src/HOL/Tools/datatype_abs_proofs.ML
author blanchet
Mon Feb 09 10:37:59 2009 +0100 (2009-02-09)
changeset 29866 6e93ae65c678
parent 29579 cb520b766e00
child 29927 ae8f42c245b2
permissions -rw-r--r--
Added Nitpick_Const_Psimp attribute, dropped the 's' in Nitpick_Const_Simps, and killed the Nitpick_Ind_Intros attribute.
This should now be all.
berghofe@5177
     1
(*  Title:      HOL/Tools/datatype_abs_proofs.ML
wenzelm@11539
     2
    Author:     Stefan Berghofer, TU Muenchen
berghofe@5177
     3
berghofe@5177
     4
Proofs and defintions independent of concrete representation
berghofe@5177
     5
of datatypes  (i.e. requiring only abstract properties such as
berghofe@5177
     6
injectivity / distinctness of constructors and induction)
berghofe@5177
     7
berghofe@5177
     8
 - case distinction (exhaustion) theorems
berghofe@5177
     9
 - characteristic equations for primrec combinators
berghofe@5177
    10
 - characteristic equations for case combinators
berghofe@5177
    11
 - equations for splitting "P (case ...)" expressions
wenzelm@29264
    12
 - "nchotomy" and "case_cong" theorems for TFL
berghofe@5177
    13
*)
berghofe@5177
    14
berghofe@5177
    15
signature DATATYPE_ABS_PROOFS =
berghofe@5177
    16
sig
berghofe@13641
    17
  val prove_casedist_thms : string list ->
berghofe@13641
    18
    DatatypeAux.descr list -> (string * sort) list -> thm ->
wenzelm@18728
    19
    attribute list -> theory -> thm list * theory
berghofe@13641
    20
  val prove_primrec_thms : bool -> string list ->
berghofe@13641
    21
    DatatypeAux.descr list -> (string * sort) list ->
berghofe@5177
    22
      DatatypeAux.datatype_info Symtab.table -> thm list list -> thm list list ->
haftmann@18314
    23
        simpset -> thm -> theory -> (string list * thm list) * theory
berghofe@13641
    24
  val prove_case_thms : bool -> string list ->
berghofe@13641
    25
    DatatypeAux.descr list -> (string * sort) list ->
haftmann@18314
    26
      string list -> thm list -> theory -> (thm list list * string list) * theory
berghofe@13641
    27
  val prove_split_thms : string list ->
berghofe@13641
    28
    DatatypeAux.descr list -> (string * sort) list ->
berghofe@5177
    29
      thm list list -> thm list list -> thm list -> thm list list -> theory ->
haftmann@18314
    30
        (thm * thm) list * theory
berghofe@13641
    31
  val prove_nchotomys : string list -> DatatypeAux.descr list ->
haftmann@18314
    32
    (string * sort) list -> thm list -> theory -> thm list * theory
berghofe@13641
    33
  val prove_weak_case_congs : string list -> DatatypeAux.descr list ->
haftmann@18314
    34
    (string * sort) list -> theory -> thm list * theory
berghofe@13641
    35
  val prove_case_congs : string list ->
berghofe@13641
    36
    DatatypeAux.descr list -> (string * sort) list ->
haftmann@18314
    37
      thm list -> thm list list -> theory -> thm list * theory
berghofe@5177
    38
end;
berghofe@5177
    39
wenzelm@8436
    40
structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS =
berghofe@5177
    41
struct
berghofe@5177
    42
berghofe@5177
    43
open DatatypeAux;
berghofe@5177
    44
berghofe@5177
    45
(************************ case distinction theorems ***************************)
berghofe@5177
    46
wenzelm@8436
    47
fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy =
berghofe@5177
    48
  let
wenzelm@6427
    49
    val _ = message "Proving case distinction theorems ...";
berghofe@5177
    50
skalberg@15570
    51
    val descr' = List.concat descr;
berghofe@5177
    52
    val recTs = get_rec_types descr' sorts;
skalberg@15570
    53
    val newTs = Library.take (length (hd descr), recTs);
berghofe@5177
    54
berghofe@8477
    55
    val {maxidx, ...} = rep_thm induct;
wenzelm@8305
    56
    val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@5177
    57
berghofe@5177
    58
    fun prove_casedist_thm ((i, t), T) =
berghofe@5177
    59
      let
berghofe@5177
    60
        val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
