src/HOL/Tools/inductive_package.ML
author wenzelm
Fri Mar 31 21:55:27 2000 +0200 (2000-03-31)
changeset 8634 3f34637cb9c0
parent 8433 8ae16c770fc8
child 8720 840c75ab2a7f
permissions -rw-r--r--
use Attrib.add_del_args;
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
wenzelm@8316
    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
berghofe@7710
    39
  val mono_add_global: theory attribute
berghofe@7710
    40
  val mono_del_global: theory attribute
berghofe@7710
    41
  val get_monos: theory -> thm list
wenzelm@6424
    42
  val add_inductive_i: bool -> bool -> bstring -> bool -> bool -> bool -> term list ->
wenzelm@6521
    43
    theory attribute list -> ((bstring * term) * theory attribute list) list ->
wenzelm@6521
    44
      thm list -> thm list -> theory -> theory *
wenzelm@6424
    45
      {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
wenzelm@6437
    46
       intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
wenzelm@6521
    47
  val add_inductive: bool -> bool -> string list -> Args.src list ->
wenzelm@6521
    48
    ((bstring * string) * Args.src list) list -> (xstring * Args.src list) list ->
wenzelm@6521
    49
      (xstring * Args.src list) list -> theory -> theory *
wenzelm@6424
    50
      {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
wenzelm@6437
    51
       intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
wenzelm@7107
    52
  val inductive_cases: (((bstring * Args.src list) * xstring) * string list) * Comment.text
wenzelm@7107
    53
    -> theory -> theory
wenzelm@7107
    54
  val inductive_cases_i: (((bstring * theory attribute list) * string) * term list) * Comment.text
wenzelm@7107
    55
    -> theory -> theory
wenzelm@6437
    56
  val setup: (theory -> theory) list
berghofe@5094
    57
end;
berghofe@5094
    58
wenzelm@6424
    59
structure InductivePackage: INDUCTIVE_PACKAGE =
berghofe@5094
    60
struct
berghofe@5094
    61
berghofe@7710
    62
(*** theory data ***)
berghofe@7710
    63
berghofe@7710
    64
(* data kind 'HOL/inductive' *)
berghofe@7710
    65
berghofe@7710
    66
type inductive_info =
berghofe@7710
    67
  {names: string list, coind: bool} * {defs: thm list, elims: thm list, raw_induct: thm,
berghofe@7710
    68
    induct: thm, intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm};
berghofe@7710
    69
berghofe@7710
    70
structure InductiveArgs =
berghofe@7710
    71
struct
berghofe@7710
    72
  val name = "HOL/inductive";
berghofe@7710
    73
  type T = inductive_info Symtab.table * thm list;
berghofe@7710
    74
berghofe@7710
    75
  val empty = (Symtab.empty, []);
berghofe@7710
    76
  val copy = I;
berghofe@7710
    77
  val prep_ext = I;
berghofe@7710
    78
  fun merge ((tab1, monos1), (tab2, monos2)) = (Symtab.merge (K true) (tab1, tab2),
berghofe@7710
    79
    Library.generic_merge Thm.eq_thm I I monos1 monos2);
berghofe@7710
    80
berghofe@7710
    81
  fun print sg (tab, monos) =
berghofe@7710
    82
    (Pretty.writeln (Pretty.strs ("(co)inductives:" ::
berghofe@7710
    83
       map #1 (Sign.cond_extern_table sg Sign.constK tab)));
berghofe@7710
    84
     Pretty.writeln (Pretty.big_list "monotonicity rules:" (map Display.pretty_thm monos)));
berghofe@7710
    85
end;
berghofe@7710
    86
berghofe@7710
    87
structure InductiveData = TheoryDataFun(InductiveArgs);
berghofe@7710
    88
val print_inductives = InductiveData.print;
berghofe@7710
    89
berghofe@7710
    90
berghofe@7710
    91
(* get and put data *)
berghofe@7710
    92
berghofe@7710
    93
fun get_inductive thy name =
berghofe@7710
    94
  (case Symtab.lookup (fst (InductiveData.get thy), name) of
berghofe@7710
    95
    Some info => info
berghofe@7710
    96
  | None => error ("Unknown (co)inductive set " ^ quote name));
berghofe@7710
    97
berghofe@7710
    98
fun put_inductives names info thy =
berghofe@7710
    99
  let
berghofe@7710
   100
    fun upd ((tab, monos), name) = (Symtab.update_new ((name, info), tab), monos);
berghofe@7710
   101
    val tab_monos = foldl upd (InductiveData.get thy, names)
berghofe@7710
   102
      handle Symtab.DUP name => error ("Duplicate definition of (co)inductive set " ^ quote name);
berghofe@7710
   103
  in InductiveData.put tab_monos thy end;
berghofe@7710
   104
wenzelm@8277
   105
berghofe@7710
   106
berghofe@7710
   107
(** monotonicity rules **)
berghofe@7710
   108
wenzelm@8277
   109
val get_monos = snd o InductiveData.get;
wenzelm@8277
   110
fun put_monos thms thy = InductiveData.put (fst (InductiveData.get thy), thms) thy;
wenzelm@8277
   111
berghofe@7710
   112
fun mk_mono thm =
berghofe@7710
   113
  let
berghofe@7710
   114
    fun eq2mono thm' = [standard (thm' RS (thm' RS eq_to_mono))] @
berghofe@7710
   115
      (case concl_of thm of
berghofe@7710
   116
          (_ $ (_ $ (Const ("Not", _) $ _) $ _)) => []
berghofe@7710
   117
        | _ => [standard (thm' RS (thm' RS eq_to_mono2))]);
berghofe@7710
   118
    val concl = concl_of thm
berghofe@7710
   119
  in
berghofe@7710
   120
    if Logic.is_equals concl then
berghofe@7710
   121
      eq2mono (thm RS meta_eq_to_obj_eq)
berghofe@7710
   122
    else if can (HOLogic.dest_eq o HOLogic.dest_Trueprop) concl then
berghofe@7710
   123
      eq2mono thm
berghofe@7710
   124
    else [thm]
berghofe@7710
   125
  end;
berghofe@7710
   126
wenzelm@8634
   127
wenzelm@8634
   128
(* attributes *)
berghofe@7710
   129
berghofe@7710
   130
local
berghofe@7710
   131
berghofe@7710
   132
fun map_rules_global f thy = put_monos (f (get_monos thy)) thy;
berghofe@7710
   133
berghofe@7710
   134
fun add_mono thm rules = Library.gen_union Thm.eq_thm (mk_mono thm, rules);
berghofe@7710
   135
fun del_mono thm rules = Library.gen_rems Thm.eq_thm (rules, mk_mono thm);
berghofe@7710
   136
berghofe@7710
   137
fun mk_att f g (x, thm) = (f (g thm) x, thm);
berghofe@7710
   138
berghofe@7710
   139
in
wenzelm@8634
   140
  val mono_add_global = mk_att map_rules_global add_mono;
wenzelm@8634
   141
