src/HOL/Tools/Datatype/datatype_abs_proofs.ML
author wenzelm
Thu Nov 12 22:02:11 2009 +0100 (2009-11-12)
changeset 33643 b275f26a638b
parent 33459 a4a38ed813f7
child 33669 ae9a2ea9a989
permissions -rw-r--r--
eliminated obsolete "internal" kind -- collapsed to unspecific "";
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
haftmann@31737
    17
  include DATATYPE_COMMON
haftmann@31737
    18
  val prove_casedist_thms : config -> string list ->
haftmann@31668
    19
    descr list -> (string * sort) list -> thm ->
wenzelm@18728
    20
    attribute list -> theory -> thm list * theory
haftmann@31737
    21
  val prove_primrec_thms : config -> string list ->
haftmann@31668
    22
    descr list -> (string * sort) list ->
haftmann@32915
    23
      (string -> thm list) -> thm list list -> thm list list * thm list list ->
haftmann@32915
    24
        thm -> theory -> (string list * thm list) * theory
haftmann@31737
    25
  val prove_case_thms : config -> string list ->
haftmann@31668
    26
    descr list -> (string * sort) list ->
haftmann@18314
    27
      string list -> thm list -> theory -> (thm list list * string list) * theory
haftmann@31737
    28
  val prove_split_thms : config -> string list ->
haftmann@31668
    29
    descr list -> (string * sort) list ->
berghofe@5177
    30
      thm list list -> thm list list -> thm list -> thm list list -> theory ->
haftmann@18314
    31
        (thm * thm) list * theory
haftmann@31737
    32
  val prove_nchotomys : config -> string list -> descr list ->
haftmann@18314
    33
    (string * sort) list -> thm list -> theory -> thm list * theory
haftmann@31668
    34
  val prove_weak_case_congs : string list -> descr list ->
haftmann@18314
    35
    (string * sort) list -> theory -> thm list * theory
berghofe@13641
    36
  val prove_case_congs : string list ->
haftmann@31668
    37
    descr list -> (string * sort) list ->
haftmann@18314
    38
      thm list -> thm list list -> theory -> thm list * theory
berghofe@5177
    39
end;
berghofe@5177
    40
wenzelm@8436
    41
structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS =
berghofe@5177
    42
struct
berghofe@5177
    43
berghofe@5177
    44
open DatatypeAux;
berghofe@5177
    45
berghofe@5177
    46
(************************ case distinction theorems ***************************)
berghofe@5177
    47
haftmann@31737
    48
fun prove_casedist_thms (config : config) new_type_names descr sorts induct case_names_exhausts thy =
berghofe@5177
    49
  let
haftmann@31668
    50
    val _ = message config "Proving case distinction theorems ...";
berghofe@5177
    51
wenzelm@32952
    52
    val descr' = flat descr;
berghofe@5177
    53
    val recTs = get_rec_types descr' sorts;
skalberg@15570
    54
    val newTs = Library.take (length (hd descr), recTs);
berghofe@5177
    55
berghofe@8477
    56
    val {maxidx, ...} = rep_thm induct;
wenzelm@8305
    57
    val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@5177
    58
haftmann@33063
    59
    fun prove_casedist_thm (i, (T, t)) =
berghofe@5177
    60
      let
berghofe@5177
    61
        val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
berghofe@5177
    62
          Abs ("z", T', Const ("True", T''))) induct_Ps;
berghofe@8477
    63
        val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $
berghofe@5177
    64
          Var (("P", 0), HOLogic.boolT))
skalberg@15570
    65
        val insts = Library.take (i, dummyPs) @ (P::(Library.drop (i + 1, dummyPs)));
wenzelm@17985
    66
        val cert = cterm_of thy;
berghofe@5177
    67
        val insts' = (map cert induct_Ps) ~~ (map cert insts);
haftmann@32905
    68
        val induct' = refl RS ((nth
haftmann@32905
    69
          (split_conj_thm (cterm_instantiate insts' induct)) i) RSN (2, rev_mp))
berghofe@5177
    70
wenzelm@17985
    71
      in
