src/HOL/Tools/datatype_abs_proofs.ML
author berghofe
Wed Mar 15 23:36:46 2000 +0100 (2000-03-15)
changeset 8477 17231d71171a
parent 8436 8a87fa482baf
child 8601 8fb3a81b4ccf
permissions -rw-r--r--
- Fixed bug in prove_casedist_thms (proof failed because of
name clashes)
- Now returns theorems with correct names in derivations
berghofe@5177
     1
(*  Title:      HOL/Tools/datatype_abs_proofs.ML
berghofe@5177
     2
    ID:         $Id$
berghofe@5177
     3
    Author:     Stefan Berghofer
berghofe@5177
     4
    Copyright   1998  TU Muenchen
berghofe@5177
     5
berghofe@5177
     6
Proofs and defintions independent of concrete representation
berghofe@5177
     7
of datatypes  (i.e. requiring only abstract properties such as
berghofe@5177
     8
injectivity / distinctness of constructors and induction)
berghofe@5177
     9
berghofe@5177
    10
 - case distinction (exhaustion) theorems
berghofe@5177
    11
 - characteristic equations for primrec combinators
berghofe@5177
    12
 - characteristic equations for case combinators
berghofe@5177
    13
 - equations for splitting "P (case ...)" expressions
berghofe@5177
    14
 - datatype size function
berghofe@5177
    15
 - "nchotomy" and "case_cong" theorems for TFL
berghofe@5177
    16
berghofe@5177
    17
*)
berghofe@5177
    18
berghofe@5177
    19
signature DATATYPE_ABS_PROOFS =
berghofe@5177
    20
sig
berghofe@5177
    21
  val prove_casedist_thms : string list -> (int * (string * DatatypeAux.dtyp list *
berghofe@5177
    22
    (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
wenzelm@8436
    23
      thm -> theory attribute list -> theory -> theory * thm list
berghofe@5661
    24
  val prove_primrec_thms : bool -> string list -> (int * (string * DatatypeAux.dtyp list *
berghofe@5177
    25
    (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
berghofe@5177
    26
      DatatypeAux.datatype_info Symtab.table -> thm list list -> thm list list ->
berghofe@8477
    27
        simpset -> thm -> theory -> theory * (string list * thm list)
berghofe@5661
    28
  val prove_case_thms : bool -> string list -> (int * (string * DatatypeAux.dtyp list *
berghofe@5177
    29
    (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
wenzelm@8436
    30
      string list -> thm list -> theory -> theory * (thm list list * string list)
berghofe@5177
    31
  val prove_split_thms : string list -> (int * (string * DatatypeAux.dtyp list *
berghofe@5177
    32
    (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
berghofe@5177
    33
      thm list list -> thm list list -> thm list -> thm list list -> theory ->
berghofe@5177
    34
        theory * (thm * thm) list
berghofe@5661
    35
  val prove_size_thms : bool -> string list -> (int * (string * DatatypeAux.dtyp list *
berghofe@5177
    36
    (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
berghofe@5177
    37
      string list -> thm list -> theory -> theory * thm list
berghofe@5177
    38
  val prove_nchotomys : string list -> (int * (string * DatatypeAux.dtyp list *
berghofe@5177
    39
    (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
berghofe@5177
    40
      thm list -> theory -> theory * thm list
berghofe@5177
    41
  val prove_case_congs : string list -> (int * (string * DatatypeAux.dtyp list *
berghofe@5177
    42
    (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
berghofe@5177
    43
      thm list -> thm list list -> theory -> theory * thm list
berghofe@5177
    44
end;
berghofe@5177
    45
wenzelm@8436
    46
structure DatatypeAbsProofs: DATATYPE_ABS_PROOFS =
berghofe@5177
    47
struct
berghofe@5177
    48
berghofe@5177
    49
open DatatypeAux;
berghofe@5177
    50
wenzelm@6394
    51
val thin = read_instantiate_sg (Theory.sign_of Set.thy) [("V", "?X : ?Y")] thin_rl;
berghofe@5177
    52
berghofe@5177
    53
val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of distinct_lemma);
berghofe@5177
    54
berghofe@5177
    55
(************************ case distinction theorems ***************************)
berghofe@5177
    56
wenzelm@8436
    57
fun prove_casedist_thms new_type_names descr sorts induct case_names_exhausts thy =
