src/HOL/Tools/inductive_package.ML
author wenzelm
Tue Jul 27 22:03:24 1999 +0200 (1999-07-27)
changeset 7107 ce69de572bca
parent 7020 75ff179df7b7
child 7152 44d46a112127
permissions -rw-r--r--
inductive_cases(_i): Isar interface to mk_cases;
berghofe@5094
     1
(*  Title:      HOL/Tools/inductive_package.ML
berghofe@5094
     2
    ID:         $Id$
berghofe@5094
     3
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
berghofe@5094
     4
                Stefan Berghofer,   TU Muenchen
berghofe@5094
     5
    Copyright   1994  University of Cambridge
berghofe@5094
     6
                1998  TU Muenchen     
berghofe@5094
     7
wenzelm@6424
     8
(Co)Inductive Definition module for HOL.
berghofe@5094
     9
berghofe@5094
    10
Features:
wenzelm@6424
    11
  * least or greatest fixedpoints
wenzelm@6424
    12
  * user-specified product and sum constructions
wenzelm@6424
    13
  * mutually recursive definitions
wenzelm@6424
    14
  * definitions involving arbitrary monotone operators
wenzelm@6424
    15
  * automatically proves introduction and elimination rules
berghofe@5094
    16
wenzelm@6424
    17
The recursive sets must *already* be declared as constants in the
wenzelm@6424
    18
current theory!
berghofe@5094
    19
berghofe@5094
    20
  Introduction rules have the form
berghofe@5094
    21
  [| ti:M(Sj), ..., P(x), ... |] ==> t: Sk |]
berghofe@5094
    22
  where M is some monotone operator (usually the identity)
berghofe@5094
    23
  P(x) is any side condition on the free variables
berghofe@5094
    24
  ti, t are any terms
berghofe@5094
    25
  Sj, Sk are two of the sets being defined in mutual recursion
berghofe@5094
    26
wenzelm@6424
    27
Sums are used only for mutual recursion.  Products are used only to
wenzelm@6424
    28
derive "streamlined" induction rules for relations.
berghofe@5094
    29
*)
berghofe@5094
    30
berghofe@5094
    31
signature INDUCTIVE_PACKAGE =
berghofe@5094
    32
sig
wenzelm@6424
    33
  val quiet_mode: bool ref
berghofe@7020
    34
  val unify_consts: Sign.sg -> term list -> term list -> term list * term list
wenzelm@6437
    35
  val get_inductive: theory -> string ->
wenzelm@6437
    36
    {names: string list, coind: bool} * {defs: thm list, elims: thm list, raw_induct: thm,
wenzelm@6437
    37
      induct: thm, intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
wenzelm@6437
    38
  val print_inductives: theory -> unit
wenzelm@6424
    39
  val add_inductive_i: bool -> bool -> bstring -> bool -> bool -> bool -> term list ->
wenzelm@6521
    40
    theory attribute list -> ((bstring * term) * theory attribute list) list ->
wenzelm@6521
    41
      thm list -> thm list -> theory -> theory *
wenzelm@6424
    42
      {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
wenzelm@6437
    43
       intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
wenzelm@6521
    44
  val add_inductive: bool -> bool -> string list -> Args.src list ->
wenzelm@6521
    45
    ((bstring * string) * Args.src list) list -> (xstring * Args.src list) list ->
wenzelm@6521
    46
      (xstring * Args.src list) list -> theory -> theory *
wenzelm@6424
    47
      {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
wenzelm@6437
    48
       intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
wenzelm@7107
    49
  val inductive_cases: (((bstring * Args.src list) * xstring) * string list) * Comment.text
wenzelm@7107
    50
    -> theory -> theory
wenzelm@7107
    51
  val inductive_cases_i: (((bstring * theory attribute list) * string) * term list) * Comment.text
wenzelm@7107
    52
    -> theory -> theory
wenzelm@6437
    53
  val setup: (theory -> theory) list
berghofe@5094
    54
end;
berghofe@5094
    55
wenzelm@6424
    56
structure InductivePackage: INDUCTIVE_PACKAGE =
berghofe@5094
    57
struct
berghofe@5094
    58
wenzelm@7107
    59
wenzelm@6424
    60
(** utilities **)
wenzelm@6424
    61
wenzelm@6424
    62
(* messages *)
wenzelm@6424
    63
berghofe@5662
    64
val quiet_mode = ref false;
berghofe@5662
    65
fun message s = if !quiet_mode then () else writeln s;
berghofe@5662
    66
wenzelm@6424
    67
fun coind_prefix true = "co"
wenzelm@6424
    68
  | coind_prefix false = "";
wenzelm@6424
    69
wenzelm@6424
    70
berghofe@7020
    71
(* the following code ensures that each recursive set *)
berghofe@7020
    72
(* always has the same type in all introduction rules *)
berghofe@7020
    73
berghofe@7020
    74
fun unify_consts sign cs intr_ts =
berghofe@7020
    75
  (let
berghofe@7020
    76
    val {tsig, ...} = Sign.rep_sg sign;
berghofe@7020
    77
    val add_term_consts_2 =
berghofe@7020
    78
      foldl_aterms (fn (cs, Const c) => c ins cs | (cs, _) => cs);
berghofe@7020
    79
    fun varify (t, (i, ts)) =
berghofe@7020
    80
      let val t' = map_term_types (incr_tvar (i + 1)) (Type.varify (t, []))
berghofe@7020
    81
      in (maxidx_of_term t', t'::ts) end;
berghofe@7020
    82
    val (i, cs') = foldr varify (cs, (~1, []));
berghofe@7020
    83
    val (i', intr_ts') = foldr varify (intr_ts, (i, []));
berghofe@7020
    84
    val rec_consts = foldl add_term_consts_2 ([], cs');
berghofe@7020
    85
    val intr_consts = foldl add_term_consts_2 ([], intr_ts');
berghofe@7020
    86
    fun unify (env, (cname, cT)) =
berghofe@7020
    87
      let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
berghofe@7020
    88
      in foldl (fn ((env', j'), Tp) => (Type.unify tsig j' env' Tp))