wenzelm@32970
    72
        Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@26711
    73
          (fn {prems, ...} => EVERY
wenzelm@17985
    74
            [rtac induct' 1,
wenzelm@17985
    75
             REPEAT (rtac TrueI 1),
wenzelm@17985
    76
             REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
wenzelm@20046
    77
             REPEAT (rtac TrueI 1)])
berghofe@5177
    78
      end;
berghofe@5177
    79
haftmann@33063
    80
    val casedist_thms = map_index prove_casedist_thm
haftmann@33063
    81
      (newTs ~~ DatatypeProp.make_casedists descr sorts)
haftmann@18314
    82
  in
haftmann@18314
    83
    thy
haftmann@18314
    84
    |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms
haftmann@18314
    85
  end;
berghofe@5177
    86
berghofe@5177
    87
berghofe@5177
    88
(*************************** primrec combinators ******************************)
berghofe@5177
    89
haftmann@31737
    90
fun prove_primrec_thms (config : config) new_type_names descr sorts
haftmann@32915
    91
    injects_of constr_inject (dist_rewrites, other_dist_rewrites) induct thy =
berghofe@5177
    92
  let
haftmann@31668
    93
    val _ = message config "Constructing primrec combinators ...";
berghofe@5661
    94
berghofe@5661
    95
    val big_name = space_implode "_" new_type_names;
haftmann@32124
    96
    val thy0 = Sign.add_path big_name thy;
berghofe@5177
    97
wenzelm@32952
    98
    val descr' = flat descr;
berghofe@5177
    99
    val recTs = get_rec_types descr' sorts;
wenzelm@30190
   100
    val used = List.foldr OldTerm.add_typ_tfree_names [] recTs;
skalberg@15570
   101
    val newTs = Library.take (length (hd descr), recTs);
berghofe@5177
   102
wenzelm@8305
   103
    val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@5177
   104
berghofe@5661
   105
    val big_rec_name' = big_name ^ "_rec_set";
berghofe@21021
   106
    val rec_set_names' =
berghofe@21021
   107
      if length descr' = 1 then [big_rec_name'] else
berghofe@21021
   108
        map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int)
berghofe@21021
   109
          (1 upto (length descr'));
haftmann@28965
   110
    val rec_set_names = map (Sign.full_bname thy0) rec_set_names';
berghofe@5177
   111
berghofe@15459
   112
    val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
berghofe@5177
   113
berghofe@21021
   114
    val rec_set_Ts = map (fn (T1, T2) =>
berghofe@21021
   115
      reccomb_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts);
berghofe@5177
   116
berghofe@5177
   117
    val rec_fns = map (uncurry (mk_Free "f"))
berghofe@5177
   118
      (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
berghofe@21021
   119
    val rec_sets' = map (fn c => list_comb (Free c, rec_fns))
berghofe@21021
   120
      (rec_set_names' ~~ rec_set_Ts);
berghofe@5177
   121
    val rec_sets = map (fn c => list_comb (Const c, rec_fns))
berghofe@5177
   122
      (rec_set_names ~~ rec_set_Ts);
berghofe@5177
   123
berghofe@5177
   124
    (* introduction rules for graph of primrec function *)
berghofe@5177
   125
haftmann@32906
   126
    fun make_rec_intr T rec_set (cname, cargs) (rec_intr_ts, l) =
berghofe@5177
   127
      let
wenzelm@33338
   128
        fun mk_prem (dt, U) (j, k, prems, t1s, t2s) =
berghofe@7015
   129
          let val free1 = mk_Free "x" U j
berghofe@13641
   130
          in (case (strip_dtyp dt, strip_type U) of
berghofe@13641
   131
             ((_, DtRec m), (Us, _)) =>
berghofe@13641
   132
               let
haftmann@32905
   133
                 val free2 = mk_Free "y" (Us ---> nth rec_result_Ts m) k;
berghofe@13641
   134
                 val i = length Us
berghofe@13641
   135
               in (j + 1, k + 1, HOLogic.mk_Trueprop (HOLogic.list_all
haftmann@32905
   136
                     (map (pair "x") Us, nth rec_sets' m $
