src/HOL/Nominal/nominal.ML
author haftmann
Fri Jun 19 17:23:21 2009 +0200 (2009-06-19)
changeset 31723 f5cafe803b55
parent 31671 src/HOL/Nominal/nominal_package.ML@81e5e8ffe92f
child 31737 b3f63611784e
permissions -rw-r--r--
discontinued ancient tradition to suffix certain ML module names with "_package"
haftmann@31723
     1
(*  Title:      HOL/Nominal/nominal.ML
berghofe@19494
     2
    Author:     Stefan Berghofer and Christian Urban, TU Muenchen
berghofe@19494
     3
berghofe@19494
     4
Nominal datatype package for Isabelle/HOL.
berghofe@19494
     5
*)
berghofe@17870
     6
haftmann@31723
     7
signature NOMINAL =
berghofe@17870
     8
sig
haftmann@31671
     9
  val add_nominal_datatype : DatatypeAux.datatype_config -> string list ->
haftmann@31671
    10
    (string list * bstring * mixfix *
haftmann@31671
    11
      (bstring * string list * mixfix) list) list -> theory -> theory
berghofe@22433
    12
  type descr
berghofe@21540
    13
  type nominal_datatype_info
berghofe@21540
    14
  val get_nominal_datatypes : theory -> nominal_datatype_info Symtab.table
berghofe@21540
    15
  val get_nominal_datatype : theory -> string -> nominal_datatype_info option
berghofe@22311
    16
  val mk_perm: typ list -> term -> term -> term
berghofe@22529
    17
  val perm_of_pair: term * term -> term
berghofe@22529
    18
  val mk_not_sym: thm list -> thm list
berghofe@22529
    19
  val perm_simproc: simproc
berghofe@25823
    20
  val fresh_const: typ -> typ -> term
berghofe@28373
    21
  val fresh_star_const: typ -> typ -> term
berghofe@17870
    22
end
berghofe@17870
    23
haftmann@31723
    24
structure Nominal : NOMINAL =
berghofe@17870
    25
struct
berghofe@17870
    26
berghofe@22274
    27
val finite_emptyI = thm "finite.emptyI";
wenzelm@21669
    28
val finite_Diff = thm "finite_Diff";
wenzelm@21669
    29
val finite_Un = thm "finite_Un";
wenzelm@21669
    30
val Un_iff = thm "Un_iff";
wenzelm@21669
    31
val In0_eq = thm "In0_eq";
wenzelm@21669
    32
val In1_eq = thm "In1_eq";
wenzelm@21669
    33
val In0_not_In1 = thm "In0_not_In1";
wenzelm@21669
    34
val In1_not_In0 = thm "In1_not_In0";
wenzelm@21669
    35
val Un_assoc = thm "Un_assoc";
wenzelm@21669
    36
val Collect_disj_eq = thm "Collect_disj_eq";
wenzelm@21669
    37
val empty_def = thm "empty_def";
berghofe@24459
    38
val empty_iff = thm "empty_iff";
wenzelm@21669
    39
berghofe@17870
    40
open DatatypeAux;
berghofe@18068
    41
open NominalAtoms;
berghofe@17870
    42
haftmann@31723
    43
(** FIXME: Datatype should export this function **)
berghofe@18016
    44
berghofe@18016
    45
local
berghofe@18016
    46
berghofe@18016
    47
fun dt_recs (DtTFree _) = []
berghofe@18016
    48
  | dt_recs (DtType (_, dts)) = List.concat (map dt_recs dts)
berghofe@18016
    49
  | dt_recs (DtRec i) = [i];
berghofe@18016
    50
berghofe@18016
    51
fun dt_cases (descr: descr) (_, args, constrs) =
berghofe@18016
    52
  let
wenzelm@30364
    53
    fun the_bname i = Long_Name.base_name (#1 (valOf (AList.lookup (op =) descr i)));
berghofe@19133
    54
    val bnames = map the_bname (distinct op = (List.concat (map dt_recs args)));
wenzelm@30364
    55
  in map (fn (c, _) => space_implode "_" (Long_Name.base_name c :: bnames)) constrs end;
berghofe@18016
    56
berghofe@18016
    57
berghofe@18016
    58
fun induct_cases descr =
berghofe@18016
    59
  DatatypeProp.indexify_names (List.concat (map (dt_cases descr) (map #2 descr)));
berghofe@18016
    60
berghofe@18016
    61
fun exhaust_cases descr i = dt_cases descr (valOf (AList.lookup (op =) descr i));
berghofe@18016
    62
berghofe@18016
    63
in
berghofe@18016
    64
berghofe@18016
    65
fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
berghofe@18016
    66
berghofe@18016
    67
fun mk_case_names_exhausts descr new =
berghofe@18016
    68
  map (RuleCases.case_names o exhaust_cases descr o #1)
berghofe@18016
    69
    (List.filter (fn ((_, (name, _, _))) => name mem_string new) descr);
berghofe@18016
    70
berghofe@18016
    71
end;
berghofe@18016
    72
wenzelm@22846
    73
(* theory data *)
berghofe@21540
    74
berghofe@22433
    75
type descr = (int * (string * dtyp list * (string * (dtyp list * dtyp) list) list)) list;
berghofe@22433
    76
berghofe@21540
    77
type nominal_datatype_info =
berghofe@21540
    78
  {index : int,
berghofe@21540
    79
   descr : descr,
berghofe@21540
    80
   sorts : (string * sort) list,
berghofe@21540
    81
   rec_names : string list,
berghofe@21540
    82
   rec_rewrites : thm list,
berghofe@21540
    83
   induction : thm,
berghofe@21540
    84
   distinct : thm list,
berghofe@21540
    85
   inject : thm list};
berghofe@21540
    86
berghofe@21540
    87
structure NominalDatatypesData = TheoryDataFun
wenzelm@22846
    88
(
berghofe@21540
    89
  type T = nominal_datatype_info Symtab.table;
berghofe@21540
    90
  val empty = Symtab.empty;
berghofe@21540
    91
  val copy = I;
berghofe@21540
    92
  val extend = I;
berghofe@21540
    93
  fun merge _ tabs : T = Symtab.merge (K true) tabs;
wenzelm@22846
    94
);
berghofe@21540
    95
berghofe@21540
    96
val get_nominal_datatypes = NominalDatatypesData.get;
berghofe@21540
    97
val put_nominal_datatypes = NominalDatatypesData.put;
berghofe@21540
    98
val map_nominal_datatypes = NominalDatatypesData.map;
berghofe@21540
    99
val get_nominal_datatype = Symtab.lookup o get_nominal_datatypes;
wenzelm@22846
   100
berghofe@21540
   101
berghofe@21540
   102
(**** make datatype info ****)
berghofe@21540
   103
berghofe@21540
   104
fun make_dt_info descr sorts induct reccomb_names rec_thms
berghofe@21540
   105
    (((i, (_, (tname, _, _))), distinct), inject) =
berghofe@21540
   106
  (tname,
berghofe@21540
   107
   {index = i,
berghofe@21540
   108
    descr = descr,
berghofe@21540
   109
    sorts = sorts,
berghofe@21540
   110
    rec_names = reccomb_names,
berghofe@21540
   111
    rec_rewrites = rec_thms,
berghofe@21540
   112
    induction = induct,
berghofe@21540
   113
    distinct = distinct,
berghofe@21540
   114
    inject = inject});
berghofe@21540
   115
berghofe@18016
   116
(*******************************)
berghofe@18016
   117
berghofe@17870
   118
val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma);
berghofe@17870
   119
berghofe@17870
   120
berghofe@18658
   121
(** simplification procedure for sorting permutations **)
berghofe@18658
   122
berghofe@18658
   123
val dj_cp = thm "dj_cp";
berghofe@18658
   124
berghofe@18658
   125
fun dest_permT (Type ("fun", [Type ("List.list", [Type ("*", [T, _])]),
berghofe@18658
   126
      Type ("fun", [_, U])])) = (T, U);
berghofe@18658
   127
berghofe@19494
   128
fun permTs_of (Const ("Nominal.perm", T) $ t $ u) = fst (dest_permT T) :: permTs_of u
berghofe@18658
   129
  | permTs_of _ = [];
berghofe@18658
   130
berghofe@19494
   131
fun perm_simproc' thy ss (Const ("Nominal.perm", T) $ t $ (u as Const ("Nominal.perm", U) $ r $ s)) =
berghofe@18658
   132
      let
berghofe@18658
   133
        val (aT as Type (a, []), S) = dest_permT T;
berghofe@18658
   134
        val (bT as Type (b, []), _) = dest_permT U
berghofe@18658
   135
      in if aT mem permTs_of u andalso aT <> bT then
berghofe@18658
   136
          let
berghofe@28731
   137
            val cp = cp_inst_of thy a b;
berghofe@28731
   138
            val dj = dj_thm_of thy b a;
berghofe@18658
   139
            val dj_cp' = [cp, dj] MRS dj_cp;
berghofe@18658
   140
            val cert = SOME o cterm_of thy
berghofe@18658
   141
          in
berghofe@18658
   142
            SOME (mk_meta_eq (Drule.instantiate' [SOME (ctyp_of thy S)]
berghofe@18658
   143
              [cert t, cert r, cert s] dj_cp'))
berghofe@18658
   144
          end
berghofe@18658
   145
        else NONE
berghofe@18658
   146
      end
berghofe@18658
   147
  | perm_simproc' thy ss _ = NONE;
berghofe@18658
   148
berghofe@18658
   149
val perm_simproc =
wenzelm@25985
   150
  Simplifier.simproc (the_context ()) "perm_simp" ["pi1 \<bullet> (pi2 \<bullet> x)"] perm_simproc';
berghofe@18658
   151
berghofe@18658
   152
val meta_spec = thm "meta_spec";
berghofe@18658
   153
wenzelm@18582
   154
fun projections rule =
wenzelm@19874
   155
  ProjectRule.projections (ProofContext.init (Thm.theory_of_thm rule)) rule
wenzelm@18582
   156
  |> map (standard #> RuleCases.save rule);
wenzelm@18582
   157
berghofe@20267
   158
val supp_prod = thm "supp_prod";
berghofe@20376
   159
val fresh_prod = thm "fresh_prod";
berghofe@20376
   160
val supports_fresh = thm "supports_fresh";
wenzelm@22812
   161
val supports_def = thm "Nominal.supports_def";
berghofe@20376
   162
val fresh_def = thm "fresh_def";
berghofe@20376
   163
val supp_def = thm "supp_def";
berghofe@20376
   164
val rev_simps = thms "rev.simps";
haftmann@23029
   165
val app_simps = thms "append.simps";
berghofe@25951
   166
val at_fin_set_supp = thm "at_fin_set_supp";
berghofe@25951
   167
val at_fin_set_fresh = thm "at_fin_set_fresh";
berghofe@25951
   168
val abs_fun_eq1 = thm "abs_fun_eq1";
berghofe@20267
   169
berghofe@21021
   170
val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq];
berghofe@21021
   171
berghofe@22311
   172
fun mk_perm Ts t u =
berghofe@22311
   173
  let
berghofe@22311
   174
    val T = fastype_of1 (Ts, t);
berghofe@22311
   175
    val U = fastype_of1 (Ts, u)
berghofe@22311
   176
  in Const ("Nominal.perm", T --> U --> U) $ t $ u end;
berghofe@22311
   177
berghofe@22529
   178
fun perm_of_pair (x, y) =
berghofe@22529
   179
  let
berghofe@22529
   180
    val T = fastype_of x;
berghofe@22529
   181
    val pT = mk_permT T
berghofe@22529
   182
  in Const ("List.list.Cons", HOLogic.mk_prodT (T, T) --> pT --> pT) $
berghofe@22529
   183
    HOLogic.mk_prod (x, y) $ Const ("List.list.Nil", pT)
berghofe@22529
   184
  end;
berghofe@22529
   185
berghofe@22529
   186
fun mk_not_sym ths = maps (fn th => case prop_of th of
berghofe@25951
   187
    _ $ (Const ("Not", _) $ (Const ("op =", _) $ _ $ _)) => [th, th RS not_sym]
berghofe@22529
   188
  | _ => [th]) ths;
berghofe@22529
   189
berghofe@25823
   190
fun fresh_const T U = Const ("Nominal.fresh", T --> U --> HOLogic.boolT);
berghofe@28373
   191
fun fresh_star_const T U =
berghofe@28373
   192
  Const ("Nominal.fresh_star", HOLogic.mk_setT T --> U --> HOLogic.boolT);
berghofe@25823
   193
haftmann@31671
   194
fun gen_add_nominal_datatype prep_typ config new_type_names dts thy =
berghofe@17870
   195
  let
berghofe@17870
   196
    (* this theory is used just for parsing *)
wenzelm@21365
   197
berghofe@17870
   198
    val tmp_thy = thy |>
berghofe@17870
   199
      Theory.copy |>
wenzelm@24712
   200
      Sign.add_types (map (fn (tvs, tname, mx, _) =>
wenzelm@30345
   201
        (Binding.name tname, length tvs, mx)) dts);
berghofe@17870
   202
berghofe@17870
   203
    val atoms = atoms_of thy;
berghofe@17870
   204
berghofe@17870
   205
    fun prep_constr ((constrs, sorts), (cname, cargs, mx)) =
wenzelm@22578
   206
      let val (cargs', sorts') = Library.foldl (prep_typ tmp_thy) (([], sorts), cargs)
berghofe@17870
   207
      in (constrs @ [(cname, cargs', mx)], sorts') end
berghofe@17870
   208
berghofe@17870
   209
    fun prep_dt_spec ((dts, sorts), (tvs, tname, mx, constrs)) =
berghofe@17870
   210
      let val (constrs', sorts') = Library.foldl prep_constr (([], sorts), constrs)
berghofe@17870
   211
      in (dts @ [(tvs, tname, mx, constrs')], sorts') end
berghofe@17870
   212
berghofe@17870
   213
    val (dts', sorts) = Library.foldl prep_dt_spec (([], []), dts);
berghofe@28736
   214
    val tyvars = map (map (fn s =>
berghofe@28736
   215
      (s, the (AList.lookup (op =) sorts s))) o #1) dts';
berghofe@17870
   216
berghofe@28731
   217
    fun inter_sort thy S S' = Type.inter_sort (Sign.tsig_of thy) (S, S');
berghofe@28731
   218
    fun augment_sort_typ thy S =
berghofe@28731
   219
      let val S = Sign.certify_sort thy S
berghofe@28731
   220
      in map_type_tfree (fn (s, S') => TFree (s,
berghofe@28731
   221
        if member (op = o apsnd fst) sorts s then inter_sort thy S S' else S'))
berghofe@28731
   222
      end;
berghofe@28731
   223
    fun augment_sort thy S = map_types (augment_sort_typ thy S);
berghofe@28731
   224
berghofe@17870
   225
    val types_syntax = map (fn (tvs, tname, mx, constrs) => (tname, mx)) dts';
berghofe@17870
   226
    val constr_syntax = map (fn (tvs, tname, mx, constrs) =>
berghofe@17870
   227
      map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts';
berghofe@17870
   228
berghofe@17870
   229
    val ps = map (fn (_, n, _, _) =>
haftmann@28965
   230
      (Sign.full_bname tmp_thy n, Sign.full_bname tmp_thy (n ^ "_Rep"))) dts;
berghofe@17870
   231
    val rps = map Library.swap ps;
berghofe@17870
   232
wenzelm@21365
   233
    fun replace_types (Type ("Nominal.ABS", [T, U])) =
berghofe@19494
   234
          Type ("fun", [T, Type ("Nominal.noption", [replace_types U])])
berghofe@17870
   235
      | replace_types (Type (s, Ts)) =
berghofe@17870
   236
          Type (getOpt (AList.lookup op = ps s, s), map replace_types Ts)
berghofe@17870
   237
      | replace_types T = T;
berghofe@17870
   238
wenzelm@30345
   239
    val dts'' = map (fn (tvs, tname, mx, constrs) => (tvs, Binding.name (tname ^ "_Rep"), NoSyn,
wenzelm@30345
   240
      map (fn (cname, cargs, mx) => (Binding.name (cname ^ "_Rep"),
berghofe@28731
   241
        map replace_types cargs, NoSyn)) constrs)) dts';
berghofe@17870
   242
berghofe@17870
   243
    val new_type_names' = map (fn n => n ^ "_Rep") new_type_names;
haftmann@28965
   244
    val full_new_type_names' = map (Sign.full_bname thy) new_type_names';
berghofe@17870
   245
urbanc@18045
   246
    val ({induction, ...},thy1) =
haftmann@31723
   247
      Datatype.add_datatype config new_type_names' dts'' thy;
berghofe@17870
   248
berghofe@17870
   249
    val SOME {descr, ...} = Symtab.lookup
haftmann@31723
   250
      (Datatype.get_datatypes thy1) (hd full_new_type_names');
berghofe@28731
   251
    fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i);
berghofe@18107
   252
wenzelm@26651
   253
    val big_name = space_implode "_" new_type_names;
wenzelm@26651
   254
wenzelm@26651
   255
berghofe@17870
   256
    (**** define permutation functions ****)
berghofe@17870
   257
berghofe@17870
   258
    val permT = mk_permT (TFree ("'x", HOLogic.typeS));
berghofe@17870
   259
    val pi = Free ("pi", permT);
berghofe@17870
   260
    val perm_types = map (fn (i, _) =>
berghofe@17870
   261
      let val T = nth_dtyp i
berghofe@17870
   262
      in permT --> T --> T end) descr;
berghofe@26680
   263
    val perm_names' = DatatypeProp.indexify_names (map (fn (i, _) =>
berghofe@26680
   264
      "perm_" ^ name_of_typ (nth_dtyp i)) descr);
berghofe@19494
   265
    val perm_names = replicate (length new_type_names) "Nominal.perm" @
haftmann@28965
   266
      map (Sign.full_bname thy1) (List.drop (perm_names', length new_type_names));
berghofe@17870
   267
    val perm_names_types = perm_names ~~ perm_types;
berghofe@26680
   268
    val perm_names_types' = perm_names' ~~ perm_types;
berghofe@17870
   269
berghofe@26680
   270
    val perm_eqs = maps (fn (i, (_, _, constrs)) =>
berghofe@17870
   271
      let val T = nth_dtyp i
wenzelm@21365
   272
      in map (fn (cname, dts) =>
berghofe@17870
   273
        let
berghofe@28731
   274
          val Ts = map (typ_of_dtyp descr sorts) dts;
berghofe@28641
   275
          val names = Name.variant_list ["pi"] (DatatypeProp.make_tnames Ts);
berghofe@17870
   276
          val args = map Free (names ~~ Ts);
berghofe@17870
   277
          val c = Const (cname, Ts ---> T);
berghofe@17870
   278
          fun perm_arg (dt, x) =
berghofe@17870
   279
            let val T = type_of x
berghofe@17870
   280
            in if is_rec_type dt then
berghofe@17870
   281
                let val (Us, _) = strip_type T
berghofe@17870
   282
                in list_abs (map (pair "x") Us,
berghofe@26680
   283
                  Free (nth perm_names_types' (body_index dt)) $ pi $
berghofe@17870
   284
                    list_comb (x, map (fn (i, U) =>
berghofe@19494
   285
                      Const ("Nominal.perm", permT --> U --> U) $
berghofe@17870
   286
                        (Const ("List.rev", permT --> permT) $ pi) $
berghofe@17870
   287
                        Bound i) ((length Us - 1 downto 0) ~~ Us)))
berghofe@17870
   288
                end
berghofe@19494
   289
              else Const ("Nominal.perm", permT --> T --> T) $ pi $ x
wenzelm@21365
   290
            end;
berghofe@17870
   291
        in
haftmann@28965
   292
          (Attrib.empty_binding, HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@26680
   293
            (Free (nth perm_names_types' i) $
berghofe@17870
   294
               Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $
berghofe@17870
   295
               list_comb (c, args),
berghofe@26680
   296
             list_comb (c, map perm_arg (dts ~~ args)))))
berghofe@17870
   297
        end) constrs
berghofe@26680
   298
      end) descr;
berghofe@17870
   299
berghofe@26689
   300
    val (perm_simps, thy2) =
haftmann@31723
   301
      Primrec.add_primrec_overloaded
berghofe@26689
   302
        (map (fn (s, sT) => (s, sT, false))
berghofe@26689
   303
           (List.take (perm_names' ~~ perm_names_types, length new_type_names)))
haftmann@28965
   304
        (map (fn s => (Binding.name s, NONE, NoSyn)) perm_names') perm_eqs thy1;
berghofe@17870
   305
berghofe@17870
   306
    (**** prove that permutation functions introduced by unfolding are ****)
berghofe@17870
   307
    (**** equivalent to already existing permutation functions         ****)