berghofe@5177
    58
  let
wenzelm@6427
    59
    val _ = message "Proving case distinction theorems ...";
berghofe@5177
    60
berghofe@5177
    61
    val descr' = flat descr;
berghofe@5177
    62
    val recTs = get_rec_types descr' sorts;
berghofe@5177
    63
    val newTs = take (length (hd descr), recTs);
berghofe@5177
    64
berghofe@8477
    65
    val {maxidx, ...} = rep_thm induct;
wenzelm@8305
    66
    val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@5177
    67
berghofe@5177
    68
    fun prove_casedist_thm ((i, t), T) =
berghofe@5177
    69
      let
berghofe@5177
    70
        val dummyPs = map (fn (Var (_, Type (_, [T', T'']))) =>
berghofe@5177
    71
          Abs ("z", T', Const ("True", T''))) induct_Ps;
berghofe@8477
    72
        val P = Abs ("z", T, HOLogic.imp $ HOLogic.mk_eq (Var (("a", maxidx+1), T), Bound 0) $
berghofe@5177
    73
          Var (("P", 0), HOLogic.boolT))
berghofe@5177
    74
        val insts = take (i, dummyPs) @ (P::(drop (i + 1, dummyPs)));
wenzelm@6394
    75
        val cert = cterm_of (Theory.sign_of thy);
berghofe@5177
    76
        val insts' = (map cert induct_Ps) ~~ (map cert insts);
berghofe@5177
    77
        val induct' = refl RS ((nth_elem (i,
berghofe@5177
    78
          split_conj_thm (cterm_instantiate insts' induct))) RSN (2, rev_mp))
berghofe@5177
    79
berghofe@5177
    80
      in prove_goalw_cterm [] (cert t) (fn prems =>
berghofe@5177
    81
        [rtac induct' 1,
berghofe@5177
    82
         REPEAT (rtac TrueI 1),
berghofe@5177
    83
         REPEAT ((rtac impI 1) THEN (eresolve_tac prems 1)),
berghofe@5177
    84
         REPEAT (rtac TrueI 1)])
berghofe@5177
    85
      end;
berghofe@5177
    86
berghofe@5177
    87
    val casedist_thms = map prove_casedist_thm ((0 upto (length newTs - 1)) ~~
berghofe@5177
    88
      (DatatypeProp.make_casedists descr sorts) ~~ newTs)
wenzelm@8436
    89
  in thy |> store_thms_atts "exhaust" new_type_names (map single case_names_exhausts) casedist_thms end;
berghofe@5177
    90
berghofe@5177
    91
berghofe@5177
    92
(*************************** primrec combinators ******************************)
berghofe@5177
    93
berghofe@5661
    94
fun prove_primrec_thms flat_names new_type_names descr sorts
berghofe@7015
    95
    (dt_info : datatype_info Symtab.table) constr_inject dist_rewrites dist_ss induct thy =
berghofe@5177
    96
  let
wenzelm@6427
    97
    val _ = message "Constructing primrec combinators ...";
berghofe@5661
    98
berghofe@7015
    99
    val fun_rel_comp_name = Sign.intern_const (sign_of Relation.thy) "fun_rel_comp";
berghofe@7015
   100
    val [fun_rel_comp_def, o_def] =
berghofe@7015
   101
      map (get_thm Relation.thy) ["fun_rel_comp_def", "o_def"];
berghofe@7015
   102
berghofe@5661
   103
    val big_name = space_implode "_" new_type_names;
berghofe@5661
   104
    val thy0 = add_path flat_names big_name thy;
berghofe@5177
   105
berghofe@5177
   106
    val descr' = flat descr;
berghofe@5177
   107
    val recTs = get_rec_types descr' sorts;
berghofe@5578
   108
    val used = foldr add_typ_tfree_names (recTs, []);
berghofe@5177
   109
    val newTs = take (length (hd descr), recTs);
berghofe@5177
   110
wenzelm@8305
   111
    val induct_Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@5177
   112
berghofe@5661
   113
    val big_rec_name' = big_name ^ "_rec_set";
wenzelm@6394
   114
    val rec_set_names = map (Sign.full_name (Theory.sign_of thy0))
berghofe@5177
   115
      (if length descr' = 1 then [big_rec_name'] else
berghofe@5177
   116
        (map ((curry (op ^) (big_rec_name' ^ "_")) o string_of_int)
berghofe@5177
   117
          (1 upto (length descr'))));
berghofe@5177
   118
berghofe@5578
   119
    val rec_result_Ts = map TFree (variantlist (replicate (length descr') "'t", used) ~~
berghofe@5578
   120
      replicate (length descr') HOLogic.termS);
berghofe@5177
   121
berghofe@5177
   122
    val reccomb_fn_Ts = flat (map (fn (i, (_, _, constrs)) =>
berghofe@5177
   123
      map (fn (_, cargs) =>
berghofe@5177
   124
        let
berghofe@7015