berghofe@21021
   137
                       app_bnds free1 i $ app_bnds free2 i)) :: prems,
berghofe@5177
   138
                   free1::t1s, free2::t2s)
berghofe@5177
   139
               end
berghofe@5177
   140
           | _ => (j + 1, k, prems, free1::t1s, t2s))
berghofe@5177
   141
          end;
berghofe@5177
   142
berghofe@5177
   143
        val Ts = map (typ_of_dtyp descr' sorts) cargs;
wenzelm@33338
   144
        val (_, _, prems, t1s, t2s) = fold_rev mk_prem (cargs ~~ Ts) (1, 1, [], [], [])
berghofe@5177
   145
berghofe@21021
   146
      in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop
berghofe@21021
   147
        (rec_set $ list_comb (Const (cname, Ts ---> T), t1s) $
haftmann@32905
   148
          list_comb (nth rec_fns l, t1s @ t2s)))], l + 1)
berghofe@5177
   149
      end;
berghofe@5177
   150
haftmann@32906
   151
    val (rec_intr_ts, _) = fold (fn ((d, T), set_name) =>
haftmann@32906
   152
      fold (make_rec_intr T set_name) (#3 (snd d)))
haftmann@32906
   153
        (descr' ~~ recTs ~~ rec_sets') ([], 0);
berghofe@5177
   154
wenzelm@21365
   155
    val ({intrs = rec_intrs, elims = rec_elims, ...}, thy1) =
wenzelm@33278
   156
      thy0
wenzelm@33278
   157
      |> Sign.map_naming Name_Space.conceal
wenzelm@33278
   158
      |> Inductive.add_inductive_global (serial ())
wenzelm@33643
   159
          {quiet_mode = #quiet config, verbose = false, kind = "",
haftmann@28965
   160
            alt_name = Binding.name big_rec_name', coind = false, no_elim = false, no_ind = true,
wenzelm@29389
   161
            skip_mono = true, fork_mono = false}
haftmann@28965
   162
          (map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts))
wenzelm@26128
   163
          (map dest_Free rec_fns)
wenzelm@33278
   164
          (map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) []
wenzelm@33278
   165
      ||> Sign.restore_naming thy0
wenzelm@33278
   166
      ||> Theory.checkpoint;
berghofe@5177
   167
berghofe@5177
   168
    (* prove uniqueness and termination of primrec combinators *)
berghofe@5177
   169
haftmann@31668
   170
    val _ = message config "Proving termination and uniqueness of primrec functions ...";
berghofe@5177
   171
haftmann@32906
   172
    fun mk_unique_tac ((((i, (tname, _, constrs)), elim), T), T') (tac, intrs) =
berghofe@5177
   173
      let
berghofe@21021
   174
        val distinct_tac =
berghofe@5177
   175
          (if i < length newTs then
haftmann@32905
   176
             full_simp_tac (HOL_ss addsimps (nth dist_rewrites i)) 1
haftmann@32915
   177
           else full_simp_tac (HOL_ss addsimps (flat other_dist_rewrites)) 1);
berghofe@5177
   178
berghofe@5177
   179
        val inject = map (fn r => r RS iffD1)
haftmann@32905
   180
          (if i < length newTs then nth constr_inject i
haftmann@32729
   181
            else injects_of tname);
berghofe@5177
   182
haftmann@32906
   183
        fun mk_unique_constr_tac n (cname, cargs) (tac, intr::intrs, j) =
berghofe@5177
   184
          let
haftmann@32729
   185
            val k = length (filter is_rec_type cargs)
berghofe@5177
   186
berghofe@5177
   187
          in (EVERY [DETERM tac,
berghofe@5177
   188
                REPEAT (etac ex1E 1), rtac ex1I 1,
berghofe@5177
   189
                DEPTH_SOLVE_1 (ares_tac [intr] 1),
berghofe@13641
   190
                REPEAT_DETERM_N k (etac thin_rl 1 THEN rotate_tac 1 1),
berghofe@5177
   191
                etac elim 1,
berghofe@5177
   192
                REPEAT_DETERM_N j distinct_tac,
berghofe@21021
   193
                TRY (dresolve_tac inject 1),
berghofe@5177
   194
                REPEAT (etac conjE 1), hyp_subst_tac 1,
berghofe@13641
   195
                REPEAT (EVERY [etac allE 1, dtac mp 1, atac 1]),
berghofe@5177
   196
                TRY (hyp_subst_tac 1),
berghofe@5177