berghofe@17870
   308
berghofe@17870
   309
    val _ = warning ("length descr: " ^ string_of_int (length descr));
berghofe@17870
   310
    val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names));
berghofe@17870
   311
berghofe@17870
   312
    val perm_indnames = DatatypeProp.make_tnames (map body_type perm_types);
wenzelm@26343
   313
    val perm_fun_def = PureThy.get_thm thy2 "perm_fun_def";
berghofe@17870
   314
berghofe@17870
   315
    val unfolded_perm_eq_thms =
berghofe@17870
   316
      if length descr = length new_type_names then []
berghofe@17870
   317
      else map standard (List.drop (split_conj_thm
wenzelm@20046
   318
        (Goal.prove_global thy2 [] []
berghofe@17870
   319
          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   320
            (map (fn (c as (s, T), x) =>
berghofe@17870
   321
               let val [T1, T2] = binder_types T
berghofe@17870
   322
               in HOLogic.mk_eq (Const c $ pi $ Free (x, T2),
berghofe@19494
   323
                 Const ("Nominal.perm", T) $ pi $ Free (x, T2))
berghofe@17870
   324
               end)
berghofe@18010
   325
             (perm_names_types ~~ perm_indnames))))
berghofe@18010
   326
          (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@17870
   327
            ALLGOALS (asm_full_simp_tac
berghofe@17870
   328
              (simpset_of thy2 addsimps [perm_fun_def]))])),
berghofe@17870
   329
        length new_type_names));
berghofe@17870
   330
berghofe@17870
   331
    (**** prove [] \<bullet> t = t ****)
berghofe@17870
   332
berghofe@17870
   333
    val _ = warning "perm_empty_thms";
berghofe@17870
   334
berghofe@17870
   335
    val perm_empty_thms = List.concat (map (fn a =>
berghofe@17870
   336
      let val permT = mk_permT (Type (a, []))
berghofe@17870
   337
      in map standard (List.take (split_conj_thm
wenzelm@20046
   338
        (Goal.prove_global thy2 [] []
berghofe@28731
   339
          (augment_sort thy2 [pt_class_of thy2 a]
berghofe@28731
   340
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@28731
   341
              (map (fn ((s, T), x) => HOLogic.mk_eq
berghofe@28731
   342
                  (Const (s, permT --> T --> T) $
berghofe@28731
   343
                     Const ("List.list.Nil", permT) $ Free (x, T),
berghofe@28731
   344
                   Free (x, T)))
berghofe@28731
   345
               (perm_names ~~
berghofe@28731
   346
                map body_type perm_types ~~ perm_indnames)))))
berghofe@18010
   347
          (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@17870
   348
            ALLGOALS (asm_full_simp_tac (simpset_of thy2))])),
berghofe@17870
   349
        length new_type_names))
berghofe@17870
   350
      end)
berghofe@17870
   351
      atoms);
berghofe@17870
   352
berghofe@17870
   353
    (**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****)
berghofe@17870
   354
berghofe@17870
   355
    val _ = warning "perm_append_thms";
berghofe@17870
   356
berghofe@17870
   357
    (*FIXME: these should be looked up statically*)
wenzelm@26343
   358
    val at_pt_inst = PureThy.get_thm thy2 "at_pt_inst";
wenzelm@26343
   359
    val pt2 = PureThy.get_thm thy2 "pt2";
berghofe@17870
   360
berghofe@17870
   361
    val perm_append_thms = List.concat (map (fn a =>
berghofe@17870
   362
      let
berghofe@17870
   363
        val permT = mk_permT (Type (a, []));
berghofe@17870
   364
        val pi1 = Free ("pi1", permT);
berghofe@17870
   365
        val pi2 = Free ("pi2", permT);
berghofe@28731
   366
        val pt_inst = pt_inst_of thy2 a;
berghofe@17870
   367
        val pt2' = pt_inst RS pt2;
wenzelm@30364
   368
        val pt2_ax = PureThy.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "2") a);
berghofe@17870
   369
      in List.take (map standard (split_conj_thm
wenzelm@20046
   370
        (Goal.prove_global thy2 [] []
berghofe@28731
   371
           (augment_sort thy2 [pt_class_of thy2 a]
berghofe@17870
   372
             (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   373
                (map (fn ((s, T), x) =>
berghofe@17870
   374
                    let val perm = Const (s, permT --> T --> T)
berghofe@17870
   375
                    in HOLogic.mk_eq
haftmann@23029
   376
                      (perm $ (Const ("List.append", permT --> permT --> permT) $
berghofe@17870
   377
                         pi1 $ pi2) $ Free (x, T),
berghofe@17870
   378
                       perm $ pi1 $ (perm $ pi2 $ Free (x, T)))
berghofe@17870
   379
                    end)
berghofe@17870
   380
                  (perm_names ~~
berghofe@28731
   381
                   map body_type perm_types ~~ perm_indnames)))))
berghofe@18010
   382
           (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@17870
   383
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt2', pt2_ax]))]))),
berghofe@17870
   384
         length new_type_names)
berghofe@17870
   385
      end) atoms);
berghofe@17870
   386
berghofe@17870
   387
    (**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****)
berghofe@17870
   388
berghofe@17870
   389
    val _ = warning "perm_eq_thms";
berghofe@17870
   390
wenzelm@26343
   391
    val pt3 = PureThy.get_thm thy2 "pt3";
wenzelm@26343
   392
    val pt3_rev = PureThy.get_thm thy2 "pt3_rev";
berghofe@17870
   393
berghofe@17870
   394
    val perm_eq_thms = List.concat (map (fn a =>
berghofe@17870
   395
      let
berghofe@17870
   396
        val permT = mk_permT (Type (a, []));
berghofe@17870
   397
        val pi1 = Free ("pi1", permT);
berghofe@17870
   398
        val pi2 = Free ("pi2", permT);
berghofe@28731
   399
        val at_inst = at_inst_of thy2 a;
berghofe@28731
   400
        val pt_inst = pt_inst_of thy2 a;
berghofe@17870
   401
        val pt3' = pt_inst RS pt3;
berghofe@17870
   402
        val pt3_rev' = at_inst RS (pt_inst RS pt3_rev);
wenzelm@30364
   403
        val pt3_ax = PureThy.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "3") a);
berghofe@17870
   404
      in List.take (map standard (split_conj_thm
berghofe@28731
   405
        (Goal.prove_global thy2 [] []
berghofe@28731
   406
          (augment_sort thy2 [pt_class_of thy2 a] (Logic.mk_implies
berghofe@19494
   407
             (HOLogic.mk_Trueprop (Const ("Nominal.prm_eq",
berghofe@17870
   408
                permT --> permT --> HOLogic.boolT) $ pi1 $ pi2),
berghofe@17870
   409
              HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   410
                (map (fn ((s, T), x) =>
berghofe@17870
   411
                    let val perm = Const (s, permT --> T --> T)
berghofe@17870
   412
                    in HOLogic.mk_eq
berghofe@17870
   413
                      (perm $ pi1 $ Free (x, T),
berghofe@17870
   414
                       perm $ pi2 $ Free (x, T))
berghofe@17870
   415
                    end)
berghofe@17870
   416
                  (perm_names ~~
berghofe@28731
   417
                   map body_type perm_types ~~ perm_indnames))))))
berghofe@18010
   418
           (fn _ => EVERY [indtac induction perm_indnames 1,
berghofe@17870
   419
              ALLGOALS (asm_full_simp_tac (simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))),
berghofe@17870
   420
         length new_type_names)
berghofe@17870
   421
      end) atoms);
berghofe@17870
   422
berghofe@17870
   423
    (**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****)
berghofe@17870
   424
wenzelm@26343
   425
    val cp1 = PureThy.get_thm thy2 "cp1";
wenzelm@26343
   426
    val dj_cp = PureThy.get_thm thy2 "dj_cp";
wenzelm@26343
   427
    val pt_perm_compose = PureThy.get_thm thy2 "pt_perm_compose";
wenzelm@26343
   428
    val pt_perm_compose_rev = PureThy.get_thm thy2 "pt_perm_compose_rev";
wenzelm@26343
   429
    val dj_perm_perm_forget = PureThy.get_thm thy2 "dj_perm_perm_forget";
berghofe@17870
   430
berghofe@17870
   431
    fun composition_instance name1 name2 thy =
berghofe@17870
   432
      let
berghofe@28731
   433
        val cp_class = cp_class_of thy name1 name2;
berghofe@28731
   434
        val pt_class =
berghofe@28731
   435
          if name1 = name2 then [pt_class_of thy name1]
berghofe@28731
   436
          else [];
berghofe@17870
   437
        val permT1 = mk_permT (Type (name1, []));
berghofe@17870
   438
        val permT2 = mk_permT (Type (name2, []));
berghofe@28731
   439
        val Ts = map body_type perm_types;
berghofe@28731
   440
        val cp_inst = cp_inst_of thy name1 name2;
berghofe@17870
   441
        val simps = simpset_of thy addsimps (perm_fun_def ::
berghofe@17870
   442
          (if name1 <> name2 then
berghofe@28731
   443
             let val dj = dj_thm_of thy name2 name1
berghofe@17870
   444
             in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end
berghofe@17870
   445
           else
berghofe@17870
   446
             let
berghofe@28731
   447
               val at_inst = at_inst_of thy name1;
berghofe@28731
   448
               val pt_inst = pt_inst_of thy name1;
berghofe@17870
   449
             in
berghofe@17870
   450
               [cp_inst RS cp1 RS sym,
berghofe@17870
   451
                at_inst RS (pt_inst RS pt_perm_compose) RS sym,
berghofe@17870
   452
                at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym]
berghofe@17870
   453
            end))
berghofe@28736
   454
        val sort = Sign.certify_sort thy (cp_class :: pt_class);
wenzelm@20046
   455
        val thms = split_conj_thm (Goal.prove_global thy [] []
berghofe@28736
   456
          (augment_sort thy sort
berghofe@17870
   457
            (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@17870
   458
              (map (fn ((s, T), x) =>
berghofe@17870
   459
                  let
berghofe@17870
   460
                    val pi1 = Free ("pi1", permT1);
berghofe@17870
   461
                    val pi2 = Free ("pi2", permT2);
berghofe@17870
   462
                    val perm1 = Const (s, permT1 --> T --> T);
berghofe@17870
   463
                    val perm2 = Const (s, permT2 --> T --> T);
berghofe@19494
   464
                    val perm3 = Const ("Nominal.perm", permT1 --> permT2 --> permT2)
berghofe@17870
   465
                  in HOLogic.mk_eq
berghofe@17870
   466
                    (perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)),
berghofe@17870
   467
                     perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T)))
berghofe@17870
   468
                  end)
berghofe@28731
   469
                (perm_names ~~ Ts ~~ perm_indnames)))))
berghofe@18010
   470
          (fn _ => EVERY [indtac induction perm_indnames 1,
wenzelm@20046
   471
             ALLGOALS (asm_full_simp_tac simps)]))
berghofe@17870
   472
      in
berghofe@28736
   473
        fold (fn (s, tvs) => fn thy => AxClass.prove_arity
berghofe@28736
   474
            (s, map (inter_sort thy sort o snd) tvs, [cp_class])
haftmann@24218
   475
            (Class.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy)
berghofe@28736
   476
          (full_new_type_names' ~~ tyvars) thy
berghofe@17870
   477
      end;
berghofe@17870
   478
urbanc@18381
   479
    val (perm_thmss,thy3) = thy2 |>
berghofe@17870
   480
      fold (fn name1 => fold (composition_instance name1) atoms) atoms |>
berghofe@28731
   481
      fold (fn atom => fn thy =>
berghofe@28731
   482
        let val pt_name = pt_class_of thy atom
berghofe@28731
   483
        in
berghofe@28736
   484
          fold (fn (s, tvs) => fn thy => AxClass.prove_arity
berghofe@28736
   485
              (s, map (inter_sort thy [pt_name] o snd) tvs, [pt_name])
berghofe@28731
   486
              (EVERY
berghofe@28731
   487
                [Class.intro_classes_tac [],
berghofe@28731
   488
                 resolve_tac perm_empty_thms 1,
berghofe@28731
   489
                 resolve_tac perm_append_thms 1,
berghofe@28736
   490
                 resolve_tac perm_eq_thms 1, assume_tac 1]) thy)
berghofe@28736
   491
            (full_new_type_names' ~~ tyvars) thy
berghofe@28731
   492
        end) atoms |>
berghofe@17870
   493
      PureThy.add_thmss
haftmann@29585
   494
        [((Binding.name (space_implode "_" new_type_names ^ "_unfolded_perm_eq"),
krauss@18759
   495
          unfolded_perm_eq_thms), [Simplifier.simp_add]),
haftmann@29585
   496
         ((Binding.name (space_implode "_" new_type_names ^ "_perm_empty"),
krauss@18759
   497
          perm_empty_thms), [Simplifier.simp_add]),
haftmann@29585
   498
         ((Binding.name (space_implode "_" new_type_names ^ "_perm_append"),
krauss@18759
   499
          perm_append_thms), [Simplifier.simp_add]),
haftmann@29585
   500
         ((Binding.name (space_implode "_" new_type_names ^ "_perm_eq"),
krauss@18759
   501
          perm_eq_thms), [Simplifier.simp_add])];
wenzelm@21365
   502
berghofe@17870
   503
    (**** Define representing sets ****)
berghofe@17870
   504
berghofe@17870
   505
    val _ = warning "representing sets";
berghofe@17870
   506
berghofe@21021
   507
    val rep_set_names = DatatypeProp.indexify_names
berghofe@21021
   508
      (map (fn (i, _) => name_of_typ (nth_dtyp i) ^ "_set") descr);
berghofe@17870
   509
    val big_rep_name =
berghofe@17870
   510
      space_implode "_" (DatatypeProp.indexify_names (List.mapPartial
berghofe@19494
   511
        (fn (i, ("Nominal.noption", _, _)) => NONE
berghofe@17870
   512
          | (i, _) => SOME (name_of_typ (nth_dtyp i))) descr)) ^ "_set";
berghofe@17870
   513
    val _ = warning ("big_rep_name: " ^ big_rep_name);
berghofe@17870
   514
berghofe@17870
   515
    fun strip_option (dtf as DtType ("fun", [dt, DtRec i])) =
berghofe@17870
   516
          (case AList.lookup op = descr i of
berghofe@19494
   517
             SOME ("Nominal.noption", _, [(_, [dt']), _]) =>
berghofe@17870
   518
               apfst (cons dt) (strip_option dt')
berghofe@17870
   519
           | _ => ([], dtf))
berghofe@19494
   520
      | strip_option (DtType ("fun", [dt, DtType ("Nominal.noption", [dt'])])) =
berghofe@18261
   521
          apfst (cons dt) (strip_option dt')
berghofe@17870
   522
      | strip_option dt = ([], dt);
berghofe@17870
   523
berghofe@28731
   524
    val dt_atomTs = distinct op = (map (typ_of_dtyp descr sorts)
berghofe@18280
   525
      (List.concat (map (fn (_, (_, _, cs)) => List.concat
berghofe@18280
   526
        (map (List.concat o map (fst o strip_option) o snd) cs)) descr)));
berghofe@28731
   527
    val dt_atoms = map (fst o dest_Type) dt_atomTs;
berghofe@18280
   528
berghofe@17870
   529
    fun make_intr s T (cname, cargs) =
berghofe@17870
   530
      let
wenzelm@21365
   531
        fun mk_prem (dt, (j, j', prems, ts)) =
berghofe@17870
   532
          let
berghofe@17870
   533
            val (dts, dt') = strip_option dt;
berghofe@17870
   534
            val (dts', dt'') = strip_dtyp dt';
berghofe@28731
   535
            val Ts = map (typ_of_dtyp descr sorts) dts;
berghofe@28731
   536
            val Us = map (typ_of_dtyp descr sorts) dts';
berghofe@28731
   537
            val T = typ_of_dtyp descr sorts dt'';
berghofe@17870
   538
            val free = mk_Free "x" (Us ---> T) j;
berghofe@17870
   539
            val free' = app_bnds free (length Us);
berghofe@17870
   540
            fun mk_abs_fun (T, (i, t)) =
berghofe@17870
   541
              let val U = fastype_of t
berghofe@19494
   542
              in (i + 1, Const ("Nominal.abs_fun", [T, U, T] --->
berghofe@19494
   543
                Type ("Nominal.noption", [U])) $ mk_Free "y" T i $ t)
berghofe@17870
   544
              end
berghofe@17870
   545
          in (j + 1, j' + length Ts,
berghofe@17870
   546
            case dt'' of
berghofe@17870
   547
                DtRec k => list_all (map (pair "x") Us,
berghofe@21021
   548
                  HOLogic.mk_Trueprop (Free (List.nth (rep_set_names, k),
berghofe@21021
   549
                    T --> HOLogic.boolT) $ free')) :: prems
berghofe@17870
   550
              | _ => prems,
wenzelm@30190
   551
            snd (List.foldr mk_abs_fun (j', free) Ts) :: ts)
berghofe@17870
   552
          end;
berghofe@17870
   553
wenzelm@30190
   554
        val (_, _, prems, ts) = List.foldr mk_prem (1, 1, [], []) cargs;
berghofe@21021
   555
        val concl = HOLogic.mk_Trueprop (Free (s, T --> HOLogic.boolT) $
berghofe@21021
   556
          list_comb (Const (cname, map fastype_of ts ---> T), ts))
berghofe@17870
   557
      in Logic.list_implies (prems, concl)
berghofe@17870
   558
      end;
berghofe@17870
   559
berghofe@21021
   560
    val (intr_ts, (rep_set_names', recTs')) =
berghofe@21021
   561
      apfst List.concat (apsnd ListPair.unzip (ListPair.unzip (List.mapPartial
berghofe@19494
   562
        (fn ((_, ("Nominal.noption", _, _)), _) => NONE
berghofe@17870
   563
          | ((i, (_, _, constrs)), rep_set_name) =>
berghofe@17870
   564
              let val T = nth_dtyp i
berghofe@17870
   565
              in SOME (map (make_intr rep_set_name T) constrs,
berghofe@21021
   566
                (rep_set_name, T))
berghofe@17870
   567
              end)
berghofe@21021
   568
                (descr ~~ rep_set_names))));
haftmann@28965
   569
    val rep_set_names'' = map (Sign.full_bname thy3) rep_set_names';
berghofe@17870
   570
wenzelm@21365
   571
    val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy4) =
haftmann@31723
   572
        Inductive.add_inductive_global (serial_string ())
wenzelm@26475
   573
          {quiet_mode = false, verbose = false, kind = Thm.internalK,
haftmann@28965
   574
           alt_name = Binding.name big_rep_name, coind = false, no_elim = true, no_ind = false,
wenzelm@29389
   575
           skip_mono = true, fork_mono = false}
haftmann@28965
   576
