src/HOL/Tools/inductive.ML
author wenzelm
Sun Apr 17 21:42:47 2011 +0200 (2011-04-17)
changeset 42381 309ec68442c6
parent 42364 8c674b3b8e44
child 42439 9efdd0af15ac
permissions -rw-r--r--
added Binding.print convenience, which includes quote already;
haftmann@31723
     1
(*  Title:      HOL/Tools/inductive.ML
berghofe@5094
     2
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
wenzelm@21367
     3
    Author:     Stefan Berghofer and Markus Wenzel, TU Muenchen
berghofe@5094
     4
wenzelm@6424
     5
(Co)Inductive Definition module for HOL.
berghofe@5094
     6
berghofe@5094
     7
Features:
wenzelm@6424
     8
  * least or greatest fixedpoints
wenzelm@6424
     9
  * mutually recursive definitions
wenzelm@6424
    10
  * definitions involving arbitrary monotone operators
wenzelm@6424
    11
  * automatically proves introduction and elimination rules
berghofe@5094
    12
berghofe@5094
    13
  Introduction rules have the form
berghofe@21024
    14
  [| M Pj ti, ..., Q x, ... |] ==> Pk t
berghofe@5094
    15
  where M is some monotone operator (usually the identity)
berghofe@21024
    16
  Q x is any side condition on the free variables
berghofe@5094
    17
  ti, t are any terms
berghofe@21024
    18
  Pj, Pk are two of the predicates being defined in mutual recursion
berghofe@5094
    19
*)
berghofe@5094
    20
haftmann@31723
    21
signature BASIC_INDUCTIVE =
berghofe@5094
    22
sig
wenzelm@33458
    23
  type inductive_result =
wenzelm@33458
    24
    {preds: term list, elims: thm list, raw_induct: thm,
bulwahn@37734
    25
     induct: thm, inducts: thm list, intrs: thm list, eqs: thm list}
wenzelm@21526
    26
  val morph_result: morphism -> inductive_result -> inductive_result
wenzelm@33458
    27
  type inductive_info = {names: string list, coind: bool} * inductive_result
wenzelm@21526
    28
  val the_inductive: Proof.context -> string -> inductive_info
wenzelm@21367
    29
  val print_inductives: Proof.context -> unit
wenzelm@18728
    30
  val mono_add: attribute
wenzelm@18728
    31
  val mono_del: attribute
wenzelm@21367
    32
  val get_monos: Proof.context -> thm list
wenzelm@21367
    33
  val mk_cases: Proof.context -> term -> thm
wenzelm@10910
    34
  val inductive_forall_name: string
wenzelm@10910
    35
  val inductive_forall_def: thm
wenzelm@10910
    36
  val rulify: thm -> thm
wenzelm@28839
    37
  val inductive_cases: (Attrib.binding * string list) list -> local_theory ->
wenzelm@28084
    38
    thm list list * local_theory
wenzelm@28839
    39
  val inductive_cases_i: (Attrib.binding * term list) list -> local_theory ->
wenzelm@28084
    40
    thm list list * local_theory
wenzelm@33458
    41
  type inductive_flags =
wenzelm@33669
    42
    {quiet_mode: bool, verbose: bool, alt_name: binding, coind: bool,
wenzelm@33669
    43
      no_elim: bool, no_ind: bool, skip_mono: bool, fork_mono: bool}
wenzelm@24815
    44
  val add_inductive_i:
haftmann@29581
    45
    inductive_flags -> ((binding * typ) * mixfix) list ->
wenzelm@28084
    46
    (string * typ) list -> (Attrib.binding * term) list -> thm list -> local_theory ->
wenzelm@28084
    47
    inductive_result * local_theory
wenzelm@28083
    48
  val add_inductive: bool -> bool ->
haftmann@29581
    49
    (binding * string option * mixfix) list ->
haftmann@29581
    50
    (binding * string option * mixfix) list ->
wenzelm@28084
    51
    (Attrib.binding * string) list ->
wenzelm@28083
    52
    (Facts.ref * Attrib.src list) list ->
wenzelm@29388
    53
    bool -> local_theory -> inductive_result * local_theory
wenzelm@33726
    54
  val add_inductive_global: inductive_flags ->
haftmann@29581
    55
    ((binding * typ) * mixfix) list -> (string * typ) list -> (Attrib.binding * term) list ->
wenzelm@28084
    56
    thm list -> theory -> inductive_result * theory
berghofe@22789
    57
  val arities_of: thm -> (string * int) list
berghofe@22789
    58
  val params_of: thm -> term list
berghofe@22789
    59
  val partition_rules: thm -> thm list -> (string * thm list) list
berghofe@25822
    60
  val partition_rules': thm -> (thm * 'a) list -> (string * (thm * 'a) list) list
berghofe@22789
    61
  val unpartition_rules: thm list -> (string * 'a list) list -> 'a list
berghofe@22789
    62
  val infer_intro_vars: thm -> int -> thm list -> term list list
wenzelm@18708
    63
  val setup: theory -> theory
berghofe@5094
    64
end;
berghofe@5094
    65
haftmann@31723
    66
signature INDUCTIVE =
berghofe@23762
    67
sig
haftmann@31723
    68
  include BASIC_INDUCTIVE
wenzelm@33458
    69
  type add_ind_def =
wenzelm@33458
    70
    inductive_flags ->
wenzelm@33458
    71
    term list -> (Attrib.binding * term) list -> thm list ->
wenzelm@33458
    72
    term list -> (binding * mixfix) list ->
wenzelm@33458
    73
    local_theory -> inductive_result * local_theory
bulwahn@35757
    74
  val declare_rules: binding -> bool -> bool -> string list -> term list ->
berghofe@34986
    75
    thm list -> binding list -> Attrib.src list list -> (thm * string list * int) list ->
bulwahn@37734
    76
    thm list -> thm -> local_theory -> thm list * thm list * thm list * thm * thm list * local_theory
berghofe@23762
    77
  val add_ind_def: add_ind_def
wenzelm@28083
    78
  val gen_add_inductive_i: add_ind_def -> inductive_flags ->
haftmann@29581
    79
    ((binding * typ) * mixfix) list -> (string * typ) list -> (Attrib.binding * term) list ->
wenzelm@28084
    80
    thm list -> local_theory -> inductive_result * local_theory
wenzelm@28083
    81
  val gen_add_inductive: add_ind_def -> bool -> bool ->
haftmann@29581
    82
    (binding * string option * mixfix) list ->
haftmann@29581
    83
    (binding * string option * mixfix) list ->
wenzelm@28084
    84
    (Attrib.binding * string) list -> (Facts.ref * Attrib.src list) list ->
wenzelm@29388
    85
    bool -> local_theory -> inductive_result * local_theory
wenzelm@36958
    86
  val gen_ind_decl: add_ind_def -> bool -> (bool -> local_theory -> local_theory) parser
berghofe@23762
    87
end;
berghofe@23762
    88
haftmann@31723
    89
structure Inductive: INDUCTIVE =
berghofe@5094
    90
struct
berghofe@5094
    91
wenzelm@9598
    92
wenzelm@10729
    93
(** theory context references **)
wenzelm@10729
    94
wenzelm@11991
    95
val inductive_forall_name = "HOL.induct_forall";
haftmann@32602
    96
val inductive_forall_def = @{thm induct_forall_def};
wenzelm@11991
    97
val inductive_conj_name = "HOL.induct_conj";
haftmann@32602
    98
val inductive_conj_def = @{thm induct_conj_def};
haftmann@32602
    99
val inductive_conj = @{thms induct_conj};
haftmann@32602
   100
val inductive_atomize = @{thms induct_atomize};
haftmann@32602
   101
val inductive_rulify = @{thms induct_rulify};
haftmann@32602
   102
val inductive_rulify_fallback = @{thms induct_rulify_fallback};
wenzelm@10729
   103
berghofe@21024
   104
val notTrueE = TrueI RSN (2, notE);
berghofe@21024
   105
val notFalseI = Seq.hd (atac 1 notI);
wenzelm@32181
   106
wenzelm@32181
   107
val simp_thms' = map mk_meta_eq
wenzelm@32181
   108
  @{lemma "(~True) = False" "(~False) = True"
wenzelm@32181
   109
      "(True --> P) = P" "(False --> P) = True"
wenzelm@32181
   110
      "(P & True) = P" "(True & P) = P"
wenzelm@32181
   111
    by (fact simp_thms)+};
berghofe@21024
   112
haftmann@41075
   113
val simp_thms'' = map mk_meta_eq [@{thm inf_fun_def}, @{thm inf_bool_def}] @ simp_thms';
haftmann@32652
   114
haftmann@32652
   115
val simp_thms''' = map mk_meta_eq
haftmann@41075
   116
  [@{thm le_fun_def}, @{thm le_bool_def}, @{thm sup_fun_def}, @{thm sup_bool_def}];
wenzelm@10729
   117
wenzelm@10729
   118
wenzelm@22846
   119
(** context data **)
berghofe@7710
   120
berghofe@21024
   121
type inductive_result =
berghofe@23762
   122
  {preds: term list, elims: thm list, raw_induct: thm,
bulwahn@37734
   123
   induct: thm, inducts: thm list, intrs: thm list, eqs: thm list};
berghofe@7710
   124
bulwahn@37734
   125
fun morph_result phi {preds, elims, raw_induct: thm, induct, inducts, intrs, eqs} =
wenzelm@21526
   126
  let
wenzelm@21526
   127
    val term = Morphism.term phi;
wenzelm@21526
   128
    val thm = Morphism.thm phi;
wenzelm@21526
   129
    val fact = Morphism.fact phi;
wenzelm@21526
   130
  in
berghofe@23762
   131
   {preds = map term preds, elims = fact elims, raw_induct = thm raw_induct,
bulwahn@37734
   132
    induct = thm induct, inducts = fact inducts, intrs = fact intrs, eqs = fact eqs}