   125
          val Ts = map (typ_of_dtyp descr' sorts) cargs;
berghofe@7015
   126
          val recs = filter (is_rec_type o fst) (cargs ~~ Ts);
berghofe@7015
   127
berghofe@7015
   128
          fun mk_argT (DtRec k, _) = nth_elem (k, rec_result_Ts)
berghofe@7015
   129
            | mk_argT (DtType ("fun", [_, DtRec k]), Type ("fun", [T, _])) =
berghofe@7015
   130
               T --> nth_elem (k, rec_result_Ts);
berghofe@7015
   131
berghofe@7015
   132
          val argTs = Ts @ map mk_argT recs
berghofe@5177
   133
        in argTs ---> nth_elem (i, rec_result_Ts)
berghofe@5177
   134
        end) constrs) descr');
berghofe@5177
   135
berghofe@5177
   136
    val rec_set_Ts = map (fn (T1, T2) => reccomb_fn_Ts ---> HOLogic.mk_setT
berghofe@5177
   137
      (HOLogic.mk_prodT (T1, T2))) (recTs ~~ rec_result_Ts);
berghofe@5177
   138
berghofe@5177
   139
    val rec_fns = map (uncurry (mk_Free "f"))
berghofe@5177
   140
      (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
berghofe@5177
   141
    val rec_sets = map (fn c => list_comb (Const c, rec_fns))
berghofe@5177
   142
      (rec_set_names ~~ rec_set_Ts);
berghofe@5177
   143
berghofe@5177
   144
    (* introduction rules for graph of primrec function *)
berghofe@5177
   145
berghofe@5177
   146
    fun make_rec_intr T set_name ((rec_intr_ts, l), (cname, cargs)) =
berghofe@5177
   147
      let
berghofe@7015
   148
        fun mk_prem ((dt, U), (j, k, prems, t1s, t2s)) =
berghofe@7015
   149
          let val free1 = mk_Free "x" U j
berghofe@7015
   150
          in (case (dt, U) of
berghofe@7015
   151
             (DtRec m, _) =>
berghofe@5177
   152
               let val free2 = mk_Free "y" (nth_elem (m, rec_result_Ts)) k
berghofe@5177
   153
               in (j + 1, k + 1, (HOLogic.mk_Trueprop (HOLogic.mk_mem
berghofe@5177
   154
                 (HOLogic.mk_prod (free1, free2), nth_elem (m, rec_sets))))::prems,
berghofe@5177
   155
                   free1::t1s, free2::t2s)
berghofe@5177
   156
               end
berghofe@7015
   157
           | (DtType ("fun", [_, DtRec m]), U' as Type ("fun", [T', _])) =>
berghofe@7015
   158
               let val free2 = mk_Free "y" (T' --> nth_elem (m, rec_result_Ts)) k
berghofe@7015
   159
               in (j + 1, k + 1, (HOLogic.mk_Trueprop (HOLogic.mk_mem (free2,
berghofe@7015
   160
                 Const (fun_rel_comp_name, [U', snd (strip_type (nth_elem (m, rec_set_Ts)))] --->
berghofe@7015
   161
                   HOLogic.mk_setT (T' --> nth_elem (m, rec_result_Ts))) $
berghofe@7015
   162
                     free1 $ nth_elem (m, rec_sets))))::prems, free1::t1s, free2::t2s)
berghofe@7015
   163
               end
berghofe@5177
   164
           | _ => (j + 1, k, prems, free1::t1s, t2s))
berghofe@5177
   165
          end;
berghofe@5177
   166
berghofe@5177
   167
        val Ts = map (typ_of_dtyp descr' sorts) cargs;
berghofe@7015
   168
        val (_, _, prems, t1s, t2s) = foldr mk_prem (cargs ~~ Ts, (1, 1, [], [], []))
berghofe@5177
   169
berghofe@5177
   170
      in (rec_intr_ts @ [Logic.list_implies (prems, HOLogic.mk_Trueprop (HOLogic.mk_mem
berghofe@5177
   171
        (HOLogic.mk_prod (list_comb (Const (cname, Ts ---> T), t1s),
berghofe@5177
   172
          list_comb (nth_elem (l, rec_fns), t1s @ t2s)), set_name)))], l + 1)
berghofe@5177
   173
      end;
berghofe@5177
   174
berghofe@5177
   175
    val (rec_intr_ts, _) = foldl (fn (x, ((d, T), set_name)) =>
berghofe@5177
   176
      foldl (make_rec_intr T set_name) (x, #3 (snd d)))
berghofe@5177
   177
        (([], 0), descr' ~~ recTs ~~ rec_sets);
berghofe@5177
   178
berghofe@5177
   179
    val (thy1, {intrs = rec_intrs, elims = rec_elims, ...}) =
berghofe@5661
   180
      setmp InductivePackage.quiet_mode (!quiet_mode)
berghofe@5661
   181
        (InductivePackage.add_inductive_i false true big_rec_name' false false true
berghofe@7015
   182
           rec_sets [] (map (fn x => (("", x), [])) rec_intr_ts) [fun_rel_comp_mono] []) thy0;
berghofe@5177
   183
berghofe@5177
   184
    (* prove uniqueness and termination of primrec combinators *)