          (map (fn (s, T) => ((Binding.name s, T --> HOLogic.boolT), NoSyn))
wenzelm@26128
   577
             (rep_set_names' ~~ recTs'))
haftmann@28965
   578
          [] (map (fn x => (Attrib.empty_binding, x)) intr_ts) [] thy3;
berghofe@17870
   579
berghofe@17870
   580
    (**** Prove that representing set is closed under permutation ****)
berghofe@17870
   581
berghofe@17870
   582
    val _ = warning "proving closure under permutation...";
berghofe@17870
   583
wenzelm@26343
   584
    val abs_perm = PureThy.get_thms thy4 "abs_perm";
berghofe@25951
   585
berghofe@17870
   586
    val perm_indnames' = List.mapPartial
berghofe@19494
   587
      (fn (x, (_, ("Nominal.noption", _, _))) => NONE | (x, _) => SOME x)
berghofe@17870
   588
      (perm_indnames ~~ descr);
berghofe@17870
   589
berghofe@17870
   590
    fun mk_perm_closed name = map (fn th => standard (th RS mp))
wenzelm@20046
   591
      (List.take (split_conj_thm (Goal.prove_global thy4 [] []
berghofe@28731
   592
        (augment_sort thy4
berghofe@28731
   593
          (pt_class_of thy4 name :: map (cp_class_of thy4 name) (dt_atoms \ name))
berghofe@28731
   594
          (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map
berghofe@28731
   595
            (fn ((s, T), x) =>
berghofe@28731
   596
               let
berghofe@28731
   597
                 val S = Const (s, T --> HOLogic.boolT);
berghofe@28731
   598
                 val permT = mk_permT (Type (name, []))
berghofe@28731
   599
               in HOLogic.mk_imp (S $ Free (x, T),
berghofe@28731
   600
                 S $ (Const ("Nominal.perm", permT --> T --> T) $
berghofe@28731
   601
                   Free ("pi", permT) $ Free (x, T)))
berghofe@28731
   602
               end) (rep_set_names'' ~~ recTs' ~~ perm_indnames')))))
berghofe@28731
   603
        (fn _ => EVERY
berghofe@17870
   604
           [indtac rep_induct [] 1,
berghofe@17870
   605
            ALLGOALS (simp_tac (simpset_of thy4 addsimps
berghofe@25951
   606
              (symmetric perm_fun_def :: abs_perm))),
berghofe@28731
   607
            ALLGOALS (resolve_tac rep_intrs THEN_ALL_NEW assume_tac)])),
berghofe@17870
   608
        length new_type_names));
berghofe@17870
   609
berghofe@17870
   610
    val perm_closed_thmss = map mk_perm_closed atoms;
berghofe@17870
   611
berghofe@17870
   612
    (**** typedef ****)
berghofe@17870
   613
berghofe@17870
   614
    val _ = warning "defining type...";
berghofe@17870
   615
berghofe@18366
   616
    val (typedefs, thy6) =
wenzelm@26651
   617
      thy4
berghofe@21021
   618
      |> fold_map (fn ((((name, mx), tvs), (cname, U)), name') => fn thy =>
haftmann@31723
   619
          Typedef.add_typedef false (SOME (Binding.name name'))
wenzelm@30345
   620
            (Binding.name name, map fst tvs, mx)
berghofe@21021
   621
            (Const ("Collect", (U --> HOLogic.boolT) --> HOLogic.mk_setT U) $
berghofe@21021
   622
               Const (cname, U --> HOLogic.boolT)) NONE
berghofe@21021
   623
            (rtac exI 1 THEN rtac CollectI 1 THEN
berghofe@17870
   624
              QUIET_BREADTH_FIRST (has_fewer_prems 1)
wenzelm@26475
   625
              (resolve_tac rep_intrs 1)) thy |> (fn ((_, r), thy) =>
berghofe@17870
   626
        let
berghofe@28736
   627
          val permT = mk_permT
berghofe@28736
   628
            (TFree (Name.variant (map fst tvs) "'a", HOLogic.typeS));
berghofe@17870
   629
          val pi = Free ("pi", permT);
berghofe@28736
   630
          val T = Type (Sign.intern_type thy name, map TFree tvs);
berghofe@18366
   631
        in apfst (pair r o hd)
haftmann@29585
   632
          (PureThy.add_defs_unchecked true [((Binding.name ("prm_" ^ name ^ "_def"), Logic.mk_equals
berghofe@19494
   633
            (Const ("Nominal.perm", permT --> T --> T) $ pi $ Free ("x", T),
berghofe@17870
   634
             Const (Sign.intern_const thy ("Abs_" ^ name), U --> T) $
berghofe@19494
   635
               (Const ("Nominal.perm", permT --> U --> U) $ pi $
berghofe@17870
   636
                 (Const (Sign.intern_const thy ("Rep_" ^ name), T --> U) $
berghofe@17870
   637
                   Free ("x", T))))), [])] thy)
berghofe@17870
   638
        end))
berghofe@18366
   639
          (types_syntax ~~ tyvars ~~
berghofe@21021
   640
            List.take (rep_set_names'' ~~ recTs', length new_type_names) ~~
berghofe@21021
   641
            new_type_names);
berghofe@17870
   642
berghofe@17870
   643
    val perm_defs = map snd typedefs;
berghofe@21021
   644
    val Abs_inverse_thms = map (collect_simp o #Abs_inverse o fst) typedefs;
berghofe@18016
   645
    val Rep_inverse_thms = map (#Rep_inverse o fst) typedefs;
berghofe@21021
   646
    val Rep_thms = map (collect_simp o #Rep o fst) typedefs;
berghofe@17870
   647
berghofe@18016
   648
berghofe@17870
   649
    (** prove that new types are in class pt_<name> **)
berghofe@17870
   650
berghofe@17870
   651
    val _ = warning "prove that new types are in class pt_<name> ...";
berghofe@17870
   652
berghofe@28731
   653
    fun pt_instance (atom, perm_closed_thms) =
berghofe@21021
   654
      fold (fn ((((((Abs_inverse, Rep_inverse), Rep),
berghofe@17870
   655
        perm_def), name), tvs), perm_closed) => fn thy =>
berghofe@28731
   656
          let
berghofe@28731
   657
            val pt_class = pt_class_of thy atom;
berghofe@28736
   658
            val sort = Sign.certify_sort thy
berghofe@28736
   659
              (pt_class :: map (cp_class_of thy atom) (dt_atoms \ atom))
berghofe@28731
   660
          in AxClass.prove_arity
berghofe@17870
   661
            (Sign.intern_type thy name,
berghofe@28736
   662
              map (inter_sort thy sort o snd) tvs, [pt_class])
haftmann@24218
   663
            (EVERY [Class.intro_classes_tac [],
berghofe@17870
   664
              rewrite_goals_tac [perm_def],
berghofe@17870
   665
              asm_full_simp_tac (simpset_of thy addsimps [Rep_inverse]) 1,
berghofe@17870
   666
              asm_full_simp_tac (simpset_of thy addsimps
berghofe@17870
   667
                [Rep RS perm_closed RS Abs_inverse]) 1,
wenzelm@26343
   668
              asm_full_simp_tac (HOL_basic_ss addsimps [PureThy.get_thm thy
wenzelm@30364
   669
                ("pt_" ^ Long_Name.base_name atom ^ "3")]) 1]) thy
berghofe@28731
   670
          end)
berghofe@21021
   671
        (Abs_inverse_thms ~~ Rep_inverse_thms ~~ Rep_thms ~~ perm_defs ~~
berghofe@21021
   672
           new_type_names ~~ tyvars ~~ perm_closed_thms);
berghofe@17870
   673
berghofe@17870
   674
berghofe@17870
   675
    (** prove that new types are in class cp_<name1>_<name2> **)
berghofe@17870
   676
berghofe@17870
   677
    val _ = warning "prove that new types are in class cp_<name1>_<name2> ...";
berghofe@17870
   678
berghofe@17870
   679
    fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy =
berghofe@17870
   680
      let
berghofe@28731
   681
        val cp_class = cp_class_of thy atom1 atom2;
berghofe@28736
   682
        val sort = Sign.certify_sort thy
berghofe@28736
   683
          (pt_class_of thy atom1 :: map (cp_class_of thy atom1) (dt_atoms \ atom1) @
berghofe@28736
   684
           (if atom1 = atom2 then [cp_class_of thy atom1 atom1] else
berghofe@28736
   685
            pt_class_of thy atom2 :: map (cp_class_of thy atom2) (dt_atoms \ atom2)));
berghofe@28731
   686
        val cp1' = cp_inst_of thy atom1 atom2 RS cp1
berghofe@21021
   687
      in fold (fn ((((((Abs_inverse, Rep),
berghofe@17870
   688
        perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy =>
berghofe@19275
   689
          AxClass.prove_arity
berghofe@17870
   690
            (Sign.intern_type thy name,
berghofe@28736
   691
              map (inter_sort thy sort o snd) tvs, [cp_class])
haftmann@24218
   692
            (EVERY [Class.intro_classes_tac [],
berghofe@17870
   693
              rewrite_goals_tac [perm_def],
berghofe@17870
   694
              asm_full_simp_tac (simpset_of thy addsimps
berghofe@17870
   695
                ((Rep RS perm_closed1 RS Abs_inverse) ::
berghofe@17870
   696
                 (if atom1 = atom2 then []
berghofe@17870
   697
                  else [Rep RS perm_closed2 RS Abs_inverse]))) 1,
berghofe@18016
   698
              cong_tac 1,
berghofe@17870
   699
              rtac refl 1,
berghofe@17870
   700
              rtac cp1' 1]) thy)
berghofe@21021
   701
        (Abs_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ new_type_names ~~
berghofe@21021
   702
           tyvars ~~ perm_closed_thms1 ~~ perm_closed_thms2) thy
berghofe@17870
   703
      end;
berghofe@17870
   704
berghofe@17870
   705
    val thy7 = fold (fn x => fn thy => thy |>
berghofe@17870
   706
      pt_instance x |>
berghofe@28731
   707
      fold (cp_instance x) (atoms ~~ perm_closed_thmss))
berghofe@28731
   708
        (atoms ~~ perm_closed_thmss) thy6;
berghofe@17870
   709
berghofe@17870
   710
    (**** constructors ****)
berghofe@17870
   711
berghofe@17870
   712
    fun mk_abs_fun (x, t) =
berghofe@17870
   713
      let
berghofe@17870
   714
        val T = fastype_of x;
berghofe@17870
   715
        val U = fastype_of t
berghofe@17870
   716
      in
berghofe@19494
   717
        Const ("Nominal.abs_fun", T --> U --> T -->
berghofe@19494
   718
          Type ("Nominal.noption", [U])) $ x $ t
berghofe@17870
   719
      end;
berghofe@17870
   720
wenzelm@30190
   721
    val (ty_idxs, _) = List.foldl
berghofe@19494
   722
      (fn ((i, ("Nominal.noption", _, _)), p) => p
berghofe@18016
   723
        | ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr;
berghofe@18016
   724
berghofe@18016
   725
    fun reindex (DtType (s, dts)) = DtType (s, map reindex dts)
berghofe@18016
   726
      | reindex (DtRec i) = DtRec (the (AList.lookup op = ty_idxs i))
berghofe@18016
   727
      | reindex dt = dt;
berghofe@18016
   728
berghofe@18016
   729
    fun strip_suffix i s = implode (List.take (explode s, size s - i));
berghofe@18016
   730
berghofe@18016
   731
    (** strips the "_Rep" in type names *)
wenzelm@21365
   732
    fun strip_nth_name i s =
wenzelm@30364
   733
      let val xs = Long_Name.explode s;
wenzelm@30364
   734
      in Long_Name.implode (Library.nth_map (length xs - i) (strip_suffix 4) xs) end;
berghofe@18016
   735
haftmann@31458
   736
    val (descr'', ndescr) = ListPair.unzip (map_filter
berghofe@19494
   737
      (fn (i, ("Nominal.noption", _, _)) => NONE
berghofe@18107
   738
        | (i, (s, dts, constrs)) =>
berghofe@18107
   739
             let
berghofe@18107
   740
               val SOME index = AList.lookup op = ty_idxs i;
haftmann@31458
   741
               val (constrs2, constrs1) =
haftmann@31458
   742
                 map_split (fn (cname, cargs) =>
haftmann@31458
   743
                   apsnd (pair (strip_nth_name 2 (strip_nth_name 1 cname)))
haftmann@31458
   744
                   (fold_map (fn dt => fn dts =>
berghofe@18107
   745
                     let val (dts', dt') = strip_option dt
haftmann@31458
   746
                     in ((length dts, length dts'), dts @ dts' @ [reindex dt']) end)
haftmann@31458
   747
                       cargs [])) constrs
berghofe@18107
   748
             in SOME ((index, (strip_nth_name 1 s,  map reindex dts, constrs1)),
berghofe@18107
   749
               (index, constrs2))
berghofe@18107
   750
             end) descr);
urbanc@18045
   751
berghofe@19489
   752
    val (descr1, descr2) = chop (length new_type_names) descr'';
berghofe@18016
   753
    val descr' = [descr1, descr2];
berghofe@18016
   754
berghofe@19710
   755
    fun partition_cargs idxs xs = map (fn (i, j) =>
berghofe@19710
   756
      (List.take (List.drop (xs, i), j), List.nth (xs, i + j))) idxs;
berghofe@19710
   757
berghofe@19833
   758
    val pdescr = map (fn ((i, (s, dts, constrs)), (_, idxss)) => (i, (s, dts,
berghofe@19833
   759
      map (fn ((cname, cargs), idxs) => (cname, partition_cargs idxs cargs))
berghofe@19833
   760
        (constrs ~~ idxss)))) (descr'' ~~ ndescr);
berghofe@19833
   761
berghofe@28731
   762
    fun nth_dtyp' i = typ_of_dtyp descr'' sorts (DtRec i);
berghofe@17870
   763
berghofe@17870
   764
    val rep_names = map (fn s =>
berghofe@17870
   765
      Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names;
berghofe@17870
   766
    val abs_names = map (fn s =>
berghofe@17870
   767
      Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names;
berghofe@17870
   768
berghofe@28731
   769
    val recTs = get_rec_types descr'' sorts;
berghofe@18016
   770
    val newTs' = Library.take (length new_type_names, recTs');
berghofe@18016
   771
    val newTs = Library.take (length new_type_names, recTs);
berghofe@17870
   772
haftmann@28965
   773
    val full_new_type_names = map (Sign.full_bname thy) new_type_names;
berghofe@17870
   774
berghofe@19833
   775
    fun make_constr_def tname T T' ((thy, defs, eqns),
berghofe@19833
   776
        (((cname_rep, _), (cname, cargs)), (cname', mx))) =
berghofe@17870
   777
      let
berghofe@19833
   778
        fun constr_arg ((dts, dt), (j, l_args, r_args)) =
berghofe@17870
   779
          let
berghofe@28731
   780
            val xs = map (fn (dt, i) => mk_Free "x" (typ_of_dtyp descr'' sorts dt) i)
berghofe@17870
   781
              (dts ~~ (j upto j + length dts - 1))
berghofe@28731
   782
            val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts)
berghofe@18261
   783
          in
berghofe@18261
   784
            (j + length dts + 1,
berghofe@18261
   785
             xs @ x :: l_args,
wenzelm@30190
   786
             List.foldr mk_abs_fun
berghofe@19833
   787
               (case dt of
berghofe@18261
   788
                  DtRec k => if k < length new_type_names then
berghofe@28731
   789
                      Const (List.nth (rep_names, k), typ_of_dtyp descr'' sorts dt -->
berghofe@28731
   790
                        typ_of_dtyp descr sorts dt) $ x
berghofe@18261
   791
                    else error "nested recursion not (yet) supported"
berghofe@18261
   792
                | _ => x) xs :: r_args)
berghofe@17870
   793
          end
berghofe@17870
   794
wenzelm@30190
   795
        val (_, l_args, r_args) = List.foldr constr_arg (1, [], []) cargs;
wenzelm@22578
   796
        val abs_name = Sign.intern_const thy ("Abs_" ^ tname);
wenzelm@22578
   797
        val rep_name = Sign.intern_const thy ("Rep_" ^ tname);
berghofe@17870
   798
        val constrT = map fastype_of l_args ---> T;
berghofe@19833
   799
        val lhs = list_comb (Const (cname, constrT), l_args);
berghofe@19833
   800
        val rhs = list_comb (Const (cname_rep, map fastype_of r_args ---> T'), r_args);
berghofe@17870
   801
        val def = Logic.mk_equals (lhs, Const (abs_name, T' --> T) $ rhs);
berghofe@17870
   802
        val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17870
   803
          (Const (rep_name, T --> T') $ lhs, rhs));
wenzelm@30364
   804
        val def_name = (Long_Name.base_name cname) ^ "_def";
berghofe@18366
   805
        val ([def_thm], thy') = thy |>
wenzelm@30345
   806
          Sign.add_consts_i [(Binding.name cname', constrT, mx)] |>
haftmann@29585
   807
          (PureThy.add_defs false o map Thm.no_attributes) [(Binding.name def_name, def)]
berghofe@17870
   808
      in (thy', defs @ [def_thm], eqns @ [eqn]) end;
berghofe@17870
   809
berghofe@19833
   810
    fun dt_constr_defs ((thy, defs, eqns, dist_lemmas), ((((((_, (_, _, constrs)),
berghofe@19833
   811
        (_, (_, _, constrs'))), tname), T), T'), constr_syntax)) =
berghofe@17870
   812
      let
berghofe@17870
   813
        val rep_const = cterm_of thy
berghofe@17870
   814
          (Const (Sign.intern_const thy ("Rep_" ^ tname), T --> T'));
berghofe@17870
   815
        val dist = standard (cterm_instantiate [(cterm_of thy distinct_f, rep_const)] distinct_lemma);
berghofe@17870
   816
        val (thy', defs', eqns') = Library.foldl (make_constr_def tname T T')
wenzelm@24712
   817
          ((Sign.add_path tname thy, defs, []), constrs ~~ constrs' ~~ constr_syntax)
berghofe@17870
   818
      in
haftmann@31671
   819
        (parent_path (#flat_names config) thy', defs', eqns @ [eqns'], dist_lemmas @ [dist])
berghofe@17870
   820
      end;
berghofe@17870
   821
berghofe@17870
   822
    val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = Library.foldl dt_constr_defs
berghofe@17870
   823
      ((thy7, [], [], []), List.take (descr, length new_type_names) ~~
berghofe@19833
   824
        List.take (pdescr, length new_type_names) ~~
berghofe@17870
   825
        new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax);
berghofe@17870
   826
berghofe@21021
   827
    val abs_inject_thms = map (collect_simp o #Abs_inject o fst) typedefs
berghofe@21021
   828
    val rep_inject_thms = map (#Rep_inject o fst) typedefs
berghofe@17870
   829
berghofe@17870
   830
    (* prove theorem  Rep_i (Constr_j ...) = Constr'_j ...  *)
wenzelm@21365
   831
berghofe@17870
   832
    fun prove_constr_rep_thm eqn =
berghofe@17870
   833
      let
berghofe@17870
   834
        val inj_thms = map (fn r => r RS iffD1) abs_inject_thms;
berghofe@21021
   835
        val rewrites = constr_defs @ map mk_meta_eq Rep_inverse_thms
wenzelm@20046
   836
      in Goal.prove_global thy8 [] [] eqn (fn _ => EVERY
berghofe@17870
   837
        [resolve_tac inj_thms 1,
berghofe@17870
   838
         rewrite_goals_tac rewrites,
berghofe@17870
   839
         rtac refl 3,
berghofe@17870
   840
         resolve_tac rep_intrs 2,
berghofe@21021
   841
         REPEAT (resolve_tac Rep_thms 1)])
berghofe@17870
   842
      end;
berghofe@17870
   843
berghofe@17870
   844
    val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns;