  val mono_del_global = mk_att map_rules_global del_mono;
berghofe@7710
   142
end;
berghofe@7710
   143
berghofe@7710
   144
val mono_attr =
wenzelm@8634
   145
 (Attrib.add_del_args mono_add_global mono_del_global,
wenzelm@8634
   146
  Attrib.add_del_args Attrib.undef_local_attribute Attrib.undef_local_attribute);
berghofe@7710
   147
berghofe@7710
   148
wenzelm@7107
   149
wenzelm@6424
   150
(** utilities **)
wenzelm@6424
   151
wenzelm@6424
   152
(* messages *)
wenzelm@6424
   153
berghofe@5662
   154
val quiet_mode = ref false;
berghofe@5662
   155
fun message s = if !quiet_mode then () else writeln s;
berghofe@5662
   156
wenzelm@6424
   157
fun coind_prefix true = "co"
wenzelm@6424
   158
  | coind_prefix false = "";
wenzelm@6424
   159
wenzelm@6424
   160
berghofe@7020
   161
(* the following code ensures that each recursive set *)
berghofe@7020
   162
(* always has the same type in all introduction rules *)
berghofe@7020
   163
berghofe@7020
   164
fun unify_consts sign cs intr_ts =
berghofe@7020
   165
  (let
berghofe@7020
   166
    val {tsig, ...} = Sign.rep_sg sign;
berghofe@7020
   167
    val add_term_consts_2 =
berghofe@7020
   168
      foldl_aterms (fn (cs, Const c) => c ins cs | (cs, _) => cs);
berghofe@7020
   169
    fun varify (t, (i, ts)) =
berghofe@7020
   170
      let val t' = map_term_types (incr_tvar (i + 1)) (Type.varify (t, []))
berghofe@7020
   171
      in (maxidx_of_term t', t'::ts) end;
berghofe@7020
   172
    val (i, cs') = foldr varify (cs, (~1, []));
berghofe@7020
   173
    val (i', intr_ts') = foldr varify (intr_ts, (i, []));
berghofe@7020
   174
    val rec_consts = foldl add_term_consts_2 ([], cs');
berghofe@7020
   175
    val intr_consts = foldl add_term_consts_2 ([], intr_ts');
berghofe@7020
   176
    fun unify (env, (cname, cT)) =
berghofe@7020
   177
      let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
berghofe@7020
   178
      in foldl (fn ((env', j'), Tp) => (Type.unify tsig j' env' Tp))
berghofe@7020
   179
          (env, (replicate (length consts) cT) ~~ consts)
berghofe@7020
   180
      end;
berghofe@8410
   181
    val (env, _) = foldl unify ((Vartab.empty, i'), rec_consts);
berghofe@8410
   182
    fun typ_subst_TVars_2 env T = let val T' = typ_subst_TVars_Vartab env T
berghofe@7020
   183
      in if T = T' then T else typ_subst_TVars_2 env T' end;
berghofe@7020
   184
    val subst = fst o Type.freeze_thaw o
berghofe@7020
   185
      (map_term_types (typ_subst_TVars_2 env))
berghofe@7020
   186
berghofe@7020
   187
  in (map subst cs', map subst intr_ts')
berghofe@7020
   188
  end) handle Type.TUNIFY =>
berghofe@7020
   189
    (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
berghofe@7020
   190
berghofe@7020
   191
wenzelm@6424
   192
(* misc *)
wenzelm@6424
   193
berghofe@5094
   194
val Const _ $ (vimage_f $ _) $ _ = HOLogic.dest_Trueprop (concl_of vimageD);
berghofe@5094
   195
wenzelm@6394
   196
val vimage_name = Sign.intern_const (Theory.sign_of Vimage.thy) "op -``";
wenzelm@6394
   197
val mono_name = Sign.intern_const (Theory.sign_of Ord.thy) "mono";
berghofe@5094
   198
berghofe@5094
   199
(* make injections needed in mutually recursive definitions *)
berghofe@5094
   200
berghofe@5094
   201
fun mk_inj cs sumT c x =
berghofe@5094
   202
  let
berghofe@5094
   203
    fun mk_inj' T n i =
berghofe@5094
   204
      if n = 1 then x else
berghofe@5094
   205
      let val n2 = n div 2;
berghofe@5094
   206
          val Type (_, [T1, T2]) = T
berghofe@5094
   207
      in
berghofe@5094
   208
        if i <= n2 then
berghofe@5094
   209
          Const ("Inl", T1 --> T) $ (mk_inj' T1 n2 i)
berghofe@5094
   210
        else
berghofe@5094
   211
          Const ("Inr", T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2))
berghofe@5094
   212
      end
berghofe@5094
   213
  in mk_inj' sumT (length cs) (1 + find_index_eq c cs)
berghofe@5094
   214
  end;
berghofe@5094
   215
berghofe@5094
   216
(* make "vimage" terms for selecting out components of mutually rec.def. *)
berghofe@5094
   217
berghofe@5094
   218
fun mk_vimage cs sumT t c = if length cs < 2 then t else
berghofe@5094
   219
  let
berghofe@5094
   220
    val cT = HOLogic.dest_setT (fastype_of c);
berghofe@5094
   221
    val vimageT = [cT --> sumT, HOLogic.mk_setT sumT] ---> HOLogic.mk_setT cT
berghofe@5094
   222
  in
berghofe@5094
   223
    Const (vimage_name, vimageT) $
berghofe@5094
   224
      Abs ("y", cT, mk_inj cs sumT c (Bound 0)) $ t
berghofe@5094
   225
  end;
berghofe@5094
   226
wenzelm@6424
   227
wenzelm@6424
   228
wenzelm@6424
   229
(** well-formedness checks **)
berghofe@5094
   230
berghofe@5094
   231
fun err_in_rule sign t msg = error ("Ill-formed introduction rule\n" ^
berghofe@5094
   232
  (Sign.string_of_term sign t) ^ "\n" ^ msg);
berghofe@5094
   233
berghofe@5094
   234
fun err_in_prem sign t p msg = error ("Ill-formed premise\n" ^
berghofe@5094
   235
  (Sign.string_of_term sign p) ^ "\nin introduction rule\n" ^
berghofe@5094
   236
  (Sign.string_of_term sign t) ^ "\n" ^ msg);
berghofe@5094
   237
berghofe@5094
   238
val msg1 = "Conclusion of introduction rule must have form\
berghofe@5094
   239
          \ ' t : S_i '";
berghofe@7710
   240
val msg2 = "Non-atomic premise";
berghofe@5094
   241
val msg3 = "Recursion term on left of member symbol";
berghofe@5094
   242
berghofe@5094
   243
fun check_rule sign cs r =
berghofe@5094
   244
  let
berghofe@7710
   245
    fun check_prem prem = if can HOLogic.dest_Trueprop prem then ()
berghofe@7710
   246
      else err_in_prem sign r prem msg2;
berghofe@5094
   247
berghofe@7710
   248
  in (case HOLogic.dest_Trueprop (Logic.strip_imp_concl r) of
berghofe@7710
   249
        (Const ("op :", _) $ t $ u) =>
berghofe@7710
   250
          if u mem cs then
berghofe@7710
   251
            if exists (Logic.occs o (rpair t)) cs then
berghofe@7710
   252
              err_in_rule sign r msg3
berghofe@7710
   253
            else
berghofe@7710
   254