berghofe@5177
   185
wenzelm@6427
   186
    val _ = message "Proving termination and uniqueness of primrec functions ...";
berghofe@5177
   187
berghofe@5177
   188
    fun mk_unique_tac ((tac, intrs), ((((i, (tname, _, constrs)), elim), T), T')) =
berghofe@5177
   189
      let
berghofe@5177
   190
        val distinct_tac = (etac Pair_inject 1) THEN
berghofe@5177
   191
          (if i < length newTs then
berghofe@5177
   192
             full_simp_tac (HOL_ss addsimps (nth_elem (i, dist_rewrites))) 1
berghofe@7015
   193
           else full_simp_tac dist_ss 1);
berghofe@5177
   194
berghofe@5177
   195
        val inject = map (fn r => r RS iffD1)
berghofe@5177
   196
          (if i < length newTs then nth_elem (i, constr_inject)
berghofe@5177
   197
            else #inject (the (Symtab.lookup (dt_info, tname))));
berghofe@5177
   198
berghofe@5177
   199
        fun mk_unique_constr_tac n ((tac, intr::intrs, j), (cname, cargs)) =
berghofe@5177
   200
          let
berghofe@5177
   201
            val k = length (filter is_rec_type cargs)
berghofe@5177
   202
berghofe@5177
   203
          in (EVERY [DETERM tac,
berghofe@7015
   204
                REPEAT (dtac fun_rel_comp_unique 1),
berghofe@5177
   205
                REPEAT (etac ex1E 1), rtac ex1I 1,
berghofe@5177
   206
                DEPTH_SOLVE_1 (ares_tac [intr] 1),
berghofe@5177
   207
                REPEAT_DETERM_N k (etac thin 1),
berghofe@5177
   208
                etac elim 1,
berghofe@5177
   209
                REPEAT_DETERM_N j distinct_tac,
berghofe@5177
   210
                etac Pair_inject 1, TRY (dresolve_tac inject 1),
berghofe@5177
   211
                REPEAT (etac conjE 1), hyp_subst_tac 1,
berghofe@5177
   212
                REPEAT (etac allE 1),
berghofe@5177
   213
                REPEAT (dtac mp 1 THEN atac 1),
berghofe@5177
   214
                TRY (hyp_subst_tac 1),
berghofe@5177
   215
                rtac refl 1,
berghofe@5177
   216
                REPEAT_DETERM_N (n - j - 1) distinct_tac],
berghofe@5177
   217
              intrs, j + 1)
berghofe@5177
   218
          end;
berghofe@5177
   219
berghofe@5177
   220
        val (tac', intrs', _) = foldl (mk_unique_constr_tac (length constrs))
berghofe@5177
   221
          ((tac, intrs, 0), constrs);
berghofe@5177
   222
berghofe@5177
   223
      in (tac', intrs') end;
berghofe@5177
   224
berghofe@5177
   225
    val rec_unique_thms =
berghofe@5177
   226
      let
berghofe@5177
   227
        val rec_unique_ts = map (fn (((set_t, T1), T2), i) =>
berghofe@5177
   228
          Const ("Ex1", (T2 --> HOLogic.boolT) --> HOLogic.boolT) $
berghofe@5177
   229
            absfree ("y", T2, HOLogic.mk_mem (HOLogic.mk_prod
berghofe@5177
   230
              (mk_Free "x" T1 i, Free ("y", T2)), set_t)))
berghofe@5177
   231
                (rec_sets ~~ recTs ~~ rec_result_Ts ~~ (1 upto length recTs));
wenzelm@6394
   232
        val cert = cterm_of (Theory.sign_of thy1)
berghofe@5177
   233
        val insts = map (fn ((i, T), t) => absfree ("x" ^ (string_of_int i), T, t))
berghofe@5177
   234
          ((1 upto length recTs) ~~ recTs ~~ rec_unique_ts);
berghofe@5177
   235
        val induct' = cterm_instantiate ((map cert induct_Ps) ~~
berghofe@5177
   236
          (map cert insts)) induct;
berghofe@5177
   237
        val (tac, _) = foldl mk_unique_tac
berghofe@5177
   238
          ((rtac induct' 1, rec_intrs), descr' ~~ rec_elims ~~ recTs ~~ rec_result_Ts)
berghofe@5177
   239
berghofe@5177
   240
      in split_conj_thm (prove_goalw_cterm []
berghofe@5177
   241
        (cert (HOLogic.mk_Trueprop (mk_conj rec_unique_ts))) (K [tac]))
berghofe@5177
   242
      end;
berghofe@5177
   243
berghofe@5177
   244
    val rec_total_thms = map (fn r =>
berghofe@5177
   245
      r RS ex1_implies_ex RS (select_eq_Ex RS iffD2)) rec_unique_thms;
berghofe@5177
   246
berghofe@5177
   247
    (* define primrec combinators *)
berghofe@5177
   248
berghofe@5177
   249
    val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
wenzelm@6394
   250
    val reccomb_names = map (Sign.full_name (Theory.sign_of thy1))