berghofe@17870
   845
berghofe@17870
   846
    (* prove theorem  pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *)
berghofe@17870
   847
berghofe@17870
   848
    fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th =>
berghofe@17870
   849
      let
berghofe@21021
   850
        val _ $ (_ $ (Rep $ x)) = Logic.unvarify (prop_of th);
berghofe@17870
   851
        val Type ("fun", [T, U]) = fastype_of Rep;
berghofe@17870
   852
        val permT = mk_permT (Type (atom, []));
berghofe@17870
   853
        val pi = Free ("pi", permT);
berghofe@17870
   854
      in
berghofe@28731
   855
        Goal.prove_global thy8 [] []
berghofe@28731
   856
          (augment_sort thy8
berghofe@28731
   857
            (pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (dt_atoms \ atom))
berghofe@28731
   858
            (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@28731
   859
              (Const ("Nominal.perm", permT --> U --> U) $ pi $ (Rep $ x),
berghofe@28731
   860
               Rep $ (Const ("Nominal.perm", permT --> T --> T) $ pi $ x)))))
berghofe@18010
   861
          (fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @
wenzelm@20046
   862
            perm_closed_thms @ Rep_thms)) 1)
berghofe@17870
   863
      end) Rep_thms;
berghofe@17870
   864
berghofe@17870
   865
    val perm_rep_perm_thms = List.concat (map prove_perm_rep_perm
berghofe@17870
   866
      (atoms ~~ perm_closed_thmss));
berghofe@17870
   867
berghofe@17870
   868
    (* prove distinctness theorems *)
berghofe@17870
   869
berghofe@28731
   870
    val distinct_props = DatatypeProp.make_distincts descr' sorts;
haftmann@27300
   871
    val dist_rewrites = map2 (fn rep_thms => fn dist_lemma =>
haftmann@27300
   872
      dist_lemma :: rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])
haftmann@27300
   873
        constr_rep_thmss dist_lemmas;
berghofe@17870
   874
haftmann@26969
   875
    fun prove_distinct_thms _ (_, []) = []
haftmann@26969
   876
      | prove_distinct_thms (p as (rep_thms, dist_lemma)) (k, t :: ts) =
berghofe@17870
   877
          let
wenzelm@20046
   878
            val dist_thm = Goal.prove_global thy8 [] [] t (fn _ =>
wenzelm@20046
   879
              simp_tac (simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1)
haftmann@27300
   880
          in dist_thm :: standard (dist_thm RS not_sym) ::
haftmann@27300
   881
            prove_distinct_thms p (k, ts)
berghofe@17870
   882
          end;
berghofe@17870
   883
haftmann@26969
   884
    val distinct_thms = map2 prove_distinct_thms
haftmann@26969
   885
      (constr_rep_thmss ~~ dist_lemmas) distinct_props;
berghofe@17870
   886
berghofe@17870
   887
    (** prove equations for permutation functions **)
berghofe@17870
   888
berghofe@17870
   889
    val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@19833
   890
      let val T = nth_dtyp' i
berghofe@17870
   891
      in List.concat (map (fn (atom, perm_closed_thms) =>
wenzelm@21365
   892
          map (fn ((cname, dts), constr_rep_thm) =>
berghofe@17870
   893
        let
berghofe@17870
   894
          val cname = Sign.intern_const thy8
wenzelm@30364
   895
            (Long_Name.append tname (Long_Name.base_name cname));
berghofe@17870
   896
          val permT = mk_permT (Type (atom, []));
berghofe@17870
   897
          val pi = Free ("pi", permT);
berghofe@17870
   898
berghofe@17870
   899
          fun perm t =
berghofe@17870
   900
            let val T = fastype_of t
berghofe@19494
   901
            in Const ("Nominal.perm", permT --> T --> T) $ pi $ t end;
berghofe@17870
   902
berghofe@19833
   903
          fun constr_arg ((dts, dt), (j, l_args, r_args)) =
berghofe@17870
   904
            let
berghofe@28731
   905
              val Ts = map (typ_of_dtyp descr'' sorts) dts;
berghofe@17870
   906
              val xs = map (fn (T, i) => mk_Free "x" T i)
berghofe@17870
   907
                (Ts ~~ (j upto j + length dts - 1))
berghofe@28731
   908
              val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts)
berghofe@18261
   909
            in
berghofe@18261
   910
              (j + length dts + 1,
berghofe@18261
   911
               xs @ x :: l_args,
berghofe@18261
   912
               map perm (xs @ [x]) @ r_args)
berghofe@17870
   913
            end
berghofe@17870
   914
wenzelm@30190
   915
          val (_, l_args, r_args) = List.foldr constr_arg (1, [], []) dts;
berghofe@17870
   916
          val c = Const (cname, map fastype_of l_args ---> T)
berghofe@17870
   917
        in
wenzelm@20046
   918
          Goal.prove_global thy8 [] []
berghofe@28731
   919
            (augment_sort thy8
berghofe@28731
   920
              (pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (dt_atoms \ atom))
berghofe@28731
   921
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@28731
   922
                (perm (list_comb (c, l_args)), list_comb (c, r_args)))))
berghofe@18010
   923
            (fn _ => EVERY
berghofe@17870
   924
              [simp_tac (simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1,
berghofe@17870
   925
               simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @
berghofe@17870
   926
                 constr_defs @ perm_closed_thms)) 1,
berghofe@17870
   927
               TRY (simp_tac (HOL_basic_ss addsimps
berghofe@17870
   928
                 (symmetric perm_fun_def :: abs_perm)) 1),
berghofe@17870
   929
               TRY (simp_tac (HOL_basic_ss addsimps
berghofe@17870
   930
                 (perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @
wenzelm@20046
   931
                    perm_closed_thms)) 1)])
berghofe@17870
   932
        end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss))
berghofe@19833
   933
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   934
berghofe@17870
   935
    (** prove injectivity of constructors **)
berghofe@17870
   936
berghofe@17870
   937
    val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms;
wenzelm@26343
   938
    val alpha = PureThy.get_thms thy8 "alpha";
wenzelm@26343
   939
    val abs_fresh = PureThy.get_thms thy8 "abs_fresh";
berghofe@17870
   940
berghofe@28731
   941
    val pt_cp_sort =
berghofe@28731
   942
      map (pt_class_of thy8) dt_atoms @
berghofe@28731
   943
      maps (fn s => map (cp_class_of thy8 s) (dt_atoms \ s)) dt_atoms;
berghofe@28731
   944
berghofe@17870
   945
    val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) =>
berghofe@19833
   946
      let val T = nth_dtyp' i
berghofe@17870
   947
      in List.mapPartial (fn ((cname, dts), constr_rep_thm) =>
berghofe@17870
   948
        if null dts then NONE else SOME
berghofe@17870
   949
        let
berghofe@17870
   950
          val cname = Sign.intern_const thy8
wenzelm@30364
   951
            (Long_Name.append tname (Long_Name.base_name cname));
berghofe@17870
   952
berghofe@19833
   953
          fun make_inj ((dts, dt), (j, args1, args2, eqs)) =
berghofe@17870
   954
            let
berghofe@28731
   955
              val Ts_idx = map (typ_of_dtyp descr'' sorts) dts ~~ (j upto j + length dts - 1);
berghofe@17870
   956
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
berghofe@17870
   957
              val ys = map (fn (T, i) => mk_Free "y" T i) Ts_idx;
berghofe@28731
   958
              val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts);
berghofe@28731
   959
              val y = mk_Free "y" (typ_of_dtyp descr'' sorts dt) (j + length dts)
berghofe@18261
   960
            in
berghofe@18261
   961
              (j + length dts + 1,
berghofe@18261
   962
               xs @ (x :: args1), ys @ (y :: args2),
berghofe@18261
   963
               HOLogic.mk_eq
wenzelm@30190
   964
                 (List.foldr mk_abs_fun x xs, List.foldr mk_abs_fun y ys) :: eqs)
berghofe@17870
   965
            end;
berghofe@17870
   966
wenzelm@30190
   967
          val (_, args1, args2, eqs) = List.foldr make_inj (1, [], [], []) dts;
berghofe@17870
   968
          val Ts = map fastype_of args1;
berghofe@17870
   969
          val c = Const (cname, Ts ---> T)
berghofe@17870
   970
        in
berghofe@28731
   971
          Goal.prove_global thy8 [] []
berghofe@28731
   972
            (augment_sort thy8 pt_cp_sort
berghofe@28731
   973
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@28731
   974
                (HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)),
berghofe@28731
   975
                 foldr1 HOLogic.mk_conj eqs))))
berghofe@18010
   976
            (fn _ => EVERY
berghofe@17870
   977
               [asm_full_simp_tac (simpset_of thy8 addsimps (constr_rep_thm ::
berghofe@17870
   978
                  rep_inject_thms')) 1,
berghofe@17870
   979
                TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def ::
berghofe@17870
   980
                  alpha @ abs_perm @ abs_fresh @ rep_inject_thms @
berghofe@28731
   981
                  perm_rep_perm_thms)) 1)])
berghofe@17870
   982
        end) (constrs ~~ constr_rep_thms)
berghofe@19833
   983
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss);
berghofe@17870
   984
berghofe@17872
   985
    (** equations for support and freshness **)
berghofe@17872
   986
berghofe@17872
   987
    val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip
berghofe@17872
   988
      (map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') =>
berghofe@19833
   989
      let val T = nth_dtyp' i
berghofe@17872
   990
      in List.concat (map (fn (cname, dts) => map (fn atom =>
berghofe@17872
   991
        let
berghofe@17872
   992
          val cname = Sign.intern_const thy8
wenzelm@30364
   993
            (Long_Name.append tname (Long_Name.base_name cname));
berghofe@17872
   994
          val atomT = Type (atom, []);
berghofe@17872
   995
berghofe@19833
   996
          fun process_constr ((dts, dt), (j, args1, args2)) =
berghofe@17872
   997
            let
berghofe@28731
   998
              val Ts_idx = map (typ_of_dtyp descr'' sorts) dts ~~ (j upto j + length dts - 1);
berghofe@17872
   999
              val xs = map (fn (T, i) => mk_Free "x" T i) Ts_idx;
berghofe@28731
  1000
              val x = mk_Free "x" (typ_of_dtyp descr'' sorts dt) (j + length dts)
berghofe@18261
  1001
            in
berghofe@18261
  1002
              (j + length dts + 1,
wenzelm@30190
  1003
               xs @ (x :: args1), List.foldr mk_abs_fun x xs :: args2)
berghofe@17872
  1004
            end;
berghofe@17872
  1005
wenzelm@30190
  1006
          val (_, args1, args2) = List.foldr process_constr (1, [], []) dts;
berghofe@17872
  1007
          val Ts = map fastype_of args1;
berghofe@17872
  1008
          val c = list_comb (Const (cname, Ts ---> T), args1);
berghofe@17872
  1009
          fun supp t =
berghofe@19494
  1010
            Const ("Nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t;
berghofe@25823
  1011
          fun fresh t = fresh_const atomT (fastype_of t) $ Free ("a", atomT) $ t;
wenzelm@20046
  1012
          val supp_thm = Goal.prove_global thy8 [] []
berghofe@28731
  1013
            (augment_sort thy8 pt_cp_sort
berghofe@17872
  1014
              (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@17872
  1015
                (supp c,
haftmann@30450
  1016
                 if null dts then HOLogic.mk_set atomT []
haftmann@30304
  1017
                 else foldr1 (HOLogic.mk_binop @{const_name Un}) (map supp args2)))))
berghofe@17872
  1018
            (fn _ =>
berghofe@18010
  1019
              simp_tac (HOL_basic_ss addsimps (supp_def ::
berghofe@17872
  1020
                 Un_assoc :: de_Morgan_conj :: Collect_disj_eq :: finite_Un ::
berghofe@22274
  1021
                 symmetric empty_def :: finite_emptyI :: simp_thms @
wenzelm@20046
  1022
                 abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1)
berghofe@17872
  1023
        in
berghofe@17872
  1024
          (supp_thm,
berghofe@28731
  1025
           Goal.prove_global thy8 [] [] (augment_sort thy8 pt_cp_sort
berghofe@28731
  1026
             (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@28731
  1027
               (fresh c,
berghofe@28731
  1028
                if null dts then HOLogic.true_const
berghofe@28731
  1029
                else foldr1 HOLogic.mk_conj (map fresh args2)))))
berghofe@17872
  1030
             (fn _ =>
berghofe@24459
  1031
               simp_tac (HOL_ss addsimps [Un_iff, empty_iff, fresh_def, supp_thm]) 1))
berghofe@17872
  1032
        end) atoms) constrs)
berghofe@19833
  1033
      end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps')));
berghofe@17872
  1034
berghofe@18107
  1035
    (**** weak induction theorem ****)
berghofe@18016
  1036
berghofe@18016
  1037
    fun mk_indrule_lemma ((prems, concls), (((i, _), T), U)) =
berghofe@18016
  1038
      let
berghofe@18016
  1039
        val Rep_t = Const (List.nth (rep_names, i), T --> U) $
berghofe@18016
  1040
          mk_Free "x" T i;
berghofe@18016
  1041
berghofe@18016
  1042
        val Abs_t =  Const (List.nth (abs_names, i), U --> T)
berghofe@18016
  1043
berghofe@21021
  1044
      in (prems @ [HOLogic.imp $
berghofe@21021
  1045
            (Const (List.nth (rep_set_names'', i), U --> HOLogic.boolT) $ Rep_t) $
berghofe@18016
  1046
              (mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))],
berghofe@18016
  1047
          concls @ [mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ mk_Free "x" T i])
berghofe@18016
  1048
      end;
berghofe@18016
  1049
berghofe@18016
  1050
    val (indrule_lemma_prems, indrule_lemma_concls) =
berghofe@18107
  1051
      Library.foldl mk_indrule_lemma (([], []), (descr'' ~~ recTs ~~ recTs'));
berghofe@18016
  1052
wenzelm@20046
  1053
    val indrule_lemma = Goal.prove_global thy8 [] []
berghofe@18016
  1054
      (Logic.mk_implies
berghofe@18016
  1055
        (HOLogic.mk_Trueprop (mk_conj indrule_lemma_prems),
berghofe@18016
  1056
         HOLogic.mk_Trueprop (mk_conj indrule_lemma_concls))) (fn _ => EVERY
berghofe@18016
  1057
           [REPEAT (etac conjE 1),
berghofe@18016
  1058
            REPEAT (EVERY
berghofe@18016
  1059
              [TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1,
wenzelm@20046
  1060
               etac mp 1, resolve_tac Rep_thms 1])]);
berghofe@18016
  1061
berghofe@18016
  1062
    val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma)));
berghofe@18016
  1063
    val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else
berghofe@18016
  1064
      map (Free o apfst fst o dest_Var) Ps;
berghofe@18016
  1065
    val indrule_lemma' = cterm_instantiate
berghofe@18016
  1066
      (map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma;
berghofe@18016
  1067
berghofe@19833
  1068
    val Abs_inverse_thms' = map (fn r => r RS subst) Abs_inverse_thms;
berghofe@18016
  1069
berghofe@28731
  1070
    val dt_induct_prop = DatatypeProp.make_ind descr' sorts;
wenzelm@20046
  1071
    val dt_induct = Goal.prove_global thy8 []
berghofe@18016
  1072
      (Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop)
wenzelm@26711
  1073
      (fn {prems, ...} => EVERY
berghofe@18016
  1074
        [rtac indrule_lemma' 1,
berghofe@25674
  1075
         (indtac rep_induct [] THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1,
berghofe@18016
  1076
         EVERY (map (fn (prem, r) => (EVERY
berghofe@18016
  1077
           [REPEAT (eresolve_tac Abs_inverse_thms' 1),
berghofe@18016
  1078
            simp_tac (HOL_basic_ss addsimps [symmetric r]) 1,
berghofe@18016
  1079
            DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)]))
wenzelm@20046
  1080
                (prems ~~ constr_defs))]);
berghofe@18016
  1081
berghofe@18107
  1082
    val case_names_induct = mk_case_names_induct descr'';
berghofe@18016
  1083
berghofe@18066
  1084
    (**** prove that new datatypes have finite support ****)
berghofe@18066
  1085
urbanc@18246
  1086
    val _ = warning "proving finite support for the new datatype";
urbanc@18246
  1087
berghofe@18066
  1088
    val indnames = DatatypeProp.make_tnames recTs;
berghofe@18066
  1089
wenzelm@26343
  1090
    val abs_supp = PureThy.get_thms thy8 "abs_supp";
wenzelm@26343
  1091
    val supp_atm = PureThy.get_thms thy8 "supp_atm";
berghofe@18066
  1092
berghofe@18066
  1093
    val finite_supp_thms = map (fn atom =>
berghofe@18066
  1094
      let val atomT = Type (atom, [])
berghofe@18066
  1095
      in map standard (List.take
berghofe@28731
  1096
        (split_conj_thm (Goal.prove_global thy8 [] []
berghofe@28731
  1097
           (augment_sort thy8 (fs_class_of thy8 atom :: pt_cp_sort)
berghofe@28731
  1098
             (HOLogic.mk_Trueprop
berghofe@28731
  1099
               (foldr1 HOLogic.mk_conj (map (fn (s, T) =>
berghofe@28731
  1100
                 Const ("Finite_Set.finite", HOLogic.mk_setT atomT --> HOLogic.boolT) $
berghofe@28731
  1101
                   (Const ("Nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T)))
berghofe@28731
  1102
                   (indnames ~~ recTs)))))
berghofe@18066
  1103
           (fn _ => indtac dt_induct indnames 1 THEN
berghofe@18066
  1104
            ALLGOALS (asm_full_simp_tac (simpset_of thy8 addsimps
urbanc@18067
  1105
              (abs_supp @ supp_atm @
wenzelm@30364
  1106
               PureThy.get_thms thy8 ("fs_" ^ Long_Name.base_name atom ^ "1") @
berghofe@18066
  1107
               List.concat supp_thms))))),
berghofe@18066
  1108
         length new_type_names))
berghofe@18066
  1109
      end) atoms;
berghofe@18066
  1110
krauss@18759
  1111
    val simp_atts = replicate (length new_type_names) [Simplifier.simp_add];
berghofe@18658
  1112
urbanc@22245
  1113
	(* Function to add both the simp and eqvt attributes *)
urbanc@22245
  1114