              seq check_prem (Logic.strip_imp_prems r)
berghofe@5094
   255
          else err_in_rule sign r msg1
berghofe@5094
   256
      | _ => err_in_rule sign r msg1)
berghofe@5094
   257
  end;
berghofe@5094
   258
berghofe@7020
   259
fun try' f msg sign t = (case (try f t) of
berghofe@7020
   260
      Some x => x
berghofe@7020
   261
    | None => error (msg ^ Sign.string_of_term sign t));
berghofe@5094
   262
wenzelm@6424
   263
berghofe@5094
   264
wenzelm@6424
   265
(*** properties of (co)inductive sets ***)
wenzelm@6424
   266
wenzelm@6424
   267
(** elimination rules **)
berghofe@5094
   268
wenzelm@8375
   269
fun mk_elims cs cTs params intr_ts intr_names =
berghofe@5094
   270
  let
berghofe@5094
   271
    val used = foldr add_term_names (intr_ts, []);
berghofe@5094
   272
    val [aname, pname] = variantlist (["a", "P"], used);
berghofe@5094
   273
    val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
berghofe@5094
   274
berghofe@5094
   275
    fun dest_intr r =
berghofe@5094
   276
      let val Const ("op :", _) $ t $ u =
berghofe@5094
   277
        HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   278
      in (u, t, Logic.strip_imp_prems r) end;
berghofe@5094
   279
wenzelm@8380
   280
    val intrs = map dest_intr intr_ts ~~ intr_names;
berghofe@5094
   281
berghofe@5094
   282
    fun mk_elim (c, T) =
berghofe@5094
   283
      let
berghofe@5094
   284
        val a = Free (aname, T);
berghofe@5094
   285
berghofe@5094
   286
        fun mk_elim_prem (_, t, ts) =
berghofe@5094
   287
          list_all_free (map dest_Free ((foldr add_term_frees (t::ts, [])) \\ params),
berghofe@5094
   288
            Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (a, t)) :: ts, P));
wenzelm@8375
   289
        val c_intrs = (filter (equal c o #1 o #1) intrs);
berghofe@5094
   290
      in
wenzelm@8375
   291
        (Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (a, c)) ::
wenzelm@8375
   292
          map mk_elim_prem (map #1 c_intrs), P), map #2 c_intrs)
berghofe@5094
   293
      end
berghofe@5094
   294
  in
berghofe@5094
   295
    map mk_elim (cs ~~ cTs)
berghofe@5094
   296
  end;
berghofe@5094
   297
        
wenzelm@6424
   298
wenzelm@6424
   299
wenzelm@6424
   300
(** premises and conclusions of induction rules **)
berghofe@5094
   301
berghofe@5094
   302
fun mk_indrule cs cTs params intr_ts =
berghofe@5094
   303
  let
berghofe@5094
   304
    val used = foldr add_term_names (intr_ts, []);
berghofe@5094
   305
berghofe@5094
   306
    (* predicates for induction rule *)
berghofe@5094
   307
berghofe@5094
   308
    val preds = map Free (variantlist (if length cs < 2 then ["P"] else
berghofe@5094
   309
      map (fn i => "P" ^ string_of_int i) (1 upto length cs), used) ~~
berghofe@5094
   310
        map (fn T => T --> HOLogic.boolT) cTs);
berghofe@5094
   311
berghofe@5094
   312
    (* transform an introduction rule into a premise for induction rule *)
berghofe@5094
   313
berghofe@5094
   314
    fun mk_ind_prem r =
berghofe@5094
   315
      let
berghofe@5094
   316
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5094
   317
berghofe@7710
   318
        val pred_of = curry (Library.gen_assoc (op aconv)) (cs ~~ preds);
berghofe@5094
   319
berghofe@7710
   320
        fun subst (s as ((m as Const ("op :", T)) $ t $ u)) =
berghofe@7710
   321
              (case pred_of u of
berghofe@7710
   322
                  None => (m $ fst (subst t) $ fst (subst u), None)
berghofe@7710
   323
                | Some P => (HOLogic.conj $ s $ (P $ t), Some (s, P $ t)))
berghofe@7710
   324
          | subst s =
berghofe@7710
   325
              (case pred_of s of
berghofe@7710
   326
                  Some P => (HOLogic.mk_binop "op Int"
berghofe@7710
   327
                    (s, HOLogic.Collect_const (HOLogic.dest_setT
berghofe@7710
   328
                      (fastype_of s)) $ P), None)
berghofe@7710
   329
                | None => (case s of
berghofe@7710
   330
                     (t $ u) => (fst (subst t) $ fst (subst u), None)
berghofe@7710
   331
                   | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), None)
berghofe@7710
   332
                   | _ => (s, None)));
berghofe@7710
   333
berghofe@7710
   334
        fun mk_prem (s, prems) = (case subst s of
berghofe@7710
   335
              (_, Some (t, u)) => t :: u :: prems
berghofe@7710
   336
            | (t, _) => t :: prems);
berghofe@7710
   337
          
berghofe@5094
   338
        val Const ("op :", _) $ t $ u =
berghofe@5094
   339
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   340
berghofe@5094
   341
      in list_all_free (frees,
berghofe@7710
   342
           Logic.list_implies (map HOLogic.mk_Trueprop (foldr mk_prem
berghofe@5094
   343
             (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r), [])),
berghofe@7710
   344
               HOLogic.mk_Trueprop (the (pred_of u) $ t)))
berghofe@5094
   345
      end;
berghofe@5094
   346
berghofe@5094
   347
    val ind_prems = map mk_ind_prem intr_ts;
berghofe@5094
   348
berghofe@5094
   349
    (* make conclusions for induction rules *)
berghofe@5094
   350
berghofe@5094
   351
    fun mk_ind_concl ((c, P), (ts, x)) =
berghofe@5094
   352
      let val T = HOLogic.dest_setT (fastype_of c);
berghofe@5094
   353
          val Ts = HOLogic.prodT_factors T;
berghofe@5094
   354
          val (frees, x') = foldr (fn (T', (fs, s)) =>
berghofe@5094
   355
            ((Free (s, T'))::fs, bump_string s)) (Ts, ([], x));
berghofe@5094
   356
          val tuple = HOLogic.mk_tuple T frees;
berghofe@5094
   357
      in ((HOLogic.mk_binop "op -->"
berghofe@5094
   358
        (HOLogic.mk_mem (tuple, c), P $ tuple))::ts, x')
berghofe@5094
   359
      end;
berghofe@5094
   360
berghofe@7710
   361
    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@5094
   362
        (fst (foldr mk_ind_concl (cs ~~ preds, ([], "xa")))))
berghofe@5094
   363
berghofe@5094
   364
  in (preds, ind_prems, mutual_ind_concl)
berghofe@5094