   197
                rtac refl 1,
berghofe@5177
   198
                REPEAT_DETERM_N (n - j - 1) distinct_tac],
berghofe@5177
   199
              intrs, j + 1)
berghofe@5177
   200
          end;
berghofe@5177
   201
haftmann@32906
   202
        val (tac', intrs', _) = fold (mk_unique_constr_tac (length constrs))
haftmann@32906
   203
          constrs (tac, intrs, 0);
berghofe@5177
   204
berghofe@5177
   205
      in (tac', intrs') end;
berghofe@5177
   206
berghofe@5177
   207
    val rec_unique_thms =
berghofe@5177
   208
      let
berghofe@5177
   209
        val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
berghofe@5177
   210
          Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
berghofe@21021
   211
            absfree ("y", T2, set_t $ mk_Free "x" T1 i $ Free ("y", T2)))
berghofe@21021
   212
              (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
wenzelm@17985
   213
        val cert = cterm_of thy1
berghofe@5177
   214
        val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
berghofe@5177
   215
          ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
berghofe@5177
   216
        val induct' = cterm_instantiate ((map cert induct_Ps) ~~
berghofe@5177
   217
          (map cert insts)) induct;
haftmann@32906
   218
        val (tac, _) = fold mk_unique_tac (descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts)
haftmann@32906
   219
           (((rtac induct' THEN_ALL_NEW ObjectLogic.atomize_prems_tac) 1
haftmann@32906
   220
              THEN rewrite_goals_tac [mk_meta_eq choice_eq], rec_intrs));
berghofe@5177
   221
wenzelm@32970
   222
      in split_conj_thm (Skip_Proof.prove_global thy1 [] []
wenzelm@20046
   223
        (HOLogic.mk_Trueprop (mk_conj rec_unique_ts)) (K tac))
berghofe@5177
   224
      end;
berghofe@5177
   225
wenzelm@11435
   226
    val rec_total_thms = map (fn r => r RS theI') rec_unique_thms;
berghofe@5177
   227
berghofe@5177
   228
    (* define primrec combinators *)
berghofe@5177
   229
berghofe@5177
   230
    val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
haftmann@28965
   231
    val reccomb_names = map (Sign.full_bname thy1)
berghofe@5177
   232
      (if length descr' = 1 then [big_reccomb_name] else
berghofe@5177
   233
        (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
berghofe@5177
   234
          (1 upto (length descr'))));
berghofe@5177
   235
    val reccombs = map (fn ((name, T), T') => list_comb
berghofe@5177
   236
      (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
berghofe@5177
   237
        (reccomb_names ~~ recTs ~~ rec_result_Ts);
berghofe@5177
   238
haftmann@18358
   239
    val (reccomb_defs, thy2) =
haftmann@18358
   240
      thy1
wenzelm@24712
   241
      |> Sign.add_consts_i (map (fn ((name, T), T') =>
wenzelm@30364
   242
          (Binding.name (Long_Name.base_name name), reccomb_fn_Ts @ [T] ---> T', NoSyn))
haftmann@18358
   243
          (reccomb_names ~~ recTs ~~ rec_result_Ts))
haftmann@27691
   244
      |> (PureThy.add_defs false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
wenzelm@30364
   245
          (Binding.name (Long_Name.base_name name ^ "_def"), Logic.mk_equals (comb, absfree ("x", T,
wenzelm@11435
   246
           Const ("The", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
berghofe@21021
   247
             set $ Free ("x", T) $ Free ("y", T'))))))
haftmann@18358
   248
               (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts))
haftmann@32124
   249
      ||> Sign.parent_path
wenzelm@28361
   250
      ||> Theory.checkpoint;
berghofe@5177
   251
berghofe@5177
   252
berghofe@5177
   253
    (* prove characteristic equations for primrec combinators *)
berghofe@5177
   254
haftmann@31668
   255
    val _ = message config "Proving characteristic theorems for primrec combinators ..."