        (* These two attributes are duplicated on all the types in the mutual nominal datatypes *)
urbanc@22245
  1115
urbanc@22245
  1116
    val simp_eqvt_atts = replicate (length new_type_names) [Simplifier.simp_add, NominalThmDecls.eqvt_add];
urbanc@22245
  1117
 
berghofe@18658
  1118
    val (_, thy9) = thy8 |>
wenzelm@24712
  1119
      Sign.add_path big_name |>
haftmann@29585
  1120
      PureThy.add_thms [((Binding.name "induct", dt_induct), [case_names_induct])] ||>>
haftmann@29585
  1121
      PureThy.add_thmss [((Binding.name "inducts", projections dt_induct), [case_names_induct])] ||>
wenzelm@24712
  1122
      Sign.parent_path ||>>
berghofe@18658
  1123
      DatatypeAux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms ||>>
berghofe@18658
  1124
      DatatypeAux.store_thmss "constr_rep" new_type_names constr_rep_thmss ||>>
urbanc@22231
  1125
      DatatypeAux.store_thmss_atts "perm" new_type_names simp_eqvt_atts perm_simps' ||>>
berghofe@18658
  1126
      DatatypeAux.store_thmss "inject" new_type_names inject_thms ||>>
berghofe@18658
  1127
      DatatypeAux.store_thmss "supp" new_type_names supp_thms ||>>
berghofe@18658
  1128
      DatatypeAux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms ||>
berghofe@18658
  1129
      fold (fn (atom, ths) => fn thy =>
berghofe@28736
  1130
        let
berghofe@28736
  1131
          val class = fs_class_of thy atom;
berghofe@28736
  1132
          val sort = Sign.certify_sort thy (class :: pt_cp_sort)
berghofe@28736
  1133
        in fold (fn Type (s, Ts) => AxClass.prove_arity
berghofe@28736
  1134
          (s, map (inter_sort thy sort o snd o dest_TFree) Ts, [class])
berghofe@28736
  1135
          (Class.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy
berghofe@18658
  1136
        end) (atoms ~~ finite_supp_thms);
berghofe@18658
  1137
berghofe@18107
  1138
    (**** strong induction theorem ****)
berghofe@18107
  1139
berghofe@18107
  1140
    val pnames = if length descr'' = 1 then ["P"]
berghofe@18107
  1141
      else map (fn i => "P" ^ string_of_int i) (1 upto length descr'');
berghofe@18245
  1142
    val ind_sort = if null dt_atomTs then HOLogic.typeS
berghofe@28731
  1143
      else Sign.certify_sort thy9 (map (fs_class_of thy9) dt_atoms);
berghofe@18107
  1144
    val fsT = TFree ("'n", ind_sort);
berghofe@18658
  1145
    val fsT' = TFree ("'n", HOLogic.typeS);
berghofe@18107
  1146
berghofe@18658
  1147
    val fresh_fs = map (fn (s, T) => (T, Free (s, fsT' --> HOLogic.mk_setT T)))
berghofe@18658
  1148
      (DatatypeProp.indexify_names (replicate (length dt_atomTs) "f") ~~ dt_atomTs);
berghofe@18658
  1149
berghofe@18658
  1150
    fun make_pred fsT i T =
berghofe@18302
  1151
      Free (List.nth (pnames, i), fsT --> T --> HOLogic.boolT);
berghofe@18107
  1152
berghofe@19851
  1153
    fun mk_fresh1 xs [] = []
berghofe@19851
  1154
      | mk_fresh1 xs ((y as (_, T)) :: ys) = map (fn x => HOLogic.mk_Trueprop
berghofe@19851
  1155
            (HOLogic.mk_not (HOLogic.mk_eq (Free y, Free x))))
berghofe@19851
  1156
              (filter (fn (_, U) => T = U) (rev xs)) @
berghofe@19851
  1157
          mk_fresh1 (y :: xs) ys;
berghofe@19851
  1158
berghofe@19851
  1159
    fun mk_fresh2 xss [] = []
berghofe@19851
  1160
      | mk_fresh2 xss ((p as (ys, _)) :: yss) = List.concat (map (fn y as (_, T) =>
berghofe@19851
  1161
            map (fn (_, x as (_, U)) => HOLogic.mk_Trueprop
berghofe@25823
  1162
              (fresh_const T U $ Free y $ Free x)) (rev xss @ yss)) ys) @
berghofe@19851
  1163
          mk_fresh2 (p :: xss) yss;
berghofe@19851
  1164
berghofe@18658
  1165
    fun make_ind_prem fsT f k T ((cname, cargs), idxs) =
berghofe@18107
  1166
      let
berghofe@18107
  1167
        val recs = List.filter is_rec_type cargs;
berghofe@28731
  1168
        val Ts = map (typ_of_dtyp descr'' sorts) cargs;
berghofe@28731
  1169
        val recTs' = map (typ_of_dtyp descr'' sorts) recs;
wenzelm@20071
  1170
        val tnames = Name.variant_list pnames (DatatypeProp.make_tnames Ts);
berghofe@18107
  1171
        val rec_tnames = map fst (List.filter (is_rec_type o snd) (tnames ~~ cargs));
berghofe@18107
  1172
        val frees = tnames ~~ Ts;
berghofe@19710
  1173
        val frees' = partition_cargs idxs frees;
wenzelm@20071
  1174
        val z = (Name.variant tnames "z", fsT);
berghofe@18107
  1175
berghofe@18107
  1176
        fun mk_prem ((dt, s), T) =
berghofe@18107
  1177
          let
berghofe@18107
  1178
            val (Us, U) = strip_type T;
berghofe@18107
  1179
            val l = length Us
berghofe@18107
  1180
          in list_all (z :: map (pair "x") Us, HOLogic.mk_Trueprop
berghofe@18658
  1181
            (make_pred fsT (body_index dt) U $ Bound l $ app_bnds (Free (s, T)) l))
berghofe@18107
  1182
          end;
berghofe@18107
  1183
berghofe@18107
  1184
        val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs');
berghofe@18107
  1185
        val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop
berghofe@19710
  1186
            (f T (Free p) (Free z))) (List.concat (map fst frees')) @
berghofe@19710
  1187
          mk_fresh1 [] (List.concat (map fst frees')) @
berghofe@19710
  1188
          mk_fresh2 [] frees'
berghofe@18107
  1189
berghofe@18302
  1190
      in list_all_free (frees @ [z], Logic.list_implies (prems' @ prems,
berghofe@18658
  1191
        HOLogic.mk_Trueprop (make_pred fsT k T $ Free z $
berghofe@18302
  1192
          list_comb (Const (cname, Ts ---> T), map Free frees))))
berghofe@18107
  1193
      end;
berghofe@18107
  1194
berghofe@18107
  1195
    val ind_prems = List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
berghofe@18658
  1196
      map (make_ind_prem fsT (fn T => fn t => fn u =>
berghofe@25823
  1197
        fresh_const T fsT $ t $ u) i T)
berghofe@18658
  1198
          (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs));
berghofe@18107
  1199
    val tnames = DatatypeProp.make_tnames recTs;
wenzelm@20071
  1200
    val zs = Name.variant_list tnames (replicate (length descr'') "z");
berghofe@18107
  1201
    val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
berghofe@18658
  1202
      (map (fn ((((i, _), T), tname), z) =>
berghofe@18658
  1203
        make_pred fsT i T $ Free (z, fsT) $ Free (tname, T))
berghofe@18658
  1204
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
berghofe@18107
  1205
    val induct = Logic.list_implies (ind_prems, ind_concl);
berghofe@18107
  1206
berghofe@18658
  1207
    val ind_prems' =
berghofe@18658
  1208
      map (fn (_, f as Free (_, T)) => list_all_free ([("x", fsT')],
berghofe@26806
  1209
        HOLogic.mk_Trueprop (Const ("Finite_Set.finite",
berghofe@26806
  1210
          (snd (split_last (binder_types T)) --> HOLogic.boolT) -->
berghofe@26806
  1211
            HOLogic.boolT) $ (f $ Free ("x", fsT'))))) fresh_fs @
berghofe@18658
  1212
      List.concat (map (fn (((i, (_, _, constrs)), (_, idxss)), T) =>
berghofe@18658
  1213
        map (make_ind_prem fsT' (fn T => fn t => fn u => HOLogic.Not $
berghofe@18658
  1214
          HOLogic.mk_mem (t, the (AList.lookup op = fresh_fs T) $ u)) i T)
berghofe@18658
  1215
            (constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs));
berghofe@18658
  1216
    val ind_concl' = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
berghofe@18658
  1217
      (map (fn ((((i, _), T), tname), z) =>
berghofe@18658
  1218
        make_pred fsT' i T $ Free (z, fsT') $ Free (tname, T))
berghofe@18658
  1219
        (descr'' ~~ recTs ~~ tnames ~~ zs)));
berghofe@18658
  1220
    val induct' = Logic.list_implies (ind_prems', ind_concl');
berghofe@18658
  1221
berghofe@18658
  1222
    val aux_ind_vars =
berghofe@18658
  1223
      (DatatypeProp.indexify_names (replicate (length dt_atomTs) "pi") ~~
berghofe@18658
  1224
       map mk_permT dt_atomTs) @ [("z", fsT')];
berghofe@18658
  1225
    val aux_ind_Ts = rev (map snd aux_ind_vars);
berghofe@18658
  1226
    val aux_ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
berghofe@18658
  1227
      (map (fn (((i, _), T), tname) =>
berghofe@18658
  1228
        HOLogic.list_all (aux_ind_vars, make_pred fsT' i T $ Bound 0 $
berghofe@22311
  1229
          fold_rev (mk_perm aux_ind_Ts) (map Bound (length dt_atomTs downto 1))
berghofe@22311
  1230
            (Free (tname, T))))
berghofe@18658
  1231
        (descr'' ~~ recTs ~~ tnames)));
berghofe@18658
  1232
berghofe@28731
  1233
    val fin_set_supp = map (fn s =>
berghofe@28731
  1234
      at_inst_of thy9 s RS at_fin_set_supp) dt_atoms;
berghofe@28731
  1235
    val fin_set_fresh = map (fn s =>
berghofe@28731
  1236
      at_inst_of thy9 s RS at_fin_set_fresh) dt_atoms;
berghofe@25951
  1237
    val pt1_atoms = map (fn Type (s, _) =>
wenzelm@30364
  1238
      PureThy.get_thm thy9 ("pt_" ^ Long_Name.base_name s ^ "1")) dt_atomTs;
berghofe@25951
  1239
    val pt2_atoms = map (fn Type (s, _) =>
wenzelm@30364
  1240
      PureThy.get_thm thy9 ("pt_" ^ Long_Name.base_name s ^ "2") RS sym) dt_atomTs;
wenzelm@26343
  1241
    val exists_fresh' = PureThy.get_thms thy9 "exists_fresh'";
wenzelm@26343
  1242
    val fs_atoms = PureThy.get_thms thy9 "fin_supp";
wenzelm@26343
  1243
    val abs_supp = PureThy.get_thms thy9 "abs_supp";
wenzelm@26343
  1244
    val perm_fresh_fresh = PureThy.get_thms thy9 "perm_fresh_fresh";
wenzelm@26343
  1245
    val calc_atm = PureThy.get_thms thy9 "calc_atm";
wenzelm@26343
  1246
    val fresh_atm = PureThy.get_thms thy9 "fresh_atm";
wenzelm@26343
  1247
    val fresh_left = PureThy.get_thms thy9 "fresh_left";
wenzelm@26343
  1248
    val perm_swap = PureThy.get_thms thy9 "perm_swap";
berghofe@18658
  1249
berghofe@25951
  1250
    fun obtain_fresh_name' ths ts T (freshs1, freshs2, ctxt) =
berghofe@18658
  1251
      let
berghofe@25951
  1252
        val p = foldr1 HOLogic.mk_prod (ts @ freshs1);
berghofe@25951
  1253
        val ex = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop
berghofe@25951
  1254
            (HOLogic.exists_const T $ Abs ("x", T,
berghofe@25951
  1255
              fresh_const T (fastype_of p) $
berghofe@25951
  1256
                Bound 0 $ p)))
berghofe@25951
  1257
          (fn _ => EVERY
berghofe@25951
  1258
            [resolve_tac exists_fresh' 1,
berghofe@25951
  1259
             simp_tac (HOL_ss addsimps (supp_prod :: finite_Un :: fs_atoms @
berghofe@25951
  1260
               fin_set_supp @ ths)) 1]);
berghofe@25951
  1261
        val (([cx], ths), ctxt') = Obtain.result
berghofe@25951
  1262
          (fn _ => EVERY
berghofe@25951
  1263
            [etac exE 1,
berghofe@25951
  1264
             full_simp_tac (HOL_ss addsimps (fresh_prod :: fresh_atm)) 1,
berghofe@25951
  1265
             REPEAT (etac conjE 1)])
berghofe@25951
  1266
          [ex] ctxt
berghofe@25951
  1267
      in (freshs1 @ [term_of cx], freshs2 @ ths, ctxt') end;
berghofe@25951
  1268
berghofe@25951
  1269
    fun fresh_fresh_inst thy a b =
berghofe@25951
  1270
      let
berghofe@25951
  1271
        val T = fastype_of a;
berghofe@25951
  1272
        val SOME th = find_first (fn th => case prop_of th of
berghofe@25951
  1273
            _ $ (_ $ (Const (_, Type (_, [U, _])) $ _ $ _)) $ _ => U = T
berghofe@25951
  1274
          | _ => false) perm_fresh_fresh
berghofe@18658
  1275
      in
berghofe@25951
  1276
        Drule.instantiate' []
berghofe@25951
  1277
          [SOME (cterm_of thy a), NONE, SOME (cterm_of thy b)] th
berghofe@18658
  1278
      end;
urbanc@18104
  1279
berghofe@28731
  1280
    val fs_cp_sort =
berghofe@28731
  1281
      map (fs_class_of thy9) dt_atoms @
berghofe@28731
  1282
      maps (fn s => map (cp_class_of thy9 s) (dt_atoms \ s)) dt_atoms;
berghofe@28731
  1283
berghofe@19710
  1284
    (**********************************************************************
berghofe@19710
  1285
      The subgoals occurring in the proof of induct_aux have the
berghofe@19710
  1286
      following parameters:
berghofe@19710
  1287
berghofe@25951
  1288
        x_1 ... x_k p_1 ... p_m z
berghofe@19710
  1289
berghofe@19710
  1290
      where
berghofe@19710
  1291
berghofe@19710
  1292
        x_i : constructor arguments (introduced by weak induction rule)
berghofe@19710
  1293
        p_i : permutations (one for each atom type in the data type)
berghofe@19710
  1294
        z   : freshness context
berghofe@19710
  1295
    ***********************************************************************)
berghofe@19710
  1296
berghofe@19710
  1297
    val _ = warning "proving strong induction theorem ...";
berghofe@19710
  1298
berghofe@28731
  1299
    val induct_aux = Goal.prove_global thy9 []
berghofe@28731
  1300
        (map (augment_sort thy9 fs_cp_sort) ind_prems')
berghofe@28731
  1301
        (augment_sort thy9 fs_cp_sort ind_concl') (fn {prems, context} =>
berghofe@25951
  1302
      let
berghofe@25951
  1303
        val (prems1, prems2) = chop (length dt_atomTs) prems;
berghofe@25951
  1304
        val ind_ss2 = HOL_ss addsimps
berghofe@25951
  1305
          finite_Diff :: abs_fresh @ abs_supp @ fs_atoms;
berghofe@25951
  1306
        val ind_ss1 = ind_ss2 addsimps fresh_left @ calc_atm @
berghofe@25951
  1307
          fresh_atm @ rev_simps @ app_simps;
berghofe@25951
  1308
        val ind_ss3 = HOL_ss addsimps abs_fun_eq1 ::
berghofe@25951
  1309
          abs_perm @ calc_atm @ perm_swap;
berghofe@25951
  1310
        val ind_ss4 = HOL_basic_ss addsimps fresh_left @ prems1 @
berghofe@25951
  1311
          fin_set_fresh @ calc_atm;
berghofe@25951
  1312
        val ind_ss5 = HOL_basic_ss addsimps pt1_atoms;
berghofe@25951
  1313
        val ind_ss6 = HOL_basic_ss addsimps flat perm_simps';
berghofe@28731
  1314
        val th = Goal.prove context [] []
berghofe@28731
  1315
          (augment_sort thy9 fs_cp_sort aux_ind_concl)
berghofe@25951
  1316
          (fn {context = context1, ...} =>
berghofe@25951
  1317
             EVERY (indtac dt_induct tnames 1 ::
berghofe@25951
  1318
               maps (fn ((_, (_, _, constrs)), (_, constrs')) =>
berghofe@25951
  1319
                 map (fn ((cname, cargs), is) =>
berghofe@25951
  1320
                   REPEAT (rtac allI 1) THEN
berghofe@25951
  1321
                   SUBPROOF (fn {prems = iprems, params, concl,
berghofe@25951
  1322
                       context = context2, ...} =>
berghofe@18658
  1323
                     let
berghofe@25951
  1324
                       val concl' = term_of concl;
berghofe@25951
  1325
                       val _ $ (_ $ _ $ u) = concl';
berghofe@25951
  1326
                       val U = fastype_of u;
berghofe@25951
  1327
                       val (xs, params') =
berghofe@25951
  1328
                         chop (length cargs) (map term_of params);
berghofe@25951
  1329
                       val Ts = map fastype_of xs;
berghofe@25951
  1330
                       val cnstr = Const (cname, Ts ---> U);
berghofe@25951
  1331
                       val (pis, z) = split_last params';
berghofe@25951
  1332
                       val mk_pi = fold_rev (mk_perm []) pis;
berghofe@25951
  1333
                       val xs' = partition_cargs is xs;
berghofe@25951
  1334
                       val xs'' = map (fn (ts, u) => (map mk_pi ts, mk_pi u)) xs';
berghofe@25951
  1335
                       val ts = maps (fn (ts, u) => ts @ [u]) xs'';
berghofe@25951
  1336
                       val (freshs1, freshs2, context3) = fold (fn t =>
berghofe@25951
  1337
                         let val T = fastype_of t
berghofe@25951
  1338
                         in obtain_fresh_name' prems1
berghofe@25951
  1339
                           (the (AList.lookup op = fresh_fs T) $ z :: ts) T
berghofe@25951
  1340
                         end) (maps fst xs') ([], [], context2);
berghofe@25951
  1341
                       val freshs1' = unflat (map fst xs') freshs1;
berghofe@25951
  1342
                       val freshs2' = map (Simplifier.simplify ind_ss4)
berghofe@25951
  1343
                         (mk_not_sym freshs2);
berghofe@25951
  1344
                       val ind_ss1' = ind_ss1 addsimps freshs2';
berghofe@25951
  1345
                       val ind_ss3' = ind_ss3 addsimps freshs2';
berghofe@25951
  1346
                       val rename_eq =
berghofe@25951
  1347
                         if forall (null o fst) xs' then []
berghofe@25951
  1348
                         else [Goal.prove context3 [] []
berghofe@25951
  1349
                           (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@25951
  1350
                             (list_comb (cnstr, ts),
berghofe@25951
  1351
                              list_comb (cnstr, maps (fn ((bs, t), cs) =>
berghofe@25951
  1352
                                cs @ [fold_rev (mk_perm []) (map perm_of_pair
berghofe@25951
  1353
                                  (bs ~~ cs)) t]) (xs'' ~~ freshs1')))))
berghofe@25951
  1354
                           (fn _ => EVERY
berghofe@25951
  1355
                              (simp_tac (HOL_ss addsimps flat inject_thms) 1 ::
berghofe@25951
  1356
                               REPEAT (FIRSTGOAL (rtac conjI)) ::
berghofe@25951
  1357
                               maps (fn ((bs, t), cs) =>
berghofe@25951
  1358
                                 if null bs then []
berghofe@25951
  1359
                                 else rtac sym 1 :: maps (fn (b, c) =>
berghofe@25951
  1360
                                   [rtac trans 1, rtac sym 1,
berghofe@25951
  1361
                                    rtac (fresh_fresh_inst thy9 b c) 1,
berghofe@25951
  1362
                                    simp_tac ind_ss1' 1,
berghofe@25951
  1363
                                    simp_tac ind_ss2 1,
berghofe@25951
  1364