   365
  end;
berghofe@5094
   366
wenzelm@6424
   367
berghofe@5094
   368
wenzelm@8316
   369
(** prepare cases and induct rules **)
wenzelm@8316
   370
wenzelm@8316
   371
(*
wenzelm@8316
   372
  transform mutual rule:
wenzelm@8316
   373
    HH ==> (x1:A1 --> P1 x1) & ... & (xn:An --> Pn xn)
wenzelm@8316
   374
  into i-th projection:
wenzelm@8316
   375
    xi:Ai ==> HH ==> Pi xi
wenzelm@8316
   376
*)
wenzelm@8316
   377
wenzelm@8316
   378
fun project_rules [name] rule = [(name, rule)]
wenzelm@8316
   379
  | project_rules names mutual_rule =
wenzelm@8316
   380
      let
wenzelm@8316
   381
        val n = length names;
wenzelm@8316
   382
        fun proj i =
wenzelm@8316
   383
          (if i < n then (fn th => th RS conjunct1) else I)
wenzelm@8316
   384
            (Library.funpow (i - 1) (fn th => th RS conjunct2) mutual_rule)
wenzelm@8316
   385
            RS mp |> Thm.permute_prems 0 ~1 |> Drule.standard;
wenzelm@8316
   386
      in names ~~ map proj (1 upto n) end;
wenzelm@8316
   387
wenzelm@8375
   388
fun add_cases_induct no_elim no_ind names elims induct induct_cases =
wenzelm@8316
   389
  let
wenzelm@8375
   390
    fun cases_spec (name, elim) = (("", elim), [InductMethod.cases_set_global name]);
wenzelm@8375
   391
    val cases_specs = if no_elim then [] else map2 cases_spec (names, elims);
wenzelm@8316
   392
wenzelm@8375
   393
    fun induct_spec (name, th) =
wenzelm@8380
   394
      (("", th), [RuleCases.case_names induct_cases, InductMethod.induct_set_global name]);
wenzelm@8401
   395
    val induct_specs = if no_ind then [] else map induct_spec (project_rules names induct);
wenzelm@8433
   396
  in #1 o PureThy.add_thms (cases_specs @ induct_specs) end;
wenzelm@8316
   397
wenzelm@8316
   398
wenzelm@8316
   399
wenzelm@6424
   400
(*** proofs for (co)inductive sets ***)
wenzelm@6424
   401
wenzelm@6424
   402
(** prove monotonicity **)
berghofe@5094
   403
berghofe@5094
   404
fun prove_mono setT fp_fun monos thy =
berghofe@5094
   405
  let
wenzelm@6427
   406
    val _ = message "  Proving monotonicity ...";
berghofe@5094
   407
wenzelm@6394
   408
    val mono = prove_goalw_cterm [] (cterm_of (Theory.sign_of thy) (HOLogic.mk_Trueprop
berghofe@5094
   409
      (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun)))
berghofe@7710
   410
        (fn _ => [rtac monoI 1, REPEAT (ares_tac (get_monos thy @ flat (map mk_mono monos)) 1)])
berghofe@5094
   411
berghofe@5094
   412
  in mono end;
berghofe@5094
   413
wenzelm@6424
   414
wenzelm@6424
   415
wenzelm@6424
   416
(** prove introduction rules **)
berghofe@5094
   417
berghofe@5094
   418
fun prove_intrs coind mono fp_def intr_ts con_defs rec_sets_defs thy =
berghofe@5094
   419
  let
wenzelm@6427
   420
    val _ = message "  Proving the introduction rules ...";
berghofe@5094
   421
berghofe@5094
   422
    val unfold = standard (mono RS (fp_def RS
berghofe@5094
   423
      (if coind then def_gfp_Tarski else def_lfp_Tarski)));
berghofe@5094
   424
berghofe@5094
   425
    fun select_disj 1 1 = []
berghofe@5094
   426
      | select_disj _ 1 = [rtac disjI1]
berghofe@5094
   427
      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
berghofe@5094
   428
berghofe@5094
   429
    val intrs = map (fn (i, intr) => prove_goalw_cterm rec_sets_defs
wenzelm@6394
   430
      (cterm_of (Theory.sign_of thy) intr) (fn prems =>
berghofe@5094
   431
       [(*insert prems and underlying sets*)
berghofe@5094
   432
       cut_facts_tac prems 1,
berghofe@5094
   433
       stac unfold 1,
berghofe@5094
   434
       REPEAT (resolve_tac [vimageI2, CollectI] 1),
berghofe@5094
   435
       (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
berghofe@5094
   436
       EVERY1 (select_disj (length intr_ts) i),
berghofe@5094
   437
       (*Not ares_tac, since refl must be tried before any equality assumptions;
berghofe@5094
   438
         backtracking may occur if the premises have extra variables!*)
berghofe@5094
   439
       DEPTH_SOLVE_1 (resolve_tac [refl,exI,conjI] 1 APPEND assume_tac 1),
berghofe@5094
   440
       (*Now solve the equations like Inl 0 = Inl ?b2*)
berghofe@5094
   441
       rewrite_goals_tac con_defs,
berghofe@5094
   442
       REPEAT (rtac refl 1)])) (1 upto (length intr_ts) ~~ intr_ts)
berghofe@5094
   443
berghofe@5094
   444
  in (intrs, unfold) end;
berghofe@5094
   445
wenzelm@6424
   446
wenzelm@6424
   447
wenzelm@6424
   448
(** prove elimination rules **)
berghofe@5094
   449
wenzelm@8375
   450
fun prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy =
berghofe@5094
   451
  let
wenzelm@6427
   452
    val _ = message "  Proving the elimination rules ...";
berghofe@5094
   453
berghofe@7710
   454
    val rules1 = [CollectE, disjE, make_elim vimageD, exE];
berghofe@7710
   455
    val rules2 = [conjE, Inl_neq_Inr, Inr_neq_Inl] @
berghofe@5094
   456
      map make_elim [Inl_inject, Inr_inject];
wenzelm@8375
   457
  in
wenzelm@8375
   458
    map (fn (t, cases) => prove_goalw_cterm rec_sets_defs
wenzelm@6394
   459
      (cterm_of (Theory.sign_of thy) t) (fn prems =>
berghofe@5094
   460
        [cut_facts_tac [hd prems] 1,
berghofe@5094
   461
         dtac (unfold RS subst) 1,
berghofe@5094
   462
         REPEAT (FIRSTGOAL (eresolve_tac rules1)),
berghofe@5094
   463
         REPEAT (FIRSTGOAL (eresolve_tac rules2)),
berghofe@5094
   464
         EVERY (map (fn prem =>
wenzelm@8375
   465
           DEPTH_SOLVE_1 (ares_tac [prem, conjI] 1)) (tl prems))])
wenzelm@8375
   466
      |> RuleCases.name cases)
wenzelm@8375
   467
      (mk_elims cs cTs params intr_ts intr_names)
wenzelm@8375
   468
  end;
berghofe@5094
   469
wenzelm@6424
   470
berghofe@5094
   471
(** derivation of simplified elimination rules **)
berghofe@5094
   472
berghofe@5094
   473
(*Applies freeness of the given constructors, which *must* be unfolded by
berghofe@5094
   474
  the given defs.  Cannot simply use the local con_defs because con_defs=[] 
berghofe@5094
   475
  for inference systems.