berghofe@7020
    89
          (env, (replicate (length consts) cT) ~~ consts)
berghofe@7020
    90
      end;
berghofe@7020
    91
    val (env, _) = foldl unify (([], i'), rec_consts);
berghofe@7020
    92
    fun typ_subst_TVars_2 env T = let val T' = typ_subst_TVars env T
berghofe@7020
    93
      in if T = T' then T else typ_subst_TVars_2 env T' end;
berghofe@7020
    94
    val subst = fst o Type.freeze_thaw o
berghofe@7020
    95
      (map_term_types (typ_subst_TVars_2 env))
berghofe@7020
    96
berghofe@7020
    97
  in (map subst cs', map subst intr_ts')
berghofe@7020
    98
  end) handle Type.TUNIFY =>
berghofe@7020
    99
    (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
berghofe@7020
   100
berghofe@7020
   101
wenzelm@6424
   102
(* misc *)
wenzelm@6424
   103
wenzelm@7107
   104
(*for proving monotonicity of recursion operator*)
wenzelm@7107
   105
val default_monos = basic_monos @ [vimage_mono];
berghofe@5094
   106
berghofe@5094
   107
val Const _ $ (vimage_f $ _) $ _ = HOLogic.dest_Trueprop (concl_of vimageD);
berghofe@5094
   108
berghofe@5094
   109
(*Delete needless equality assumptions*)
berghofe@5094
   110
val refl_thin = prove_goal HOL.thy "!!P. [| a=a;  P |] ==> P"
berghofe@5094
   111
     (fn _ => [assume_tac 1]);
berghofe@5094
   112
berghofe@5094
   113
(*For simplifying the elimination rule*)
berghofe@5120
   114
val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE, Pair_inject];
berghofe@5094
   115
wenzelm@6394
   116
val vimage_name = Sign.intern_const (Theory.sign_of Vimage.thy) "op -``";
wenzelm@6394
   117
val mono_name = Sign.intern_const (Theory.sign_of Ord.thy) "mono";
berghofe@5094
   118
berghofe@5094
   119
(* make injections needed in mutually recursive definitions *)
berghofe@5094
   120
berghofe@5094
   121
fun mk_inj cs sumT c x =
berghofe@5094
   122
  let
berghofe@5094
   123
    fun mk_inj' T n i =
berghofe@5094
   124
      if n = 1 then x else
berghofe@5094
   125
      let val n2 = n div 2;
berghofe@5094
   126
          val Type (_, [T1, T2]) = T
berghofe@5094
   127
      in
berghofe@5094
   128
        if i <= n2 then
berghofe@5094
   129
          Const ("Inl", T1 --> T) $ (mk_inj' T1 n2 i)
berghofe@5094
   130
        else
berghofe@5094
   131
          Const ("Inr", T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2))
berghofe@5094
   132
      end
berghofe@5094
   133
  in mk_inj' sumT (length cs) (1 + find_index_eq c cs)
berghofe@5094
   134
  end;
berghofe@5094
   135
berghofe@5094
   136
(* make "vimage" terms for selecting out components of mutually rec.def. *)
berghofe@5094
   137
berghofe@5094
   138
fun mk_vimage cs sumT t c = if length cs < 2 then t else
berghofe@5094
   139
  let
berghofe@5094
   140
    val cT = HOLogic.dest_setT (fastype_of c);
berghofe@5094
   141
    val vimageT = [cT --> sumT, HOLogic.mk_setT sumT] ---> HOLogic.mk_setT cT
berghofe@5094
   142
  in
berghofe@5094
   143
    Const (vimage_name, vimageT) $
berghofe@5094
   144
      Abs ("y", cT, mk_inj cs sumT c (Bound 0)) $ t
berghofe@5094
   145
  end;
berghofe@5094
   146
wenzelm@6424
   147
wenzelm@6424
   148
wenzelm@6424
   149
(** well-formedness checks **)
berghofe@5094
   150
berghofe@5094
   151
fun err_in_rule sign t msg = error ("Ill-formed introduction rule\n" ^
berghofe@5094
   152
  (Sign.string_of_term sign t) ^ "\n" ^ msg);
berghofe@5094
   153
berghofe@5094
   154
fun err_in_prem sign t p msg = error ("Ill-formed premise\n" ^
berghofe@5094
   155
  (Sign.string_of_term sign p) ^ "\nin introduction rule\n" ^
berghofe@5094
   156
  (Sign.string_of_term sign t) ^ "\n" ^ msg);
berghofe@5094
   157
berghofe@5094
   158
val msg1 = "Conclusion of introduction rule must have form\
berghofe@5094
   159
          \ ' t : S_i '";
berghofe@5094
   160
val msg2 = "Premises mentioning recursive sets must have form\
berghofe@5094
   161
          \ ' t : M S_i '";
berghofe@5094
   162
val msg3 = "Recursion term on left of member symbol";
berghofe@5094
   163
berghofe@5094
   164
fun check_rule sign cs r =
berghofe@5094
   165
  let
berghofe@5094
   166
    fun check_prem prem = if exists (Logic.occs o (rpair prem)) cs then
berghofe@5094
   167
         (case prem of
berghofe@5094
   168
           (Const ("op :", _) $ t $ u) =>
berghofe@5094
   169
             if exists (Logic.occs o (rpair t)) cs then
berghofe@5094
   170
               err_in_prem sign r prem msg3 else ()
berghofe@5094
   171
         | _ => err_in_prem sign r prem msg2)
berghofe@5094
   172
        else ()
berghofe@5094
   173
berghofe@5094
   174
  in (case (HOLogic.dest_Trueprop o Logic.strip_imp_concl) r of
berghofe@5094
   175
        (Const ("op :", _) $ _ $ u) =>
wenzelm@6424
   176
          if u mem cs then seq (check_prem o HOLogic.dest_Trueprop)
berghofe@5094
   177
            (Logic.strip_imp_prems r)
berghofe@5094
   178
          else err_in_rule sign r msg1
berghofe@5094
   179
      | _ => err_in_rule sign r msg1)
berghofe@5094
   180
  end;
berghofe@5094
   181
berghofe@7020
   182
fun try' f msg sign t = (case (try f t) of
berghofe@7020
   183
      Some x => x
berghofe@7020
   184
    | None => error (msg ^ Sign.string_of_term sign t));
berghofe@5094
   185
wenzelm@6424
   186
berghofe@5094
   187
wenzelm@6437
   188
(*** theory data ***)
wenzelm@6437
   189
wenzelm@6437
   190
(* data kind 'HOL/inductive' *)
wenzelm@6437
   191
wenzelm@6437
   192
type inductive_info =
wenzelm@6437
   193
