  1079
    fun massage_simple_notes base =
blanchet@51780
  1080
      filter_out (null o #2)
blanchet@51780
  1081
      #> map (fn (thmN, thms, attrs) =>
blanchet@55410
  1082
        ((Binding.qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
  1083
blanchet@51780
  1084
    val massage_multi_notes =
blanchet@51780
  1085
      maps (fn (thmN, thmss, attrs) =>
blanchet@53792
  1086
        map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@55410
  1087
            ((Binding.qualify true fp_b_name (Binding.name thmN), attrs T_name), [(thms, [])]))
blanchet@53792
  1088
          fp_b_names fpTs thmss)
blanchet@53792
  1089
      #> filter_out (null o fst o hd o snd);
blanchet@51780
  1090
blanchet@52310
  1091
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctrXs_Tsss;
blanchet@49203
  1092
    val ns = map length ctr_Tsss;
blanchet@49212
  1093
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
  1094
    val mss = map (map length) ctr_Tsss;
blanchet@49203
  1095
blanchet@55867
  1096
    val ((xtor_co_recs, recs_args_types, corecs_args_types), lthy') =
blanchet@55867
  1097
      mk_co_recs_prelims fp ctr_Tsss fpTs Cs absTs repTs ns mss (map co_rec_of xtor_co_iterss0)
blanchet@55867
  1098
        lthy;
blanchet@49210
  1099
traytel@55803
  1100
    fun define_ctrs_dtrs_for_type (((((((((((((((((((((((((((fp_bnf, fp_b), fpT), ctor), dtor),
blanchet@55867
  1101
              xtor_co_rec), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
traytel@55803
  1102
            pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), abs),
traytel@55803
  1103
          abs_inject), abs_inverse), type_definition), ctr_bindings), ctr_mixfixes), ctr_Tss),
traytel@55803
  1104
        disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
  1105
      let
blanchet@49498
  1106
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
  1107
traytel@55803
  1108
        val ctr_absT = domain_type (fastype_of ctor);
blanchet@49119
  1109
blanchet@52968
  1110
        val ((((w, xss), yss), u'), names_lthy) =
blanchet@49204
  1111
          no_defs_lthy
traytel@55803
  1112
          |> yield_singleton (mk_Frees "w") ctr_absT
blanchet@49370
  1113
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
  1114
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
  1115
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
  1116
blanchet@49498
  1117
        val u = Free (u', fpT);
blanchet@49121
  1118
blanchet@49129
  1119
        val ctr_rhss =
traytel@55803
  1120
          map2 (fn k => fn xs => fold_rev Term.lambda xs (ctor $ mk_absumprod ctr_absT abs n k xs))
traytel@55803
  1121
            ks xss;
blanchet@49121
  1122
traytel@53569
  1123
        val maybe_conceal_def_binding = Thm.def_binding
traytel@53569
  1124
          #> Config.get no_defs_lthy bnf_note_all = false ? Binding.conceal;
traytel@53569
  1125
blanchet@52968
  1126
        val ((raw_ctrs, raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
  1127
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
traytel@53569
  1128
              Local_Theory.define ((b, mx), ((maybe_conceal_def_binding b, []), rhs)) #>> apsnd snd)
blanchet@52968
  1129
            ctr_bindings ctr_mixfixes ctr_rhss
blanchet@49121
  1130
          ||> `Local_Theory.restore;
blanchet@49121
  1131
blanchet@49121
  1132
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
  1133
blanchet@49121
  1134
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
  1135
        val ctr_defs' =
blanchet@49585
  1136
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
  1137
blanchet@49203
  1138
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
  1139
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
  1140
blanchet@51897
  1141
        fun wrap_ctrs lthy =
blanchet@49123
  1142
          let
traytel@50170
  1143