berghofe@5177
   251
      (if length descr' = 1 then [big_reccomb_name] else
berghofe@5177
   252
        (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
berghofe@5177
   253
          (1 upto (length descr'))));
berghofe@5177
   254
    val reccombs = map (fn ((name, T), T') => list_comb
berghofe@5177
   255
      (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
berghofe@5177
   256
        (reccomb_names ~~ recTs ~~ rec_result_Ts);
berghofe@5177
   257
wenzelm@8436
   258
    val (thy2, reccomb_defs) = thy1 |>
berghofe@5177
   259
      Theory.add_consts_i (map (fn ((name, T), T') =>
berghofe@5177
   260
        (Sign.base_name name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
berghofe@5177
   261
          (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
wenzelm@7904
   262
      (PureThy.add_defs_i o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') =>
berghofe@7015
   263
        ((Sign.base_name name) ^ "_def", Logic.mk_equals (comb, absfree ("x", T,
berghofe@5177
   264
           Const ("Eps", (T' --> HOLogic.boolT) --> T') $ absfree ("y", T',
berghofe@7015
   265
             HOLogic.mk_mem (HOLogic.mk_prod (Free ("x", T), Free ("y", T')), set))))))
wenzelm@8436
   266
               (reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)) |>>
berghofe@5661
   267
      parent_path flat_names;
berghofe@5177
   268
berghofe@5177
   269
berghofe@5177
   270
    (* prove characteristic equations for primrec combinators *)
berghofe@5177
   271
wenzelm@6427
   272
    val _ = message "Proving characteristic theorems for primrec combinators ..."
berghofe@5177
   273
berghofe@5177
   274
    val rec_thms = map (fn t => prove_goalw_cterm reccomb_defs
wenzelm@6394
   275
      (cterm_of (Theory.sign_of thy2) t) (fn _ =>
berghofe@5177
   276
        [rtac select1_equality 1,
berghofe@5177
   277
         resolve_tac rec_unique_thms 1,
berghofe@5177
   278
         resolve_tac rec_intrs 1,
berghofe@7015
   279
         rewrite_goals_tac [o_def, fun_rel_comp_def],
berghofe@7015
   280
         REPEAT ((rtac CollectI 1 THEN rtac allI 1) ORELSE resolve_tac rec_total_thms 1)]))
berghofe@5177
   281
           (DatatypeProp.make_primrecs new_type_names descr sorts thy2)
berghofe@5177
   282
berghofe@5177
   283
  in
berghofe@8477
   284
    thy2 |> Theory.add_path (space_implode "_" new_type_names) |>
berghofe@8477
   285
    PureThy.add_thmss [(("recs", rec_thms), [])] |>>
berghofe@8477
   286
    Theory.parent_path |> apsnd (pair reccomb_names o flat)
berghofe@5177
   287
  end;
berghofe@5177
   288
berghofe@8477
   289
berghofe@5177
   290
(***************************** case combinators *******************************)
berghofe@5177
   291
berghofe@5661
   292
fun prove_case_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
berghofe@5177
   293
  let
wenzelm@6427
   294
    val _ = message "Proving characteristic theorems for case combinators ...";
berghofe@5661
   295
berghofe@5661
   296
    val thy1 = add_path flat_names (space_implode "_" new_type_names) thy;
berghofe@5177
   297
berghofe@5177
   298
    val descr' = flat descr;
berghofe@5177
   299
    val recTs = get_rec_types descr' sorts;
berghofe@5578
   300
    val used = foldr add_typ_tfree_names (recTs, []);
berghofe@5177
   301
    val newTs = take (length (hd descr), recTs);
berghofe@5578
   302
    val T' = TFree (variant used "'t", HOLogic.termS);
berghofe@5177
   303
berghofe@7015
   304
    fun mk_dummyT (DtRec _) = T'
berghofe@7015
   305
      | mk_dummyT (DtType ("fun", [T, _])) = typ_of_dtyp descr' sorts T --> T'
berghofe@7015
   306
berghofe@5177
   307
    val case_dummy_fns = map (fn (_, (_, _, constrs)) => map (fn (_, cargs) =>
berghofe@5177
   308
      let
berghofe@5177
   309
        val Ts = map (typ_of_dtyp descr' sorts) cargs;
berghofe@7015
   310
        val Ts' = map mk_dummyT (filter is_rec_type cargs)
berghofe@5578
   311
      in Const ("arbitrary", Ts @ Ts' ---> T')
berghofe@5177
   312
      end) constrs) descr';
berghofe@5177
   313
berghofe@5177
   314
    val case_names = map (fn s =>
wenzelm@6394
   315