berghofe@5177
    61
          Abs ("z", T', Const ("True", T''))) induct_Ps;
berghofe@8477
    62
        val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $
berghofe@5177
    63
          Var (("P", 0), HOLogic.boolT))
skalberg@15570
    64
        val insts = Library.take (i, dummyPs) @ (P::(Library.drop (i + 1, dummyPs)));
wenzelm@17985
    65
        val cert = cterm_of thy;
berghofe@5177
    66
        val insts' = (map cert induct_Ps) ~~ (map cert insts);
skalberg@15570
    67
        val induct' = refl RS ((List.nth
skalberg@15570
    68
          (split_conj_thm (cterm_instantiate insts' induct), i)) RSN (2, rev_mp))
berghofe@5177
    69
wenzelm@17985
    70
      in
berghofe@26531
    71
        SkipProof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@26711
    72
          (fn {prems, ...} => EVERY
wenzelm@17985
    73
            [rtac induct' 1,
wenzelm@17985
    74
             REPEAT (rtac TrueI 1),
wenzelm@17985
    75
             REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
wenzelm@20046
    76
             REPEAT (rtac TrueI 1)])
berghofe@5177
    77
      end;
berghofe@5177
    78
berghofe@5177
    79
    val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~
berghofe@5177
    80
      (DatatypeProp.make_casedists descr sorts) ~~ newTs)
haftmann@18314
    81
  in
haftmann@18314
    82
    thy
haftmann@18314
    83
    |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms
haftmann@18314
    84
  end;
berghofe@5177
    85
berghofe@5177
    86
berghofe@5177
    87
(*************************** primrec combinators ******************************)
berghofe@5177
    88
berghofe@5661
    89
fun prove_primrec_thms flat_names new_type_names descr sorts
berghofe@7015
    90
    (dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy =
berghofe@5177
    91
  let
wenzelm@6427
    92
    val _ = message "Constructing primrec combinators ...";
berghofe@5661
    93
berghofe@5661
    94
    val big_name = space_implode "_" new_type_names;
berghofe@5661
    95
    val thy0 = add_path flat_names big_name thy;
berghofe@5177
    96
skalberg@15570
    97
    val descr' = List.concat descr;
berghofe@5177
    98
    val recTs = get_rec_types descr' sorts;
wenzelm@29270
    99
    val used = foldr OldTerm.add_typ_tfree_names [] recTs;
skalberg@15570
   100
    val newTs = Library.take (length (hd descr), recTs);
berghofe@5177
   101
wenzelm@8305
   102
    val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@5177
   103
berghofe@5661
   104
    val big_rec_name' = big_name ^ "_rec_set";
berghofe@21021
   105
    val rec_set_names' =
berghofe@21021
   106
      if length descr' = 1 then [big_rec_name'] else
berghofe@21021
   107
        map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int)
berghofe@21021
   108
          (1 upto (length descr'));
haftmann@28965
   109
    val rec_set_names = map (Sign.full_bname thy0) rec_set_names';
berghofe@5177
   110
berghofe@15459
   111
    val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
berghofe@5177
   112
berghofe@21021
   113
    val rec_set_Ts = map (fn (T1, T2) =>
berghofe@21021
   114
      reccomb_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts);
berghofe@5177
   115
berghofe@5177
   116
    val rec_fns = map (uncurry (mk_Free "f"))
berghofe@5177
   117
      (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
berghofe@21021
   118
    val rec_sets' = map (fn c => list_comb (Free c, rec_fns))
berghofe@21021
   119
      (rec_set_names' ~~ rec_set_Ts);
berghofe@5177
   120
    val rec_sets = map (fn c => list_comb (Const c, rec_fns))
berghofe@5177
   121
      (rec_set_names ~~ rec_set_Ts);
berghofe@5177
   122
berghofe@5177
   123
    (* introduction rules for graph of primrec function *)
berghofe@5177
   124
berghofe@21021
   125
    fun make_rec_intr T rec_set ((rec_intr_ts, l), (cname, cargs)) =
berghofe@5177
   126
      let
berghofe@7015
   127
        fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) =
berghofe@7015
   128
          let val free1 = mk_Free "x" U j