berghofe@5094
   476
 *)
berghofe@5094
   477
wenzelm@7107
   478
(*cprop should have the form t:Si where Si is an inductive set*)
wenzelm@8336
   479
fun mk_cases_i solved elims ss cprop =
wenzelm@7107
   480
  let
wenzelm@7107
   481
    val prem = Thm.assume cprop;
wenzelm@8336
   482
    val tac = if solved then InductMethod.con_elim_solved_tac else InductMethod.con_elim_tac;
wenzelm@8336
   483
    fun mk_elim rl = Drule.standard (Tactic.rule_by_tactic (tac ss) (prem RS rl));
wenzelm@7107
   484
  in
wenzelm@7107
   485
    (case get_first (try mk_elim) elims of
wenzelm@7107
   486
      Some r => r
wenzelm@7107
   487
    | None => error (Pretty.string_of (Pretty.block
wenzelm@7107
   488
        [Pretty.str "mk_cases: proposition not of form 't : S_i'", Pretty.fbrk,
wenzelm@7107
   489
          Display.pretty_cterm cprop])))
wenzelm@7107
   490
  end;
wenzelm@7107
   491
paulson@6141
   492
fun mk_cases elims s =
wenzelm@8336
   493
  mk_cases_i false elims (simpset()) (Thm.read_cterm (Thm.sign_of_thm (hd elims)) (s, propT));
wenzelm@7107
   494
wenzelm@7107
   495
wenzelm@7107
   496
(* inductive_cases(_i) *)
wenzelm@7107
   497
wenzelm@7107
   498
fun gen_inductive_cases prep_att prep_const prep_prop
wenzelm@7107
   499
    ((((name, raw_atts), raw_set), raw_props), comment) thy =
wenzelm@7107
   500
  let
wenzelm@7107
   501
    val sign = Theory.sign_of thy;
wenzelm@7107
   502
wenzelm@7107
   503
    val atts = map (prep_att thy) raw_atts;
wenzelm@7107
   504
    val (_, {elims, ...}) = get_inductive thy (prep_const sign raw_set);
wenzelm@7107
   505
    val cprops = map (Thm.cterm_of sign o prep_prop (ProofContext.init thy)) raw_props;
wenzelm@8336
   506
    val thms = map (mk_cases_i true elims (Simplifier.simpset_of thy)) cprops;
wenzelm@7107
   507
  in
wenzelm@7107
   508
    thy
wenzelm@7107
   509
    |> IsarThy.have_theorems_i (((name, atts), map Thm.no_attributes thms), comment)
berghofe@5094
   510
  end;
berghofe@5094
   511
wenzelm@7107
   512
val inductive_cases =
wenzelm@7107
   513
  gen_inductive_cases Attrib.global_attribute Sign.intern_const ProofContext.read_prop;
wenzelm@7107
   514
wenzelm@7107
   515
val inductive_cases_i = gen_inductive_cases (K I) (K I) ProofContext.cert_prop;
wenzelm@7107
   516
wenzelm@6424
   517
wenzelm@6424
   518
wenzelm@6424
   519
(** prove induction rule **)
berghofe@5094
   520
berghofe@5094
   521
fun prove_indrule cs cTs sumT rec_const params intr_ts mono
berghofe@5094
   522
    fp_def rec_sets_defs thy =
berghofe@5094
   523
  let
wenzelm@6427
   524
    val _ = message "  Proving the induction rule ...";
berghofe@5094
   525
wenzelm@6394
   526
    val sign = Theory.sign_of thy;
berghofe@5094
   527
berghofe@7293
   528
    val sum_case_rewrites = (case ThyInfo.lookup_theory "Datatype" of
berghofe@7293
   529
        None => []
berghofe@7293
   530
      | Some thy' => map mk_meta_eq (PureThy.get_thms thy' "sum.cases"));
berghofe@7293
   531
berghofe@5094
   532
    val (preds, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
berghofe@5094
   533
berghofe@5094
   534
    (* make predicate for instantiation of abstract induction rule *)
berghofe@5094
   535
berghofe@5094
   536
    fun mk_ind_pred _ [P] = P
berghofe@5094
   537
      | mk_ind_pred T Ps =
berghofe@5094
   538
         let val n = (length Ps) div 2;
berghofe@5094
   539
             val Type (_, [T1, T2]) = T
berghofe@7293
   540
         in Const ("Datatype.sum.sum_case",
berghofe@5094
   541
           [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
berghofe@5094
   542
             mk_ind_pred T1 (take (n, Ps)) $ mk_ind_pred T2 (drop (n, Ps))
berghofe@5094
   543
         end;
berghofe@5094
   544
berghofe@5094
   545
    val ind_pred = mk_ind_pred sumT preds;
berghofe@5094
   546
berghofe@5094
   547
    val ind_concl = HOLogic.mk_Trueprop
berghofe@5094
   548
      (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
berghofe@5094
   549
        (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
berghofe@5094
   550
berghofe@5094
   551
    (* simplification rules for vimage and Collect *)
berghofe@5094
   552
berghofe@5094
   553
    val vimage_simps = if length cs < 2 then [] else
berghofe@5094
   554
      map (fn c => prove_goalw_cterm [] (cterm_of sign
berghofe@5094
   555
        (HOLogic.mk_Trueprop (HOLogic.mk_eq
berghofe@5094
   556
          (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
berghofe@5094
   557
           HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
berghofe@5094
   558
             nth_elem (find_index_eq c cs, preds)))))
berghofe@7293
   559
        (fn _ => [rtac vimage_Collect 1, rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   560
          rtac refl 1])) cs;
berghofe@5094
   561
berghofe@5094
   562
    val induct = prove_goalw_cterm [] (cterm_of sign
berghofe@5094
   563
      (Logic.list_implies (ind_prems, ind_concl))) (fn prems =>
berghofe@5094
   564
        [rtac (impI RS allI) 1,
berghofe@5094
   565
         DETERM (etac (mono RS (fp_def RS def_induct)) 1),
berghofe@7710
   566
         rewrite_goals_tac (map mk_meta_eq (vimage_Int::Int_Collect::vimage_simps)),
berghofe@5094
   567
         fold_goals_tac rec_sets_defs,
berghofe@5094
   568
         (*This CollectE and disjE separates out the introduction rules*)
berghofe@7710
   569
         REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE, exE])),
berghofe@5094
   570
         (*Now break down the individual cases.  No disjE here in case