berghofe@5177
   256
wenzelm@32970
   257
    val rec_thms = map (fn t => Skip_Proof.prove_global thy2 [] [] t
wenzelm@17985
   258
      (fn _ => EVERY
wenzelm@17985
   259
        [rewrite_goals_tac reccomb_defs,
wenzelm@17985
   260
         rtac the1_equality 1,
berghofe@5177
   261
         resolve_tac rec_unique_thms 1,
berghofe@5177
   262
         resolve_tac rec_intrs 1,
wenzelm@20046
   263
         REPEAT (rtac allI 1 ORELSE resolve_tac rec_total_thms 1)]))
berghofe@5177
   264
           (DatatypeProp.make_primrecs new_type_names descr sorts thy2)
berghofe@5177
   265
berghofe@5177
   266
  in
haftmann@18314
   267
    thy2
wenzelm@24712
   268
    |> Sign.add_path (space_implode "_" new_type_names)
blanchet@33056
   269
    |> PureThy.add_thmss [((Binding.name "recs", rec_thms), [Nitpick_Simps.add])]
wenzelm@24712
   270
    ||> Sign.parent_path
wenzelm@28361
   271
    ||> Theory.checkpoint
haftmann@32906
   272
    |-> (fn thms => pair (reccomb_names, flat thms))
berghofe@5177
   273
  end;
berghofe@5177
   274
berghofe@8477
   275
berghofe@5177
   276
(***************************** case combinators *******************************)
berghofe@5177
   277
haftmann@31737
   278
fun prove_case_thms (config : config) new_type_names descr sorts reccomb_names primrec_thms thy =
berghofe@5177
   279
  let
haftmann@31668
   280
    val _ = message config "Proving characteristic theorems for case combinators ...";
berghofe@5661
   281
haftmann@32124
   282
    val thy1 = Sign.add_path (space_implode "_" new_type_names) thy;
berghofe@5177
   283
wenzelm@32952
   284
    val descr' = flat descr;
berghofe@5177
   285
    val recTs = get_rec_types descr' sorts;
wenzelm@30190
   286
    val used = List.foldr OldTerm.add_typ_tfree_names [] recTs;
skalberg@15570
   287
    val newTs = Library.take (length (hd descr), recTs);
wenzelm@20071
   288
    val T' = TFree (Name.variant used "'t", HOLogic.typeS);
berghofe@5177
   289
berghofe@13641
   290
    fun mk_dummyT dt = binder_types (typ_of_dtyp descr' sorts dt) ---> T';
berghofe@7015
   291
berghofe@5177
   292
    val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
berghofe@5177
   293
      let
berghofe@5177
   294
        val Ts = map (typ_of_dtyp descr' sorts) cargs;
wenzelm@33317
   295
        val Ts' = map mk_dummyT (filter is_rec_type cargs)
haftmann@28524
   296
      in Const (@{const_name undefined}, Ts @ Ts' ---> T')
berghofe@5177
   297
      end) constrs) descr';
berghofe@5177
   298
haftmann@28965
   299
    val case_names = map (fn s => Sign.full_bname thy1 (s ^ "_case")) new_type_names;
berghofe@5177
   300
berghofe@5177
   301
    (* define case combinators via primrec combinators *)
berghofe@5177
   302
haftmann@32906
   303
    val (case_defs, thy2) = fold (fn ((((i, (_, _, constrs)), T), name), recname) => fn (defs, thy) =>
berghofe@5177
   304
        let
haftmann@32906
   305
          val (fns1, fns2) = split_list (map (fn ((_, cargs), j) =>
berghofe@5177
   306
            let
berghofe@5177
   307
              val Ts = map (typ_of_dtyp descr' sorts) cargs;
wenzelm@33317
   308
              val Ts' = Ts @ map mk_dummyT (filter is_rec_type cargs);
berghofe@5177
   309
              val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
skalberg@15570
   310
              val frees = Library.take (length cargs, frees');
berghofe@5177
   311
              val free = mk_Free "f" (Ts ---> T') j
berghofe@5177
   312
            in
berghofe@5177
   313
             (free, list_abs_free (map dest_Free frees',
berghofe@5177
   314
               list_comb (free, frees)))
berghofe@5177
   315
            end) (constrs ~~ (1 upto length constrs)));
berghofe@5177
   316
berghofe@5177
   317
          val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
wenzelm@32952
   318
          val fns = flat (Library.take (i, case_dummy_fns)) @
wenzelm@32952
   319