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
  1144
              let
blanchet@49585
  1145
                val ctor_iff_dtor_thm =
blanchet@49585
  1146
                  let
blanchet@49585
  1147
                    val goal =
blanchet@49585
  1148
                      fold_rev Logic.all [w, u]
blanchet@49585
  1149
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
  1150
                  in
wenzelm@51551
  1151
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
  1152
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [ctr_absT, fpT])
blanchet@49585
  1153
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@55409
  1154
                    |> Morphism.thm phi
blanchet@49585
  1155
                    |> Thm.close_derivation
blanchet@49585
  1156
                  end;
blanchet@49585
  1157
blanchet@49585
  1158
                val sumEN_thm' =
traytel@55803
  1159
                  unfold_thms lthy @{thms unit_all_eq1} (mk_absumprodE type_definition ms)
blanchet@49585
  1160
                  |> Morphism.thm phi;
blanchet@49135
  1161
              in
blanchet@49585
  1162
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
  1163
              end;
blanchet@49135
  1164
blanchet@49585
  1165
            val inject_tacss =
traytel@55803
  1166
              map2 (fn ctr_def => fn 0 => [] | _ => [fn {context = ctxt, ...} =>
traytel@55803
  1167
                mk_inject_tac ctxt ctr_def ctor_inject abs_inject]) ctr_defs ms;
blanchet@49585
  1168
blanchet@49585
  1169
            val half_distinct_tacss =
blanchet@49585
  1170
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
traytel@55803
  1171
                  mk_half_distinct_tac ctxt ctor_inject abs_inject [def, def']))
traytel@55803
  1172
                (mk_half_pairss (`I ctr_defs));
blanchet@49585
  1173
blanchet@52968
  1174
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss;
blanchet@49585
  1175
blanchet@49585
  1176
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@55469
  1177
blanchet@55469
  1178
            fun ctr_spec_of disc_b ctr0 sel_bs sel_defs = (((disc_b, ctr0), sel_bs), sel_defs);
blanchet@55469
  1179
            val ctr_specs = map4 ctr_spec_of disc_bindings ctrs0 sel_bindingss sel_defaultss;
blanchet@49123
  1180
          in
blanchet@55469
  1181
            free_constructors tacss ((wrap_opts, standard_binding), ctr_specs) lthy
blanchet@49123
  1182
          end;
blanchet@49121
  1183
blanchet@55397
  1184
        fun derive_maps_sets_rels (ctr_sugar as {case_cong, ...} : ctr_sugar, lthy) =
blanchet@51835
  1185
          if live = 0 then
blanchet@51840
  1186
            ((([], [], [], []), ctr_sugar), lthy)
blanchet@51835
  1187
          else
blanchet@51835
  1188
            let
blanchet@51835
  1189
              val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@51835
  1190
              val nones = replicate live NONE;
blanchet@49585
  1191
blanchet@51835
  1192
              val ctor_cong =
blanchet@52207
  1193
                if fp = Least_FP then
blanchet@51835
  1194
                  Drule.dummy_thm
blanchet@51835
  1195
                else
blanchet@51835
  1196
                  let val ctor' = mk_ctor Bs ctor in
blanchet@51835
  1197
                    cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51835
  1198
                  end;
blanchet@49585
  1199
traytel@55803
  1200
              fun mk_cIn ctor k xs =
traytel@55803
  1201
                let val absT = domain_type (fastype_of ctor) in
traytel@55803
  1202
                  mk_absumprod absT abs n k xs
traytel@55803
  1203
                  |> fp = Greatest_FP ? curry (op $) ctor
traytel@55803
  1204
                  |> certify lthy
traytel@55803
  1205
                end;
blanchet@49585
  1206
traytel@55803
  1207
              val cxIns = map2 (mk_cIn ctor) ks xss;
traytel@55803
  1208