                                    simp_tac ind_ss3' 1]) (bs ~~ cs))
berghofe@25951
  1365
                                 (xs'' ~~ freshs1')))];
berghofe@25951
  1366
                       val th = Goal.prove context3 [] [] concl' (fn _ => EVERY
berghofe@25951
  1367
                         [simp_tac (ind_ss6 addsimps rename_eq) 1,
berghofe@25951
  1368
                          cut_facts_tac iprems 1,
berghofe@25951
  1369
                          (resolve_tac prems THEN_ALL_NEW
berghofe@25951
  1370
                            SUBGOAL (fn (t, i) => case Logic.strip_assums_concl t of
berghofe@25951
  1371
                                _ $ (Const ("Nominal.fresh", _) $ _ $ _) =>
berghofe@25951
  1372
                                  simp_tac ind_ss1' i
berghofe@25951
  1373
                              | _ $ (Const ("Not", _) $ _) =>
berghofe@25951
  1374
                                  resolve_tac freshs2' i
berghofe@25951
  1375
                              | _ => asm_simp_tac (HOL_basic_ss addsimps
berghofe@25951
  1376
                                  pt2_atoms addsimprocs [perm_simproc]) i)) 1])
berghofe@25951
  1377
                       val final = ProofContext.export context3 context2 [th]
berghofe@18658
  1378
                     in
berghofe@25951
  1379
                       resolve_tac final 1
berghofe@25951
  1380
                     end) context1 1) (constrs ~~ constrs')) (descr'' ~~ ndescr)))
berghofe@25951
  1381
      in
berghofe@25951
  1382
        EVERY
berghofe@25951
  1383
          [cut_facts_tac [th] 1,
wenzelm@27228
  1384
           REPEAT (eresolve_tac [conjE, @{thm allE_Nil}] 1),
berghofe@25951
  1385
           REPEAT (etac allE 1),
berghofe@25951
  1386
           REPEAT (TRY (rtac conjI 1) THEN asm_full_simp_tac ind_ss5 1)]
berghofe@25951
  1387
      end);
berghofe@18658
  1388
berghofe@18658
  1389
    val induct_aux' = Thm.instantiate ([],
berghofe@28731
  1390
      map (fn (s, v as Var (_, T)) =>
berghofe@28731
  1391
        (cterm_of thy9 v, cterm_of thy9 (Free (s, T))))
berghofe@28731
  1392
          (pnames ~~ map head_of (HOLogic.dest_conj
berghofe@28731
  1393
             (HOLogic.dest_Trueprop (concl_of induct_aux)))) @
berghofe@18658
  1394
      map (fn (_, f) =>
berghofe@18658
  1395
        let val f' = Logic.varify f
berghofe@18658
  1396
        in (cterm_of thy9 f',
berghofe@19494
  1397
          cterm_of thy9 (Const ("Nominal.supp", fastype_of f')))
berghofe@18658
  1398
        end) fresh_fs) induct_aux;
berghofe@18658
  1399
berghofe@28731
  1400
    val induct = Goal.prove_global thy9 []
berghofe@28731
  1401
      (map (augment_sort thy9 fs_cp_sort) ind_prems)
berghofe@28731
  1402
      (augment_sort thy9 fs_cp_sort ind_concl)
wenzelm@26711
  1403
      (fn {prems, ...} => EVERY
berghofe@18658
  1404
         [rtac induct_aux' 1,
berghofe@25951
  1405
          REPEAT (resolve_tac fs_atoms 1),
berghofe@18658
  1406
          REPEAT ((resolve_tac prems THEN_ALL_NEW
wenzelm@20046
  1407
            (etac meta_spec ORELSE' full_simp_tac (HOL_basic_ss addsimps [fresh_def]))) 1)])
berghofe@18658
  1408
berghofe@18658
  1409
    val (_, thy10) = thy9 |>
wenzelm@24712
  1410
      Sign.add_path big_name |>
haftmann@29585
  1411
      PureThy.add_thms [((Binding.name "strong_induct'", induct_aux), [])] ||>>
haftmann@29585
  1412
      PureThy.add_thms [((Binding.name "strong_induct", induct), [case_names_induct])] ||>>
haftmann@29585
  1413
      PureThy.add_thmss [((Binding.name "strong_inducts", projections induct), [case_names_induct])];
berghofe@18658
  1414
berghofe@19322
  1415
    (**** recursion combinator ****)
berghofe@19251
  1416
berghofe@19322
  1417
    val _ = warning "defining recursion combinator ...";
berghofe@19251
  1418
wenzelm@30190
  1419
    val used = List.foldr OldTerm.add_typ_tfree_names [] recTs;
berghofe@19251
  1420
berghofe@28731
  1421
    val (rec_result_Ts', rec_fn_Ts') = DatatypeProp.make_primrec_Ts descr' sorts used;
berghofe@19985
  1422
wenzelm@21365
  1423
    val rec_sort = if null dt_atomTs then HOLogic.typeS else
berghofe@28731
  1424
      Sign.certify_sort thy10 pt_cp_sort;
berghofe@19985
  1425
berghofe@19985
  1426
    val rec_result_Ts = map (fn TFree (s, _) => TFree (s, rec_sort)) rec_result_Ts';
berghofe@19985
  1427
    val rec_fn_Ts = map (typ_subst_atomic (rec_result_Ts' ~~ rec_result_Ts)) rec_fn_Ts';
berghofe@19251
  1428
berghofe@21021
  1429
    val rec_set_Ts = map (fn (T1, T2) =>
berghofe@21021
  1430
      rec_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts);
berghofe@19251
  1431
berghofe@19322
  1432
    val big_rec_name = big_name ^ "_rec_set";
berghofe@21021
  1433
    val rec_set_names' =
berghofe@21021
  1434
      if length descr'' = 1 then [big_rec_name] else
berghofe@21021
  1435
        map ((curry (op ^) (big_rec_name ^ "_")) o string_of_int)
berghofe@21021
  1436
          (1 upto (length descr''));
haftmann@28965
  1437
    val rec_set_names =  map (Sign.full_bname thy10) rec_set_names';
berghofe@19251
  1438
berghofe@19322
  1439
    val rec_fns = map (uncurry (mk_Free "f"))
berghofe@19322
  1440
      (rec_fn_Ts ~~ (1 upto (length rec_fn_Ts)));
berghofe@21021
  1441
    val rec_sets' = map (fn c => list_comb (Free c, rec_fns))
berghofe@21021
  1442
      (rec_set_names' ~~ rec_set_Ts);
berghofe@19322
  1443
    val rec_sets = map (fn c => list_comb (Const c, rec_fns))
berghofe@19322
  1444
      (rec_set_names ~~ rec_set_Ts);
berghofe@19251
  1445
berghofe@19322
  1446
    (* introduction rules for graph of recursion function *)
berghofe@19251
  1447
berghofe@20145
  1448
    val rec_preds = map (fn (a, T) =>
berghofe@20145
  1449
      Free (a, T --> HOLogic.boolT)) (pnames ~~ rec_result_Ts);
berghofe@20145
  1450
berghofe@20267
  1451
    fun mk_fresh3 rs [] = []
berghofe@20267
  1452
      | mk_fresh3 rs ((p as (ys, z)) :: yss) = List.concat (map (fn y as (_, T) =>
berghofe@20267
  1453
            List.mapPartial (fn ((_, (_, x)), r as (_, U)) => if z = x then NONE
berghofe@20267
  1454
              else SOME (HOLogic.mk_Trueprop
berghofe@25823
  1455
                (fresh_const T U $ Free y $ Free r))) rs) ys) @
berghofe@20267
  1456
          mk_fresh3 rs yss;
berghofe@20267
  1457
berghofe@21088
  1458
    (* FIXME: avoid collisions with other variable names? *)
berghofe@21088
  1459
    val rec_ctxt = Free ("z", fsT');
berghofe@21088
  1460
berghofe@20397
  1461
    fun make_rec_intr T p rec_set ((rec_intr_ts, rec_prems, rec_prems',
berghofe@20397
  1462
          rec_eq_prems, l), ((cname, cargs), idxs)) =
berghofe@19251
  1463
      let
berghofe@28731
  1464
        val Ts = map (typ_of_dtyp descr'' sorts) cargs;
berghofe@19851
  1465
        val frees = map (fn i => "x" ^ string_of_int i) (1 upto length Ts) ~~ Ts;
berghofe@19851
  1466
        val frees' = partition_cargs idxs frees;
berghofe@21088
  1467
        val binders = List.concat (map fst frees');
berghofe@20411
  1468
        val atomTs = distinct op = (maps (map snd o fst) frees');
berghofe@19851
  1469
        val recs = List.mapPartial
berghofe@20145
  1470
          (fn ((_, DtRec i), p) => SOME (i, p) | _ => NONE)
berghofe@19851
  1471
          (partition_cargs idxs cargs ~~ frees');
berghofe@19851
  1472
        val frees'' = map (fn i => "y" ^ string_of_int i) (1 upto length recs) ~~
berghofe@19851
  1473
          map (fn (i, _) => List.nth (rec_result_Ts, i)) recs;
berghofe@20145
  1474
        val prems1 = map (fn ((i, (_, x)), y) => HOLogic.mk_Trueprop
berghofe@21021
  1475
          (List.nth (rec_sets', i) $ Free x $ Free y)) (recs ~~ frees'');
berghofe@20145
  1476
        val prems2 =
berghofe@20145
  1477
          map (fn f => map (fn p as (_, T) => HOLogic.mk_Trueprop
berghofe@25823
  1478
            (fresh_const T (fastype_of f) $ Free p $ f)) binders) rec_fns;
berghofe@21088
  1479
        val prems3 = mk_fresh1 [] binders @ mk_fresh2 [] frees';
berghofe@20145
  1480
        val prems4 = map (fn ((i, _), y) =>
berghofe@20145
  1481
          HOLogic.mk_Trueprop (List.nth (rec_preds, i) $ Free y)) (recs ~~ frees'');
berghofe@20267
  1482
        val prems5 = mk_fresh3 (recs ~~ frees'') frees';
berghofe@20411
  1483
        val prems6 = maps (fn aT => map (fn y as (_, T) => HOLogic.mk_Trueprop
berghofe@22274
  1484
          (Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $
berghofe@22274
  1485
             (Const ("Nominal.supp", T --> HOLogic.mk_setT aT) $ Free y)))
berghofe@20411
  1486
               frees'') atomTs;
berghofe@21088
  1487
        val prems7 = map (fn x as (_, T) => HOLogic.mk_Trueprop
berghofe@25823
  1488
          (fresh_const T fsT' $ Free x $ rec_ctxt)) binders;
berghofe@20145
  1489
        val result = list_comb (List.nth (rec_fns, l), map Free (frees @ frees''));
berghofe@20376
  1490
        val result_freshs = map (fn p as (_, T) =>
berghofe@25823
  1491
          fresh_const T (fastype_of result) $ Free p $ result) binders;
berghofe@20145
  1492
        val P = HOLogic.mk_Trueprop (p $ result)
berghofe@20145
  1493
      in
berghofe@20145
  1494
        (rec_intr_ts @ [Logic.list_implies (List.concat prems2 @ prems3 @ prems1,
berghofe@21021
  1495
           HOLogic.mk_Trueprop (rec_set $
berghofe@21021
  1496
             list_comb (Const (cname, Ts ---> T), map Free frees) $ result))],
berghofe@20145
  1497
         rec_prems @ [list_all_free (frees @ frees'', Logic.list_implies (prems4, P))],
berghofe@21054
  1498
         rec_prems' @ map (fn fr => list_all_free (frees @ frees'',
berghofe@21088
  1499
           Logic.list_implies (List.nth (prems2, l) @ prems3 @ prems5 @ prems7 @ prems6 @ [P],
berghofe@21054
  1500
             HOLogic.mk_Trueprop fr))) result_freshs,
berghofe@20397
  1501
         rec_eq_prems @ [List.concat prems2 @ prems3],
berghofe@20145
  1502
         l + 1)
berghofe@19251
  1503
      end;
berghofe@19251
  1504
berghofe@20397
  1505
    val (rec_intr_ts, rec_prems, rec_prems', rec_eq_prems, _) =
berghofe@20145
  1506
      Library.foldl (fn (x, ((((d, d'), T), p), rec_set)) =>
berghofe@20145
  1507
        Library.foldl (make_rec_intr T p rec_set) (x, #3 (snd d) ~~ snd d'))
berghofe@21021
  1508
          (([], [], [], [], 0), descr'' ~~ ndescr ~~ recTs ~~ rec_preds ~~ rec_sets');
berghofe@19251
  1509
wenzelm@21365
  1510
    val ({intrs = rec_intrs, elims = rec_elims, raw_induct = rec_induct, ...}, thy11) =
berghofe@21055
  1511
      thy10 |>
haftmann@31723
  1512
        Inductive.add_inductive_global (serial_string ())
haftmann@31671
  1513
          {quiet_mode = #quiet config, verbose = false, kind = Thm.internalK,
haftmann@28965
  1514
           alt_name = Binding.name big_rec_name, coind = false, no_elim = false, no_ind = false,
wenzelm@29389
  1515
           skip_mono = true, fork_mono = false}
haftmann@28965
  1516
          (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts))
wenzelm@26128
  1517
          (map dest_Free rec_fns)
haftmann@28965
  1518
          (map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) [] ||>
wenzelm@30364
  1519
      PureThy.hide_fact true (Long_Name.append (Sign.full_bname thy10 big_rec_name) "induct");
berghofe@19251
  1520
berghofe@19985
  1521
    (** equivariance **)
berghofe@19985
  1522
wenzelm@26343
  1523
    val fresh_bij = PureThy.get_thms thy11 "fresh_bij";
wenzelm@26343
  1524
    val perm_bij = PureThy.get_thms thy11 "perm_bij";
berghofe@19985
  1525
berghofe@19985
  1526
    val (rec_equiv_thms, rec_equiv_thms') = ListPair.unzip (map (fn aT =>
berghofe@19985
  1527
      let
berghofe@19985
  1528
        val permT = mk_permT aT;
berghofe@19985
  1529
        val pi = Free ("pi", permT);
berghofe@22311
  1530
        val rec_fns_pi = map (mk_perm [] pi o uncurry (mk_Free "f"))
berghofe@19985
  1531
          (rec_fn_Ts ~~ (1 upto (length rec_fn_Ts)));
berghofe@19985
  1532
        val rec_sets_pi = map (fn c => list_comb (Const c, rec_fns_pi))
berghofe@19985
  1533
          (rec_set_names ~~ rec_set_Ts);
berghofe@19985
  1534
        val ps = map (fn ((((T, U), R), R'), i) =>
berghofe@19985
  1535
          let
berghofe@19985
  1536
            val x = Free ("x" ^ string_of_int i, T);
berghofe@19985
  1537
            val y = Free ("y" ^ string_of_int i, U)
berghofe@19985
  1538
          in
berghofe@22311
  1539
            (R $ x $ y, R' $ mk_perm [] pi x $ mk_perm [] pi y)
berghofe@19985
  1540
          end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ rec_sets_pi ~~ (1 upto length recTs));
berghofe@19985
  1541
        val ths = map (fn th => standard (th RS mp)) (split_conj_thm
wenzelm@20046
  1542
          (Goal.prove_global thy11 [] []
berghofe@28731
  1543
            (augment_sort thy1 pt_cp_sort
berghofe@28731
  1544
              (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map HOLogic.mk_imp ps))))
berghofe@19985
  1545
            (fn _ => rtac rec_induct 1 THEN REPEAT
berghofe@27450
  1546
               (simp_tac (Simplifier.theory_context thy11 HOL_basic_ss
berghofe@27450
  1547
                  addsimps flat perm_simps'
berghofe@27450
  1548
                  addsimprocs [NominalPermeq.perm_simproc_app]) 1 THEN
berghofe@19985
  1549
                (resolve_tac rec_intrs THEN_ALL_NEW
berghofe@19985
  1550
                 asm_simp_tac (HOL_ss addsimps (fresh_bij @ perm_bij))) 1))))
wenzelm@20046
  1551
        val ths' = map (fn ((P, Q), th) =>
wenzelm@20046
  1552
          Goal.prove_global thy11 [] []
berghofe@28731
  1553
            (augment_sort thy1 pt_cp_sort
berghofe@28731
  1554
              (Logic.mk_implies (HOLogic.mk_Trueprop Q, HOLogic.mk_Trueprop P)))
berghofe@19985
  1555
            (fn _ => dtac (Thm.instantiate ([],
berghofe@19985
  1556
                 [(cterm_of thy11 (Var (("pi", 0), permT)),
berghofe@19985
  1557
                   cterm_of thy11 (Const ("List.rev", permT --> permT) $ pi))]) th) 1 THEN
wenzelm@20046
  1558
               NominalPermeq.perm_simp_tac HOL_ss 1)) (ps ~~ ths)
berghofe@19985
  1559
      in (ths, ths') end) dt_atomTs);
berghofe@19985
  1560
berghofe@19985
  1561
    (** finite support **)
berghofe@19985
  1562
berghofe@19985
  1563
    val rec_fin_supp_thms = map (fn aT =>
berghofe@19985
  1564
      let
wenzelm@30364
  1565
        val name = Long_Name.base_name (fst (dest_Type aT));
wenzelm@26343
  1566
        val fs_name = PureThy.get_thm thy11 ("fs_" ^ name ^ "1");
berghofe@19985
  1567
        val aset = HOLogic.mk_setT aT;
berghofe@22274
  1568
        val finite = Const ("Finite_Set.finite", aset --> HOLogic.boolT);
berghofe@22274
  1569
        val fins = map (fn (f, T) => HOLogic.mk_Trueprop
berghofe@22274
  1570
          (finite $ (Const ("Nominal.supp", T --> aset) $ f)))
berghofe@19985
  1571
            (rec_fns ~~ rec_fn_Ts)
berghofe@19985
  1572
      in
berghofe@19985
  1573
        map (fn th => standard (th RS mp)) (split_conj_thm
berghofe@28731
  1574
          (Goal.prove_global thy11 []
berghofe@28731
  1575
            (map (augment_sort thy11 fs_cp_sort) fins)
berghofe@28731
  1576
            (augment_sort thy11 fs_cp_sort
berghofe@28731
  1577
              (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@28731
  1578
                (map (fn (((T, U), R), i) =>
berghofe@28731
  1579
                   let
berghofe@28731
  1580
                     val x = Free ("x" ^ string_of_int i, T);
berghofe@28731
  1581
                     val y = Free ("y" ^ string_of_int i, U)
berghofe@28731
  1582
                   in
berghofe@28731
  1583
                     HOLogic.mk_imp (R $ x $ y,
berghofe@28731
  1584
                       finite $ (Const ("Nominal.supp", U --> aset) $ y))
berghofe@28731
  1585
                   end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~
berghofe@28731
  1586
                     (1 upto length recTs))))))
wenzelm@26711
  1587
            (fn {prems = fins, ...} =>
wenzelm@26711
  1588
              (rtac rec_induct THEN_ALL_NEW cut_facts_tac fins) 1 THEN REPEAT
berghofe@19985
  1589
               (NominalPermeq.finite_guess_tac (HOL_ss addsimps [fs_name]) 1))))
berghofe@19985
  1590
      end) dt_atomTs;
berghofe@19985
  1591
berghofe@20376
  1592
    (** freshness **)
berghofe@20376
  1593
berghofe@20376
  1594
    val finite_premss = map (fn aT =>
berghofe@22274
  1595
      map (fn (f, T) => HOLogic.mk_Trueprop
berghofe@22274
  1596
        (Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $
berghofe@22274
  1597
           (Const ("Nominal.supp", T --> HOLogic.mk_setT aT) $ f)))
berghofe@20376
  1598
           (rec_fns ~~ rec_fn_Ts)) dt_atomTs;
berghofe@20376
  1599
berghofe@28731
  1600
    val rec_fns' = map (augment_sort thy11 fs_cp_sort) rec_fns;
berghofe@28731
  1601
berghofe@20376
  1602
    val rec_fresh_thms = map (fn ((aT, eqvt_ths), finite_prems) =>
berghofe@20376
  1603
      let
wenzelm@30364
  1604
        val name = Long_Name.base_name (fst (dest_Type aT));
wenzelm@26343
  1605
        val fs_name = PureThy.get_thm thy11 ("fs_" ^ name ^ "1");
berghofe@20376
  1606
        val a = Free ("a", aT);
berghofe@20376
  1607
        val freshs = map (fn (f, fT) => HOLogic.mk_Trueprop
berghofe@25823
  1608
          (fresh_const aT fT $ a $ f)) (rec_fns ~~ rec_fn_Ts)
berghofe@20376
  1609
      in
berghofe@20376
  1610
        map (fn (((T, U), R), eqvt_th) =>
berghofe@20376
  1611
          let
berghofe@28731
  1612
            val x = Free ("x", augment_sort_typ thy11 fs_cp_sort T);
berghofe@20376
  1613
            val y = Free ("y", U);
berghofe@20376
  1614
            val y' = Free ("y'", U)
berghofe@20376
  1615
          in
berghofe@28731
  1616
            standard (Goal.prove (ProofContext.init thy11) []
berghofe@28731
  1617
              (map (augment_sort thy11 fs_cp_sort)