wenzelm@21526
   133
  end;
wenzelm@21526
   134
berghofe@21024
   135
type inductive_info =
berghofe@21024
   136
  {names: string list, coind: bool} * inductive_result;
berghofe@21024
   137
wenzelm@33519
   138
structure InductiveData = Generic_Data
wenzelm@22846
   139
(
berghofe@7710
   140
  type T = inductive_info Symtab.table * thm list;
berghofe@7710
   141
  val empty = (Symtab.empty, []);
wenzelm@16432
   142
  val extend = I;
wenzelm@33519
   143
  fun merge ((tab1, monos1), (tab2, monos2)) : T =
wenzelm@24039
   144
    (Symtab.merge (K true) (tab1, tab2), Thm.merge_thms (monos1, monos2));
wenzelm@22846
   145
);
berghofe@7710
   146
wenzelm@21526
   147
val get_inductives = InductiveData.get o Context.Proof;
wenzelm@22846
   148
wenzelm@22846
   149
fun print_inductives ctxt =
wenzelm@22846
   150
  let
wenzelm@22846
   151
    val (tab, monos) = get_inductives ctxt;
wenzelm@42361
   152
    val space = Consts.space_of (Proof_Context.consts_of ctxt);
wenzelm@22846
   153
  in
wenzelm@42358
   154
    [Pretty.strs ("(co)inductives:" :: map #1 (Name_Space.extern_table ctxt (space, tab))),
wenzelm@32091
   155
     Pretty.big_list "monotonicity rules:" (map (Display.pretty_thm ctxt) monos)]
wenzelm@22846
   156
    |> Pretty.chunks |> Pretty.writeln
wenzelm@22846
   157
  end;
berghofe@7710
   158
berghofe@7710
   159
berghofe@7710
   160
(* get and put data *)
berghofe@7710
   161
wenzelm@21367
   162
fun the_inductive ctxt name =
wenzelm@21526
   163
  (case Symtab.lookup (#1 (get_inductives ctxt)) name of
berghofe@21024
   164
    NONE => error ("Unknown (co)inductive predicate " ^ quote name)
skalberg@15531
   165
  | SOME info => info);
wenzelm@9598
   166
wenzelm@25380
   167
fun put_inductives names info = InductiveData.map
wenzelm@25380
   168
  (apfst (fold (fn name => Symtab.update (name, info)) names));
berghofe@7710
   169
wenzelm@8277
   170
berghofe@7710
   171
berghofe@7710
   172
(** monotonicity rules **)
berghofe@7710
   173
wenzelm@21526
   174
val get_monos = #2 o get_inductives;
wenzelm@21367
   175
val map_monos = InductiveData.map o apsnd;
wenzelm@8277
   176
berghofe@7710
   177
fun mk_mono thm =
berghofe@7710
   178
  let
berghofe@33933
   179
    fun eq2mono thm' = thm' RS (thm' RS eq_to_mono);
haftmann@32652
   180
    fun dest_less_concl thm = dest_less_concl (thm RS @{thm le_funD})
haftmann@32652
   181
      handle THM _ => thm RS @{thm le_boolD}
berghofe@7710
   182
  in
berghofe@33933
   183
    case concl_of thm of
berghofe@22275
   184
      Const ("==", _) $ _ $ _ => eq2mono (thm RS meta_eq_to_obj_eq)
haftmann@38864
   185
    | _ $ (Const (@{const_name HOL.eq}, _) $ _ $ _) => eq2mono thm
haftmann@35092
   186
    | _ $ (Const (@{const_name Orderings.less_eq}, _) $ _ $ _) =>
berghofe@33933
   187
      dest_less_concl (Seq.hd (REPEAT (FIRSTGOAL
berghofe@33933
   188
        (resolve_tac [@{thm le_funI}, @{thm le_boolI'}])) thm))
berghofe@33933
   189
    | _ => thm
wenzelm@32091
   190
  end handle THM _ =>
wenzelm@32091
   191
    error ("Bad monotonicity theorem:\n" ^ Display.string_of_thm_without_context thm);
berghofe@7710
   192
berghofe@33933
   193
val mono_add = Thm.declaration_attribute (map_monos o Thm.add_thm o mk_mono);
berghofe@33933
   194
val mono_del = Thm.declaration_attribute (map_monos o Thm.del_thm o mk_mono);
berghofe@7710
   195
berghofe@7710
   196
wenzelm@7107
   197
bulwahn@38665
   198
(** equations **)
bulwahn@38665
   199
bulwahn@38665
   200
structure Equation_Data = Generic_Data
bulwahn@38665
   201
(
bulwahn@38665
   202
  type T = thm Item_Net.T;
bulwahn@38665
   203
  val empty = Item_Net.init (op aconv o pairself Thm.prop_of)
bulwahn@38665
   204
    (single o fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o Thm.prop_of);
bulwahn@38665
   205
  val extend = I;
bulwahn@38665
   206
  val merge = Item_Net.merge;
bulwahn@38665
   207
);
bulwahn@38665
   208
bulwahn@38665
   209
val add_equation = Thm.declaration_attribute (Equation_Data.map o Item_Net.update)
bulwahn@38665
   210
bulwahn@38665
   211
bulwahn@38665
   212
wenzelm@10735
   213
(** misc utilities **)
wenzelm@6424
   214
wenzelm@26477
   215
fun message quiet_mode s = if quiet_mode then () else writeln s;
wenzelm@26477
   216
fun clean_message quiet_mode s = if ! quick_and_dirty then () else message quiet_mode s;
berghofe@5662
   217
wenzelm@6424
   218
fun coind_prefix true = "co"
wenzelm@6424
   219
  | coind_prefix false = "";
wenzelm@6424
   220
wenzelm@24133
   221
fun log (b:int) m n = if m >= n then 0 else 1 + log b (b * m) n;
wenzelm@6424
   222
berghofe@21024
   223
fun make_bool_args f g [] i = []
berghofe@21024
   224
  | make_bool_args f g (x :: xs) i =
berghofe@21024
   225
      (if i mod 2 = 0 then f x else g x) :: make_bool_args f g xs (i div 2);
berghofe@21024
   226
berghofe@21024
   227
fun make_bool_args' xs =
berghofe@21024
   228
  make_bool_args (K HOLogic.false_const) (K HOLogic.true_const) xs;
berghofe@21024
   229
haftmann@33957
   230
fun arg_types_of k c = drop k (binder_types (fastype_of c));
haftmann@33077
   231
wenzelm@40316
   232
fun find_arg T x [] = raise Fail "find_arg"
berghofe@21024
   233
  | find_arg T x ((p as (_, (SOME _, _))) :: ps) =
berghofe@21024
   234
      apsnd (cons p) (find_arg T x ps)
berghofe@21024
   235
  | find_arg T x ((p as (U, (NONE, y))) :: ps) =
wenzelm@23577
   236
      if (T: typ) = U then (y, (U, (SOME x, y)) :: ps)
berghofe@21024
   237
      else apsnd (cons p) (find_arg T x ps);
berghofe@7020
   238
berghofe@21024
   239
fun make_args Ts xs =
haftmann@28524
   240
  map (fn (T, (NONE, ())) => Const (@{const_name undefined}, T) | (_, (SOME t, ())) => t)
berghofe@21024
   241
    (fold (fn (t, T) => snd o find_arg T t) xs (map (rpair (NONE, ())) Ts));
berghofe@7020
   242
berghofe@21024
   243
fun make_args' Ts xs Us =
berghofe@21024
   244
  fst (fold_map (fn T => find_arg T ()) Us (Ts ~~ map (pair NONE) xs));
berghofe@7020
   245
berghofe@21024
   246
fun dest_predicate cs params t =
berghofe@5094
   247
  let
berghofe@21024
   248
    val k = length params;
berghofe@21024
   249
    val (c, ts) = strip_comb t;
berghofe@21024
   250
    val (xs, ys) = chop k ts;
haftmann@31986
   251
    val i = find_index (fn c' => c' = c) cs;
berghofe@21024
   252
  in
berghofe@21024
   253
    if xs = params andalso i >= 0 then
haftmann@33077
   254
      SOME (c, i, ys, chop (length ys) (arg_types_of k c))
berghofe@21024
   255
    else NONE
berghofe@5094
   256
  end;
berghofe@5094
   257
berghofe@21024
   258
fun mk_names a 0 = []
berghofe@21024
   259
  | mk_names a 1 = [a]
berghofe@21024
   260
  | mk_names a n = map (fn i => a ^ string_of_int i) (1 upto n);
berghofe@10988
   261
bulwahn@37734
   262
fun select_disj 1 1 = []
bulwahn@37734
   263
  | select_disj _ 1 = [rtac disjI1]
bulwahn@37734
   264
  | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
wenzelm@6424
   265
wenzelm@6424
   266
wenzelm@10729
   267
(** process rules **)
wenzelm@10729
   268
wenzelm@10729
   269
local
berghofe@5094
   270
berghofe@23762
   271
fun err_in_rule ctxt name t msg =
wenzelm@42381
   272
  error (cat_lines ["Ill-formed introduction rule " ^ Binding.print name,
wenzelm@24920
   273
    Syntax.string_of_term ctxt t, msg]);
wenzelm@10729
   274
berghofe@23762
   275
fun err_in_prem ctxt name t p msg =
wenzelm@24920
   276
  error (cat_lines ["Ill-formed premise", Syntax.string_of_term ctxt p,
wenzelm@42381
   277
    "in introduction rule " ^ Binding.print name, Syntax.string_of_term ctxt t, msg]);
berghofe@5094
   278
berghofe@21024
   279
val bad_concl = "Conclusion of introduction rule must be an inductive predicate";
wenzelm@10729
   280
berghofe@21024
   281
val bad_ind_occ = "Inductive predicate occurs in argument of inductive predicate";
berghofe@21024
   282
berghofe@21024
   283
val bad_app = "Inductive predicate must be applied to parameter(s) ";
paulson@11358
   284
wenzelm@41228
   285
fun atomize_term thy = Raw_Simplifier.rewrite_term thy inductive_atomize [];
wenzelm@10729
   286
wenzelm@10729
   287
in
berghofe@5094
   288
wenzelm@28083
   289
fun check_rule ctxt cs params ((binding, att), rule) =
wenzelm@10729
   290
  let
berghofe@21024
   291
    val params' = Term.variant_frees rule (Logic.strip_params rule);
berghofe@21024
   292
    val frees = rev (map Free params');
berghofe@21024
   293