            fns2 @ flat (Library.drop (i + 1, case_dummy_fns));
berghofe@5177
   320
          val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
wenzelm@30364
   321
          val decl = ((Binding.name (Long_Name.base_name name), caseT), NoSyn);
wenzelm@30364
   322
          val def = (Binding.name (Long_Name.base_name name ^ "_def"),
berghofe@5177
   323
            Logic.mk_equals (list_comb (Const (name, caseT), fns1),
wenzelm@32952
   324
              list_comb (reccomb, (flat (Library.take (i, case_dummy_fns))) @
wenzelm@32952
   325
                fns2 @ (flat (Library.drop (i + 1, case_dummy_fns))) )));
haftmann@18358
   326
          val ([def_thm], thy') =
haftmann@18358
   327
            thy
wenzelm@33173
   328
            |> Sign.declare_const decl |> snd
haftmann@27691
   329
            |> (PureThy.add_defs false o map Thm.no_attributes) [def];
berghofe@5177
   330
wenzelm@8436
   331
        in (defs @ [def_thm], thy')
haftmann@32906
   332
        end) (hd descr ~~ newTs ~~ case_names ~~
haftmann@32906
   333
          Library.take (length newTs, reccomb_names)) ([], thy1)
wenzelm@28361
   334
      ||> Theory.checkpoint;
berghofe@5177
   335
wenzelm@32970
   336
    val case_thms = map (map (fn t => Skip_Proof.prove_global thy2 [] [] t
wenzelm@20046
   337
      (fn _ => EVERY [rewrite_goals_tac (case_defs @ map mk_meta_eq primrec_thms), rtac refl 1])))
berghofe@8477
   338
          (DatatypeProp.make_cases new_type_names descr sorts thy2)
berghofe@8477
   339
  in
haftmann@18314
   340
    thy2
wenzelm@33459
   341
    |> Context.theory_map ((fold o fold) Nitpick_Simps.add_thm case_thms)
haftmann@32124
   342
    |> Sign.parent_path
haftmann@18314
   343
    |> store_thmss "cases" new_type_names case_thms
haftmann@18314
   344
    |-> (fn thmss => pair (thmss, case_names))
berghofe@8477
   345
  end;
berghofe@5177
   346
berghofe@5177
   347
berghofe@5177
   348
(******************************* case splitting *******************************)
berghofe@5177
   349
haftmann@31737
   350
fun prove_split_thms (config : config) new_type_names descr sorts constr_inject dist_rewrites
berghofe@5177
   351
    casedist_thms case_thms thy =
berghofe@5177
   352
  let
haftmann@31668
   353
    val _ = message config "Proving equations for case splitting ...";
berghofe@5177
   354
haftmann@31668
   355
    val descr' = flat descr;
berghofe@5177
   356
    val recTs = get_rec_types descr' sorts;
skalberg@15570
   357
    val newTs = Library.take (length (hd descr), recTs);
berghofe@5177
   358
berghofe@5177
   359
    fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
berghofe@5177
   360
        exhaustion), case_thms'), T) =
berghofe@5177
   361
      let
wenzelm@17985
   362
        val cert = cterm_of thy;
berghofe@5177
   363
        val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
berghofe@5177
   364
        val exhaustion' = cterm_instantiate
berghofe@5177
   365
          [(cert lhs, cert (Free ("x", T)))] exhaustion;
wenzelm@17985
   366
        val tacf = K (EVERY [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
wenzelm@17985
   367
          (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))])
berghofe@5177
   368
      in
wenzelm@32970
   369
        (Skip_Proof.prove_global thy [] [] t1 tacf,
wenzelm@32970
   370
         Skip_Proof.prove_global thy [] [] t2 tacf)
berghofe@5177
   371
      end;
berghofe@5177
   372
berghofe@5177
   373
    val split_thm_pairs = map prove_split_thms
berghofe@5177
   374
      ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
berghofe@5177
   375
        dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
berghofe@5177
   376
berghofe@5177
   377
    val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
berghofe@5177
   378
berghofe@5177
   379
  in
haftmann@18314
   380
    thy
haftmann@18314
   381
    |> store_thms "split" new_type_names split_thms