              val cyIns = map2 (mk_cIn (map_types B_ify ctor)) ks yss;
blanchet@49585
  1209
blanchet@51835
  1210
              fun mk_map_thm ctr_def' cxIn =
blanchet@51835
  1211
                fold_thms lthy [ctr_def']
traytel@55803
  1212
                  (unfold_thms lthy (o_apply :: pre_map_def ::
traytel@55803
  1213
                       (if fp = Least_FP then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map @
traytel@55803
  1214
                       abs_inverses)
blanchet@51835
  1215
                     (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@52207
  1216
                        (if fp = Least_FP then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@51835
  1217
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1218
blanchet@51835
  1219
              fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@51835
  1220
                fold_thms lthy [ctr_def']
blanchet@53290
  1221
                  (unfold_thms lthy (pre_set_defs @ nested_set_maps @ nesting_set_maps @
traytel@55803
  1222
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_set @
traytel@55803
  1223
                       abs_inverses)
blanchet@51835
  1224
                     (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@51835
  1225
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1226
blanchet@51835
  1227
              fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49127
  1228
blanchet@51835
  1229
              val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@51835
  1230
              val set_thmss = map mk_set_thms fp_set_thms;
blanchet@55463
  1231
              val set_thms = flat set_thmss;
blanchet@51835
  1232
blanchet@51835
  1233
              val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
  1234
blanchet@51835
  1235
              fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@51835
  1236
                fold_thms lthy ctr_defs'
traytel@55803
  1237
                  (unfold_thms lthy (pre_rel_def :: abs_inverse ::
traytel@55803
  1238
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_rel @
traytel@55803
  1239
                       @{thms vimage2p_def Inl_Inr_False})
blanchet@53266
  1240
                     (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@51835
  1241
                |> postproc
blanchet@51835
  1242
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1243
blanchet@51835
  1244
              fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@51835
  1245
                mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
  1246
blanchet@51835
  1247
              val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
  1248
blanchet@51835
  1249
              fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@51835
  1250
                mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@51835
  1251
                  cxIn cyIn;
blanchet@49121
  1252
blanchet@51835
  1253
              fun mk_other_half_rel_distinct_thm thm =
blanchet@51835
  1254
                flip_rels lthy live thm
blanchet@51835
  1255
                RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
  1256
blanchet@51835
  1257
              val half_rel_distinct_thmss =
blanchet@51835
  1258
                map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@51835
  1259
              val other_half_rel_distinct_thmss =
blanchet@51835
  1260
                map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@51835
  1261
              val (rel_distinct_thms, _) =
blanchet@51835
  1262
                join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
  1263
blanchet@55463
  1264
              val rel_eq_thms =
blanchet@55463
  1265
                map (fn th => th RS @{thm eq_False[THEN iffD2]}) rel_distinct_thms @
blanchet@55463
  1266