  {names: string list, coind: bool} * {defs: thm list, elims: thm list, raw_induct: thm,
wenzelm@6437
   194
    induct: thm, intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm};
wenzelm@6437
   195
wenzelm@6437
   196
structure InductiveArgs =
wenzelm@6437
   197
struct
wenzelm@6437
   198
  val name = "HOL/inductive";
wenzelm@6437
   199
  type T = inductive_info Symtab.table;
wenzelm@6437
   200
wenzelm@6437
   201
  val empty = Symtab.empty;
wenzelm@6556
   202
  val copy = I;
wenzelm@6437
   203
  val prep_ext = I;
wenzelm@6437
   204
  val merge: T * T -> T = Symtab.merge (K true);
wenzelm@6437
   205
wenzelm@6437
   206
  fun print sg tab =
wenzelm@6437
   207
    Pretty.writeln (Pretty.strs ("(co)inductives:" ::
wenzelm@6851
   208
      map #1 (Sign.cond_extern_table sg Sign.constK tab)));
wenzelm@6437
   209
end;
wenzelm@6437
   210
wenzelm@6437
   211
structure InductiveData = TheoryDataFun(InductiveArgs);
wenzelm@6437
   212
val print_inductives = InductiveData.print;
wenzelm@6437
   213
wenzelm@6437
   214
wenzelm@6437
   215
(* get and put data *)
wenzelm@6437
   216
wenzelm@6437
   217
fun get_inductive thy name =
wenzelm@6437
   218
  (case Symtab.lookup (InductiveData.get thy, name) of
wenzelm@6437
   219
    Some info => info
wenzelm@6437
   220
  | None => error ("Unknown (co)inductive set " ^ quote name));
wenzelm@6437
   221
wenzelm@6437
   222
fun put_inductives names info thy =
wenzelm@6437
   223
  let
wenzelm@6437
   224
    fun upd (tab, name) = Symtab.update_new ((name, info), tab);
wenzelm@6437
   225
    val tab = foldl upd (InductiveData.get thy, names)
wenzelm@6437
   226
      handle Symtab.DUP name => error ("Duplicate definition of (co)inductive set " ^ quote name);
wenzelm@6437
   227
  in InductiveData.put tab thy end;
wenzelm@6437
   228
wenzelm@6437
   229
wenzelm@6437
   230
wenzelm@6424
   231
(*** properties of (co)inductive sets ***)
wenzelm@6424
   232
wenzelm@6424
   233
(** elimination rules **)
berghofe@5094
   234
berghofe@5094
   235
fun mk_elims cs cTs params intr_ts =
berghofe@5094
   236
  let
berghofe@5094
   237
    val used = foldr add_term_names (intr_ts, []);
berghofe@5094
   238
    val [aname, pname] = variantlist (["a", "P"], used);
berghofe@5094
   239
    val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
berghofe@5094
   240
berghofe@5094
   241
    fun dest_intr r =
berghofe@5094
   242
      let val Const ("op :", _) $ t $ u =
berghofe@5094
   243
        HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   244
      in (u, t, Logic.strip_imp_prems r) end;
berghofe@5094
   245
berghofe@5094
   246
    val intrs = map dest_intr intr_ts;
berghofe@5094
   247
berghofe@5094
   248
    fun mk_elim (c, T) =
berghofe@5094
   249
      let
berghofe@5094
   250
        val a = Free (aname, T);
berghofe@5094
   251
berghofe@5094
   252
        fun mk_elim_prem (_, t, ts) =
berghofe@5094
   253
          list_all_free (map dest_Free ((foldr add_term_frees (t::ts, [])) \\ params),
berghofe@5094
   254
            Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (a, t)) :: ts, P));
berghofe@5094
   255
      in
berghofe@5094
   256
        Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (a, c)) ::
berghofe@5094
   257
          map mk_elim_prem (filter (equal c o #1) intrs), P)
berghofe@5094
   258
      end
berghofe@5094
   259
  in
berghofe@5094
   260
    map mk_elim (cs ~~ cTs)
berghofe@5094
   261
  end;
berghofe@5094
   262
        
wenzelm@6424
   263
wenzelm@6424
   264
wenzelm@6424
   265
(** premises and conclusions of induction rules **)
berghofe@5094
   266
berghofe@5094
   267
fun mk_indrule cs cTs params intr_ts =
berghofe@5094
   268
  let
berghofe@5094
   269
    val used = foldr add_term_names (intr_ts, []);
berghofe@5094
   270
berghofe@5094
   271
    (* predicates for induction rule *)
berghofe@5094
   272
berghofe@5094
   273
    val preds = map Free (variantlist (if length cs < 2 then ["P"] else
berghofe@5094
   274
      map (fn i => "P" ^ string_of_int i) (1 upto length cs), used) ~~
berghofe@5094
   275
        map (fn T => T --> HOLogic.boolT) cTs);
berghofe@5094
   276
berghofe@5094
   277
    (* transform an introduction rule into a premise for induction rule *)
berghofe@5094
   278
berghofe@5094
   279
    fun mk_ind_prem r =
berghofe@5094
   280
      let
berghofe@5094
   281
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5094
   282
berghofe@5094
   283
        fun subst (prem as (Const ("op :", T) $ t $ u), prems) =
berghofe@5094
   284
              let val n = find_index_eq u cs in
berghofe@5094
   285
                if n >= 0 then prem :: (nth_elem (n, preds)) $ t :: prems else
berghofe@5094
   286
                  (subst_free (map (fn (c, P) => (c, HOLogic.mk_binop "op Int"
berghofe@5094
   287
                    (c, HOLogic.Collect_const (HOLogic.dest_setT
berghofe@5094
   288
                      (fastype_of c)) $ P))) (cs ~~ preds)) prem)::prems
berghofe@5094
   289
              end
berghofe@5094
   290
          | subst (prem, prems) = prem::prems;
berghofe@5094
   291
berghofe@5094
   292
        val Const ("op :", _) $ t $ u =
berghofe@5094
   293
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   294
berghofe@5094
   295
      in list_all_free (frees,
berghofe@5094
   296
           Logic.list_implies (map HOLogic.mk_Trueprop (foldr subst
berghofe@5094
   297
             (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r), [])),
berghofe@5094
   298