berghofe@13641
   129
          in (case (strip_dtyp dt, strip_type U) of
berghofe@13641
   130
             ((_, DtRec m), (Us, _)) =>
berghofe@13641
   131
               let
skalberg@15570
   132
                 val free2 = mk_Free "y" (Us ---> List.nth (rec_result_Ts, m)) k;
berghofe@13641
   133
                 val i = length Us
berghofe@13641
   134
               in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all
berghofe@21021
   135
                     (map (pair "x") Us, List.nth (rec_sets', m) $
berghofe@21021
   136
                       app_bnds free1 i $ app_bnds free2 i)) :: prems,
berghofe@5177
   137
                   free1::t1s, free2::t2s)
berghofe@5177
   138
               end
berghofe@5177
   139
           | _ => (j + 1, k, prems, free1::t1s, t2s))
berghofe@5177
   140
          end;
berghofe@5177
   141
berghofe@5177
   142
        val Ts = map (typ_of_dtyp descr' sorts) cargs;
skalberg@15574
   143
        val (_, _, prems, t1s, t2s) = foldr mk_prem (1, 1, [], [], []) (cargs ~~ Ts)
berghofe@5177
   144
berghofe@21021
   145
      in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop
berghofe@21021
   146
        (rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $
berghofe@21021
   147
          list_comb (List.nth (rec_fns, l), t1s @ t2s)))], l + 1)
berghofe@5177
   148
      end;
berghofe@5177
   149
skalberg@15570
   150
    val (rec_intr_ts, _) = Library.foldl (fn (x, ((d, T), set_name)) =>
skalberg@15570
   151
      Library.foldl (make_rec_intr T set_name) (x, #3 (snd d)))
berghofe@21021
   152
        (([], 0), descr' ~~ recTs ~~ rec_sets');
berghofe@5177
   153
wenzelm@21365
   154
    val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) =
wenzelm@26475
   155
        InductivePackage.add_inductive_global (serial_string ())
wenzelm@26475
   156
          {quiet_mode = ! quiet_mode, verbose = false, kind = Thm.internalK,
haftmann@28965
   157
            alt_name = Binding.name big_rec_name', coind = false, no_elim = false, no_ind = true,
wenzelm@29389
   158
            skip_mono = true, fork_mono = false}
haftmann@28965
   159
          (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts))
wenzelm@26128
   160
          (map dest_Free rec_fns)
haftmann@28965
   161
          (map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) [] thy0;
berghofe@5177
   162
berghofe@5177
   163
    (* prove uniqueness and termination of primrec combinators *)
berghofe@5177
   164
wenzelm@6427
   165
    val _ = message "Proving termination and uniqueness of primrec functions ...";
berghofe@5177
   166
berghofe@5177
   167
    fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) =
berghofe@5177
   168
      let
berghofe@21021
   169
        val distinct_tac =
berghofe@5177
   170
          (if i < length newTs then
skalberg@15570
   171
             full_simp_tac (HOL_ss addsimps (List.nth (dist_rewrites, i))) 1
berghofe@7015
   172
           else full_simp_tac dist_ss 1);
berghofe@5177
   173
berghofe@5177
   174
        val inject = map (fn r => r RS iffD1)
skalberg@15570
   175
          (if i < length newTs then List.nth (constr_inject, i)
wenzelm@17412
   176
            else #inject (the (Symtab.lookup dt_info tname)));
berghofe@5177
   177
berghofe@5177
   178
        fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) =
berghofe@5177
   179
          let
skalberg@15570
   180
            val k = length (List.filter is_rec_type cargs)
berghofe@5177
   181
berghofe@5177
   182
          in (EVERY [DETERM tac,
berghofe@5177
   183
                REPEAT (etac ex1E 1), rtac ex1I 1,
berghofe@5177
   184
                DEPTH_SOLVE_1 (ares_tac [intr] 1),
berghofe@13641
   185
                REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
berghofe@5177
   186
                etac elim 1,
berghofe@5177
   187
                REPEAT_DETERM_N j distinct_tac,
berghofe@21021
   188
                TRY (dresolve_tac inject 1),
berghofe@5177
   189
                REPEAT (etac conjE 1), hyp_subst_tac 1,