    val concl = subst_bounds (frees, Logic.strip_assums_concl rule);
berghofe@21024
   294
    val prems = map (curry subst_bounds frees) (Logic.strip_assums_hyp rule);
berghofe@23762
   295
    val rule' = Logic.list_implies (prems, concl);
wenzelm@42361
   296
    val aprems = map (atomize_term (Proof_Context.theory_of ctxt)) prems;
berghofe@21024
   297
    val arule = list_all_free (params', Logic.list_implies (aprems, concl));
berghofe@21024
   298
berghofe@21024
   299
    fun check_ind err t = case dest_predicate cs params t of
berghofe@21024
   300
        NONE => err (bad_app ^
wenzelm@24920
   301
          commas (map (Syntax.string_of_term ctxt) params))
berghofe@21024
   302
      | SOME (_, _, ys, _) =>
berghofe@21024
   303
          if exists (fn c => exists (fn t => Logic.occs (c, t)) ys) cs
berghofe@21024
   304
          then err bad_ind_occ else ();
berghofe@21024
   305
berghofe@21024
   306
    fun check_prem' prem t =
haftmann@36692
   307
      if member (op =) cs (head_of t) then
wenzelm@42381
   308
        check_ind (err_in_prem ctxt binding rule prem) t
berghofe@21024
   309
      else (case t of
berghofe@21024
   310
          Abs (_, _, t) => check_prem' prem t
berghofe@21024
   311
        | t $ u => (check_prem' prem t; check_prem' prem u)
berghofe@21024
   312
        | _ => ());
berghofe@5094
   313
wenzelm@10729
   314
    fun check_prem (prem, aprem) =
berghofe@21024
   315
      if can HOLogic.dest_Trueprop aprem then check_prem' prem prem
wenzelm@42381
   316
      else err_in_prem ctxt binding rule prem "Non-atomic premise";
wenzelm@10729
   317
  in
paulson@11358
   318
    (case concl of
wenzelm@35364
   319
       Const (@{const_name Trueprop}, _) $ t =>
haftmann@36692
   320
         if member (op =) cs (head_of t) then
wenzelm@42381
   321
           (check_ind (err_in_rule ctxt binding rule') t;
berghofe@21024
   322
            List.app check_prem (prems ~~ aprems))
wenzelm@42381
   323
         else err_in_rule ctxt binding rule' bad_concl
wenzelm@42381
   324
     | _ => err_in_rule ctxt binding rule' bad_concl);
wenzelm@28083
   325
    ((binding, att), arule)
wenzelm@10729
   326
  end;
berghofe@5094
   327
berghofe@24744
   328
val rulify =
wenzelm@18222
   329
  hol_simplify inductive_conj
wenzelm@18463
   330
  #> hol_simplify inductive_rulify
wenzelm@18463
   331
  #> hol_simplify inductive_rulify_fallback
wenzelm@30552
   332
  #> Simplifier.norm_hhf;
wenzelm@10729
   333
wenzelm@10729
   334
end;
wenzelm@10729
   335
berghofe@5094
   336
wenzelm@6424
   337
berghofe@21024
   338
(** proofs for (co)inductive predicates **)
wenzelm@6424
   339
berghofe@26534
   340
(* prove monotonicity *)
berghofe@5094
   341
berghofe@36642
   342
fun prove_mono quiet_mode skip_mono fork_mono predT fp_fun monos ctxt =
wenzelm@29388
   343
 (message (quiet_mode orelse skip_mono andalso !quick_and_dirty orelse fork_mono)
berghofe@26534
   344
    "  Proving monotonicity ...";
wenzelm@32970
   345
  (if skip_mono then Skip_Proof.prove else if fork_mono then Goal.prove_future else Goal.prove) ctxt
berghofe@36642
   346
    [] []
wenzelm@17985
   347
    (HOLogic.mk_Trueprop
wenzelm@24815
   348
      (Const (@{const_name Orderings.mono}, (predT --> predT) --> HOLogic.boolT) $ fp_fun))
wenzelm@25380
   349
    (fn _ => EVERY [rtac @{thm monoI} 1,
haftmann@32652
   350
      REPEAT (resolve_tac [@{thm le_funI}, @{thm le_boolI'}] 1),
berghofe@21024
   351
      REPEAT (FIRST
berghofe@21024
   352
        [atac 1,
berghofe@33933
   353
         resolve_tac (map mk_mono monos @ get_monos ctxt) 1,
haftmann@32652
   354
         etac @{thm le_funE} 1, dtac @{thm le_boolD} 1])]));
berghofe@5094
   355
wenzelm@6424
   356
wenzelm@10735
   357
(* prove introduction rules *)
berghofe@5094
   358
berghofe@36642
   359
fun prove_intrs quiet_mode coind mono fp_def k intr_ts rec_preds_defs ctxt ctxt' =
berghofe@5094
   360
  let
wenzelm@26477
   361
    val _ = clean_message quiet_mode "  Proving the introduction rules ...";
berghofe@5094
   362
berghofe@21024
   363
    val unfold = funpow k (fn th => th RS fun_cong)
berghofe@21024
   364
      (mono RS (fp_def RS
haftmann@32652
   365
        (if coind then @{thm def_gfp_unfold} else @{thm def_lfp_unfold})));
berghofe@5094
   366
berghofe@21024
   367
    val rules = [refl, TrueI, notFalseI, exI, conjI];
berghofe@21024
   368
berghofe@36642
   369
    val intrs = map_index (fn (i, intr) =>
berghofe@36642
   370
      Skip_Proof.prove ctxt [] [] intr (fn _ => EVERY
berghofe@21024
   371
       [rewrite_goals_tac rec_preds_defs,
berghofe@21024
   372
        rtac (unfold RS iffD2) 1,
berghofe@21024
   373
        EVERY1 (select_disj (length intr_ts) (i + 1)),
wenzelm@17985
   374
        (*Not ares_tac, since refl must be tried before any equality assumptions;
wenzelm@17985
   375
          backtracking may occur if the premises have extra variables!*)
berghofe@36642
   376
        DEPTH_SOLVE_1 (resolve_tac rules 1 APPEND assume_tac 1)])
wenzelm@42361
   377
       |> singleton (Proof_Context.export ctxt ctxt')) intr_ts
berghofe@5094
   378
berghofe@5094
   379
  in (intrs, unfold) end;
berghofe@5094
   380
wenzelm@6424
   381
wenzelm@10735
   382
(* prove elimination rules *)
berghofe@5094
   383
berghofe@36642
   384
fun prove_elims quiet_mode cs params intr_ts intr_names unfold rec_preds_defs ctxt ctxt''' =
berghofe@5094
   385
  let
wenzelm@26477
   386
    val _ = clean_message quiet_mode "  Proving the elimination rules ...";
berghofe@5094
   387
berghofe@36642
   388
    val ([pname], ctxt') = Variable.variant_fixes ["P"] ctxt;
berghofe@21024
   389
    val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
berghofe@21024
   390
berghofe@21024
   391
    fun dest_intr r =
berghofe@21024
   392
      (the (dest_predicate cs params (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))),
berghofe@21024
   393
       Logic.strip_assums_hyp r, Logic.strip_params r);
berghofe@21024
   394
berghofe@21024
   395
    val intrs = map dest_intr intr_ts ~~ intr_names;
berghofe@21024
   396
berghofe@21024
   397
    val rules1 = [disjE, exE, FalseE];
berghofe@21024
   398
    val rules2 = [conjE, FalseE, notTrueE];
berghofe@21024
   399
berghofe@21024
   400
    fun prove_elim c =
berghofe@21024
   401
      let
haftmann@33077
   402
        val Ts = arg_types_of (length params) c;
berghofe@21024
   403
        val (anames, ctxt'') = Variable.variant_fixes (mk_names "a" (length Ts)) ctxt';
berghofe@21024
   404
        val frees = map Free (anames ~~ Ts);
berghofe@21024
   405
berghofe@21024
   406
        fun mk_elim_prem ((_, _, us, _), ts, params') =
berghofe@21024
   407
          list_all (params',
berghofe@21024
   408
            Logic.list_implies (map (HOLogic.mk_Trueprop o HOLogic.mk_eq)
berghofe@21024
   409
              (frees ~~ us) @ ts, P));
wenzelm@33317
   410
        val c_intrs = filter (equal c o #1 o #1 o #1) intrs;
berghofe@21024
   411
        val prems = HOLogic.mk_Trueprop (list_comb (c, params @ frees)) ::
berghofe@21024
   412
           map mk_elim_prem (map #1 c_intrs)
berghofe@21024
   413
      in
wenzelm@32970
   414
        (Skip_Proof.prove ctxt'' [] prems P
berghofe@21024
   415
          (fn {prems, ...} => EVERY
berghofe@21024
   416
            [cut_facts_tac [hd prems] 1,
berghofe@21024
   417
             rewrite_goals_tac rec_preds_defs,
berghofe@21024
   418
             dtac (unfold RS iffD1) 1,
berghofe@21024
   419
             REPEAT (FIRSTGOAL (eresolve_tac rules1)),
berghofe@21024
   420
             REPEAT (FIRSTGOAL (eresolve_tac rules2)),
berghofe@21024
   421
             EVERY (map (fn prem =>
berghofe@21024
   422
               DEPTH_SOLVE_1 (ares_tac [rewrite_rule rec_preds_defs prem, conjI] 1)) (tl prems))])
wenzelm@42361
   423
          |> singleton (Proof_Context.export ctxt'' ctxt'''),
berghofe@34986
   424
         map #2 c_intrs, length Ts)
berghofe@21024
   425
      end
berghofe@21024
   426
berghofe@21024
   427
   in map prove_elim cs end;
berghofe@5094
   428
bulwahn@37734
   429
(* prove simplification equations *)
wenzelm@6424
   430
wenzelm@37901
   431
fun prove_eqs quiet_mode cs params intr_ts intrs (elims: (thm * bstring list * int) list) ctxt ctxt'' =
bulwahn@37734
   432
  let
bulwahn@37734
   433
    val _ = clean_message quiet_mode "  Proving the simplification rules ...";
bulwahn@37734
   434
    
bulwahn@37734
   435
    fun dest_intr r =
bulwahn@37734
   436