berghofe@28731
  1618
                (finite_prems @
berghofe@28731
  1619
                   [HOLogic.mk_Trueprop (R $ x $ y),
berghofe@28731
  1620
                    HOLogic.mk_Trueprop (HOLogic.mk_all ("y'", U,
berghofe@28731
  1621
                      HOLogic.mk_imp (R $ x $ y', HOLogic.mk_eq (y', y)))),
berghofe@28731
  1622
                    HOLogic.mk_Trueprop (fresh_const aT T $ a $ x)] @
berghofe@28731
  1623
                 freshs))
berghofe@25823
  1624
              (HOLogic.mk_Trueprop (fresh_const aT U $ a $ y))
berghofe@20376
  1625
              (fn {prems, context} =>
berghofe@20376
  1626
                 let
berghofe@20376
  1627
                   val (finite_prems, rec_prem :: unique_prem ::
berghofe@20376
  1628
                     fresh_prems) = chop (length finite_prems) prems;
berghofe@20376
  1629
                   val unique_prem' = unique_prem RS spec RS mp;
berghofe@20376
  1630
                   val unique = [unique_prem', unique_prem' RS sym] MRS trans;
berghofe@20376
  1631
                   val _ $ (_ $ (_ $ S $ _)) $ _ = prop_of supports_fresh;
berghofe@28731
  1632
                   val tuple = foldr1 HOLogic.mk_prod (x :: rec_fns')
berghofe@20376
  1633
                 in EVERY
berghofe@20376
  1634
                   [rtac (Drule.cterm_instantiate
berghofe@20376
  1635
                      [(cterm_of thy11 S,
berghofe@20376
  1636
                        cterm_of thy11 (Const ("Nominal.supp",
berghofe@20376
  1637
                          fastype_of tuple --> HOLogic.mk_setT aT) $ tuple))]
berghofe@20376
  1638
                      supports_fresh) 1,
berghofe@20376
  1639
                    simp_tac (HOL_basic_ss addsimps
berghofe@20376
  1640
                      [supports_def, symmetric fresh_def, fresh_prod]) 1,
berghofe@20376
  1641
                    REPEAT_DETERM (resolve_tac [allI, impI] 1),
berghofe@20376
  1642
                    REPEAT_DETERM (etac conjE 1),
berghofe@20376
  1643
                    rtac unique 1,
berghofe@20376
  1644
                    SUBPROOF (fn {prems = prems', params = [a, b], ...} => EVERY
berghofe@20376
  1645
                      [cut_facts_tac [rec_prem] 1,
berghofe@20376
  1646
                       rtac (Thm.instantiate ([],
berghofe@20376
  1647
                         [(cterm_of thy11 (Var (("pi", 0), mk_permT aT)),
berghofe@20376
  1648
                           cterm_of thy11 (perm_of_pair (term_of a, term_of b)))]) eqvt_th) 1,
berghofe@20376
  1649
                       asm_simp_tac (HOL_ss addsimps
berghofe@20376
  1650
                         (prems' @ perm_swap @ perm_fresh_fresh)) 1]) context 1,
berghofe@20376
  1651
                    rtac rec_prem 1,
berghofe@20376
  1652
                    simp_tac (HOL_ss addsimps (fs_name ::
berghofe@20376
  1653
                      supp_prod :: finite_Un :: finite_prems)) 1,
berghofe@20376
  1654
                    simp_tac (HOL_ss addsimps (symmetric fresh_def ::
berghofe@20376
  1655
                      fresh_prod :: fresh_prems)) 1]
berghofe@20376
  1656
                 end))
berghofe@20376
  1657
          end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ eqvt_ths)
berghofe@20376
  1658
      end) (dt_atomTs ~~ rec_equiv_thms' ~~ finite_premss);
berghofe@20376
  1659
berghofe@20376
  1660
    (** uniqueness **)
berghofe@20376
  1661
berghofe@21088
  1662
    val fun_tuple = foldr1 HOLogic.mk_prod (rec_ctxt :: rec_fns);
berghofe@20145
  1663
    val fun_tupleT = fastype_of fun_tuple;
berghofe@20145
  1664
    val rec_unique_frees =
berghofe@20145
  1665
      DatatypeProp.indexify_names (replicate (length recTs) "x") ~~ recTs;
berghofe@20397
  1666
    val rec_unique_frees'' = map (fn (s, T) => (s ^ "'", T)) rec_unique_frees;
berghofe@20267
  1667
    val rec_unique_frees' =
berghofe@20267
  1668
      DatatypeProp.indexify_names (replicate (length recTs) "y") ~~ rec_result_Ts;
berghofe@21021
  1669
    val rec_unique_concls = map (fn ((x, U), R) =>
berghofe@20145
  1670
        Const ("Ex1", (U --> HOLogic.boolT) --> HOLogic.boolT) $
berghofe@21021
  1671
          Abs ("y", U, R $ Free x $ Bound 0))
berghofe@20145
  1672
      (rec_unique_frees ~~ rec_result_Ts ~~ rec_sets);
berghofe@20376
  1673
berghofe@20145
  1674
    val induct_aux_rec = Drule.cterm_instantiate
berghofe@28731
  1675
      (map (pairself (cterm_of thy11) o apsnd (augment_sort thy11 fs_cp_sort))
berghofe@20145
  1676
         (map (fn (aT, f) => (Logic.varify f, Abs ("z", HOLogic.unitT,
berghofe@20145
  1677
            Const ("Nominal.supp", fun_tupleT --> HOLogic.mk_setT aT) $ fun_tuple)))
berghofe@20145
  1678
              fresh_fs @
berghofe@20145
  1679
          map (fn (((P, T), (x, U)), Q) =>
berghofe@26067
  1680
           (Var ((P, 0), Logic.varifyT (fsT' --> T --> HOLogic.boolT)),
berghofe@20145
  1681
            Abs ("z", HOLogic.unitT, absfree (x, U, Q))))
berghofe@20145
  1682
              (pnames ~~ recTs ~~ rec_unique_frees ~~ rec_unique_concls) @
berghofe@20145
  1683
          map (fn (s, T) => (Var ((s, 0), Logic.varifyT T), Free (s, T)))
berghofe@20145
  1684
            rec_unique_frees)) induct_aux;
berghofe@20145
  1685
berghofe@20376
  1686
    fun obtain_fresh_name vs ths rec_fin_supp T (freshs1, freshs2, ctxt) =
berghofe@20376
  1687
      let
berghofe@20376
  1688
        val p = foldr1 HOLogic.mk_prod (vs @ freshs1);
berghofe@20376
  1689
        val ex = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop
berghofe@20376
  1690
            (HOLogic.exists_const T $ Abs ("x", T,
berghofe@25823
  1691
              fresh_const T (fastype_of p) $ Bound 0 $ p)))
berghofe@20376
  1692
          (fn _ => EVERY
berghofe@20376
  1693
            [cut_facts_tac ths 1,
berghofe@20376
  1694
             REPEAT_DETERM (dresolve_tac (the (AList.lookup op = rec_fin_supp T)) 1),
urbanc@21377
  1695
             resolve_tac exists_fresh' 1,
berghofe@20376
  1696
             asm_simp_tac (HOL_ss addsimps (supp_prod :: finite_Un :: fs_atoms)) 1]);
berghofe@20376
  1697
        val (([cx], ths), ctxt') = Obtain.result
berghofe@20376
  1698
          (fn _ => EVERY
berghofe@20376
  1699
            [etac exE 1,
berghofe@20376
  1700
             full_simp_tac (HOL_ss addsimps (fresh_prod :: fresh_atm)) 1,
berghofe@20376
  1701
             REPEAT (etac conjE 1)])
berghofe@20376
  1702
          [ex] ctxt
berghofe@20376
  1703
      in (freshs1 @ [term_of cx], freshs2 @ ths, ctxt') end;
berghofe@20376
  1704
berghofe@21088
  1705
    val finite_ctxt_prems = map (fn aT =>
berghofe@22274
  1706
      HOLogic.mk_Trueprop
berghofe@22274
  1707
        (Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $
berghofe@22274
  1708
           (Const ("Nominal.supp", fsT' --> HOLogic.mk_setT aT) $ rec_ctxt))) dt_atomTs;
berghofe@21088
  1709
berghofe@20397
  1710
    val rec_unique_thms = split_conj_thm (Goal.prove
wenzelm@21516
  1711
      (ProofContext.init thy11) (map fst rec_unique_frees)
berghofe@28731
  1712
      (map (augment_sort thy11 fs_cp_sort)
berghofe@28731
  1713
        (List.concat finite_premss @ finite_ctxt_prems @ rec_prems @ rec_prems'))
berghofe@28731
  1714
      (augment_sort thy11 fs_cp_sort
berghofe@28731
  1715
        (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj rec_unique_concls)))
berghofe@20376
  1716
      (fn {prems, context} =>
berghofe@20267
  1717
         let
berghofe@20267
  1718
           val k = length rec_fns;
berghofe@20376
  1719
           val (finite_thss, ths1) = fold_map (fn T => fn xs =>
berghofe@20376
  1720
             apfst (pair T) (chop k xs)) dt_atomTs prems;
berghofe@21088
  1721
           val (finite_ctxt_ths, ths2) = chop (length dt_atomTs) ths1;
berghofe@21088
  1722
           val (P_ind_ths, fcbs) = chop k ths2;
berghofe@20267
  1723
           val P_ths = map (fn th => th RS mp) (split_conj_thm
berghofe@20376
  1724
             (Goal.prove context
berghofe@20397
  1725
               (map fst (rec_unique_frees'' @ rec_unique_frees')) []
berghofe@28731
  1726
               (augment_sort thy11 fs_cp_sort
berghofe@28731
  1727
                 (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@28731
  1728
                    (map (fn (((x, y), S), P) => HOLogic.mk_imp
berghofe@28731
  1729
                      (S $ Free x $ Free y, P $ (Free y)))
berghofe@28731
  1730
                        (rec_unique_frees'' ~~ rec_unique_frees' ~~
berghofe@28731
  1731
                           rec_sets ~~ rec_preds)))))
berghofe@20267
  1732
               (fn _ =>
berghofe@20267
  1733
                  rtac rec_induct 1 THEN
berghofe@20376
  1734
                  REPEAT ((resolve_tac P_ind_ths THEN_ALL_NEW assume_tac) 1))));
berghofe@20376
  1735
           val rec_fin_supp_thms' = map
berghofe@20376
  1736
             (fn (ths, (T, fin_ths)) => (T, map (curry op MRS fin_ths) ths))
berghofe@20376
  1737
             (rec_fin_supp_thms ~~ finite_thss);
berghofe@20267
  1738
         in EVERY
berghofe@20267
  1739
           ([rtac induct_aux_rec 1] @
berghofe@21088
  1740
            maps (fn ((_, finite_ths), finite_th) =>
berghofe@21088
  1741
              [cut_facts_tac (finite_th :: finite_ths) 1,
berghofe@21088
  1742
               asm_simp_tac (HOL_ss addsimps [supp_prod, finite_Un]) 1])
berghofe@21088
  1743
                (finite_thss ~~ finite_ctxt_ths) @
berghofe@20397
  1744
            maps (fn ((_, idxss), elim) => maps (fn idxs =>
berghofe@20397
  1745
              [full_simp_tac (HOL_ss addsimps [symmetric fresh_def, supp_prod, Un_iff]) 1,
berghofe@20397
  1746
               REPEAT_DETERM (eresolve_tac [conjE, ex1E] 1),
berghofe@20397
  1747
               rtac ex1I 1,
berghofe@20397
  1748
               (resolve_tac rec_intrs THEN_ALL_NEW atac) 1,
berghofe@20397
  1749
               rotate_tac ~1 1,
berghofe@20397
  1750
               ((DETERM o etac elim) THEN_ALL_NEW full_simp_tac
berghofe@21021
  1751
                  (HOL_ss addsimps List.concat distinct_thms)) 1] @
berghofe@21021
  1752
               (if null idxs then [] else [hyp_subst_tac 1,
berghofe@20397
  1753
                SUBPROOF (fn {asms, concl, prems = prems', params, context = context', ...} =>
berghofe@20376
  1754
                  let
berghofe@21021
  1755
                    val SOME prem = find_first (can (HOLogic.dest_eq o
berghofe@21021
  1756
                      HOLogic.dest_Trueprop o prop_of)) prems';
berghofe@20376
  1757
                    val _ $ (_ $ lhs $ rhs) = prop_of prem;
berghofe@20376
  1758
                    val _ $ (_ $ lhs' $ rhs') = term_of concl;
berghofe@20376
  1759
                    val rT = fastype_of lhs';
berghofe@20376
  1760
                    val (c, cargsl) = strip_comb lhs;
berghofe@20376
  1761
                    val cargsl' = partition_cargs idxs cargsl;
berghofe@20376
  1762
                    val boundsl = List.concat (map fst cargsl');
berghofe@20376
  1763
                    val (_, cargsr) = strip_comb rhs;
berghofe@20376
  1764
                    val cargsr' = partition_cargs idxs cargsr;
berghofe@20376
  1765
                    val boundsr = List.concat (map fst cargsr');
berghofe@20376
  1766
                    val (params1, _ :: params2) =
berghofe@20376
  1767
                      chop (length params div 2) (map term_of params);
berghofe@20376
  1768
                    val params' = params1 @ params2;
berghofe@20376
  1769
                    val rec_prems = filter (fn th => case prop_of th of
berghofe@28731
  1770
                        _ $ p => (case head_of p of
berghofe@28731
  1771
                          Const (s, _) => s mem rec_set_names
berghofe@28731
  1772
                        | _ => false)
berghofe@28731
  1773
                      | _ => false) prems';
berghofe@20376
  1774
                    val fresh_prems = filter (fn th => case prop_of th of
berghofe@20376
  1775
                        _ $ (Const ("Nominal.fresh", _) $ _ $ _) => true
berghofe@20376
  1776
                      | _ $ (Const ("Not", _) $ _) => true
berghofe@20376
  1777
                      | _ => false) prems';
berghofe@20376
  1778
                    val Ts = map fastype_of boundsl;
berghofe@20376
  1779
berghofe@20376
  1780
                    val _ = warning "step 1: obtaining fresh names";
berghofe@20376
  1781
                    val (freshs1, freshs2, context'') = fold
berghofe@28731
  1782
                      (obtain_fresh_name (rec_ctxt :: rec_fns' @ params')
berghofe@21088
  1783
                         (List.concat (map snd finite_thss) @
berghofe@21088
  1784
                            finite_ctxt_ths @ rec_prems)
berghofe@20376
  1785
                         rec_fin_supp_thms')
berghofe@20376
  1786
                      Ts ([], [], context');
berghofe@20376
  1787
                    val pi1 = map perm_of_pair (boundsl ~~ freshs1);
berghofe@20376
  1788
                    val rpi1 = rev pi1;
berghofe@20376
  1789
                    val pi2 = map perm_of_pair (boundsr ~~ freshs1);
berghofe@21073
  1790
                    val rpi2 = rev pi2;
berghofe@20376
  1791
berghofe@20376
  1792
                    val fresh_prems' = mk_not_sym fresh_prems;
berghofe@20376
  1793
                    val freshs2' = mk_not_sym freshs2;
berghofe@20376
  1794
berghofe@20376
  1795
                    (** as, bs, cs # K as ts, K bs us **)
berghofe@20376
  1796
                    val _ = warning "step 2: as, bs, cs # K as ts, K bs us";
berghofe@20376
  1797
                    val prove_fresh_ss = HOL_ss addsimps
berghofe@20376
  1798
                      (finite_Diff :: List.concat fresh_thms @
berghofe@20376
  1799
                       fs_atoms @ abs_fresh @ abs_supp @ fresh_atm);
berghofe@20376
  1800
                    (* FIXME: avoid asm_full_simp_tac ? *)
berghofe@20376
  1801
                    fun prove_fresh ths y x = Goal.prove context'' [] []
berghofe@25823
  1802
                      (HOLogic.mk_Trueprop (fresh_const
berghofe@25823
  1803
                         (fastype_of x) (fastype_of y) $ x $ y))
berghofe@20376
  1804
                      (fn _ => cut_facts_tac ths 1 THEN asm_full_simp_tac prove_fresh_ss 1);
berghofe@20376
  1805
                    val constr_fresh_thms =
berghofe@20376
  1806
                      map (prove_fresh fresh_prems lhs) boundsl @
berghofe@20376
  1807
                      map (prove_fresh fresh_prems rhs) boundsr @
berghofe@20376
  1808
                      map (prove_fresh freshs2 lhs) freshs1 @
berghofe@20376
  1809
                      map (prove_fresh freshs2 rhs) freshs1;
berghofe@20376
  1810
berghofe@20376
  1811
                    (** pi1 o (K as ts) = pi2 o (K bs us) **)
berghofe@20376
  1812
                    val _ = warning "step 3: pi1 o (K as ts) = pi2 o (K bs us)";
berghofe@20376
  1813
                    val pi1_pi2_eq = Goal.prove context'' [] []
berghofe@20376
  1814
                      (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@22311
  1815
                        (fold_rev (mk_perm []) pi1 lhs, fold_rev (mk_perm []) pi2 rhs)))
berghofe@20376
  1816
                      (fn _ => EVERY
berghofe@20376
  1817
                         [cut_facts_tac constr_fresh_thms 1,
berghofe@20376
  1818
                          asm_simp_tac (HOL_basic_ss addsimps perm_fresh_fresh) 1,
berghofe@20376
  1819
                          rtac prem 1]);
berghofe@20376
  1820
berghofe@20376
  1821
                    (** pi1 o ts = pi2 o us **)
berghofe@20376
  1822
                    val _ = warning "step 4: pi1 o ts = pi2 o us";
berghofe@20376
  1823
                    val pi1_pi2_eqs = map (fn (t, u) =>
berghofe@20376
  1824
                      Goal.prove context'' [] []
berghofe@20376
  1825
                        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@22311
  1826
                          (fold_rev (mk_perm []) pi1 t, fold_rev (mk_perm []) pi2 u)))
berghofe@20376
  1827
                        (fn _ => EVERY
berghofe@20376
  1828
                           [cut_facts_tac [pi1_pi2_eq] 1,
berghofe@20376
  1829
                            asm_full_simp_tac (HOL_ss addsimps
berghofe@20376
  1830
                              (calc_atm @ List.concat perm_simps' @
berghofe@20376
  1831
                               fresh_prems' @ freshs2' @ abs_perm @
berghofe@20376
  1832
                               alpha @ List.concat inject_thms)) 1]))
berghofe@20376
  1833
                        (map snd cargsl' ~~ map snd cargsr');
berghofe@20376
  1834
berghofe@20376
  1835
                    (** pi1^-1 o pi2 o us = ts **)
berghofe@20376
  1836
                    val _ = warning "step 5: pi1^-1 o pi2 o us = ts";
berghofe@20376
  1837
                    val rpi1_pi2_eqs = map (fn ((t, u), eq) =>
berghofe@20376
  1838
                      Goal.prove context'' [] []
berghofe@20376
  1839
                        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@22311
  1840
                          (fold_rev (mk_perm []) (rpi1 @ pi2) u, t)))
berghofe@20376
  1841
                        (fn _ => simp_tac (HOL_ss addsimps
berghofe@20376
  1842
                           ((eq RS sym) :: perm_swap)) 1))
berghofe@20376
  1843
                        (map snd cargsl' ~~ map snd cargsr' ~~ pi1_pi2_eqs);
berghofe@20376
  1844
berghofe@20376
  1845
                    val (rec_prems1, rec_prems2) =
berghofe@20376
  1846
                      chop (length rec_prems div 2) rec_prems;
berghofe@20376
  1847
berghofe@20376
  1848
                    (** (ts, pi1^-1 o pi2 o vs) in rec_set **)
berghofe@20376
  1849
                    val _ = warning "step 6: (ts, pi1^-1 o pi2 o vs) in rec_set";
berghofe@20376
  1850