berghofe@5094
   571
           some premise involves disjunction.*)
berghofe@7710
   572
         REPEAT (FIRSTGOAL (etac conjE ORELSE' hyp_subst_tac)),
berghofe@7293
   573
         rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   574
         EVERY (map (fn prem =>
berghofe@5149
   575
           DEPTH_SOLVE_1 (ares_tac [prem, conjI, refl] 1)) prems)]);
berghofe@5094
   576
berghofe@5094
   577
    val lemma = prove_goalw_cterm rec_sets_defs (cterm_of sign
berghofe@5094
   578
      (Logic.mk_implies (ind_concl, mutual_ind_concl))) (fn prems =>
berghofe@5094
   579
        [cut_facts_tac prems 1,
berghofe@5094
   580
         REPEAT (EVERY
berghofe@5094
   581
           [REPEAT (resolve_tac [conjI, impI] 1),
berghofe@5094
   582
            TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
berghofe@7293
   583
            rewrite_goals_tac sum_case_rewrites,
berghofe@5094
   584
            atac 1])])
berghofe@5094
   585
berghofe@5094
   586
  in standard (split_rule (induct RS lemma))
berghofe@5094
   587
  end;
berghofe@5094
   588
wenzelm@6424
   589
wenzelm@6424
   590
wenzelm@6424
   591
(*** specification of (co)inductive sets ****)
wenzelm@6424
   592
wenzelm@6424
   593
(** definitional introduction of (co)inductive sets **)
berghofe@5094
   594
berghofe@5094
   595
fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@8401
   596
    atts intros monos con_defs thy params paramTs cTs cnames induct_cases =
berghofe@5094
   597
  let
wenzelm@6424
   598
    val _ = if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
wenzelm@6424
   599
      commas_quote cnames) else ();
berghofe@5094
   600
berghofe@5094
   601
    val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
berghofe@5094
   602
    val setT = HOLogic.mk_setT sumT;
berghofe@5094
   603
wenzelm@6394
   604
    val fp_name = if coind then Sign.intern_const (Theory.sign_of Gfp.thy) "gfp"
wenzelm@6394
   605
      else Sign.intern_const (Theory.sign_of Lfp.thy) "lfp";
berghofe@5094
   606
wenzelm@6424
   607
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
wenzelm@6424
   608
berghofe@5149
   609
    val used = foldr add_term_names (intr_ts, []);
berghofe@5149
   610
    val [sname, xname] = variantlist (["S", "x"], used);
berghofe@5149
   611
berghofe@5094
   612
    (* transform an introduction rule into a conjunction  *)
berghofe@5094
   613
    (*   [| t : ... S_i ... ; ... |] ==> u : S_j          *)
berghofe@5094
   614
    (* is transformed into                                *)
berghofe@5094
   615
    (*   x = Inj_j u & t : ... Inj_i -`` S ... & ...      *)
berghofe@5094
   616
berghofe@5094
   617
    fun transform_rule r =
berghofe@5094
   618
      let
berghofe@5094
   619
        val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
berghofe@5149
   620
        val subst = subst_free
berghofe@5149
   621
          (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
berghofe@5094
   622
        val Const ("op :", _) $ t $ u =
berghofe@5094
   623
          HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
berghofe@5094
   624
berghofe@5094
   625
      in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
berghofe@7710
   626
        (frees, foldr1 HOLogic.mk_conj
berghofe@5149
   627
          (((HOLogic.eq_const sumT) $ Free (xname, sumT) $ (mk_inj cs sumT u t))::
berghofe@5094
   628
            (map (subst o HOLogic.dest_Trueprop)
berghofe@5094
   629
              (Logic.strip_imp_prems r))))
berghofe@5094
   630
      end
berghofe@5094
   631
berghofe@5094
   632
    (* make a disjunction of all introduction rules *)
berghofe@5094
   633
berghofe@5149
   634
    val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) $
berghofe@7710
   635
      absfree (xname, sumT, foldr1 HOLogic.mk_disj (map transform_rule intr_ts)));
berghofe@5094
   636
berghofe@5094
   637
    (* add definiton of recursive sets to theory *)
berghofe@5094
   638
berghofe@5094
   639
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
wenzelm@6394
   640
    val full_rec_name = Sign.full_name (Theory.sign_of thy) rec_name;
berghofe@5094
   641
berghofe@5094
   642
    val rec_const = list_comb
berghofe@5094
   643
      (Const (full_rec_name, paramTs ---> setT), params);
berghofe@5094
   644
berghofe@5094
   645
    val fp_def_term = Logic.mk_equals (rec_const,
berghofe@5094
   646
      Const (fp_name, (setT --> setT) --> setT) $ fp_fun)
berghofe@5094
   647
berghofe@5094
   648
    val def_terms = fp_def_term :: (if length cs < 2 then [] else
berghofe@5094
   649
      map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
berghofe@5094
   650
wenzelm@8433
   651
    val (thy', [fp_def :: rec_sets_defs]) =
wenzelm@8433
   652
      thy
wenzelm@8433
   653
      |> (if declare_consts then
wenzelm@8433
   654
          Theory.add_consts_i (map (fn (c, n) =>
wenzelm@8433
   655
            (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
wenzelm@8433
   656
          else I)
wenzelm@8433
   657
      |> (if length cs < 2 then I
wenzelm@8433
   658
          else Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)])
wenzelm@8433
   659
      |> Theory.add_path rec_name
wenzelm@8433
   660
      |> PureThy.add_defss_i [(("defs", def_terms), [])];
berghofe@5094
   661
berghofe@5094
   662
berghofe@5094
   663
    (* prove and store theorems *)
berghofe@5094
   664
berghofe@5094
   665
    val mono = prove_mono setT fp_fun monos thy';
berghofe@5094
   666