berghofe@13641
   190
                REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
berghofe@5177
   191
                TRY (hyp_subst_tac 1),
berghofe@5177
   192
                rtac refl 1,
berghofe@5177
   193
                REPEAT_DETERM_N (n - j - 1) distinct_tac],
berghofe@5177
   194
              intrs, j + 1)
berghofe@5177
   195
          end;
berghofe@5177
   196
skalberg@15570
   197
        val (tac', intrs', _) = Library.foldl (mk_unique_constr_tac (length constrs))
berghofe@5177
   198
          ((tac, intrs, 0), constrs);
berghofe@5177
   199
berghofe@5177
   200
      in (tac', intrs') end;
berghofe@5177
   201
berghofe@5177
   202
    val rec_unique_thms =
berghofe@5177
   203
      let
berghofe@5177
   204
        val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
berghofe@5177
   205
          Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
berghofe@21021
   206
            absfree ("y", T2, set_t $ mk_Free "x" T1 i $ Free ("y", T2)))
berghofe@21021
   207
              (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
wenzelm@17985
   208
        val cert = cterm_of thy1
berghofe@5177
   209
        val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
berghofe@5177
   210
          ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
berghofe@5177
   211
        val induct' = cterm_instantiate ((map cert induct_Ps) ~~
berghofe@5177
   212
          (map cert insts)) induct;
skalberg@15570
   213
        val (tac, _) = Library.foldl mk_unique_tac
wenzelm@23590
   214
          (((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1
wenzelm@28839
   215
              THEN rewrite_goals_tac [mk_meta_eq choice_eq], rec_intrs),
wenzelm@10911
   216
            descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts);
berghofe@5177
   217
berghofe@26531
   218
      in split_conj_thm (SkipProof.prove_global thy1 [] []
wenzelm@20046
   219
        (HOLogic.mk_Trueprop (mk_conj rec_unique_ts)) (K tac))
berghofe@5177
   220
      end;
berghofe@5177
   221
wenzelm@11435
   222
    val rec_total_thms = map (fn r => r RS theI') rec_unique_thms;
berghofe@5177
   223
berghofe@5177
   224
    (* define primrec combinators *)
berghofe@5177
   225
berghofe@5177
   226
    val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
haftmann@28965
   227
    val reccomb_names = map (Sign.full_bname thy1)
berghofe@5177
   228
      (if length descr' = 1 then [big_reccomb_name] else
berghofe@5177
   229
        (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
berghofe@5177
   230
          (1 upto (length descr'))));
berghofe@5177
   231
    val reccombs = map (fn ((name, T), T') => list_comb
berghofe@5177
   232
      (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
berghofe@5177
   233
        (reccomb_names ~~ recTs ~~ rec_result_Ts);
berghofe@5177
   234
haftmann@18358
   235
    val (reccomb_defs, thy2) =
haftmann@18358
   236
      thy1
wenzelm@24712
   237
      |> Sign.add_consts_i (map (fn ((name, T), T') =>
haftmann@18358
   238
          (Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
haftmann@18358
   239
          (reccomb_names ~~ recTs ~~ rec_result_Ts))
haftmann@27691
   240
      |> (PureThy.add_defs false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
haftmann@29579
   241
          (Binding.name (Sign.base_name name ^ "_def"), Logic.mk_equals (comb, absfree ("x", T,
wenzelm@11435
   242
           Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
berghofe@21021
   243
             set $ Free ("x", T) $ Free ("y", T'))))))
haftmann@18358
   244
               (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts))
wenzelm@28361
   245
      ||> parent_path flat_names
wenzelm@28361
   246
      ||> Theory.checkpoint;
berghofe@5177
   247
berghofe@5177
   248
berghofe@5177
   249
    (* prove characteristic equations for primrec combinators *)
berghofe@5177
   250
wenzelm@6427
   251
    val _ = message "Proving characteristic theorems for primrec combinators ..."