                    val rec_prems' = map (fn th =>
berghofe@20376
  1851
                      let
berghofe@21021
  1852
                        val _ $ (S $ x $ y) = prop_of th;
berghofe@28731
  1853
                        val Const (s, _) = head_of S;
berghofe@28731
  1854
                        val k = find_index (equal s) rec_set_names;
berghofe@20376
  1855
                        val pi = rpi1 @ pi2;
berghofe@22311
  1856
                        fun mk_pi z = fold_rev (mk_perm []) pi z;
berghofe@20376
  1857
                        fun eqvt_tac p =
berghofe@20376
  1858
                          let
berghofe@20376
  1859
                            val U as Type (_, [Type (_, [T, _])]) = fastype_of p;
berghofe@20376
  1860
                            val l = find_index (equal T) dt_atomTs;
berghofe@20376
  1861
                            val th = List.nth (List.nth (rec_equiv_thms', l), k);
berghofe@20376
  1862
                            val th' = Thm.instantiate ([],
berghofe@20376
  1863
                              [(cterm_of thy11 (Var (("pi", 0), U)),
berghofe@20376
  1864
                                cterm_of thy11 p)]) th;
berghofe@20376
  1865
                          in rtac th' 1 end;
berghofe@20376
  1866
                        val th' = Goal.prove context'' [] []
berghofe@21021
  1867
                          (HOLogic.mk_Trueprop (S $ mk_pi x $ mk_pi y))
berghofe@20376
  1868
                          (fn _ => EVERY
berghofe@20376
  1869
                             (map eqvt_tac pi @
berghofe@20376
  1870
                              [simp_tac (HOL_ss addsimps (fresh_prems' @ freshs2' @
berghofe@20376
  1871
                                 perm_swap @ perm_fresh_fresh)) 1,
berghofe@20376
  1872
                               rtac th 1]))
berghofe@20376
  1873
                      in
berghofe@20376
  1874
                        Simplifier.simplify
berghofe@20376
  1875
                          (HOL_basic_ss addsimps rpi1_pi2_eqs) th'
berghofe@20376
  1876
                      end) rec_prems2;
berghofe@20376
  1877
berghofe@20376
  1878
                    val ihs = filter (fn th => case prop_of th of
berghofe@20376
  1879
                      _ $ (Const ("All", _) $ _) => true | _ => false) prems';
berghofe@20376
  1880
berghofe@21073
  1881
                    (** pi1 o rs = pi2 o vs , rs = pi1^-1 o pi2 o vs **)
berghofe@21073
  1882
                    val _ = warning "step 7: pi1 o rs = pi2 o vs , rs = pi1^-1 o pi2 o vs";
berghofe@21073
  1883
                    val rec_eqns = map (fn (th, ih) =>
berghofe@20376
  1884
                      let
berghofe@20376
  1885
                        val th' = th RS (ih RS spec RS mp) RS sym;
berghofe@20376
  1886
                        val _ $ (_ $ lhs $ rhs) = prop_of th';
berghofe@20376
  1887
                        fun strip_perm (_ $ _ $ t) = strip_perm t
berghofe@20376
  1888
                          | strip_perm t = t;
berghofe@20376
  1889
                      in
berghofe@21073
  1890
                        Goal.prove context'' [] []
berghofe@20376
  1891
                           (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@22311
  1892
                              (fold_rev (mk_perm []) pi1 lhs,
berghofe@22311
  1893
                               fold_rev (mk_perm []) pi2 (strip_perm rhs))))
berghofe@20376
  1894
                           (fn _ => simp_tac (HOL_basic_ss addsimps
berghofe@21073
  1895
                              (th' :: perm_swap)) 1)
berghofe@21073
  1896
                      end) (rec_prems' ~~ ihs);
berghofe@20376
  1897
berghofe@21073
  1898
                    (** as # rs **)
berghofe@21073
  1899
                    val _ = warning "step 8: as # rs";
berghofe@21073
  1900
                    val rec_freshs = List.concat
berghofe@21073
  1901
                      (map (fn (rec_prem, ih) =>
berghofe@20376
  1902
                        let
berghofe@21021
  1903
                          val _ $ (S $ x $ (y as Free (_, T))) =
berghofe@20376
  1904
                            prop_of rec_prem;
berghofe@20376
  1905
                          val k = find_index (equal S) rec_sets;
berghofe@21073
  1906
                          val atoms = List.concat (List.mapPartial (fn (bs, z) =>
berghofe@21073
  1907
                            if z = x then NONE else SOME bs) cargsl')
berghofe@20376
  1908
                        in
berghofe@21073
  1909
                          map (fn a as Free (_, aT) =>
berghofe@21073
  1910
                            let val l = find_index (equal aT) dt_atomTs;
berghofe@21073
  1911
                            in
berghofe@21073
  1912
                              Goal.prove context'' [] []
berghofe@25823
  1913
                                (HOLogic.mk_Trueprop (fresh_const aT T $ a $ y))
berghofe@20376
  1914
                                (fn _ => EVERY
berghofe@20376
  1915
                                   (rtac (List.nth (List.nth (rec_fresh_thms, l), k)) 1 ::
berghofe@20376
  1916
                                    map (fn th => rtac th 1)
berghofe@20376
  1917
                                      (snd (List.nth (finite_thss, l))) @
berghofe@20376
  1918
                                    [rtac rec_prem 1, rtac ih 1,
berghofe@21073
  1919
                                     REPEAT_DETERM (resolve_tac fresh_prems 1)]))
berghofe@21073
  1920
                            end) atoms
berghofe@21073
  1921
                        end) (rec_prems1 ~~ ihs));
berghofe@20376
  1922
berghofe@20376
  1923
                    (** as # fK as ts rs , bs # fK bs us vs **)
berghofe@20376
  1924
                    val _ = warning "step 9: as # fK as ts rs , bs # fK bs us vs";
berghofe@21073
  1925
                    fun prove_fresh_result (a as Free (_, aT)) =
berghofe@20376
  1926
                      Goal.prove context'' [] []
berghofe@25823
  1927
                        (HOLogic.mk_Trueprop (fresh_const aT rT $ a $ rhs'))
berghofe@20376
  1928
                        (fn _ => EVERY
berghofe@20376
  1929
                           [resolve_tac fcbs 1,
berghofe@20376
  1930
                            REPEAT_DETERM (resolve_tac
berghofe@21073
  1931
                              (fresh_prems @ rec_freshs) 1),
berghofe@20411
  1932
                            REPEAT_DETERM (resolve_tac (maps snd rec_fin_supp_thms') 1
berghofe@20411
  1933
                              THEN resolve_tac rec_prems 1),
berghofe@20376
  1934
                            resolve_tac P_ind_ths 1,
berghofe@20376
  1935
                            REPEAT_DETERM (resolve_tac (P_ths @ rec_prems) 1)]);
wenzelm@21365
  1936
berghofe@21073
  1937
                    val fresh_results'' = map prove_fresh_result boundsl;
berghofe@21073
  1938
berghofe@21073
  1939
                    fun prove_fresh_result'' ((a as Free (_, aT), b), th) =
berghofe@21073
  1940
                      let val th' = Goal.prove context'' [] []
berghofe@25823
  1941
                        (HOLogic.mk_Trueprop (fresh_const aT rT $
berghofe@22311
  1942
                            fold_rev (mk_perm []) (rpi2 @ pi1) a $
berghofe@22311
  1943
                            fold_rev (mk_perm []) (rpi2 @ pi1) rhs'))
berghofe@21073
  1944
                        (fn _ => simp_tac (HOL_ss addsimps fresh_bij) 1 THEN
berghofe@21073
  1945
                           rtac th 1)
berghofe@21073
  1946
                      in
berghofe@21073
  1947
                        Goal.prove context'' [] []
berghofe@25823
  1948
                          (HOLogic.mk_Trueprop (fresh_const aT rT $ b $ lhs'))
berghofe@21073
  1949
                          (fn _ => EVERY
berghofe@21073
  1950
                             [cut_facts_tac [th'] 1,
berghofe@25998
  1951
                              full_simp_tac (Simplifier.theory_context thy11 HOL_ss
berghofe@25998
  1952
                                addsimps rec_eqns @ pi1_pi2_eqs @ perm_swap
berghofe@25998
  1953
                                addsimprocs [NominalPermeq.perm_simproc_app]) 1,
berghofe@21073
  1954
                              full_simp_tac (HOL_ss addsimps (calc_atm @
berghofe@21073
  1955
                                fresh_prems' @ freshs2' @ perm_fresh_fresh)) 1])
berghofe@21073
  1956
                      end;
berghofe@21073
  1957
berghofe@21073
  1958
                    val fresh_results = fresh_results'' @ map prove_fresh_result''
berghofe@21073
  1959
                      (boundsl ~~ boundsr ~~ fresh_results'');
berghofe@20376
  1960
berghofe@20376
  1961
                    (** cs # fK as ts rs , cs # fK bs us vs **)
berghofe@20376
  1962
                    val _ = warning "step 10: cs # fK as ts rs , cs # fK bs us vs";
berghofe@20376
  1963
                    fun prove_fresh_result' recs t (a as Free (_, aT)) =
berghofe@20376
  1964
                      Goal.prove context'' [] []
berghofe@25823
  1965
                        (HOLogic.mk_Trueprop (fresh_const aT rT $ a $ t))
berghofe@20376
  1966
                        (fn _ => EVERY
berghofe@20376
  1967
                          [cut_facts_tac recs 1,
berghofe@20376
  1968
                           REPEAT_DETERM (dresolve_tac
berghofe@20376
  1969
                             (the (AList.lookup op = rec_fin_supp_thms' aT)) 1),
berghofe@20376
  1970
                           NominalPermeq.fresh_guess_tac
berghofe@20376
  1971
                             (HOL_ss addsimps (freshs2 @
berghofe@20376
  1972
                                fs_atoms @ fresh_atm @
berghofe@20376
  1973
                                List.concat (map snd finite_thss))) 1]);
berghofe@20376
  1974
berghofe@20376
  1975
                    val fresh_results' =
berghofe@20376
  1976
                      map (prove_fresh_result' rec_prems1 rhs') freshs1 @
berghofe@20376
  1977
                      map (prove_fresh_result' rec_prems2 lhs') freshs1;
berghofe@20376
  1978
berghofe@20376
  1979
                    (** pi1 o (fK as ts rs) = pi2 o (fK bs us vs) **)
berghofe@20376
  1980
                    val _ = warning "step 11: pi1 o (fK as ts rs) = pi2 o (fK bs us vs)";
berghofe@20376
  1981
                    val pi1_pi2_result = Goal.prove context'' [] []
berghofe@20376
  1982
                      (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@22311
  1983
                        (fold_rev (mk_perm []) pi1 rhs', fold_rev (mk_perm []) pi2 lhs')))
berghofe@27450
  1984
                      (fn _ => simp_tac (Simplifier.context context'' HOL_ss
berghofe@27450
  1985
                           addsimps pi1_pi2_eqs @ rec_eqns
berghofe@27450
  1986
                           addsimprocs [NominalPermeq.perm_simproc_app]) 1 THEN
berghofe@20376
  1987
                         TRY (simp_tac (HOL_ss addsimps
berghofe@20376
  1988
                           (fresh_prems' @ freshs2' @ calc_atm @ perm_fresh_fresh)) 1));
berghofe@20376
  1989
berghofe@20376
  1990
                    val _ = warning "final result";
berghofe@20376
  1991
                    val final = Goal.prove context'' [] [] (term_of concl)
berghofe@20376
  1992
                      (fn _ => cut_facts_tac [pi1_pi2_result RS sym] 1 THEN
berghofe@20376
  1993
                        full_simp_tac (HOL_basic_ss addsimps perm_fresh_fresh @
berghofe@20376
  1994
                          fresh_results @ fresh_results') 1);
berghofe@20376
  1995
                    val final' = ProofContext.export context'' context' [final];
berghofe@20376
  1996
                    val _ = warning "finished!"
berghofe@20376
  1997
                  in
berghofe@20376
  1998
                    resolve_tac final' 1
berghofe@20397
  1999
                  end) context 1])) idxss) (ndescr ~~ rec_elims))
berghofe@20397
  2000
         end));
berghofe@20397
  2001
berghofe@20397
  2002
    val rec_total_thms = map (fn r => r RS theI') rec_unique_thms;
berghofe@20397
  2003
berghofe@20397
  2004
    (* define primrec combinators *)
berghofe@20397
  2005
berghofe@20397
  2006
    val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
haftmann@28965
  2007
    val reccomb_names = map (Sign.full_bname thy11)
berghofe@20397
  2008
      (if length descr'' = 1 then [big_reccomb_name] else
berghofe@20397
  2009
        (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
berghofe@20397
  2010
          (1 upto (length descr''))));
berghofe@20397
  2011
    val reccombs = map (fn ((name, T), T') => list_comb
berghofe@20397
  2012
      (Const (name, rec_fn_Ts @ [T] ---> T'), rec_fns))
berghofe@20397
  2013
        (reccomb_names ~~ recTs ~~ rec_result_Ts);
berghofe@20397
  2014
berghofe@20397
  2015
    val (reccomb_defs, thy12) =
berghofe@20397
  2016
      thy11
wenzelm@24712
  2017
      |> Sign.add_consts_i (map (fn ((name, T), T') =>
wenzelm@30364
  2018
          (Binding.name (Long_Name.base_name name), rec_fn_Ts @ [T] ---> T', NoSyn))
berghofe@20397
  2019
          (reccomb_names ~~ recTs ~~ rec_result_Ts))
haftmann@27691
  2020
      |> (PureThy.add_defs false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
wenzelm@30364
  2021
          (Binding.name (Long_Name.base_name name ^ "_def"), Logic.mk_equals (comb, absfree ("x", T,
berghofe@20397
  2022
           Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
berghofe@21021
  2023
             set $ Free ("x", T) $ Free ("y", T'))))))
berghofe@20397
  2024
               (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts));
berghofe@20397
  2025
berghofe@20397
  2026
    (* prove characteristic equations for primrec combinators *)
berghofe@20397
  2027
berghofe@20397
  2028
    val rec_thms = map (fn (prems, concl) =>
berghofe@20397
  2029
      let
berghofe@20397
  2030
        val _ $ (_ $ (_ $ x) $ _) = concl;
berghofe@20397
  2031
        val (_, cargs) = strip_comb x;
berghofe@20397
  2032
        val ps = map (fn (x as Free (_, T), i) =>
berghofe@20397
  2033
          (Free ("x" ^ string_of_int i, T), x)) (cargs ~~ (1 upto length cargs));
berghofe@20397
  2034
        val concl' = subst_atomic_types (rec_result_Ts' ~~ rec_result_Ts) concl;
berghofe@21088
  2035
        val prems' = List.concat finite_premss @ finite_ctxt_prems @
berghofe@21088
  2036
          rec_prems @ rec_prems' @ map (subst_atomic ps) prems;
berghofe@20397
  2037
        fun solve rules prems = resolve_tac rules THEN_ALL_NEW
berghofe@20397
  2038
          (resolve_tac prems THEN_ALL_NEW atac)
berghofe@20397
  2039
      in
berghofe@28731
  2040
        Goal.prove_global thy12 []
berghofe@28731
  2041
          (map (augment_sort thy12 fs_cp_sort) prems')
berghofe@28731
  2042
          (augment_sort thy12 fs_cp_sort concl')
wenzelm@26711
  2043
          (fn {prems, ...} => EVERY
berghofe@20397
  2044
            [rewrite_goals_tac reccomb_defs,
berghofe@20397
  2045
             rtac the1_equality 1,
berghofe@20397
  2046
             solve rec_unique_thms prems 1,
berghofe@20397
  2047
             resolve_tac rec_intrs 1,
berghofe@20397
  2048
             REPEAT (solve (prems @ rec_total_thms) prems 1)])
berghofe@20397
  2049
      end) (rec_eq_prems ~~
berghofe@28731
  2050
        DatatypeProp.make_primrecs new_type_names descr' sorts thy12);
wenzelm@21365
  2051
berghofe@22433
  2052
    val dt_infos = map (make_dt_info pdescr sorts induct reccomb_names rec_thms)
berghofe@21540
  2053
      ((0 upto length descr1 - 1) ~~ descr1 ~~ distinct_thms ~~ inject_thms);
berghofe@21540
  2054
berghofe@19985
  2055
    (* FIXME: theorems are stored in database for testing only *)
berghofe@20397
  2056
    val (_, thy13) = thy12 |>
berghofe@20145
  2057
      PureThy.add_thmss
haftmann@29585
  2058
        [((Binding.name "rec_equiv", List.concat rec_equiv_thms), []),
haftmann@29585
  2059
         ((Binding.name "rec_equiv'", List.concat rec_equiv_thms'), []),
haftmann@29585
  2060
         ((Binding.name "rec_fin_supp", List.concat rec_fin_supp_thms), []),
haftmann@29585
  2061
         ((Binding.name "rec_fresh", List.concat rec_fresh_thms), []),
haftmann@29585
  2062
         ((Binding.name "rec_unique", map standard rec_unique_thms), []),
haftmann@29585
  2063
         ((Binding.name "recs", rec_thms), [])] ||>
wenzelm@24712
  2064
      Sign.parent_path ||>
berghofe@21540
  2065
      map_nominal_datatypes (fold Symtab.update dt_infos);
berghofe@19985
  2066
berghofe@17870
  2067
  in
berghofe@20397
  2068
    thy13
berghofe@17870
  2069
  end;
berghofe@17870
  2070
haftmann@31723
  2071
val add_nominal_datatype = gen_add_nominal_datatype Datatype.read_typ;
berghofe@17870
  2072
berghofe@17870
  2073
haftmann@31723
  2074
(* FIXME: The following stuff should be exported by Datatype *)
berghofe@17870
  2075
berghofe@17870
  2076
local structure P = OuterParse and K = OuterKeyword in
berghofe@17870
  2077
berghofe@17870
  2078
val datatype_decl =
berghofe@17870
  2079
  Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
berghofe@17870
  2080
    (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
berghofe@17870
  2081
berghofe@17870
  2082
fun mk_datatype args =
berghofe@17870
  2083
  let
berghofe@17870
  2084
    val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
berghofe@17870
  2085
    val specs = map (fn ((((_, vs), t), mx), cons) =>
berghofe@17870
  2086
      (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
haftmann@31671
  2087
  in add_nominal_datatype DatatypeAux.default_datatype_config names specs end;
berghofe@17870
  2088
wenzelm@24867
  2089
val _ =
berghofe@17870
  2090
  OuterSyntax.command "nominal_datatype" "define inductive datatypes" K.thy_decl
berghofe@17870
  2091
    (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
berghofe@17870
  2092
berghofe@17870
  2093
end;
berghofe@17870
  2094
berghofe@18261
  2095
end