      Sign.full_name (Theory.sign_of thy1) (s ^ "_case")) new_type_names;
berghofe@5177
   316
berghofe@5177
   317
    (* define case combinators via primrec combinators *)
berghofe@5177
   318
berghofe@5177
   319
    val (case_defs, thy2) = foldl (fn ((defs, thy),
berghofe@5177
   320
      ((((i, (_, _, constrs)), T), name), recname)) =>
berghofe@5177
   321
        let
berghofe@5177
   322
          val (fns1, fns2) = ListPair.unzip (map (fn ((_, cargs), j) =>
berghofe@5177
   323
            let
berghofe@5177
   324
              val Ts = map (typ_of_dtyp descr' sorts) cargs;
berghofe@7015
   325
              val Ts' = Ts @ map mk_dummyT (filter is_rec_type cargs);
berghofe@5177
   326
              val frees' = map (uncurry (mk_Free "x")) (Ts' ~~ (1 upto length Ts'));
berghofe@5177
   327
              val frees = take (length cargs, frees');
berghofe@5177
   328
              val free = mk_Free "f" (Ts ---> T') j
berghofe@5177
   329
            in
berghofe@5177
   330
             (free, list_abs_free (map dest_Free frees',
berghofe@5177
   331
               list_comb (free, frees)))
berghofe@5177
   332
            end) (constrs ~~ (1 upto length constrs)));
berghofe@5177
   333
berghofe@5177
   334
          val caseT = (map (snd o dest_Free) fns1) @ [T] ---> T';
berghofe@5177
   335
          val fns = (flat (take (i, case_dummy_fns))) @
berghofe@5177
   336
            fns2 @ (flat (drop (i + 1, case_dummy_fns)));
berghofe@5177
   337
          val reccomb = Const (recname, (map fastype_of fns) @ [T] ---> T');
berghofe@5177
   338
          val decl = (Sign.base_name name, caseT, NoSyn);
berghofe@5177
   339
          val def = ((Sign.base_name name) ^ "_def",
berghofe@5177
   340
            Logic.mk_equals (list_comb (Const (name, caseT), fns1),
berghofe@5177
   341
              list_comb (reccomb, (flat (take (i, case_dummy_fns))) @
berghofe@5177
   342
                fns2 @ (flat (drop (i + 1, case_dummy_fns))) )));
wenzelm@8436
   343
          val (thy', [def_thm]) = thy |>
wenzelm@7904
   344
            Theory.add_consts_i [decl] |> (PureThy.add_defs_i o map Thm.no_attributes) [def];
berghofe@5177
   345
wenzelm@8436
   346
        in (defs @ [def_thm], thy')
berghofe@5661
   347
        end) (([], thy1), (hd descr) ~~ newTs ~~ case_names ~~
berghofe@5177
   348
          (take (length newTs, reccomb_names)));
berghofe@5177
   349
berghofe@5177
   350
    val case_thms = map (map (fn t => prove_goalw_cterm (case_defs @
wenzelm@6394
   351
      (map mk_meta_eq primrec_thms)) (cterm_of (Theory.sign_of thy2) t)
berghofe@5177
   352
        (fn _ => [rtac refl 1])))
berghofe@8477
   353
          (DatatypeProp.make_cases new_type_names descr sorts thy2)
berghofe@5177
   354
berghofe@8477
   355
  in
berghofe@8477
   356
    thy2 |> Theory.add_trrules_i
berghofe@5661
   357
      (DatatypeProp.make_case_trrules new_type_names descr) |>
berghofe@8477
   358
    parent_path flat_names |>
berghofe@8477
   359
    store_thmss "cases" new_type_names case_thms |>
berghofe@8477
   360
    apsnd (rpair case_names)
berghofe@8477
   361
  end;
berghofe@5177
   362
berghofe@5177
   363
berghofe@5177
   364
(******************************* case splitting *******************************)
berghofe@5177
   365
berghofe@5177
   366
fun prove_split_thms new_type_names descr sorts constr_inject dist_rewrites
berghofe@5177
   367
    casedist_thms case_thms thy =
berghofe@5177
   368
  let
wenzelm@6427
   369
    val _ = message "Proving equations for case splitting ...";
berghofe@5177
   370
berghofe@5177
   371
    val descr' = flat descr;
berghofe@5177
   372
    val recTs = get_rec_types descr' sorts;
berghofe@5177
   373
    val newTs = take (length (hd descr), recTs);
berghofe@5177
   374
berghofe@5177
   375
    fun prove_split_thms ((((((t1, t2), inject), dist_rewrites'),
berghofe@5177
   376
        exhaustion), case_thms'), T) =
berghofe@5177
   377
      let
wenzelm@6394
   378
        val cert = cterm_of (Theory.sign_of thy);
berghofe@5177
   379
        val _ $ (_ $ lhs $ _) = hd (Logic.strip_assums_hyp (hd (prems_of exhaustion)));
berghofe@5177