berghofe@5177
   252
berghofe@26531
   253
    val rec_thms = map (fn t => SkipProof.prove_global thy2 [] [] t
wenzelm@17985
   254
      (fn _ => EVERY
wenzelm@17985
   255
        [rewrite_goals_tac reccomb_defs,
wenzelm@17985
   256
         rtac the1_equality 1,
berghofe@5177
   257
         resolve_tac rec_unique_thms 1,
berghofe@5177
   258
         resolve_tac rec_intrs 1,
wenzelm@20046
   259
         REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)]))
berghofe@5177
   260
           (DatatypeProp.make_primrecs new_type_names descr sorts thy2)
berghofe@5177
   261
berghofe@5177
   262
  in
haftmann@18314
   263
    thy2
wenzelm@24712
   264
    |> Sign.add_path (space_implode "_" new_type_names)
haftmann@29579
   265
    |> PureThy.add_thmss [((Binding.name "recs", rec_thms), [])]
wenzelm@24712
   266
    ||> Sign.parent_path
wenzelm@28361
   267
    ||> Theory.checkpoint
haftmann@18314
   268
    |-> (fn thms => pair (reccomb_names, Library.flat thms))
berghofe@5177
   269
  end;
berghofe@5177
   270
berghofe@8477
   271
berghofe@5177
   272
(***************************** case combinators *******************************)
berghofe@5177
   273
berghofe@5661
   274
fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
berghofe@5177
   275
  let
wenzelm@6427
   276
    val _ = message "Proving characteristic theorems for case combinators ...";
berghofe@5661
   277
berghofe@5661
   278
    val thy1 = add_path flat_names (space_implode "_" new_type_names) thy;
berghofe@5177
   279
skalberg@15570
   280
    val descr' = List.concat descr;
berghofe@5177
   281
    val recTs = get_rec_types descr' sorts;
wenzelm@29270
   282
    val used = foldr OldTerm.add_typ_tfree_names [] recTs;
skalberg@15570
   283
    val newTs = Library.take (length (hd descr), recTs);
wenzelm@20071
   284
    val T' = TFree (Name.variant used "'t", HOLogic.typeS);
berghofe@5177
   285
berghofe@13641
   286
    fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T';
berghofe@7015
   287
berghofe@5177
   288
    val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
berghofe@5177
   289
      let
berghofe@5177
   290
        val Ts = map (typ_of_dtyp descr' sorts) cargs;
skalberg@15570
   291
        val Ts' = map mk_dummyT (List.filter is_rec_type cargs)
haftmann@28524
   292
      in Const (@{const_name undefined}, Ts @ Ts' ---> T')
berghofe@5177
   293
      end) constrs) descr';
berghofe@5177
   294
haftmann@28965
   295
    val case_names = map (fn s => Sign.full_bname thy1 (s ^ "_case")) new_type_names;
berghofe@5177
   296
berghofe@5177
   297
    (* define case combinators via primrec combinators *)
berghofe@5177
   298
skalberg@15570
   299
    val (case_defs, thy2) = Library.foldl (fn ((defs, thy),
berghofe@5177
   300
      ((((i, (_, _, constrs)), T), name), recname)) =>
berghofe@5177
   301
        let
berghofe@5177
   302
          val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) =>
berghofe@5177
   303
            let
berghofe@5177
   304
              val Ts = map (typ_of_dtyp descr' sorts) cargs;
skalberg@15570
   305
              val Ts' = Ts @ map mk_dummyT (List.filter is_rec_type cargs);
berghofe@5177
   306
              val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
skalberg@15570
   307
              val frees = Library.take (length cargs, frees');
berghofe@5177
   308
              val free = mk_Free "f" (Ts ---> T') j
berghofe@5177
   309
            in
berghofe@5177
   310
             (free, list_abs_free (map dest_Free frees',
berghofe@5177
   311
               list_comb (free, frees)))
berghofe@5177
   312
            end) (constrs ~~ (1 upto length constrs)));
berghofe@5177
   313
berghofe@5177
   314
          val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
skalberg@15570
   315
          val fns = (List.concat (Library.take (i, case_dummy_fns))) @
skalberg@15570
   316
            fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns)));
berghofe@5177
   317
          val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
haftmann@28965
   318
          val decl = ((Binding.name (Sign.base_name name), caseT), NoSyn);
haftmann@29579
   319
          val def = (Binding.name (Sign.base_name name ^ "_def"),
berghofe@5177
   320
            Logic.mk_equals (list_comb (Const (name, caseT), fns1),
skalberg@15570
   321
              list_comb (reccomb, (List.concat (Library.take (i, case_dummy_fns))) @
skalberg@15570
   322
                fns2 @ (List.concat (Library.drop (i + 1, case_dummy_fns))) )));
haftmann@18358
   323
          val ([def_thm], thy') =
haftmann@18358
   324
            thy
wenzelm@24959
   325
            |> Sign.declare_const [] decl |> snd
haftmann@27691
   326
            |> (PureThy.add_defs false o map Thm.no_attributes) [def];
berghofe@5177
   327
wenzelm@8436
   328
        in (defs @ [def_thm], thy')
berghofe@5661
   329
        end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~
wenzelm@28361
   330
          (Library.take (length newTs, reccomb_names)))
wenzelm@28361
   331
      ||> Theory.checkpoint;
berghofe@5177
   332
berghofe@26531
   333
    val case_thms = map (map (fn t => SkipProof.prove_global thy2 [] [] t
wenzelm@20046
   334
      (fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1])))
berghofe@8477
   335
          (DatatypeProp.make_cases new_type_names descr sorts thy2)
berghofe@8477
   336
  in
haftmann@18314
   337
    thy2
blanchet@29866
   338
    |> Context.the_theory o fold (fold Nitpick_Const_Simp_Thms.add_thm) case_thms
blanchet@29866
   339
       o Context.Theory
haftmann@18314
   340
    |> parent_path flat_names
haftmann@18314
   341
    |> store_thmss "cases" new_type_names case_thms
haftmann@18314
   342
    |-> (fn thmss => pair (thmss, case_names))
berghofe@8477
   343
  end;
berghofe@5177
   344
berghofe@5177
   345
berghofe@5177
   346
(******************************* case splitting *******************************)
berghofe@5177
   347
berghofe@5177
   348
fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites
berghofe@5177
   349
    casedist_thms case_thms thy =
berghofe@5177
   350
  let
wenzelm@6427
   351
    val _ = message "Proving equations for case splitting ...";
berghofe@5177
   352
skalberg@15570
   353
    val descr' = List.concat descr;
berghofe@5177
   354
    val recTs = get_rec_types descr' sorts;
skalberg@15570
   355
    val newTs = Library.take (length (hd descr), recTs);
berghofe@5177
   356
berghofe@5177
   357
    fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
berghofe@5177
   358
        exhaustion), case_thms'), T) =
berghofe@5177
   359
      let
wenzelm@17985
   360
        val cert = cterm_of thy;
berghofe@5177
   361
        val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
berghofe@5177
   362
        val exhaustion' = cterm_instantiate
berghofe@5177
   363
          [(cert lhs, cert (Free ("x", T)))] exhaustion;
wenzelm@17985
   364
        val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
wenzelm@17985
   365
          (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))])
berghofe@5177
   366
      in
berghofe@26531
   367
        (SkipProof.prove_global thy [] [] t1 tacf,
berghofe@26531
   368
         SkipProof.prove_global thy [] [] t2 tacf)
berghofe@5177
   369
      end;
berghofe@5177
   370
berghofe@5177
   371
    val split_thm_pairs = map prove_split_thms
berghofe@5177
   372
      ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
berghofe@5177
   373
        dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
berghofe@5177
   374
berghofe@5177
   375
    val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
berghofe@5177
   376
berghofe@5177
   377
  in
haftmann@18314
   378
    thy
haftmann@18314
   379