      (the (dest_predicate cs params (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))),
bulwahn@37734
   437
       Logic.strip_assums_hyp r, Logic.strip_params r);
bulwahn@37734
   438
    val intr_ts' = map dest_intr intr_ts;
wenzelm@37901
   439
    fun prove_eq c (elim: thm * 'a * 'b) =
bulwahn@37734
   440
      let
bulwahn@37734
   441
        val Ts = arg_types_of (length params) c;
bulwahn@37734
   442
        val (anames, ctxt') = Variable.variant_fixes (mk_names "a" (length Ts)) ctxt;
bulwahn@37734
   443
        val frees = map Free (anames ~~ Ts);
bulwahn@37734
   444
        val c_intrs = filter (equal c o #1 o #1 o #1) (intr_ts' ~~ intrs);
bulwahn@37734
   445
        fun mk_intr_conj (((_, _, us, _), ts, params'), _) =
bulwahn@37734
   446
          let
bulwahn@37734
   447
            fun list_ex ([], t) = t
bulwahn@37734
   448
              | list_ex ((a,T)::vars, t) =
bulwahn@37734
   449
                 (HOLogic.exists_const T) $ (Abs(a, T, list_ex(vars,t)));
bulwahn@37734
   450
            val conjs = map2 (curry HOLogic.mk_eq) frees us @ (map HOLogic.dest_Trueprop ts)
bulwahn@37734
   451
          in
bulwahn@37734
   452
            list_ex (params', if null conjs then @{term True} else foldr1 HOLogic.mk_conj conjs)
bulwahn@37734
   453
          end;
bulwahn@37734
   454
        val lhs = list_comb (c, params @ frees)
bulwahn@37734
   455
        val rhs =
bulwahn@37734
   456
          if null c_intrs then @{term False} else foldr1 HOLogic.mk_disj (map mk_intr_conj c_intrs)
bulwahn@37734
   457
        val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs))
bulwahn@37734
   458
        fun prove_intr1 (i, _) = Subgoal.FOCUS_PREMS (fn {params, prems, ...} =>
bulwahn@37734
   459
            let
bulwahn@37734
   460
              val (prems', last_prem) = split_last prems
bulwahn@37734
   461
            in
bulwahn@37734
   462
              EVERY1 (select_disj (length c_intrs) (i + 1))
bulwahn@37734
   463
              THEN EVERY (replicate (length params) (rtac @{thm exI} 1))
bulwahn@37734
   464
              THEN EVERY (map (fn prem => (rtac @{thm conjI} 1 THEN rtac prem 1)) prems')
bulwahn@37734
   465
              THEN rtac last_prem 1
bulwahn@37734
   466
            end) ctxt' 1
bulwahn@37734
   467
        fun prove_intr2 (((_, _, us, _), ts, params'), intr) =
bulwahn@37734
   468
          EVERY (replicate (length params') (etac @{thm exE} 1))
bulwahn@37734
   469
          THEN EVERY (replicate (length ts + length us - 1) (etac @{thm conjE} 1))
bulwahn@37734
   470
          THEN Subgoal.FOCUS_PREMS (fn {params, prems, ...} =>
bulwahn@37734
   471
            let
bulwahn@37734
   472
              val (eqs, prems') = chop (length us) prems
bulwahn@37734
   473
              val rew_thms = map (fn th => th RS @{thm eq_reflection}) eqs
bulwahn@37734
   474
            in
bulwahn@37734
   475
              rewrite_goal_tac rew_thms 1
bulwahn@37734
   476
              THEN rtac intr 1
bulwahn@37734
   477
              THEN (EVERY (map (fn p => rtac p 1) prems'))              
bulwahn@37734
   478
            end) ctxt' 1 
bulwahn@37734
   479
      in
bulwahn@37734
   480
        Skip_Proof.prove ctxt' [] [] eq (fn {...} =>
bulwahn@37734
   481
          rtac @{thm iffI} 1 THEN etac (#1 elim) 1
bulwahn@37734
   482
          THEN EVERY (map_index prove_intr1 c_intrs)
bulwahn@37734
   483
          THEN (if null c_intrs then etac @{thm FalseE} 1 else
bulwahn@37734
   484
            let val (c_intrs', last_c_intr) = split_last c_intrs in
bulwahn@37734
   485
              EVERY (map (fn ci => etac @{thm disjE} 1 THEN prove_intr2 ci) c_intrs')
bulwahn@37734
   486
              THEN prove_intr2 last_c_intr
bulwahn@37734
   487
            end))
bulwahn@37734
   488
        |> rulify
wenzelm@42361
   489
        |> singleton (Proof_Context.export ctxt' ctxt'')
bulwahn@37734
   490
      end;  
bulwahn@37734
   491
  in
bulwahn@37734
   492
    map2 prove_eq cs elims
bulwahn@37734
   493
  end;
bulwahn@37734
   494
  
wenzelm@10735
   495
(* derivation of simplified elimination rules *)
berghofe@5094
   496
wenzelm@11682
   497
local
wenzelm@11682
   498
wenzelm@11682
   499
(*delete needless equality assumptions*)
wenzelm@29064
   500
val refl_thin = Goal.prove_global @{theory HOL} [] [] @{prop "!!P. a = a ==> P ==> P"}
haftmann@22838
   501
  (fn _ => assume_tac 1);
berghofe@21024
   502
val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE];
wenzelm@11682
   503
val elim_tac = REPEAT o Tactic.eresolve_tac elim_rls;
wenzelm@11682
   504
berghofe@23762
   505
fun simp_case_tac ss i =
berghofe@23762
   506
  EVERY' [elim_tac, asm_full_simp_tac ss, elim_tac, REPEAT o bound_hyp_subst_tac] i;
wenzelm@21367
   507
wenzelm@11682
   508
in
wenzelm@9598
   509
wenzelm@21367
   510
fun mk_cases ctxt prop =
wenzelm@7107
   511
  let
wenzelm@42361
   512
    val thy = Proof_Context.theory_of ctxt;
wenzelm@32149
   513
    val ss = simpset_of ctxt;
wenzelm@21367
   514
wenzelm@21526
   515
    fun err msg =
wenzelm@21526
   516
      error (Pretty.string_of (Pretty.block
wenzelm@24920
   517
        [Pretty.str msg, Pretty.fbrk, Syntax.pretty_term ctxt prop]));
wenzelm@21526
   518
wenzelm@24861
   519
    val elims = Induct.find_casesP ctxt prop;
wenzelm@21367
   520
wenzelm@21367
   521
    val cprop = Thm.cterm_of thy prop;
berghofe@23762
   522
    val tac = ALLGOALS (simp_case_tac ss) THEN prune_params_tac;
wenzelm@21367
   523
    fun mk_elim rl =
wenzelm@36546
   524
      Thm.implies_intr cprop (Tactic.rule_by_tactic ctxt tac (Thm.assume cprop RS rl))
wenzelm@21367
   525
      |> singleton (Variable.export (Variable.auto_fixes prop ctxt) ctxt);
wenzelm@7107
   526
  in
wenzelm@7107
   527
    (case get_first (try mk_elim) elims of
skalberg@15531
   528
      SOME r => r
wenzelm@21526
   529
    | NONE => err "Proposition not an inductive predicate:")
wenzelm@7107
   530
  end;
wenzelm@7107
   531
wenzelm@11682
   532
end;
wenzelm@11682
   533
wenzelm@21367
   534
(* inductive_cases *)
wenzelm@7107
   535
wenzelm@21367
   536
fun gen_inductive_cases prep_att prep_prop args lthy =
wenzelm@9598
   537
  let
wenzelm@42361
   538
    val thy = Proof_Context.theory_of lthy;
wenzelm@37957
   539
    val facts = args |> Par_List.map (fn ((a, atts), props) =>
wenzelm@21367
   540
      ((a, map (prep_att thy) atts),
wenzelm@37957
   541
        Par_List.map (Thm.no_attributes o single o mk_cases lthy o prep_prop lthy) props));
wenzelm@33671
   542
  in lthy |> Local_Theory.notes facts |>> map snd end;
berghofe@5094
   543
wenzelm@24509
   544
val inductive_cases = gen_inductive_cases Attrib.intern_src Syntax.read_prop;
wenzelm@24509
   545
val inductive_cases_i = gen_inductive_cases (K I) Syntax.check_prop;
wenzelm@7107
   546
wenzelm@6424
   547
wenzelm@30722
   548
val ind_cases_setup =
wenzelm@30722
   549
  Method.setup @{binding ind_cases}
wenzelm@30722
   550
    (Scan.lift (Scan.repeat1 Args.name_source --
wenzelm@30722
   551
      Scan.optional (Args.$$$ "for" |-- Scan.repeat1 Args.name) []) >>
wenzelm@30722
   552
      (fn (raw_props, fixes) => fn ctxt =>
wenzelm@30722
   553
        let
wenzelm@30722
   554
          val (_, ctxt') = Variable.add_fixes fixes ctxt;
wenzelm@30722
   555
          val props = Syntax.read_props ctxt' raw_props;
wenzelm@30722
   556
          val ctxt'' = fold Variable.declare_term props ctxt';
wenzelm@42361
   557
          val rules = Proof_Context.export ctxt'' ctxt (map (mk_cases ctxt'') props)
wenzelm@30722
   558
        in Method.erule 0 rules end))
wenzelm@30722
   559
    "dynamic case analysis on predicates";
wenzelm@9598
   560
bulwahn@37734
   561
(* derivation of simplified equation *)
wenzelm@9598
   562
bulwahn@37734
   563
fun mk_simp_eq ctxt prop =
bulwahn@37734
   564
  let
wenzelm@42361
   565
    val thy = Proof_Context.theory_of ctxt
bulwahn@37734
   566
    val ctxt' = Variable.auto_fixes prop ctxt
bulwahn@38665
   567
    val lhs_of = fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o Thm.prop_of
bulwahn@38665
   568
    val substs = Item_Net.retrieve (Equation_Data.get (Context.Proof ctxt)) (HOLogic.dest_Trueprop prop) 
bulwahn@38665
   569
      |> map_filter
bulwahn@38665
   570
        (fn eq => SOME (Pattern.match thy (lhs_of eq, HOLogic.dest_Trueprop prop)
bulwahn@38665
   571
            (Vartab.empty, Vartab.empty), eq)
bulwahn@38665
   572
          handle Pattern.MATCH => NONE)