                map2 (fn th => fn 0 => th RS @{thm eq_True[THEN iffD2]} | _ => th)
blanchet@55463
  1267
                  rel_inject_thms ms;
blanchet@55463
  1268
blanchet@54145
  1269
              val anonymous_notes =
blanchet@55397
  1270
                [([case_cong], fundefcong_attrs),
blanchet@55463
  1271
                 (rel_eq_thms, code_nitpicksimp_attrs)]
blanchet@54145
  1272
                |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@54145
  1273
blanchet@51835
  1274
              val notes =
blanchet@54145
  1275
                [(mapN, map_thms, code_nitpicksimp_attrs @ simp_attrs),
blanchet@54145
  1276
                 (rel_distinctN, rel_distinct_thms, simp_attrs),
blanchet@54145
  1277
                 (rel_injectN, rel_inject_thms, simp_attrs),
blanchet@55463
  1278
                 (setN, set_thms, code_nitpicksimp_attrs @ simp_attrs)]
blanchet@51835
  1279
                |> massage_simple_notes fp_b_name;
blanchet@51835
  1280
            in
blanchet@51840
  1281
              (((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
blanchet@55463
  1282
               lthy
blanchet@55535
  1283
               |> Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) map_thms)
blanchet@55535
  1284
               |> Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) rel_eq_thms)
blanchet@55535
  1285
               |> Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) set_thms)
blanchet@55463
  1286
               |> Local_Theory.notes (anonymous_notes @ notes)
blanchet@55463
  1287
               |> snd)
blanchet@51835
  1288
            end;
blanchet@49585
  1289
blanchet@55410
  1290
        fun mk_binding pre = Binding.qualify false fp_b_name (Binding.prefix_name (pre ^ "_") fp_b);
blanchet@49287
  1291
blanchet@55867
  1292
        fun massage_res (((maps_sets_rels, ctr_sugar), co_rec_res), lthy) =
blanchet@55867
  1293
          (((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), co_rec_res), lthy);
blanchet@49119
  1294
      in
blanchet@51897
  1295
        (wrap_ctrs
blanchet@51835
  1296
         #> derive_maps_sets_rels
blanchet@52313
  1297
         ##>>
blanchet@55867
  1298
           (if fp = Least_FP then define_rec recs_args_types mk_binding fpTs Cs reps
blanchet@55867
  1299
           else define_corec (the corecs_args_types) mk_binding fpTs Cs abss) xtor_co_rec
blanchet@51835
  1300
         #> massage_res, lthy')
blanchet@49119
  1301
      end;
blanchet@49167
  1302
blanchet@51835
  1303
    fun wrap_types_etc (wrap_types_etcs, lthy) =
blanchet@51835
  1304
      fold_map I wrap_types_etcs lthy
blanchet@52342
  1305
      |>> apsnd split_list o apfst (apsnd split_list4 o apfst split_list4 o split_list)
blanchet@52342
  1306
        o split_list;
blanchet@49226
  1307
blanchet@55856
  1308
    fun mk_simp_thms ({injects, distincts, case_thms, ...} : ctr_sugar) co_recs mapsx rel_injects
blanchet@55856
  1309
        rel_distincts setss =
blanchet@55856
  1310
      injects @ distincts @ case_thms @ co_recs @ mapsx @ rel_injects @ rel_distincts @ flat setss;
blanchet@49479
  1311
blanchet@55867
  1312
    fun derive_note_induct_recs_thms_for_types
blanchet@53476
  1313
        ((((mapss, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
blanchet@55864
  1314
          (recs, rec_defs)), lthy) =
blanchet@49202
  1315
      let
blanchet@55856
  1316
        val ((induct_thms, induct_thm, induct_attrs), (rec_thmss, iter_attrs)) =
blanchet@55867
  1317
          derive_induct_recs_thms_for_types pre_bnfs recs_args_types xtor_co_induct
blanchet@55867
  1318
            (map co_rec_of xtor_co_iter_thmss) nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss
blanchet@55867
  1319
            abs_inverses type_definitions abs_inverses ctrss ctr_defss recs rec_defs lthy;
blanchet@49201
  1320
blanchet@51830
  1321