   380
        val exhaustion' = cterm_instantiate
berghofe@5177
   381
          [(cert lhs, cert (Free ("x", T)))] exhaustion;
berghofe@5177
   382
        val tacsf = K [rtac exhaustion' 1, ALLGOALS (asm_simp_tac
berghofe@5177
   383
          (HOL_ss addsimps (dist_rewrites' @ inject @ case_thms')))]
berghofe@5177
   384
      in
berghofe@5177
   385
        (prove_goalw_cterm [] (cert t1) tacsf,
berghofe@5177
   386
         prove_goalw_cterm [] (cert t2) tacsf)
berghofe@5177
   387
      end;
berghofe@5177
   388
berghofe@5177
   389
    val split_thm_pairs = map prove_split_thms
berghofe@5177
   390
      ((DatatypeProp.make_splits new_type_names descr sorts thy) ~~ constr_inject ~~
berghofe@5177
   391
        dist_rewrites ~~ casedist_thms ~~ case_thms ~~ newTs);
berghofe@5177
   392
berghofe@5177
   393
    val (split_thms, split_asm_thms) = ListPair.unzip split_thm_pairs
berghofe@5177
   394
berghofe@5177
   395
  in
wenzelm@8436
   396
    thy |> store_thms "split" new_type_names split_thms |>>>
wenzelm@8436
   397
      store_thms "split_asm" new_type_names split_asm_thms |> apsnd ListPair.zip
berghofe@5177
   398
  end;
berghofe@5177
   399
berghofe@5177
   400
(******************************* size functions *******************************)
berghofe@5177
   401
berghofe@5661
   402
fun prove_size_thms flat_names new_type_names descr sorts reccomb_names primrec_thms thy =
berghofe@7015
   403
  if exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
berghofe@7015
   404
    (fn (DtType ("fun", [_, DtRec _])) => true | _ => false) cargs) constrs) (flat descr)
berghofe@7015
   405
  then
berghofe@7015
   406
    (thy, [])
berghofe@7015
   407
  else
berghofe@5177
   408
  let
wenzelm@6427
   409
    val _ = message "Proving equations for size function ...";
berghofe@5661
   410
berghofe@5661
   411
    val big_name = space_implode "_" new_type_names;
berghofe@5661
   412
    val thy1 = add_path flat_names big_name thy;
berghofe@5177
   413
berghofe@5177
   414
    val descr' = flat descr;
berghofe@5177
   415
    val recTs = get_rec_types descr' sorts;
berghofe@5177
   416
berghofe@5177
   417
    val big_size_name = space_implode "_" new_type_names ^ "_size";
berghofe@7015
   418
    val size_name = Sign.intern_const (Theory.sign_of (theory "Arith")) "size";
berghofe@5177
   419
    val size_names = replicate (length (hd descr)) size_name @
wenzelm@6394
   420
      map (Sign.full_name (Theory.sign_of thy1))
berghofe@5177
   421
        (if length (flat (tl descr)) = 1 then [big_size_name] else
berghofe@5177
   422
          map (fn i => big_size_name ^ "_" ^ string_of_int i)
berghofe@5177
   423
            (1 upto length (flat (tl descr))));
berghofe@5177
   424
    val def_names = map (fn i => big_size_name ^ "_def_" ^ string_of_int i)
berghofe@5177
   425
      (1 upto length recTs);
berghofe@5177
   426
wenzelm@7704
   427
    fun plus (t1, t2) = Const ("op +", [HOLogic.natT, HOLogic.natT] ---> HOLogic.natT) $ t1 $ t2;
berghofe@5177
   428
berghofe@5177
   429
    fun make_sizefun (_, cargs) =
berghofe@5177
   430
      let
berghofe@5177
   431
        val Ts = map (typ_of_dtyp descr' sorts) cargs;
berghofe@5177
   432
        val k = length (filter is_rec_type cargs);
berghofe@5177
   433
        val t = if k = 0 then HOLogic.zero else
wenzelm@7704
   434
          foldl1 plus (map Bound (k - 1 downto 0) @ [HOLogic.mk_nat 1])
berghofe@5177
   435
      in
berghofe@5177
   436
        foldr (fn (T, t') => Abs ("x", T, t')) (Ts @ replicate k HOLogic.natT, t)
berghofe@5177
   437
      end;
berghofe@5177
   438
berghofe@5177
   439
    val fs = flat (map (fn (_, (_, _, constrs)) => map make_sizefun constrs) descr');
berghofe@5177
   440
    val fTs = map fastype_of fs;
berghofe@5177
   441
wenzelm@8436
   442
    val (thy', size_def_thms) = thy1 |>
berghofe@5177
   443
      Theory.add_consts_i (map (fn (s, T) =>
berghofe@5177
   444
        (Sign.base_name s, T --> HOLogic.natT, NoSyn))
berghofe@5177
   445
          (drop (length (hd descr), size_names ~~ recTs))) |>
wenzelm@7904
   446