bulwahn@38665
   573
    val (subst, eq) = case substs of
bulwahn@38665
   574
        [s] => s
bulwahn@38665
   575
      | _ => error
bulwahn@38665
   576
        ("equations matching pattern " ^ Syntax.string_of_term ctxt prop ^ " is not unique")
bulwahn@38665
   577
    val inst = map (fn v => (cterm_of thy (Var v), cterm_of thy (Envir.subst_term subst (Var v))))
bulwahn@38665
   578
      (Term.add_vars (lhs_of eq) [])
bulwahn@38118
   579
   in
bulwahn@38118
   580
    cterm_instantiate inst eq
bulwahn@37734
   581
    |> Conv.fconv_rule (Conv.arg_conv (Conv.arg_conv
bulwahn@37734
   582
      (Simplifier.full_rewrite (simpset_of ctxt))))
bulwahn@37734
   583
    |> singleton (Variable.export ctxt' ctxt)
bulwahn@37734
   584
  end
bulwahn@37734
   585
bulwahn@37734
   586
(* inductive simps *)
bulwahn@37734
   587
bulwahn@37734
   588
fun gen_inductive_simps prep_att prep_prop args lthy =
bulwahn@37734
   589
  let
wenzelm@42361
   590
    val thy = Proof_Context.theory_of lthy;
bulwahn@37734
   591
    val facts = args |> map (fn ((a, atts), props) =>
bulwahn@37734
   592
      ((a, map (prep_att thy) atts),
bulwahn@37734
   593
        map (Thm.no_attributes o single o mk_simp_eq lthy o prep_prop lthy) props));
bulwahn@37734
   594
  in lthy |> Local_Theory.notes facts |>> map snd end;
bulwahn@37734
   595
bulwahn@37734
   596
val inductive_simps = gen_inductive_simps Attrib.intern_src Syntax.read_prop;
bulwahn@37734
   597
val inductive_simps_i = gen_inductive_simps (K I) Syntax.check_prop;
bulwahn@40902
   598
wenzelm@10735
   599
(* prove induction rule *)
berghofe@5094
   600
wenzelm@26477
   601
fun prove_indrule quiet_mode cs argTs bs xs rec_const params intr_ts mono
berghofe@36642
   602
    fp_def rec_preds_defs ctxt ctxt''' =
berghofe@5094
   603
  let
wenzelm@26477
   604
    val _ = clean_message quiet_mode "  Proving the induction rule ...";
wenzelm@42361
   605
    val thy = Proof_Context.theory_of ctxt;
berghofe@5094
   606
berghofe@21024
   607
    (* predicates for induction rule *)
berghofe@21024
   608
berghofe@36642
   609
    val (pnames, ctxt') = Variable.variant_fixes (mk_names "P" (length cs)) ctxt;
haftmann@33077
   610
    val preds = map2 (curry Free) pnames
haftmann@33077
   611
      (map (fn c => arg_types_of (length params) c ---> HOLogic.boolT) cs);
berghofe@21024
   612
berghofe@21024
   613
    (* transform an introduction rule into a premise for induction rule *)
berghofe@21024
   614
berghofe@21024
   615
    fun mk_ind_prem r =
berghofe@21024
   616
      let
wenzelm@33669
   617
        fun subst s =
wenzelm@33669
   618
          (case dest_predicate cs params s of
berghofe@21024
   619
            SOME (_, i, ys, (_, Ts)) =>
berghofe@21024
   620
              let
berghofe@21024
   621
                val k = length Ts;
berghofe@21024
   622
                val bs = map Bound (k - 1 downto 0);
wenzelm@42364
   623
                val P = list_comb (nth preds i, map (incr_boundvars k) ys @ bs);
berghofe@21024
   624
                val Q = list_abs (mk_names "x" k ~~ Ts,
berghofe@23762
   625
                  HOLogic.mk_binop inductive_conj_name
berghofe@23762
   626
                    (list_comb (incr_boundvars k s, bs), P))
berghofe@21024
   627
              in (Q, case Ts of [] => SOME (s, P) | _ => NONE) end
wenzelm@33669
   628
          | NONE =>
wenzelm@33669
   629
              (case s of
wenzelm@33669
   630
                (t $ u) => (fst (subst t) $ fst (subst u), NONE)
wenzelm@33669
   631
              | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), NONE)
wenzelm@33669
   632
              | _ => (s, NONE)));
berghofe@7293
   633
wenzelm@33338
   634
        fun mk_prem s prems =
wenzelm@33338
   635
          (case subst s of
wenzelm@33338
   636
            (_, SOME (t, u)) => t :: u :: prems
wenzelm@33338
   637
          | (t, _) => t :: prems);
berghofe@21024
   638
berghofe@21024
   639
        val SOME (_, i, ys, _) = dest_predicate cs params
berghofe@21024
   640
          (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))
berghofe@21024
   641
wenzelm@42364
   642
      in
wenzelm@42364
   643
        list_all_free (Logic.strip_params r,
wenzelm@42364
   644
          Logic.list_implies (map HOLogic.mk_Trueprop (fold_rev mk_prem
wenzelm@42364
   645
            (map HOLogic.dest_Trueprop (Logic.strip_assums_hyp r)) []),
wenzelm@42364
   646
              HOLogic.mk_Trueprop (list_comb (nth preds i, ys))))
berghofe@21024
   647
      end;
berghofe@21024
   648
berghofe@21024
   649
    val ind_prems = map mk_ind_prem intr_ts;
berghofe@21024
   650
wenzelm@21526
   651
berghofe@21024
   652
    (* make conclusions for induction rules *)
berghofe@21024
   653
berghofe@21024
   654
    val Tss = map (binder_types o fastype_of) preds;
berghofe@21024
   655
    val (xnames, ctxt'') =
berghofe@21024
   656
      Variable.variant_fixes (mk_names "x" (length (flat Tss))) ctxt';
berghofe@21024
   657
    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@21024
   658
        (map (fn (((xnames, Ts), c), P) =>
berghofe@21024
   659
           let val frees = map Free (xnames ~~ Ts)
berghofe@21024
   660
           in HOLogic.mk_imp
berghofe@21024
   661
             (list_comb (c, params @ frees), list_comb (P, frees))
berghofe@21024
   662
           end) (unflat Tss xnames ~~ Tss ~~ cs ~~ preds)));
berghofe@5094
   663
paulson@13626
   664
berghofe@5094
   665
    (* make predicate for instantiation of abstract induction rule *)
berghofe@5094
   666
berghofe@21024
   667
    val ind_pred = fold_rev lambda (bs @ xs) (foldr1 HOLogic.mk_conj
wenzelm@33338
   668
      (map_index (fn (i, P) => fold_rev (curry HOLogic.mk_imp)
wenzelm@33338
   669
         (make_bool_args HOLogic.mk_not I bs i)
wenzelm@33338
   670
         (list_comb (P, make_args' argTs xs (binder_types (fastype_of P))))) preds));
berghofe@5094
   671
berghofe@5094
   672
    val ind_concl = HOLogic.mk_Trueprop
haftmann@35092
   673
      (HOLogic.mk_binrel @{const_name Orderings.less_eq} (rec_const, ind_pred));
berghofe@5094
   674
haftmann@32652
   675
    val raw_fp_induct = (mono RS (fp_def RS @{thm def_lfp_induct}));
paulson@13626
   676
wenzelm@32970
   677
    val induct = Skip_Proof.prove ctxt'' [] ind_prems ind_concl
wenzelm@20248
   678
      (fn {prems, ...} => EVERY
wenzelm@17985
   679
        [rewrite_goals_tac [inductive_conj_def],
berghofe@21024
   680
         DETERM (rtac raw_fp_induct 1),
haftmann@32652
   681
         REPEAT (resolve_tac [@{thm le_funI}, @{thm le_boolI}] 1),
haftmann@32610
   682
         rewrite_goals_tac simp_thms'',
berghofe@21024
   683
         (*This disjE separates out the introduction rules*)
berghofe@21024
   684
         REPEAT (FIRSTGOAL (eresolve_tac [disjE, exE, FalseE])),
berghofe@5094
   685
         (*Now break down the individual cases.  No disjE here in case
berghofe@5094
   686
           some premise involves disjunction.*)
paulson@13747
   687
         REPEAT (FIRSTGOAL (etac conjE ORELSE' bound_hyp_subst_tac)),
berghofe@21024
   688
         REPEAT (FIRSTGOAL
berghofe@21024
   689
           (resolve_tac [conjI, impI] ORELSE' (etac notE THEN' atac))),
berghofe@21024
   690
         EVERY (map (fn prem => DEPTH_SOLVE_1 (ares_tac [rewrite_rule
haftmann@32610
   691
             (inductive_conj_def :: rec_preds_defs @ simp_thms'') prem,
berghofe@22980
   692
           conjI, refl] 1)) prems)]);
berghofe@5094
   693
wenzelm@32970
   694
    val lemma = Skip_Proof.prove ctxt'' [] []
wenzelm@17985
   695
      (Logic.mk_implies (ind_concl, mutual_ind_concl)) (fn _ => EVERY
berghofe@21024
   696
        [rewrite_goals_tac rec_preds_defs,
berghofe@5094
   697
         REPEAT (EVERY
berghofe@5094
   698
           [REPEAT (resolve_tac [conjI, impI] 1),
haftmann@32652
   699
            REPEAT (eresolve_tac [@{thm le_funE}, @{thm le_boolE}] 1),
berghofe@21024
   700
            atac 1,
berghofe@21024
   701
            rewrite_goals_tac simp_thms',
berghofe@21024
   702
            atac 1])])
berghofe@5094
   703
wenzelm@42361
   704
  in singleton (Proof_Context.export ctxt'' ctxt''') (induct RS lemma) end;
berghofe@5094
   705
wenzelm@6424
   706
wenzelm@6424
   707
berghofe@21024
   708
(** specification of (co)inductive predicates **)
wenzelm@10729
   709
wenzelm@33458
   710
fun mk_ind_def quiet_mode skip_mono fork_mono alt_name coind
wenzelm@33458
   711