               HOLogic.mk_Trueprop (nth_elem (find_index_eq u cs, preds) $ t)))
berghofe@5094
   299
      end;
berghofe@5094
   300
berghofe@5094
   301
    val ind_prems = map mk_ind_prem intr_ts;
berghofe@5094
   302
berghofe@5094
   303
    (* make conclusions for induction rules *)
berghofe@5094
   304
berghofe@5094
   305
    fun mk_ind_concl ((c, P), (ts, x)) =
berghofe@5094
   306
      let val T = HOLogic.dest_setT (fastype_of c);
berghofe@5094
   307
          val Ts = HOLogic.prodT_factors T;
berghofe@5094
   308
          val (frees, x') = foldr (fn (T', (fs, s)) =>
berghofe@5094
   309
            ((Free (s, T'))::fs, bump_string s)) (Ts, ([], x));
berghofe@5094
   310
          val tuple = HOLogic.mk_tuple T frees;
berghofe@5094
   311
      in ((HOLogic.mk_binop "op -->"
berghofe@5094
   312
        (HOLogic.mk_mem (tuple, c), P $ tuple))::ts, x')
berghofe@5094
   313
      end;
berghofe@5094
   314
berghofe@5094
   315
    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 (app HOLogic.conj)
berghofe@5094
   316
        (fst (foldr mk_ind_concl (cs ~~ preds, ([], "xa")))))
berghofe@5094
   317
berghofe@5094
   318
  in (preds, ind_prems, mutual_ind_concl)
berghofe@5094
   319
  end;
berghofe@5094
   320
wenzelm@6424
   321
berghofe@5094
   322
wenzelm@6424
   323
(*** proofs for (co)inductive sets ***)
wenzelm@6424
   324
wenzelm@6424
   325
(** prove monotonicity **)
berghofe@5094
   326
berghofe@5094
   327
fun prove_mono setT fp_fun monos thy =
berghofe@5094
   328
  let
wenzelm@6427
   329
    val _ = message "  Proving monotonicity ...";
berghofe@5094
   330
wenzelm@6394
   331
    val mono = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) (HOLogic.mk_Trueprop
berghofe@5094
   332
      (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun)))
wenzelm@7107
   333
        (fn _ => [rtac monoI 1, REPEAT (ares_tac (default_monos @ monos) 1)])
berghofe@5094
   334
berghofe@5094
   335
  in mono end;
berghofe@5094
   336
wenzelm@6424
   337
wenzelm@6424
   338
wenzelm@6424
   339
(** prove introduction rules **)
berghofe@5094
   340
berghofe@5094
   341
fun prove_intrs coind mono fp_def intr_ts con_defs rec_sets_defs thy =
berghofe@5094
   342
  let
wenzelm@6427
   343
    val _ = message "  Proving the introduction rules ...";
berghofe@5094
   344
berghofe@5094
   345
    val unfold = standard (mono RS (fp_def RS
berghofe@5094
   346
      (if coind then def_gfp_Tarski else def_lfp_Tarski)));
berghofe@5094
   347
berghofe@5094
   348
    fun select_disj 1 1 = []
berghofe@5094
   349
      | select_disj _ 1 = [rtac disjI1]
berghofe@5094
   350
      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
berghofe@5094
   351
berghofe@5094
   352
    val intrs = map (fn (i, intr) => prove_goalw_cterm rec_sets_defs
wenzelm@6394
   353
      (cterm_of (Theory.sign_of thy) intr) (fn prems =>
berghofe@5094
   354
       [(*insert prems and underlying sets*)
berghofe@5094
   355
       cut_facts_tac prems 1,
berghofe@5094
   356
       stac unfold 1,
berghofe@5094
   357
       REPEAT (resolve_tac [vimageI2, CollectI] 1),
berghofe@5094
   358
       (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
berghofe@5094
   359
       EVERY1 (select_disj (length intr_ts) i),
berghofe@5094
   360
       (*Not ares_tac, since refl must be tried before any equality assumptions;
berghofe@5094
   361
         backtracking may occur if the premises have extra variables!*)
berghofe@5094
   362
       DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 1 APPEND assume_tac 1),
berghofe@5094
   363
       (*Now solve the equations like Inl 0 = Inl ?b2*)
berghofe@5094
   364
       rewrite_goals_tac con_defs,
berghofe@5094
   365
       REPEAT (rtac refl 1)])) (1 upto (length intr_ts) ~~ intr_ts)
berghofe@5094
   366
berghofe@5094
   367
  in (intrs, unfold) end;
berghofe@5094
   368
wenzelm@6424
   369
wenzelm@6424
   370
wenzelm@6424
   371
(** prove elimination rules **)
berghofe@5094
   372
berghofe@5094
   373
fun prove_elims cs cTs params intr_ts unfold rec_sets_defs thy =
berghofe@5094
   374
  let
wenzelm@6427
   375
    val _ = message "  Proving the elimination rules ...";
berghofe@5094
   376
berghofe@5094
   377
    val rules1 = [CollectE, disjE, make_elim vimageD];
berghofe@5094
   378
    val rules2 = [exE, conjE, Inl_neq_Inr, Inr_neq_Inl] @
berghofe@5094
   379
      map make_elim [Inl_inject, Inr_inject];
berghofe@5094
   380
berghofe@5094
   381
    val elims = map (fn t => prove_goalw_cterm rec_sets_defs
wenzelm@6394
   382
      (cterm_of (Theory.sign_of thy) t) (fn prems =>
berghofe@5094
   383
        [cut_facts_tac [hd prems] 1,
berghofe@5094
   384
         dtac (unfold RS subst) 1,
berghofe@5094
   385
         REPEAT (FIRSTGOAL (eresolve_tac rules1)),
berghofe@5094
   386
         REPEAT (FIRSTGOAL (eresolve_tac rules2)),
berghofe@5094
   387
         EVERY (map (fn prem =>
berghofe@5149
   388
           DEPTH_SOLVE_1 (ares_tac [prem, conjI] 1)) (tl prems))]))
berghofe@5094
   389
      (mk_elims cs cTs params intr_ts)
berghofe@5094
   390
berghofe@5094
   391
  in elims end;
berghofe@5094
   392
wenzelm@6424
   393
berghofe@5094
   394
(** derivation of simplified elimination rules **)
berghofe@5094
   395
berghofe@5094
   396
(*Applies freeness of the given constructors, which *must* be unfolded by
berghofe@5094
   397
  the given defs.  Cannot simply use the local con_defs because con_defs=[] 
berghofe@5094
   398
  for inference systems.