    val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts con_defs
berghofe@5094
   667
      rec_sets_defs thy';
berghofe@5094
   668
    val elims = if no_elim then [] else
wenzelm@8375
   669
      prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs thy';
wenzelm@8312
   670
    val raw_induct = if no_ind then Drule.asm_rl else
berghofe@5094
   671
      if coind then standard (rule_by_tactic
oheimb@5553
   672
        (rewrite_tac [mk_meta_eq vimage_Un] THEN
berghofe@5094
   673
          fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
berghofe@5094
   674
      else
berghofe@5094
   675
        prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
berghofe@5094
   676
          rec_sets_defs thy';
berghofe@5108
   677
    val induct = if coind orelse no_ind orelse length cs > 1 then raw_induct
berghofe@5094
   678
      else standard (raw_induct RSN (2, rev_mp));
berghofe@5094
   679
wenzelm@8433
   680
    val (thy'', [intrs']) =
wenzelm@8433
   681
      thy'
wenzelm@6521
   682
      |> PureThy.add_thmss [(("intrs", intrs), atts)]
wenzelm@8433
   683
      |>> (#1 o PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts))
wenzelm@8433
   684
      |>> (if no_elim then I else #1 o PureThy.add_thmss [(("elims", elims), [])])
wenzelm@8433
   685
      |>> (if no_ind then I else #1 o PureThy.add_thms
wenzelm@8401
   686
        [((coind_prefix coind ^ "induct", induct), [RuleCases.case_names induct_cases])])
wenzelm@8433
   687
      |>> Theory.parent_path;
wenzelm@8312
   688
    val elims' = if no_elim then elims else PureThy.get_thms thy'' "elims";  (* FIXME improve *)
wenzelm@8312
   689
    val induct' = if no_ind then induct else PureThy.get_thm thy'' (coind_prefix coind ^ "induct");  (* FIXME improve *)
berghofe@5094
   690
  in (thy'',
berghofe@5094
   691
    {defs = fp_def::rec_sets_defs,
berghofe@5094
   692
     mono = mono,
berghofe@5094
   693
     unfold = unfold,
wenzelm@7798
   694
     intrs = intrs',
wenzelm@7798
   695
     elims = elims',
wenzelm@7798
   696
     mk_cases = mk_cases elims',
berghofe@5094
   697
     raw_induct = raw_induct,
wenzelm@7798
   698
     induct = induct'})
berghofe@5094
   699
  end;
berghofe@5094
   700
wenzelm@6424
   701
wenzelm@6424
   702
wenzelm@6424
   703
(** axiomatic introduction of (co)inductive sets **)
berghofe@5094
   704
berghofe@5094
   705
fun add_ind_axm verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@8401
   706
    atts intros monos con_defs thy params paramTs cTs cnames induct_cases =
berghofe@5094
   707
  let
berghofe@5094
   708
    val rec_name = if alt_name = "" then space_implode "_" cnames else alt_name;
berghofe@5094
   709
wenzelm@6424
   710
    val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
wenzelm@8375
   711
    val (elim_ts, elim_cases) = Library.split_list (mk_elims cs cTs params intr_ts intr_names);
berghofe@5094
   712
berghofe@5094
   713
    val (_, ind_prems, mutual_ind_concl) = mk_indrule cs cTs params intr_ts;
berghofe@5094
   714
    val ind_t = Logic.list_implies (ind_prems, mutual_ind_concl);
berghofe@5094
   715
    
wenzelm@8433
   716
    val thy' =
wenzelm@8433
   717
      thy
wenzelm@6424
   718
      |> (if declare_consts then
wenzelm@6424
   719
            Theory.add_consts_i
wenzelm@6424
   720
              (map (fn (c, n) => (n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
wenzelm@6424
   721
         else I)
wenzelm@6424
   722
      |> Theory.add_path rec_name
wenzelm@8433
   723
      |> (#1 o PureThy.add_axiomss_i [(("intrs", intr_ts), atts), (("raw_elims", elim_ts), [])])
berghofe@7710
   724
      |> (if coind then I else
wenzelm@8433
   725
            #1 o PureThy.add_axioms_i [(("raw_induct", ind_t), [apsnd (standard o split_rule)])]);
berghofe@5094
   726
wenzelm@6424
   727
    val intrs = PureThy.get_thms thy' "intrs";
wenzelm@8375
   728
    val elims = map2 (fn (th, cases) => RuleCases.name cases th)
wenzelm@8375
   729
      (PureThy.get_thms thy' "raw_elims", elim_cases);
wenzelm@8312
   730
    val raw_induct = if coind then Drule.asm_rl else PureThy.get_thm thy' "raw_induct";
berghofe@5094
   731
    val induct = if coind orelse length cs > 1 then raw_induct
berghofe@5094
   732
      else standard (raw_induct RSN (2, rev_mp));
berghofe@5094
   733
wenzelm@8433
   734
    val (thy'', ([elims'], intrs')) =
wenzelm@6424
   735
      thy'
wenzelm@8375
   736
      |> PureThy.add_thmss [(("elims", elims), [])]
wenzelm@8433
   737
      |>> (if coind then I
wenzelm@8433
   738
          else #1 o PureThy.add_thms [(("induct", induct), [RuleCases.case_names induct_cases])])
wenzelm@8433
   739
      |>>> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts)
wenzelm@8433
   740
      |>> Theory.parent_path;
wenzelm@7798
   741
    val induct' = if coind then raw_induct else PureThy.get_thm thy'' "induct";
berghofe@5094
   742
  in (thy'',
berghofe@5094
   743
    {defs = [],
wenzelm@8312
   744
     mono = Drule.asm_rl,
wenzelm@8312
   745
     unfold = Drule.asm_rl,
wenzelm@8433
   746
     intrs = intrs',
wenzelm@8433
   747
     elims = elims',
wenzelm@8433
   748
     mk_cases = mk_cases elims',
berghofe@5094
   749
     raw_induct = raw_induct,
wenzelm@7798
   750
     induct = induct'})
berghofe@5094
   751
  end;
berghofe@5094
   752
wenzelm@6424
   753
wenzelm@6424
   754
wenzelm@6424
   755
(** introduction of (co)inductive sets **)
berghofe@5094
   756
berghofe@5094
   757
fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs
wenzelm@6521
   758
    atts intros monos con_defs thy =
berghofe@5094
   759
  let
wenzelm@6424
   760
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
wenzelm@6394
   761
    val sign = Theory.sign_of thy;
berghofe@5094
   762
berghofe@5094
   763
    (*parameters should agree for all mutually recursive components*)
berghofe@5094
   764
    val (_, params) = strip_comb (hd cs);
berghofe@5094
   765
    val paramTs = map (try' (snd o dest_Free) "Parameter in recursive\
berghofe@5094
   766
      \ component is not a free variable: " sign) params;
berghofe@5094
   767
berghofe@5094
   768
    val cTs = map (try' (HOLogic.dest_setT o fastype_of)
berghofe@5094
   769
      "Recursive component not of type set: " sign) cs;
berghofe@5094
   770
wenzelm@6437
   771
    val full_cnames = map (try' (fst o dest_Const o head_of)
berghofe@5094
   772
      "Recursive set not previously declared as constant: " sign) cs;
wenzelm@6437
   773
    val cnames = map Sign.base_name full_cnames;
berghofe@5094
   774
wenzelm@6424
   775
    val _ = seq (check_rule sign cs o snd o fst) intros;
wenzelm@8401
   776
    val induct_cases = map (#1 o #1) intros;
wenzelm@6437
   777
wenzelm@6437
   778
    val (thy1, result) =
wenzelm@6437
   779
      (if ! quick_and_dirty then add_ind_axm else add_ind_def)
wenzelm@6521
   780
        verbose declare_consts alt_name coind no_elim no_ind cs atts intros monos
wenzelm@8401
   781
        con_defs thy params paramTs cTs cnames induct_cases;
wenzelm@8307
   782
    val thy2 = thy1
wenzelm@8307
   783
      |> put_inductives full_cnames ({names = full_cnames, coind = coind}, result)
wenzelm@8401
   784
      |> add_cases_induct no_elim (no_ind orelse coind) full_cnames
wenzelm@8401
   785
          (#elims result) (#induct result) induct_cases;
wenzelm@6437
   786
  in (thy2, result) end;
berghofe@5094
   787
wenzelm@6424
   788
berghofe@5094
   789
wenzelm@6424
   790
(** external interface **)
wenzelm@6424
   791
wenzelm@6521
   792
fun add_inductive verbose coind c_strings srcs intro_srcs raw_monos raw_con_defs thy =
berghofe@5094
   793
  let
wenzelm@6394
   794
    val sign = Theory.sign_of thy;
wenzelm@8100
   795
    val cs = map (term_of o Thm.read_cterm sign o rpair HOLogic.termT) c_strings;
wenzelm@6424
   796
wenzelm@6521
   797
    val atts = map (Attrib.global_attribute thy) srcs;
wenzelm@6424
   798
    val intr_names = map (fst o fst) intro_srcs;
berghofe@7710
   799
    val intr_ts = map (term_of o Thm.read_cterm sign o rpair propT o snd o fst) intro_srcs;
wenzelm@6424
   800
    val intr_atts = map (map (Attrib.global_attribute thy) o snd) intro_srcs;
berghofe@7020
   801
    val (cs', intr_ts') = unify_consts sign cs intr_ts;
berghofe@5094
   802
wenzelm@6424
   803
    val ((thy', con_defs), monos) = thy
wenzelm@6424
   804
      |> IsarThy.apply_theorems raw_monos
wenzelm@6424
   805
      |> apfst (IsarThy.apply_theorems raw_con_defs);
wenzelm@6424
   806
  in
berghofe@7020
   807
    add_inductive_i verbose false "" coind false false cs'
berghofe@7020
   808
      atts ((intr_names ~~ intr_ts') ~~ intr_atts) monos con_defs thy'
berghofe@5094
   809
  end;
berghofe@5094
   810
wenzelm@6424
   811
wenzelm@6424
   812
wenzelm@6437
   813
(** package setup **)
wenzelm@6437
   814
wenzelm@6437
   815
(* setup theory *)
wenzelm@6437
   816
wenzelm@8634
   817
val setup =
wenzelm@8634
   818
 [InductiveData.init,
wenzelm@8634
   819
  Attrib.add_attributes [("mono", mono_attr, "monotonicity rule")]];
wenzelm@6437
   820
wenzelm@6437
   821
wenzelm@6437
   822
(* outer syntax *)
wenzelm@6424
   823
wenzelm@6723
   824
local structure P = OuterParse and K = OuterSyntax.Keyword in
wenzelm@6424
   825
wenzelm@6521
   826
fun mk_ind coind (((sets, (atts, intrs)), monos), con_defs) =
wenzelm@6723
   827
  #1 o add_inductive true coind sets atts (map P.triple_swap intrs) monos con_defs;
wenzelm@6424
   828
wenzelm@6424
   829
fun ind_decl coind =
wenzelm@6729
   830
  (Scan.repeat1 P.term --| P.marg_comment) --
wenzelm@6729
   831
  (P.$$$ "intrs" |--
wenzelm@7152
   832
    P.!!! (P.opt_attribs -- Scan.repeat1 (P.opt_thm_name ":" -- P.prop --| P.marg_comment))) --
wenzelm@6729
   833
  Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1 --| P.marg_comment) [] --
wenzelm@6729
   834
  Scan.optional (P.$$$ "con_defs" |-- P.!!! P.xthms1 --| P.marg_comment) []
wenzelm@6424
   835
  >> (Toplevel.theory o mk_ind coind);
wenzelm@6424
   836
wenzelm@6723
   837
val inductiveP =
wenzelm@6723
   838
  OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
wenzelm@6723
   839
wenzelm@6723
   840
val coinductiveP =
wenzelm@6723
   841
  OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
wenzelm@6424
   842
wenzelm@7107
   843
wenzelm@7107
   844
val ind_cases =
wenzelm@7107
   845
  P.opt_thm_name "=" -- P.xname --| P.$$$ ":" -- Scan.repeat1 P.prop -- P.marg_comment
wenzelm@7107
   846
  >> (Toplevel.theory o inductive_cases);
wenzelm@7107
   847
wenzelm@7107
   848
val inductive_casesP =
wenzelm@7107
   849
  OuterSyntax.command "inductive_cases" "create simplified instances of elimination rules"
wenzelm@7107
   850
    K.thy_decl ind_cases;
wenzelm@7107
   851
wenzelm@6424
   852
val _ = OuterSyntax.add_keywords ["intrs", "monos", "con_defs"];
wenzelm@7107
   853
val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP, inductive_casesP];
wenzelm@6424
   854
berghofe@5094
   855
end;
wenzelm@6424
   856
wenzelm@6424
   857
wenzelm@6424
   858
end;