    cs intr_ts monos params cnames_syn lthy =
wenzelm@33458
   712
  let
haftmann@24915
   713
    val fp_name = if coind then @{const_name Inductive.gfp} else @{const_name Inductive.lfp};
berghofe@5094
   714
haftmann@33077
   715
    val argTs = fold (combine (op =) o arg_types_of (length params)) cs [];
berghofe@21024
   716
    val k = log 2 1 (length cs);
berghofe@21024
   717
    val predT = replicate k HOLogic.boolT ---> argTs ---> HOLogic.boolT;
wenzelm@33458
   718
    val p :: xs = map Free (Variable.variant_frees lthy intr_ts
berghofe@21024
   719
      (("p", predT) :: (mk_names "x" (length argTs) ~~ argTs)));
wenzelm@33458
   720
    val bs = map Free (Variable.variant_frees lthy (p :: xs @ intr_ts)
berghofe@21024
   721
      (map (rpair HOLogic.boolT) (mk_names "b" k)));
berghofe@21024
   722
wenzelm@33458
   723
    fun subst t =
wenzelm@33458
   724
      (case dest_predicate cs params t of
berghofe@21024
   725
        SOME (_, i, ts, (Ts, Us)) =>
berghofe@23762
   726
          let
berghofe@23762
   727
            val l = length Us;
wenzelm@33669
   728
            val zs = map Bound (l - 1 downto 0);
berghofe@21024
   729
          in
berghofe@21024
   730
            list_abs (map (pair "z") Us, list_comb (p,
berghofe@23762
   731
              make_bool_args' bs i @ make_args argTs
berghofe@23762
   732
                ((map (incr_boundvars l) ts ~~ Ts) @ (zs ~~ Us))))
berghofe@21024
   733
          end
wenzelm@33669
   734
      | NONE =>
wenzelm@33669
   735
          (case t of
wenzelm@33669
   736
            t1 $ t2 => subst t1 $ subst t2
wenzelm@33669
   737
          | Abs (x, T, u) => Abs (x, T, subst u)
wenzelm@33669
   738
          | _ => t));
berghofe@5149
   739
berghofe@5094
   740
    (* transform an introduction rule into a conjunction  *)
berghofe@21024
   741
    (*   [| p_i t; ... |] ==> p_j u                       *)
berghofe@5094
   742
    (* is transformed into                                *)
berghofe@21024
   743
    (*   b_j & x_j = u & p b_j t & ...                    *)
berghofe@5094
   744
berghofe@5094
   745
    fun transform_rule r =
berghofe@5094
   746
      let
berghofe@21024
   747
        val SOME (_, i, ts, (Ts, _)) = dest_predicate cs params
berghofe@21048
   748
          (HOLogic.dest_Trueprop (Logic.strip_assums_concl r));
berghofe@21048
   749
        val ps = make_bool_args HOLogic.mk_not I bs i @
berghofe@21048
   750
          map HOLogic.mk_eq (make_args' argTs xs Ts ~~ ts) @
berghofe@21048
   751
          map (subst o HOLogic.dest_Trueprop)
berghofe@21048
   752
            (Logic.strip_assums_hyp r)
wenzelm@33338
   753
      in
wenzelm@33338
   754
        fold_rev (fn (x, T) => fn P => HOLogic.exists_const T $ Abs (x, T, P))
wenzelm@33338
   755
          (Logic.strip_params r)
wenzelm@33338
   756
          (if null ps then HOLogic.true_const else foldr1 HOLogic.mk_conj ps)
berghofe@5094
   757
      end
berghofe@5094
   758
berghofe@5094
   759
    (* make a disjunction of all introduction rules *)
berghofe@5094
   760
berghofe@21024
   761
    val fp_fun = fold_rev lambda (p :: bs @ xs)
berghofe@21024
   762
      (if null intr_ts then HOLogic.false_const
berghofe@21024
   763
       else foldr1 HOLogic.mk_disj (map transform_rule intr_ts));
berghofe@5094
   764
berghofe@21024
   765
    (* add definiton of recursive predicates to theory *)
berghofe@5094
   766
wenzelm@28083
   767
    val rec_name =
haftmann@28965
   768
      if Binding.is_empty alt_name then
wenzelm@30223
   769
        Binding.name (space_implode "_" (map (Binding.name_of o fst) cnames_syn))
wenzelm@28083
   770
      else alt_name;
berghofe@5094
   771
wenzelm@33458
   772
    val ((rec_const, (_, fp_def)), lthy') = lthy
wenzelm@33671
   773
      |> Local_Theory.conceal
wenzelm@33766
   774
      |> Local_Theory.define
berghofe@21024
   775
        ((rec_name, case cnames_syn of [(_, syn)] => syn | _ => NoSyn),
blanchet@41792
   776
         ((Binding.empty, [Attrib.internal (K Nitpick_Unfolds.add)]),
blanchet@33577
   777
         fold_rev lambda params
wenzelm@33278
   778
           (Const (fp_name, (predT --> predT) --> predT) $ fp_fun)))
wenzelm@33671
   779
      ||> Local_Theory.restore_naming lthy;
berghofe@21024
   780
    val fp_def' = Simplifier.rewrite (HOL_basic_ss addsimps [fp_def])
wenzelm@42361
   781
      (cterm_of (Proof_Context.theory_of lthy') (list_comb (rec_const, params)));
wenzelm@33278
   782
    val specs =
wenzelm@33278
   783
      if length cs < 2 then []
wenzelm@33278
   784
      else
wenzelm@33278
   785
        map_index (fn (i, (name_mx, c)) =>
wenzelm@33278
   786
          let
wenzelm@33278
   787
            val Ts = arg_types_of (length params) c;
wenzelm@33458
   788
            val xs = map Free (Variable.variant_frees lthy intr_ts
wenzelm@33278
   789
              (mk_names "x" (length Ts) ~~ Ts))
wenzelm@33278
   790
          in
haftmann@39248
   791
            (name_mx, (apfst Binding.conceal Attrib.empty_binding, fold_rev lambda (params @ xs)
wenzelm@33278
   792
              (list_comb (rec_const, params @ make_bool_args' bs i @
wenzelm@33278
   793
                make_args argTs (xs ~~ Ts)))))
wenzelm@33278
   794
          end) (cnames_syn ~~ cs);
wenzelm@33458
   795
    val (consts_defs, lthy'') = lthy'
haftmann@39248
   796
      |> fold_map Local_Theory.define specs;
berghofe@21024
   797
    val preds = (case cs of [_] => [rec_const] | _ => map #1 consts_defs);
berghofe@5094
   798
berghofe@36642
   799
    val (_, lthy''') = Variable.add_fixes (map (fst o dest_Free) params) lthy'';
berghofe@36642
   800
    val mono = prove_mono quiet_mode skip_mono fork_mono predT fp_fun monos lthy''';
berghofe@36642
   801
    val (_, lthy'''') =
berghofe@36642
   802
      Local_Theory.note (apfst Binding.conceal Attrib.empty_binding,
wenzelm@42361
   803
        Proof_Context.export lthy''' lthy'' [mono]) lthy'';
berghofe@5094
   804
berghofe@36642
   805
  in (lthy'''', lthy''', rec_name, mono, fp_def', map (#2 o #2) consts_defs,
berghofe@21024
   806
    list_comb (rec_const, params), preds, argTs, bs, xs)
berghofe@21024
   807
  end;
berghofe@5094
   808
wenzelm@33669
   809
fun declare_rules rec_binding coind no_ind cnames
bulwahn@37734
   810
    preds intrs intr_bindings intr_atts elims eqs raw_induct lthy =
berghofe@23762
   811
  let
wenzelm@30223
   812
    val rec_name = Binding.name_of rec_binding;
haftmann@32773
   813
    fun rec_qualified qualified = Binding.qualify qualified rec_name;
wenzelm@30223
   814
    val intr_names = map Binding.name_of intr_bindings;
wenzelm@33368
   815
    val ind_case_names = Rule_Cases.case_names intr_names;
berghofe@23762
   816
    val induct =
berghofe@23762
   817
      if coind then
wenzelm@33368
   818
        (raw_induct, [Rule_Cases.case_names [rec_name],
wenzelm@33368
   819
          Rule_Cases.case_conclusion (rec_name, intr_names),
wenzelm@33368
   820
          Rule_Cases.consumes 1, Induct.coinduct_pred (hd cnames)])
berghofe@23762
   821
      else if no_ind orelse length cnames > 1 then
wenzelm@33368
   822
        (raw_induct, [ind_case_names, Rule_Cases.consumes 0])
wenzelm@33368
   823
      else (raw_induct RSN (2, rev_mp), [ind_case_names, Rule_Cases.consumes 1]);
berghofe@23762
   824
wenzelm@33458
   825
    val (intrs', lthy1) =
wenzelm@33458
   826
      lthy |>
bulwahn@35757
   827
      Spec_Rules.add
bulwahn@35757
   828
        (if coind then Spec_Rules.Co_Inductive else Spec_Rules.Inductive) (preds, intrs) |>
wenzelm@33671
   829
      Local_Theory.notes
wenzelm@33278
   830
        (map (rec_qualified false) intr_bindings ~~ intr_atts ~~
wenzelm@33278
   831
          map (fn th => [([th],
blanchet@37264
   832
           [Attrib.internal (K (Context_Rules.intro_query NONE))])]) intrs) |>>
berghofe@24744
   833
      map (hd o snd);
wenzelm@33458
   834
    val (((_, elims'), (_, [induct'])), lthy2) =
wenzelm@33458
   835
      lthy1 |>
wenzelm@33671
   836
      Local_Theory.note ((rec_qualified true (Binding.name "intros"), []), intrs') ||>>
berghofe@34986
   837
      fold_map (fn (name, (elim, cases, k)) =>
wenzelm@33671
   838
        Local_Theory.note
wenzelm@33458
   839
          ((Binding.qualify true (Long_Name.base_name name) (Binding.name "cases"),
wenzelm@33458
   840
            [Attrib.internal (K (Rule_Cases.case_names cases)),
wenzelm@33458
   841
             Attrib.internal (K (Rule_Cases.consumes 1)),