        val induct_type_attr = Attrib.internal o K o Induct.induct_type;
blanchet@51810
  1322
blanchet@55864
  1323
        val (recs', rec_thmss') =
blanchet@55867
  1324
          if is_some recs_args_types then (recs, rec_thmss)
blanchet@55864
  1325
          else (map #casex ctr_sugars, map #case_thms ctr_sugars);
blanchet@55862
  1326
blanchet@51835
  1327
        val simp_thmss =
blanchet@55856
  1328
          map6 mk_simp_thms ctr_sugars rec_thmss mapss rel_injects rel_distincts setss;
blanchet@49438
  1329
blanchet@49337
  1330
        val common_notes =
blanchet@51808
  1331
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
  1332
          |> massage_simple_notes fp_common_name;
blanchet@49337
  1333
blanchet@49226
  1334
        val notes =
blanchet@55856
  1335
          [(inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
blanchet@53808
  1336
           (recN, rec_thmss, K iter_attrs),
blanchet@49585
  1337
           (simpsN, simp_thmss, K [])]
blanchet@51780
  1338
          |> massage_multi_notes;
blanchet@49202
  1339
      in
blanchet@51824
  1340
        lthy
blanchet@55867
  1341
        |> (if is_some recs_args_types then
blanchet@55864
  1342
              Spec_Rules.add Spec_Rules.Equational (recs, flat rec_thmss)
blanchet@55862
  1343
            else
blanchet@55862
  1344
              I)
blanchet@51824
  1345
        |> Local_Theory.notes (common_notes @ notes) |> snd
traytel@55803
  1346
        |> register_fp_sugars Xs Least_FP pre_bnfs absT_infos nested_bnfs nesting_bnfs fp_res
blanchet@55864
  1347
          ctrXs_Tsss ctr_defss ctr_sugars recs' mapss [induct_thm] (map single induct_thms)
blanchet@55863
  1348
          rec_thmss' (replicate nn []) (replicate nn [])
blanchet@49202
  1349
      end;
blanchet@49202
  1350
blanchet@55867
  1351
    fun derive_note_coinduct_corecs_thms_for_types
blanchet@53476
  1352
        ((((mapss, rel_injects, rel_distincts, setss), (_, _, ctr_defss, ctr_sugars)),
blanchet@55867
  1353
          (corecs, corec_defs)), lthy) =
blanchet@49212
  1354
      let
blanchet@52345
  1355
        val (([(coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)],
blanchet@51810
  1356
              coinduct_attrs),
blanchet@55867
  1357
             (corec_thmss, corec_attrs),
blanchet@55867
  1358
             (disc_corec_thmss, disc_corec_attrs),
blanchet@55867
  1359
             (disc_corec_iff_thmss, disc_corec_iff_attrs),
blanchet@55867
  1360
             (sel_corec_thmsss, sel_corec_attrs)) =
blanchet@55867
  1361
          derive_coinduct_corecs_thms_for_types pre_bnfs (the corecs_args_types) xtor_co_induct
blanchet@55867
  1362
            dtor_injects dtor_ctors (map co_rec_of xtor_co_iter_thmss) nesting_bnfs fpTs Cs Xs
blanchet@55867
  1363
            ctrXs_Tsss kss mss ns abs_inverses abs_inverses I ctr_defss ctr_sugars corecs corec_defs
traytel@55803
  1364
            (Proof_Context.export lthy' no_defs_lthy) lthy;
blanchet@49212
  1365
blanchet@53475
  1366
        val sel_corec_thmss = map flat sel_corec_thmsss;
blanchet@53475
  1367
blanchet@51830
  1368
        val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
blanchet@49479
  1369
blanchet@55867
  1370
        val flat_corec_thms = append oo append;
blanchet@49479
  1371
blanchet@49479
  1372
        val simp_thmss =
blanchet@55856
  1373
          map6 mk_simp_thms ctr_sugars
blanchet@55867
  1374
            (map3 flat_corec_thms disc_corec_thmss disc_corec_iff_thmss sel_corec_thmss)
blanchet@53476
  1375
            mapss rel_injects rel_distincts setss;
blanchet@49479
  1376
blanchet@49342
  1377
        val common_notes =
blanchet@49591
  1378
          (if nn > 1 then
blanchet@51810
  1379
             [(coinductN, [coinduct_thm], coinduct_attrs),
blanchet@51810
  1380
              (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
blanchet@49591
  1381
           else