berghofe@5094
   399
 *)
paulson@6141
   400
fun con_elim_tac ss =
berghofe@5094
   401
  let val elim_tac = REPEAT o (eresolve_tac elim_rls)
berghofe@5094
   402
  in ALLGOALS(EVERY'[elim_tac,
paulson@6141
   403
		     asm_full_simp_tac ss,
paulson@6141
   404
		     elim_tac,
paulson@6141
   405
		     REPEAT o bound_hyp_subst_tac])
berghofe@5094
   406
     THEN prune_params_tac
berghofe@5094
   407
  end;
berghofe@5094
   408
wenzelm@7107
   409
(*cprop should have the form t:Si where Si is an inductive set*)
wenzelm@7107
   410
fun mk_cases_i elims ss cprop =
wenzelm@7107
   411
  let
wenzelm@7107
   412
    val prem = Thm.assume cprop;
wenzelm@7107
   413
    fun mk_elim rl = standard (rule_by_tactic (con_elim_tac ss) (prem RS rl));
wenzelm@7107
   414
  in
wenzelm@7107
   415
    (case get_first (try mk_elim) elims of
wenzelm@7107
   416
      Some r => r
wenzelm@7107
   417
    | None => error (Pretty.string_of (Pretty.block
wenzelm@7107
   418
        [Pretty.str "mk_cases: proposition not of form 't : S_i'", Pretty.fbrk,
wenzelm@7107
   419
          Display.pretty_cterm cprop])))
wenzelm@7107
   420
  end;
wenzelm@7107
   421
paulson@6141
   422
fun mk_cases elims s =
wenzelm@7107
   423
  mk_cases_i elims (simpset()) (Thm.read_cterm (Thm.sign_of_thm (hd elims)) (s, propT));
wenzelm@7107
   424
wenzelm@7107
   425
wenzelm@7107
   426
(* inductive_cases(_i) *)
wenzelm@7107
   427
wenzelm@7107
   428
fun gen_inductive_cases prep_att prep_const prep_prop
wenzelm@7107
   429
    ((((name, raw_atts), raw_set), raw_props), comment) thy =
wenzelm@7107
   430
  let
wenzelm@7107
   431
    val sign = Theory.sign_of thy;
wenzelm@7107
   432
wenzelm@7107
   433
    val atts = map (prep_att thy) raw_atts;
wenzelm@7107
   434
    val (_, {elims, ...}) = get_inductive thy (prep_const sign raw_set);
wenzelm@7107
   435
    val cprops = map (Thm.cterm_of sign o prep_prop (ProofContext.init thy)) raw_props;
wenzelm@7107
   436
    val thms = map (mk_cases_i elims (Simplifier.simpset_of thy)) cprops;
wenzelm@7107
   437
  in
wenzelm@7107
   438
    thy
wenzelm@7107
   439
    |> IsarThy.have_theorems_i (((name, atts), map Thm.no_attributes thms), comment)
berghofe@5094
   440
  end;
berghofe@5094
   441
wenzelm@7107
   442
val inductive_cases =
wenzelm@7107
   443
  gen_inductive_cases Attrib.global_attribute Sign.intern_const ProofContext.read_prop;
wenzelm@7107
   444
wenzelm@7107
   445
val inductive_cases_i = gen_inductive_cases (K I) (K I) ProofContext.cert_prop;
wenzelm@7107
   446
wenzelm@6424
   447
wenzelm@6424
   448
wenzelm@6424
   449
(** prove induction rule **)
berghofe@5094
   450
berghofe@5094
   451
fun prove_indrule cs cTs sumT rec_const params intr_ts mono
berghofe@5094
   452
    fp_def rec_sets_defs thy =
berghofe@5094
   453
  let
wenzelm@6427
   454
    val _ = message "  Proving the induction rule ...";
berghofe@5094
   455
wenzelm@6394
   456
    val sign = Theory.sign_of thy;
berghofe@5094
   457
berghofe@5094
   458
    val (preds, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
berghofe@5094
   459
berghofe@5094
   460
    (* make predicate for instantiation of abstract induction rule *)
berghofe@5094
   461
berghofe@5094
   462
    fun mk_ind_pred _ [P] = P
berghofe@5094
   463
      | mk_ind_pred T Ps =
berghofe@5094
   464
         let val n = (length Ps) div 2;
berghofe@5094
   465
             val Type (_, [T1, T2]) = T
berghofe@5094
   466
         in Const ("sum_case",
berghofe@5094
   467
           [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
berghofe@5094
   468
             mk_ind_pred T1 (take (n, Ps)) $ mk_ind_pred T2 (drop (n, Ps))
berghofe@5094
   469
         end;
berghofe@5094
   470
berghofe@5094
   471
    val ind_pred = mk_ind_pred sumT preds;
berghofe@5094
   472
berghofe@5094
   473
    val ind_concl = HOLogic.mk_Trueprop
berghofe@5094
   474
      (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
berghofe@5094
   475
        (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
berghofe@5094
   476
berghofe@5094
   477
    (* simplification rules for vimage and Collect *)
berghofe@5094
   478
berghofe@5094
   479
    val vimage_simps = if length cs < 2 then [] else
berghofe@5094
   480
      map (fn c => prove_goalw_cterm [] (cterm_of sign
berghofe@5094
   481
        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@5094
   482
          (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
berghofe@5094
   483
           HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
berghofe@5094
   484
             nth_elem (find_index_eq c cs, preds)))))
berghofe@5094
   485
        (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac
oheimb@5553
   486
           (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
berghofe@5094
   487
          rtac refl 1])) cs;
berghofe@5094
   488
berghofe@5094
   489
    val induct = prove_goalw_cterm [] (cterm_of sign
berghofe@5094
   490
      (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
berghofe@5094
   491
        [rtac (impI RS allI) 1,
berghofe@5094
   492
         DETERM (etac (mono RS (fp_def RS def_induct)) 1),
oheimb@5553
   493
         rewrite_goals_tac (map mk_meta_eq (vimage_Int::vimage_simps)),
berghofe@5094
   494
         fold_goals_tac rec_sets_defs,
berghofe@5094
   495