berghofe@34986
   842
             Attrib.internal (K (Rule_Cases.constraints k)),
wenzelm@33458
   843
             Attrib.internal (K (Induct.cases_pred name)),
wenzelm@33458
   844
             Attrib.internal (K (Context_Rules.elim_query NONE))]), [elim]) #>
berghofe@23762
   845
        apfst (hd o snd)) (if null elims then [] else cnames ~~ elims) ||>>
wenzelm@33671
   846
      Local_Theory.note
haftmann@32773
   847
        ((rec_qualified true (Binding.name (coind_prefix coind ^ "induct")),
wenzelm@28107
   848
          map (Attrib.internal o K) (#2 induct)), [rulify (#1 induct)]);
berghofe@23762
   849
bulwahn@37734
   850
    val (eqs', lthy3) = lthy2 |> 
bulwahn@37734
   851
      fold_map (fn (name, eq) => Local_Theory.note
bulwahn@38665
   852
          ((Binding.qualify true (Long_Name.base_name name) (Binding.name "simps"),
bulwahn@38665
   853
            [Attrib.internal (K add_equation)]), [eq])
bulwahn@37734
   854
          #> apfst (hd o snd))
bulwahn@37734
   855
        (if null eqs then [] else (cnames ~~ eqs))
bulwahn@37734
   856
    val (inducts, lthy4) =
bulwahn@37734
   857
      if no_ind orelse coind then ([], lthy3)
wenzelm@33458
   858
      else
bulwahn@37734
   859
        let val inducts = cnames ~~ Project_Rule.projects lthy3 (1 upto length cnames) induct' in
bulwahn@37734
   860
          lthy3 |>
wenzelm@33671
   861
          Local_Theory.notes [((rec_qualified true (Binding.name "inducts"), []),
wenzelm@33458
   862
            inducts |> map (fn (name, th) => ([th],
wenzelm@33458
   863
              [Attrib.internal (K ind_case_names),
wenzelm@33458
   864
               Attrib.internal (K (Rule_Cases.consumes 1)),
berghofe@35646
   865
               Attrib.internal (K (Induct.induct_pred name))])))] |>> snd o hd
wenzelm@33458
   866
        end;
bulwahn@37734
   867
  in (intrs', elims', eqs', induct', inducts, lthy4) end;
berghofe@23762
   868
berghofe@26534
   869
type inductive_flags =
wenzelm@33669
   870
  {quiet_mode: bool, verbose: bool, alt_name: binding, coind: bool,
wenzelm@33669
   871
    no_elim: bool, no_ind: bool, skip_mono: bool, fork_mono: bool};
berghofe@26534
   872
berghofe@26534
   873
type add_ind_def =
berghofe@26534
   874
  inductive_flags ->
wenzelm@28084
   875
  term list -> (Attrib.binding * term) list -> thm list ->
haftmann@29581
   876
  term list -> (binding * mixfix) list ->
wenzelm@33458
   877
  local_theory -> inductive_result * local_theory;
berghofe@23762
   878
wenzelm@33669
   879
fun add_ind_def {quiet_mode, verbose, alt_name, coind, no_elim, no_ind, skip_mono, fork_mono}
wenzelm@33458
   880
    cs intros monos params cnames_syn lthy =
berghofe@9072
   881
  let
wenzelm@25288
   882
    val _ = null cnames_syn andalso error "No inductive predicates given";
wenzelm@30223
   883
    val names = map (Binding.name_of o fst) cnames_syn;
wenzelm@26477
   884
    val _ = message (quiet_mode andalso not verbose)
wenzelm@28083
   885
      ("Proofs for " ^ coind_prefix coind ^ "inductive predicate(s) " ^ commas_quote names);
berghofe@9072
   886
wenzelm@33671
   887
    val cnames = map (Local_Theory.full_name lthy o #1) cnames_syn;  (* FIXME *)
berghofe@23762
   888
    val ((intr_names, intr_atts), intr_ts) =
wenzelm@33458
   889
      apfst split_list (split_list (map (check_rule lthy cs params) intros));
berghofe@21024
   890
berghofe@36642
   891
    val (lthy1, lthy2, rec_name, mono, fp_def, rec_preds_defs, rec_const, preds,
wenzelm@29388
   892
      argTs, bs, xs) = mk_ind_def quiet_mode skip_mono fork_mono alt_name coind cs intr_ts
wenzelm@33458
   893
        monos params cnames_syn lthy;
berghofe@9072
   894
wenzelm@26477
   895
    val (intrs, unfold) = prove_intrs quiet_mode coind mono fp_def (length bs + length xs)
berghofe@36642
   896
      intr_ts rec_preds_defs lthy2 lthy1;
wenzelm@33459
   897
    val elims =
wenzelm@33459
   898
      if no_elim then []
wenzelm@33459
   899
      else
wenzelm@33459
   900
        prove_elims quiet_mode cs params intr_ts (map Binding.name_of intr_names)
berghofe@36642
   901
          unfold rec_preds_defs lthy2 lthy1;
berghofe@22605
   902
    val raw_induct = zero_var_indexes
wenzelm@33459
   903
      (if no_ind then Drule.asm_rl
wenzelm@33459
   904
       else if coind then
wenzelm@42361
   905
         singleton (Proof_Context.export lthy2 lthy1)
wenzelm@35625
   906
           (rotate_prems ~1 (Object_Logic.rulify
wenzelm@28839
   907
             (fold_rule rec_preds_defs
haftmann@32652
   908
               (rewrite_rule simp_thms'''
haftmann@32652
   909
                (mono RS (fp_def RS @{thm def_coinduct}))))))
berghofe@21024
   910
       else
wenzelm@26477
   911
         prove_indrule quiet_mode cs argTs bs xs rec_const params intr_ts mono fp_def
berghofe@36642
   912
           rec_preds_defs lthy2 lthy1);
bulwahn@37734
   913
    val eqs =
bulwahn@37734
   914
      if no_elim then [] else prove_eqs quiet_mode cs params intr_ts intrs elims lthy2 lthy1
berghofe@5094
   915
bulwahn@37734
   916
    val elims' = map (fn (th, ns, i) => (rulify th, ns, i)) elims
bulwahn@37734
   917
    val intrs' = map rulify intrs
bulwahn@37734
   918
bulwahn@37734
   919
    val (intrs'', elims'', eqs', induct, inducts, lthy3) = declare_rules rec_name coind no_ind
bulwahn@37734
   920
      cnames preds intrs' intr_names intr_atts elims' eqs raw_induct lthy1;
berghofe@21048
   921
berghofe@21048
   922
    val result =
berghofe@21048
   923
      {preds = preds,
bulwahn@37734
   924
       intrs = intrs'',
bulwahn@37734
   925
       elims = elims'',
berghofe@21048
   926
       raw_induct = rulify raw_induct,
berghofe@35646
   927
       induct = induct,
bulwahn@37734
   928
       inducts = inducts,
bulwahn@37734
   929
       eqs = eqs'};
wenzelm@21367
   930
berghofe@36642
   931
    val lthy4 = lthy3
wenzelm@33671
   932
      |> Local_Theory.declaration false (fn phi =>
wenzelm@25380
   933
        let val result' = morph_result phi result;
wenzelm@25380
   934
        in put_inductives cnames (*global names!?*) ({names = cnames, coind = coind}, result') end);
berghofe@36642
   935
  in (result, lthy4) end;
berghofe@5094
   936
wenzelm@6424
   937
wenzelm@10735
   938
(* external interfaces *)
berghofe@5094
   939
wenzelm@26477
   940
fun gen_add_inductive_i mk_def
wenzelm@33669
   941
    (flags as {quiet_mode, verbose, alt_name, coind, no_elim, no_ind, skip_mono, fork_mono})
wenzelm@25029
   942
    cnames_syn pnames spec monos lthy =
berghofe@5094
   943
  let
wenzelm@42361
   944
    val thy = Proof_Context.theory_of lthy;
wenzelm@6424
   945
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
berghofe@5094
   946
berghofe@21766
   947
wenzelm@25029
   948
    (* abbrevs *)
wenzelm@25029
   949
wenzelm@30223
   950
    val (_, ctxt1) = Variable.add_fixes (map (Binding.name_of o fst o fst) cnames_syn) lthy;
berghofe@21766
   951
wenzelm@25029
   952
    fun get_abbrev ((name, atts), t) =
wenzelm@25029
   953
      if can (Logic.strip_assums_concl #> Logic.dest_equals) t then
wenzelm@25029
   954
        let
haftmann@29006
   955
          val _ = Binding.is_empty name andalso null atts orelse
wenzelm@25029
   956
            error "Abbreviations may not have names or attributes";
wenzelm@35624
   957
          val ((x, T), rhs) = Local_Defs.abs_def (snd (Local_Defs.cert_def ctxt1 t));
wenzelm@28083
   958
          val var =
wenzelm@30223
   959
            (case find_first (fn ((c, _), _) => Binding.name_of c = x) cnames_syn of
wenzelm@25029
   960
              NONE => error ("Undeclared head of abbreviation " ^ quote x)
wenzelm@28083
   961
            | SOME ((b, T'), mx) =>
wenzelm@25029
   962
                if T <> T' then error ("Bad type specification for abbreviation " ^ quote x)
wenzelm@28083
   963
                else (b, mx));
wenzelm@28083
   964
        in SOME (var, rhs) end
wenzelm@25029
   965
      else NONE;
berghofe@21766
   966
wenzelm@25029
   967
    val abbrevs = map_filter get_abbrev spec;
wenzelm@30223
   968
    val bs = map (Binding.name_of o fst o fst) abbrevs;
wenzelm@25029
   969
berghofe@21766
   970
wenzelm@25029
   971
    (* predicates *)
berghofe@21766
   972
wenzelm@25029
   973
    val pre_intros = filter_out (is_some o get_abbrev) spec;
wenzelm@30223
   974
    val cnames_syn' = filter_out (member (op =) bs o Binding.name_of o fst o fst) cnames_syn;
wenzelm@30223
   975