blanchet@49591
  1382
             [])
blanchet@51780
  1383
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1384
blanchet@49212
  1385
        val notes =
blanchet@51780
  1386
          [(coinductN, map single coinduct_thms,
blanchet@51810
  1387
            fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
blanchet@55867
  1388
           (corecN, corec_thmss, K corec_attrs),
blanchet@55867
  1389
           (disc_corecN, disc_corec_thmss, K disc_corec_attrs),
blanchet@55867
  1390
           (disc_corec_iffN, disc_corec_iff_thmss, K disc_corec_iff_attrs),
blanchet@55867
  1391
           (sel_corecN, sel_corec_thmss, K sel_corec_attrs),
blanchet@51780
  1392
           (simpsN, simp_thmss, K []),
blanchet@55856
  1393
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs)]
blanchet@51780
  1394
          |> massage_multi_notes;
blanchet@49212
  1395
      in
blanchet@51824
  1396
        lthy
blanchet@55864
  1397
        (* TODO: code theorems *)
blanchet@55867
  1398
        |> fold (curry (Spec_Rules.add Spec_Rules.Equational) corecs)
blanchet@55864
  1399
          [flat sel_corec_thmss, flat corec_thmss]
blanchet@54030
  1400
        |> Local_Theory.notes (common_notes @ notes) |> snd
traytel@55803
  1401
        |> register_fp_sugars Xs Greatest_FP pre_bnfs absT_infos nested_bnfs nesting_bnfs fp_res
blanchet@55867
  1402
          ctrXs_Tsss ctr_defss ctr_sugars corecs mapss [coinduct_thm, strong_coinduct_thm]
blanchet@55864
  1403
          (transpose [coinduct_thms, strong_coinduct_thms]) corec_thmss disc_corec_thmss
blanchet@55864
  1404
          sel_corec_thmsss
blanchet@49212
  1405
      end;
blanchet@49212
  1406
blanchet@52367
  1407
    val lthy'' = lthy'
blanchet@52968
  1408
      |> fold_map define_ctrs_dtrs_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ ctors ~~ dtors ~~
blanchet@55867
  1409
        xtor_co_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~ pre_set_defss ~~
blanchet@55867
  1410
        pre_rel_defs ~~ xtor_map_thms ~~ xtor_set_thmss ~~ xtor_rel_thms ~~ ns ~~ kss ~~ mss ~~
blanchet@55867
  1411
        abss ~~ abs_injects ~~ abs_inverses ~~ type_definitions ~~ ctr_bindingss ~~ ctr_mixfixess ~~
blanchet@55867
  1412
        ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ raw_sel_defaultsss)
blanchet@51835
  1413
      |> wrap_types_etc
blanchet@55867
  1414
      |> fp_case fp derive_note_induct_recs_thms_for_types
blanchet@55867
  1415
           derive_note_coinduct_corecs_thms_for_types;
blanchet@49167
  1416
blanchet@49167
  1417
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@52899
  1418
      co_prefix fp ^ "datatype"));
blanchet@49112
  1419
  in
blanchet@52367
  1420
    timer; lthy''
blanchet@49112
  1421
  end;
blanchet@49112
  1422
wenzelm@53974
  1423
fun co_datatypes x = define_co_datatypes (K I) (K I) (K I) x;
blanchet@49297
  1424
wenzelm@53974
  1425
fun co_datatype_cmd x =
wenzelm@53974
  1426
  define_co_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term x;
blanchet@49119
  1427
blanchet@55469
  1428
val parse_ctr_arg =
blanchet@55469
  1429
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
blanchet@55469
  1430
  (Parse.typ >> pair Binding.empty);
blanchet@55469
  1431
blanchet@55469
  1432
val parse_ctr_specs =
blanchet@55469
  1433
  Parse.enum1 "|" (parse_ctr_spec parse_binding parse_ctr_arg -- Parse.opt_mixfix);
blanchet@51767
  1434
blanchet@51767
  1435
val parse_spec =
blanchet@51790
  1436
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@55469
  1437
  Parse.opt_mixfix -- (@{keyword "="} |-- parse_ctr_specs);
blanchet@51767
  1438
blanchet@55469
  1439
val parse_co_datatype = parse_ctr_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1440
blanchet@52207
  1441
fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp;
blanchet@49112
  1442
blanchet@49112
  1443
end;