    |> store_thms "split" new_type_names split_thms
haftmann@18314
   380
    ||>> store_thms "split_asm" new_type_names split_asm_thms
haftmann@18314
   381
    |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2))
berghofe@5177
   382
  end;
berghofe@5177
   383
nipkow@8601
   384
fun prove_weak_case_congs new_type_names descr sorts thy =
nipkow@8601
   385
  let
nipkow@8601
   386
    fun prove_weak_case_cong t =
berghofe@26531
   387
       SkipProof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@26711
   388
         (fn {prems, ...} => EVERY [rtac ((hd prems) RS arg_cong) 1])
nipkow@8601
   389
nipkow@8601
   390
    val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs
nipkow@8601
   391
      new_type_names descr sorts thy)
nipkow@8601
   392
nipkow@8601
   393
  in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end;
berghofe@8477
   394
berghofe@5177
   395
(************************* additional theorems for TFL ************************)
berghofe@5177
   396
berghofe@5177
   397
fun prove_nchotomys new_type_names descr sorts casedist_thms thy =
berghofe@5177
   398
  let
wenzelm@6427
   399
    val _ = message "Proving additional theorems for TFL ...";
berghofe@5177
   400
berghofe@5177
   401
    fun prove_nchotomy (t, exhaustion) =
berghofe@5177
   402
      let
berghofe@5177
   403
        (* For goal i, select the correct disjunct to attack, then prove it *)
berghofe@5177
   404
        fun tac i 0 = EVERY [TRY (rtac disjI1 i),
berghofe@5177
   405
              hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
berghofe@5177
   406
          | tac i n = rtac disjI2 i THEN tac i (n - 1)
berghofe@5177
   407
      in 
berghofe@26531
   408
        SkipProof.prove_global thy [] [] t (fn _ =>
wenzelm@17985
   409
          EVERY [rtac allI 1,
berghofe@5177
   410
           exh_tac (K exhaustion) 1,
wenzelm@20046
   411
           ALLGOALS (fn i => tac i (i-1))])
berghofe@5177
   412
      end;
berghofe@5177
   413
berghofe@5177
   414
    val nchotomys =
berghofe@5177
   415
      map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
berghofe@5177
   416
wenzelm@8436
   417
  in thy |> store_thms "nchotomy" new_type_names nchotomys end;
berghofe@5177
   418
berghofe@5177
   419
fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
berghofe@5177
   420
  let
berghofe@5177
   421
    fun prove_case_cong ((t, nchotomy), case_rewrites) =
berghofe@5177
   422
      let
berghofe@5177
   423
        val (Const ("==>", _) $ tm $ _) = t;
berghofe@5177
   424
        val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
wenzelm@22578
   425
        val cert = cterm_of thy;
berghofe@5177
   426
        val nchotomy' = nchotomy RS spec;
wenzelm@29264
   427
        val [v] = Term.add_vars (concl_of nchotomy') [];
wenzelm@29264
   428
        val nchotomy'' = cterm_instantiate [(cert (Var v), cert Ma)] nchotomy'
berghofe@5177
   429
      in
berghofe@26531
   430
        SkipProof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@26711
   431
          (fn {prems, ...} => 
wenzelm@17985
   432
            let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
wenzelm@17985
   433
            in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1,
wenzelm@17985
   434
                cut_facts_tac [nchotomy''] 1,
wenzelm@17985
   435
                REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
wenzelm@17985
   436
                REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
wenzelm@20046
   437
            end)
berghofe@5177
   438
      end;
berghofe@5177
   439
berghofe@5177
   440
    val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
berghofe@5177
   441
      new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
berghofe@5177
   442
wenzelm@8436
   443
  in thy |> store_thms "case_cong" new_type_names case_congs end;
berghofe@5177
   444
berghofe@5177
   445
end;