    val cs = map (Free o apfst Binding.name_of o fst) cnames_syn';
wenzelm@25029
   976
    val ps = map Free pnames;
berghofe@5094
   977
wenzelm@30223
   978
    val (_, ctxt2) = lthy |> Variable.add_fixes (map (Binding.name_of o fst o fst) cnames_syn');
wenzelm@35624
   979
    val _ = map (fn abbr => Local_Defs.fixed_abbrev abbr ctxt2) abbrevs;
wenzelm@35624
   980
    val ctxt3 = ctxt2 |> fold (snd oo Local_Defs.fixed_abbrev) abbrevs;
wenzelm@42361
   981
    val expand = Assumption.export_term ctxt3 lthy #> Proof_Context.cert_term lthy;
wenzelm@25029
   982
wenzelm@25029
   983
    fun close_rule r = list_all_free (rev (fold_aterms
berghofe@21024
   984
      (fn t as Free (v as (s, _)) =>
wenzelm@25029
   985
          if Variable.is_fixed ctxt1 s orelse
wenzelm@25029
   986
            member (op =) ps t then I else insert (op =) v
wenzelm@25029
   987
        | _ => I) r []), r);
berghofe@5094
   988
haftmann@26736
   989
    val intros = map (apsnd (Syntax.check_term lthy #> close_rule #> expand)) pre_intros;
wenzelm@25029
   990
    val preds = map (fn ((c, _), mx) => (c, mx)) cnames_syn';
berghofe@21048
   991
  in
wenzelm@25029
   992
    lthy
wenzelm@25029
   993
    |> mk_def flags cs intros monos ps preds
wenzelm@33671
   994
    ||> fold (snd oo Local_Theory.abbrev Syntax.mode_default) abbrevs
berghofe@21048
   995
  end;
berghofe@5094
   996
wenzelm@29388
   997
fun gen_add_inductive mk_def verbose coind cnames_syn pnames_syn intro_srcs raw_monos int lthy =
berghofe@5094
   998
  let
wenzelm@30486
   999
    val ((vars, intrs), _) = lthy
wenzelm@42361
  1000
      |> Proof_Context.set_mode Proof_Context.mode_abbrev
wenzelm@30486
  1001
      |> Specification.read_spec (cnames_syn @ pnames_syn) intro_srcs;
wenzelm@24721
  1002
    val (cs, ps) = chop (length cnames_syn) vars;
wenzelm@24721
  1003
    val monos = Attrib.eval_thms lthy raw_monos;
wenzelm@33669
  1004
    val flags = {quiet_mode = false, verbose = verbose, alt_name = Binding.empty,
wenzelm@33669
  1005
      coind = coind, no_elim = false, no_ind = false, skip_mono = false, fork_mono = not int};
wenzelm@26128
  1006
  in
wenzelm@26128
  1007
    lthy
wenzelm@30223
  1008
    |> gen_add_inductive_i mk_def flags cs (map (apfst Binding.name_of o fst) ps) intrs monos
wenzelm@26128
  1009
  end;
berghofe@5094
  1010
berghofe@23762
  1011
val add_inductive_i = gen_add_inductive_i add_ind_def;
berghofe@23762
  1012
val add_inductive = gen_add_inductive add_ind_def;
berghofe@23762
  1013
wenzelm@33726
  1014
fun add_inductive_global flags cnames_syn pnames pre_intros monos thy =
wenzelm@25380
  1015
  let
haftmann@29006
  1016
    val name = Sign.full_name thy (fst (fst (hd cnames_syn)));
wenzelm@25380
  1017
    val ctxt' = thy
haftmann@38388
  1018
      |> Named_Target.theory_init
wenzelm@25380
  1019
      |> add_inductive_i flags cnames_syn pnames pre_intros monos |> snd
wenzelm@33671
  1020
      |> Local_Theory.exit;
wenzelm@25380
  1021
    val info = #2 (the_inductive ctxt' name);
wenzelm@42361
  1022
  in (info, Proof_Context.theory_of ctxt') end;
wenzelm@6424
  1023
wenzelm@6424
  1024
berghofe@22789
  1025
(* read off arities of inductive predicates from raw induction rule *)
berghofe@22789
  1026
fun arities_of induct =
berghofe@22789
  1027
  map (fn (_ $ t $ u) =>
berghofe@22789
  1028
      (fst (dest_Const (head_of t)), length (snd (strip_comb u))))
berghofe@22789
  1029
    (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@22789
  1030
berghofe@22789
  1031
(* read off parameters of inductive predicate from raw induction rule *)
berghofe@22789
  1032
fun params_of induct =
berghofe@22789
  1033
  let
berghofe@22789
  1034
    val (_ $ t $ u :: _) =
berghofe@22789
  1035
      HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct));
berghofe@22789
  1036
    val (_, ts) = strip_comb t;
berghofe@22789
  1037
    val (_, us) = strip_comb u
berghofe@22789
  1038
  in
berghofe@22789
  1039
    List.take (ts, length ts - length us)
berghofe@22789
  1040
  end;
berghofe@22789
  1041
berghofe@22789
  1042
val pname_of_intr =
berghofe@22789
  1043
  concl_of #> HOLogic.dest_Trueprop #> head_of #> dest_Const #> fst;
berghofe@22789
  1044
berghofe@22789
  1045
(* partition introduction rules according to predicate name *)
berghofe@25822
  1046
fun gen_partition_rules f induct intros =
berghofe@25822
  1047
  fold_rev (fn r => AList.map_entry op = (pname_of_intr (f r)) (cons r)) intros
berghofe@22789
  1048
    (map (rpair [] o fst) (arities_of induct));
berghofe@22789
  1049
berghofe@25822
  1050
val partition_rules = gen_partition_rules I;
berghofe@25822
  1051
fun partition_rules' induct = gen_partition_rules fst induct;
berghofe@25822
  1052
berghofe@22789
  1053
fun unpartition_rules intros xs =
berghofe@22789
  1054
  fold_map (fn r => AList.map_entry_yield op = (pname_of_intr r)
berghofe@22789
  1055
    (fn x :: xs => (x, xs)) #>> the) intros xs |> fst;
berghofe@22789
  1056
berghofe@22789
  1057
(* infer order of variables in intro rules from order of quantifiers in elim rule *)
berghofe@22789
  1058
fun infer_intro_vars elim arity intros =
berghofe@22789
  1059
  let
berghofe@22789
  1060
    val thy = theory_of_thm elim;
berghofe@22789
  1061
    val _ :: cases = prems_of elim;
berghofe@22789
  1062
    val used = map (fst o fst) (Term.add_vars (prop_of elim) []);
berghofe@22789
  1063
    fun mtch (t, u) =
berghofe@22789
  1064
      let
berghofe@22789
  1065
        val params = Logic.strip_params t;
berghofe@22789
  1066
        val vars = map (Var o apfst (rpair 0))
berghofe@22789
  1067
          (Name.variant_list used (map fst params) ~~ map snd params);
berghofe@22789
  1068
        val ts = map (curry subst_bounds (rev vars))
berghofe@22789
  1069
          (List.drop (Logic.strip_assums_hyp t, arity));
berghofe@22789
  1070
        val us = Logic.strip_imp_prems u;
berghofe@22789
  1071
        val tab = fold (Pattern.first_order_match thy) (ts ~~ us)
berghofe@22789
  1072
          (Vartab.empty, Vartab.empty);
berghofe@22789
  1073
      in
wenzelm@32035
  1074
        map (Envir.subst_term tab) vars
berghofe@22789
  1075
      end
berghofe@22789
  1076
  in
berghofe@22789
  1077
    map (mtch o apsnd prop_of) (cases ~~ intros)
berghofe@22789
  1078
  end;
berghofe@22789
  1079
berghofe@22789
  1080
wenzelm@25978
  1081
wenzelm@6437
  1082
(** package setup **)
wenzelm@6437
  1083
wenzelm@6437
  1084
(* setup theory *)
wenzelm@6437
  1085
wenzelm@8634
  1086
val setup =
wenzelm@30722
  1087
  ind_cases_setup #>
wenzelm@30528
  1088
  Attrib.setup @{binding mono} (Attrib.add_del mono_add mono_del)
wenzelm@30528
  1089
    "declaration of monotonicity rule";
wenzelm@6437
  1090
wenzelm@6437
  1091
wenzelm@6437
  1092
(* outer syntax *)
wenzelm@6424
  1093
wenzelm@36960
  1094
val _ = Keyword.keyword "monos";
wenzelm@24867
  1095
berghofe@23762
  1096
fun gen_ind_decl mk_def coind =
wenzelm@36960
  1097
  Parse.fixes -- Parse.for_fixes --
wenzelm@36954
  1098
  Scan.optional Parse_Spec.where_alt_specs [] --
wenzelm@36960
  1099
  Scan.optional (Parse.$$$ "monos" |-- Parse.!!! Parse_Spec.xthms1) []
wenzelm@26988
  1100
  >> (fn (((preds, params), specs), monos) =>
wenzelm@30486
  1101
      (snd oo gen_add_inductive mk_def true coind preds params specs monos));
berghofe@23762
  1102
berghofe@23762
  1103
val ind_decl = gen_ind_decl add_ind_def;
wenzelm@6424
  1104
wenzelm@33458
  1105
val _ =
wenzelm@36960
  1106
  Outer_Syntax.local_theory' "inductive" "define inductive predicates" Keyword.thy_decl
wenzelm@33458
  1107
    (ind_decl false);
wenzelm@33458
  1108
wenzelm@33458
  1109
val _ =
wenzelm@36960
  1110
  Outer_Syntax.local_theory' "coinductive" "define coinductive predicates" Keyword.thy_decl
wenzelm@33458
  1111
    (ind_decl true);
wenzelm@6723
  1112
wenzelm@24867
  1113
val _ =
wenzelm@36960
  1114
  Outer_Syntax.local_theory "inductive_cases"
wenzelm@36960
  1115
    "create simplified instances of elimination rules (improper)" Keyword.thy_script
wenzelm@36960
  1116
    (Parse.and_list1 Parse_Spec.specs >> (snd oo inductive_cases));
wenzelm@7107
  1117
bulwahn@37734
  1118
val _ =
bulwahn@37734
  1119
  Outer_Syntax.local_theory "inductive_simps"
bulwahn@37734
  1120
    "create simplification rules for inductive predicates" Keyword.thy_script
bulwahn@37734
  1121
    (Parse.and_list1 Parse_Spec.specs >> (snd oo inductive_simps));
bulwahn@37734
  1122
berghofe@5094
  1123
end;