      (PureThy.add_defs_i o map Thm.no_attributes) (map (fn (((s, T), def_name), rec_name) =>
berghofe@5177
   447
        (def_name, Logic.mk_equals (Const (s, T --> HOLogic.natT),
berghofe@5177
   448
          list_comb (Const (rec_name, fTs @ [T] ---> HOLogic.natT), fs))))
wenzelm@8436
   449
            (size_names ~~ recTs ~~ def_names ~~ reccomb_names)) |>>
berghofe@5661
   450
      parent_path flat_names;
berghofe@5177
   451
oheimb@5553
   452
    val rewrites = size_def_thms @ map mk_meta_eq primrec_thms;
berghofe@5177
   453
berghofe@5177
   454
    val size_thms = map (fn t => prove_goalw_cterm rewrites
wenzelm@6394
   455
      (cterm_of (Theory.sign_of thy') t) (fn _ => [rtac refl 1]))
berghofe@5177
   456
        (DatatypeProp.make_size new_type_names descr sorts thy')
berghofe@5177
   457
berghofe@5177
   458
  in
berghofe@8477
   459
    thy' |> Theory.add_path big_name |>
berghofe@8477
   460
    PureThy.add_thmss [(("size", size_thms), [])] |>>
berghofe@8477
   461
    Theory.parent_path |> apsnd flat
berghofe@5177
   462
  end;
berghofe@5177
   463
berghofe@8477
   464
berghofe@5177
   465
(************************* additional theorems for TFL ************************)
berghofe@5177
   466
berghofe@5177
   467
fun prove_nchotomys new_type_names descr sorts casedist_thms thy =
berghofe@5177
   468
  let
wenzelm@6427
   469
    val _ = message "Proving additional theorems for TFL ...";
berghofe@5177
   470
berghofe@5177
   471
    fun prove_nchotomy (t, exhaustion) =
berghofe@5177
   472
      let
berghofe@5177
   473
        (* For goal i, select the correct disjunct to attack, then prove it *)
berghofe@5177
   474
        fun tac i 0 = EVERY [TRY (rtac disjI1 i),
berghofe@5177
   475
              hyp_subst_tac i, REPEAT (rtac exI i), rtac refl i]
berghofe@5177
   476
          | tac i n = rtac disjI2 i THEN tac i (n - 1)
berghofe@5177
   477
      in 
wenzelm@6394
   478
        prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) t) (fn _ =>
berghofe@5177
   479
          [rtac allI 1,
berghofe@5177
   480
           exh_tac (K exhaustion) 1,
berghofe@5177
   481
           ALLGOALS (fn i => tac i (i-1))])
berghofe@5177
   482
      end;
berghofe@5177
   483
berghofe@5177
   484
    val nchotomys =
berghofe@5177
   485
      map prove_nchotomy (DatatypeProp.make_nchotomys descr sorts ~~ casedist_thms)
berghofe@5177
   486
wenzelm@8436
   487
  in thy |> store_thms "nchotomy" new_type_names nchotomys end;
berghofe@5177
   488
berghofe@5177
   489
fun prove_case_congs new_type_names descr sorts nchotomys case_thms thy =
berghofe@5177
   490
  let
berghofe@5177
   491
    fun prove_case_cong ((t, nchotomy), case_rewrites) =
berghofe@5177
   492
      let
berghofe@5177
   493
        val (Const ("==>", _) $ tm $ _) = t;
berghofe@5177
   494
        val (Const ("Trueprop", _) $ (Const ("op =", _) $ _ $ Ma)) = tm;
wenzelm@6394
   495
        val cert = cterm_of (Theory.sign_of thy);
berghofe@5177
   496
        val nchotomy' = nchotomy RS spec;
berghofe@5177
   497
        val nchotomy'' = cterm_instantiate
berghofe@5177
   498
          [(cert (hd (add_term_vars (concl_of nchotomy', []))), cert Ma)] nchotomy'
berghofe@5177
   499
      in
berghofe@5177
   500
        prove_goalw_cterm [] (cert t) (fn prems => 
berghofe@5177
   501
          let val simplify = asm_simp_tac (HOL_ss addsimps (prems @ case_rewrites))
berghofe@5177
   502
          in [simp_tac (HOL_ss addsimps [hd prems]) 1,
berghofe@5177
   503
              cut_facts_tac [nchotomy''] 1,
berghofe@5177
   504
              REPEAT (etac disjE 1 THEN REPEAT (etac exE 1) THEN simplify 1),
berghofe@5177
   505
              REPEAT (etac exE 1) THEN simplify 1 (* Get last disjunct *)]
berghofe@5177
   506
          end)
berghofe@5177
   507
      end;
berghofe@5177
   508
berghofe@5177
   509
    val case_congs = map prove_case_cong (DatatypeProp.make_case_congs
berghofe@5177
   510
      new_type_names descr sorts thy ~~ nchotomys ~~ case_thms)
berghofe@5177
   511
wenzelm@8436
   512
  in thy |> store_thms "case_cong" new_type_names case_congs end;
berghofe@5177
   513
berghofe@5177
   514
end;