         (*This CollectE and disjE separates out the introduction rules*)
berghofe@5094
   496
         REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE])),
berghofe@5094
   497
         (*Now break down the individual cases.  No disjE here in case
berghofe@5094
   498
           some premise involves disjunction.*)
berghofe@5094
   499
         REPEAT (FIRSTGOAL (eresolve_tac [IntE, CollectE, exE, conjE] 
berghofe@5094
   500
                     ORELSE' hyp_subst_tac)),
oheimb@5553
   501
         rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
berghofe@5094
   502
         EVERY (map (fn prem =>
berghofe@5149
   503
           DEPTH_SOLVE_1 (ares_tac [prem, conjI, refl] 1)) prems)]);
berghofe@5094
   504
berghofe@5094
   505
    val lemma = prove_goalw_cterm rec_sets_defs (cterm_of sign
berghofe@5094
   506
      (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
berghofe@5094
   507
        [cut_facts_tac prems 1,
berghofe@5094
   508
         REPEAT (EVERY
berghofe@5094
   509
           [REPEAT (resolve_tac [conjI, impI] 1),
berghofe@5094
   510
            TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
oheimb@5553
   511
            rewrite_goals_tac (map mk_meta_eq [sum_case_Inl, sum_case_Inr]),
berghofe@5094
   512
            atac 1])])
berghofe@5094
   513
berghofe@5094
   514
  in standard (split_rule (induct RS lemma))
berghofe@5094
   515
  end;
berghofe@5094
   516
wenzelm@6424
   517
wenzelm@6424
   518
wenzelm@6424
   519
(*** specification of (co)inductive sets ****)
wenzelm@6424
   520
wenzelm@6424
   521
(** definitional introduction of (co)inductive sets **)
berghofe@5094
   522
berghofe@5094
   523
fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@6521
   524
    atts intros monos con_defs thy params paramTs cTs cnames =
berghofe@5094
   525
  let
wenzelm@6424
   526
    val _ = if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
wenzelm@6424
   527
      commas_quote cnames) else ();
berghofe@5094
   528
berghofe@5094
   529
    val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
berghofe@5094
   530
    val setT = HOLogic.mk_setT sumT;
berghofe@5094
   531
wenzelm@6394
   532
    val fp_name = if coind then Sign.intern_const (Theory.sign_of Gfp.thy) "gfp"
wenzelm@6394
   533
      else Sign.intern_const (Theory.sign_of Lfp.thy) "lfp";
berghofe@5094
   534
wenzelm@6424
   535
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
wenzelm@6424
   536
berghofe@5149
   537
    val used = foldr add_term_names (intr_ts, []);
berghofe@5149
   538
    val [sname, xname] = variantlist (["S", "x"], used);
berghofe@5149
   539
berghofe@5094
   540
    (* transform an introduction rule into a conjunction  *)
berghofe@5094
   541
    (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
berghofe@5094
   542
    (* is transformed into                                *)
berghofe@5094
   543
    (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
berghofe@5094
   544
berghofe@5094
   545
    fun transform_rule r =
berghofe@5094
   546
      let
berghofe@5094
   547
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5149
   548
        val subst = subst_free
berghofe@5149
   549
          (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
berghofe@5094
   550
        val Const ("op :", _) $ t $ u =
berghofe@5094
   551
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   552
berghofe@5094
   553
      in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
berghofe@5094
   554
        (frees, foldr1 (app HOLogic.conj)
berghofe@5149
   555
          (((HOLogic.eq_const sumT) $ Free (xname, sumT) $ (mk_inj cs sumT u t))::
berghofe@5094
   556
            (map (subst o HOLogic.dest_Trueprop)
berghofe@5094
   557
              (Logic.strip_imp_prems r))))
berghofe@5094
   558
      end
berghofe@5094
   559
berghofe@5094
   560
    (* make a disjunction of all introduction rules *)
berghofe@5094
   561
berghofe@5149
   562
    val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) $
berghofe@5149
   563
      absfree (xname, sumT, foldr1 (app HOLogic.disj) (map transform_rule intr_ts)));
berghofe@5094
   564
berghofe@5094
   565
    (* add definiton of recursive sets to theory *)
berghofe@5094
   566
berghofe@5094
   567
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
wenzelm@6394
   568
    val full_rec_name = Sign.full_name (Theory.sign_of thy) rec_name;
berghofe@5094
   569
berghofe@5094
   570
    val rec_const = list_comb
berghofe@5094
   571
      (Const (full_rec_name, paramTs ---> setT), params);
berghofe@5094
   572
berghofe@5094
   573
    val fp_def_term = Logic.mk_equals (rec_const,
berghofe@5094
   574
      Const (fp_name, (setT --> setT) --> setT) $ fp_fun)
berghofe@5094
   575
berghofe@5094
   576
    val def_terms = fp_def_term :: (if length cs < 2 then [] else
berghofe@5094
   577
      map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
berghofe@5094
   578
berghofe@5094
   579
    val thy' = thy |>
berghofe@5094
   580
      (if declare_consts then
berghofe@5094
   581
        Theory.add_consts_i (map (fn (c, n) =>
berghofe@5094
   582
          (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
berghofe@5094
   583
       else I) |>
berghofe@5094
   584
      (if length cs < 2 then I else
berghofe@5094
   585
       Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)]) |>
berghofe@5094
   586
      Theory.add_path rec_name |>
berghofe@5094
   587
      PureThy.add_defss_i [(("defs", def_terms), [])];
berghofe@5094
   588
berghofe@5094
   589
    (* get definitions from theory *)
berghofe@5094
   590
wenzelm@6424
   591
    val fp_def::rec_sets_defs = PureThy.get_thms thy' "defs";
berghofe@5094
   592
berghofe@5094
   593
    (* prove and store theorems *)
berghofe@5094
   594
berghofe@5094
   595
    val mono = prove_mono setT fp_fun monos thy';
berghofe@5094
   596
    val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts con_defs
berghofe@5094
   597
      rec_sets_defs thy';
berghofe@5094
   598
    val elims = if no_elim then [] else
berghofe@5094
   599
      prove_elims cs cTs params intr_ts unfold rec_sets_defs thy';
berghofe@5094
   600
    val raw_induct = if no_ind then TrueI else
berghofe@5094
   601
      if coind then standard (rule_by_tactic
oheimb@5553
   602
        (rewrite_tac [mk_meta_eq vimage_Un] THEN
berghofe@5094
   603
          fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
berghofe@5094
   604
      else
berghofe@5094
   605
        prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
berghofe@5094
   606
          rec_sets_defs thy';
berghofe@5108
   607
    val induct = if coind orelse no_ind orelse length cs > 1 then raw_induct
berghofe@5094
   608
      else standard (raw_induct RSN (2, rev_mp));
berghofe@5094
   609
wenzelm@6424
   610
    val thy'' = thy'
wenzelm@6521
   611
      |> PureThy.add_thmss [(("intrs", intrs), atts)]
wenzelm@6424
   612
      |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
wenzelm@6424
   613
      |> (if no_elim then I else PureThy.add_thmss [(("elims", elims), [])])
wenzelm@6424
   614
      |> (if no_ind then I else PureThy.add_thms
wenzelm@6424
   615
        [((coind_prefix coind ^ "induct", induct), [])])
wenzelm@6424
   616
      |> Theory.parent_path;
berghofe@5094
   617
berghofe@5094
   618
  in (thy'',
berghofe@5094
   619
    {defs = fp_def::rec_sets_defs,
berghofe@5094
   620
     mono = mono,
berghofe@5094
   621
     unfold = unfold,
berghofe@5094
   622
     intrs = intrs,
berghofe@5094
   623
     elims = elims,
berghofe@5094
   624
     mk_cases = mk_cases elims,
berghofe@5094
   625
     raw_induct = raw_induct,
berghofe@5094
   626
     induct = induct})
berghofe@5094
   627
  end;
berghofe@5094
   628
wenzelm@6424
   629
wenzelm@6424
   630
wenzelm@6424
   631
(** axiomatic introduction of (co)inductive sets **)
berghofe@5094
   632
berghofe@5094
   633
fun add_ind_axm verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@6521
   634
    atts intros monos con_defs thy params paramTs cTs cnames =
berghofe@5094
   635
  let
wenzelm@6424
   636
    val _ = if verbose then message ("Adding axioms for " ^ coind_prefix coind ^
wenzelm@6424
   637
      "inductive set(s) " ^ commas_quote cnames) else ();
berghofe@5094
   638
berghofe@5094
   639
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
berghofe@5094
   640
wenzelm@6424
   641
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
berghofe@5094
   642
    val elim_ts = mk_elims cs cTs params intr_ts;
berghofe@5094
   643
berghofe@5094
   644
    val (_, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
berghofe@5094
   645
    val ind_t = Logic.list_implies (ind_prems, mutual_ind_concl);
berghofe@5094
   646
    
wenzelm@6424
   647
    val thy' = thy
wenzelm@6424
   648
      |> (if declare_consts then
wenzelm@6424
   649
            Theory.add_consts_i
wenzelm@6424
   650
              (map (fn (c, n) => (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
wenzelm@6424
   651
         else I)
wenzelm@6424
   652
      |> Theory.add_path rec_name
wenzelm@6521
   653
      |> PureThy.add_axiomss_i [(("intrs", intr_ts), atts), (("elims", elim_ts), [])]
wenzelm@6424
   654
      |> (if coind then I else PureThy.add_axioms_i [(("internal_induct", ind_t), [])]);
berghofe@5094
   655
wenzelm@6424
   656
    val intrs = PureThy.get_thms thy' "intrs";
wenzelm@6424
   657
    val elims = PureThy.get_thms thy' "elims";
berghofe@5094
   658
    val raw_induct = if coind then TrueI else
wenzelm@6424
   659
      standard (split_rule (PureThy.get_thm thy' "internal_induct"));
berghofe@5094
   660
    val induct = if coind orelse length cs > 1 then raw_induct
berghofe@5094
   661
      else standard (raw_induct RSN (2, rev_mp));
berghofe@5094
   662
wenzelm@6424
   663
    val thy'' =
wenzelm@6424
   664
      thy'
wenzelm@6424
   665
      |> (if coind then I else PureThy.add_thms [(("induct", induct), [])])
wenzelm@6424
   666
      |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
wenzelm@6424
   667
      |> Theory.parent_path;
berghofe@5094
   668
  in (thy'',
berghofe@5094
   669
    {defs = [],
berghofe@5094
   670
     mono = TrueI,
berghofe@5094
   671
     unfold = TrueI,
berghofe@5094
   672
     intrs = intrs,
berghofe@5094
   673
     elims = elims,
berghofe@5094
   674
     mk_cases = mk_cases elims,
berghofe@5094
   675
     raw_induct = raw_induct,
berghofe@5094
   676
     induct = induct})
berghofe@5094
   677
  end;
berghofe@5094
   678
wenzelm@6424
   679
wenzelm@6424
   680
wenzelm@6424
   681
(** introduction of (co)inductive sets **)
berghofe@5094
   682
berghofe@5094