haftmann@18314
   382
    ||>> store_thms "split_asm" new_type_names split_asm_thms
haftmann@18314
   383
    |-> (fn (thms1, thms2) => pair (thms1 ~~ thms2))
berghofe@5177
   384
  end;
berghofe@5177
   385
nipkow@8601
   386
fun prove_weak_case_congs new_type_names descr sorts thy =
nipkow@8601
   387
  let
nipkow@8601
   388
    fun prove_weak_case_cong t =
wenzelm@32970
   389
       Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@26711
   390
         (fn {prems, ...} => EVERY [rtac ((hd prems) RS arg_cong) 1])
nipkow@8601
   391
nipkow@8601
   392
    val weak_case_congs = map prove_weak_case_cong (DatatypeProp.make_weak_case_congs
nipkow@8601
   393
      new_type_names descr sorts thy)
nipkow@8601
   394
nipkow@8601
   395
  in thy |> store_thms "weak_case_cong" new_type_names weak_case_congs end;
berghofe@8477
   396
berghofe@5177
   397
(************************* additional theorems for TFL ************************)
berghofe@5177
   398
haftmann@31737
   399
fun prove_nchotomys (config : config) new_type_names descr sorts casedist_thms thy =
berghofe@5177
   400
  let
haftmann@31668
   401
    val _ = message config "Proving additional theorems for TFL ...";
berghofe@5177
   402
berghofe@5177
   403
    fun prove_nchotomy (t, exhaustion) =
berghofe@5177
   404
      let
berghofe@5177
   405
        (* For goal i, select the correct disjunct to attack, then prove it *)
berghofe@5177
   406
        fun tac i 0 = EVERY [TRY (rtac disjI1 i),
berghofe@5177
   407
              hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
berghofe@5177
   408
          | tac i n = rtac disjI2 i THEN tac i (n - 1)
berghofe@5177
   409
      in 
wenzelm@32970
   410
        Skip_Proof.prove_global thy [] [] t (fn _ =>
wenzelm@17985
   411
          EVERY [rtac allI 1,
berghofe@5177
   412
           exh_tac (K exhaustion) 1,
wenzelm@20046
   413
           ALLGOALS (fn i => tac i (i-1))])
berghofe@5177
   414
      end;
berghofe@5177
   415
berghofe@5177
   416
    val nchotomys =
berghofe@5177
   417
      map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
berghofe@5177
   418
wenzelm@8436
   419
  in thy |> store_thms "nchotomy" new_type_names nchotomys end;
berghofe@5177
   420
berghofe@5177
   421
fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
berghofe@5177
   422
  let
berghofe@5177
   423
    fun prove_case_cong ((t, nchotomy), case_rewrites) =
berghofe@5177
   424
      let
berghofe@5177
   425
        val (Const ("==>", _) $ tm $ _) = t;
berghofe@5177
   426
        val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
wenzelm@22578
   427
        val cert = cterm_of thy;
berghofe@5177
   428
        val nchotomy' = nchotomy RS spec;
wenzelm@29264
   429
        val [v] = Term.add_vars (concl_of nchotomy') [];
wenzelm@29264
   430
        val nchotomy'' = cterm_instantiate [(cert (Var v), cert Ma)] nchotomy'
berghofe@5177
   431
      in
wenzelm@32970
   432
        Skip_Proof.prove_global thy [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
wenzelm@26711
   433
          (fn {prems, ...} => 
wenzelm@17985
   434
            let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
wenzelm@17985
   435
            in EVERY [simp_tac (HOL_ss addsimps [hd prems]) 1,
wenzelm@17985
   436
                cut_facts_tac [nchotomy''] 1,
wenzelm@17985
   437
                REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
wenzelm@17985
   438
                REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
wenzelm@20046
   439
            end)
berghofe@5177
   440
      end;
berghofe@5177
   441
berghofe@5177
   442
    val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
berghofe@5177
   443
      new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
berghofe@5177
   444
wenzelm@8436
   445
  in thy |> store_thms "case_cong" new_type_names case_congs end;
berghofe@5177
   446
berghofe@5177
   447
end;