   683
fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@6521
   684
    atts intros monos con_defs thy =
berghofe@5094
   685
  let
wenzelm@6424
   686
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
wenzelm@6394
   687
    val sign = Theory.sign_of thy;
berghofe@5094
   688
berghofe@5094
   689
    (*parameters should agree for all mutually recursive components*)
berghofe@5094
   690
    val (_, params) = strip_comb (hd cs);
berghofe@5094
   691
    val paramTs = map (try' (snd o dest_Free) "Parameter in recursive\
berghofe@5094
   692
      \ component is not a free variable: " sign) params;
berghofe@5094
   693
berghofe@5094
   694
    val cTs = map (try' (HOLogic.dest_setT o fastype_of)
berghofe@5094
   695
      "Recursive component not of type set: " sign) cs;
berghofe@5094
   696
wenzelm@6437
   697
    val full_cnames = map (try' (fst o dest_Const o head_of)
berghofe@5094
   698
      "Recursive set not previously declared as constant: " sign) cs;
wenzelm@6437
   699
    val cnames = map Sign.base_name full_cnames;
berghofe@5094
   700
wenzelm@6424
   701
    val _ = assert_all Syntax.is_identifier cnames	(* FIXME why? *)
berghofe@5094
   702
       (fn a => "Base name of recursive set not an identifier: " ^ a);
wenzelm@6424
   703
    val _ = seq (check_rule sign cs o snd o fst) intros;
wenzelm@6437
   704
wenzelm@6437
   705
    val (thy1, result) =
wenzelm@6437
   706
      (if ! quick_and_dirty then add_ind_axm else add_ind_def)
wenzelm@6521
   707
        verbose declare_consts alt_name coind no_elim no_ind cs atts intros monos
wenzelm@6437
   708
        con_defs thy params paramTs cTs cnames;
wenzelm@6437
   709
    val thy2 = thy1 |> put_inductives full_cnames ({names = full_cnames, coind = coind}, result);
wenzelm@6437
   710
  in (thy2, result) end;
berghofe@5094
   711
wenzelm@6424
   712
berghofe@5094
   713
wenzelm@6424
   714
(** external interface **)
wenzelm@6424
   715
wenzelm@6521
   716
fun add_inductive verbose coind c_strings srcs intro_srcs raw_monos raw_con_defs thy =
berghofe@5094
   717
  let
wenzelm@6394
   718
    val sign = Theory.sign_of thy;
wenzelm@6394
   719
    val cs = map (readtm (Theory.sign_of thy) HOLogic.termTVar) c_strings;
wenzelm@6424
   720
wenzelm@6521
   721
    val atts = map (Attrib.global_attribute thy) srcs;
wenzelm@6424
   722
    val intr_names = map (fst o fst) intro_srcs;
wenzelm@6424
   723
    val intr_ts = map (readtm (Theory.sign_of thy) propT o snd o fst) intro_srcs;
wenzelm@6424
   724
    val intr_atts = map (map (Attrib.global_attribute thy) o snd) intro_srcs;
berghofe@7020
   725
    val (cs', intr_ts') = unify_consts sign cs intr_ts;
berghofe@5094
   726
wenzelm@6424
   727
    val ((thy', con_defs), monos) = thy
wenzelm@6424
   728
      |> IsarThy.apply_theorems raw_monos
wenzelm@6424
   729
      |> apfst (IsarThy.apply_theorems raw_con_defs);
wenzelm@6424
   730
  in
berghofe@7020
   731
    add_inductive_i verbose false "" coind false false cs'
berghofe@7020
   732
      atts ((intr_names ~~ intr_ts') ~~ intr_atts) monos con_defs thy'
berghofe@5094
   733
  end;
berghofe@5094
   734
wenzelm@6424
   735
wenzelm@6424
   736
wenzelm@6437
   737
(** package setup **)
wenzelm@6437
   738
wenzelm@6437
   739
(* setup theory *)
wenzelm@6437
   740
wenzelm@6437
   741
val setup = [InductiveData.init];
wenzelm@6437
   742
wenzelm@6437
   743
wenzelm@6437
   744
(* outer syntax *)
wenzelm@6424
   745
wenzelm@6723
   746
local structure P = OuterParse and K = OuterSyntax.Keyword in
wenzelm@6424
   747
wenzelm@6521
   748
fun mk_ind coind (((sets, (atts, intrs)), monos), con_defs) =
wenzelm@6723
   749
  #1 o add_inductive true coind sets atts (map P.triple_swap intrs) monos con_defs;
wenzelm@6424
   750
wenzelm@6424
   751
fun ind_decl coind =
wenzelm@6729
   752
  (Scan.repeat1 P.term --| P.marg_comment) --
wenzelm@6729
   753
  (P.$$$ "intrs" |--
wenzelm@6729
   754
    P.!!! (P.opt_attribs -- Scan.repeat1 (P.opt_thm_name ":" -- P.term --| P.marg_comment))) --
wenzelm@6729
   755
  Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1 --| P.marg_comment) [] --
wenzelm@6729
   756
  Scan.optional (P.$$$ "con_defs" |-- P.!!! P.xthms1 --| P.marg_comment) []
wenzelm@6424
   757
  >> (Toplevel.theory o mk_ind coind);
wenzelm@6424
   758
wenzelm@6723
   759
val inductiveP =
wenzelm@6723
   760
  OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
wenzelm@6723
   761
wenzelm@6723
   762
val coinductiveP =
wenzelm@6723
   763
  OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
wenzelm@6424
   764
wenzelm@7107
   765
wenzelm@7107
   766
val ind_cases =
wenzelm@7107
   767
  P.opt_thm_name "=" -- P.xname --| P.$$$ ":" -- Scan.repeat1 P.prop -- P.marg_comment
wenzelm@7107
   768
  >> (Toplevel.theory o inductive_cases);
wenzelm@7107
   769
wenzelm@7107
   770
val inductive_casesP =
wenzelm@7107
   771
  OuterSyntax.command "inductive_cases" "create simplified instances of elimination rules"
wenzelm@7107
   772
    K.thy_decl ind_cases;
wenzelm@7107
   773
wenzelm@6424
   774
val _ = OuterSyntax.add_keywords ["intrs", "monos", "con_defs"];
wenzelm@7107
   775
val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP, inductive_casesP];
wenzelm@6424
   776
berghofe@5094
   777
end;
wenzelm@6424
   778
wenzelm@6424
   779
wenzelm@6424
   780
end;