src/HOL/Inductive.thy
author haftmann
Wed Jan 30 10:57:44 2008 +0100 (2008-01-30)
changeset 26013 8764a1f1253b
parent 25557 ea6b11021e79
child 26793 e36a92ff543e
permissions -rw-r--r--
Theorem Inductive.lfp_ordinal_induct generalized to complete lattices
wenzelm@7700
     1
(*  Title:      HOL/Inductive.thy
wenzelm@7700
     2
    ID:         $Id$
wenzelm@10402
     3
    Author:     Markus Wenzel, TU Muenchen
wenzelm@11688
     4
*)
wenzelm@10727
     5
haftmann@24915
     6
header {* Knaster-Tarski Fixpoint Theorem and inductive definitions *}
lcp@1187
     7
nipkow@15131
     8
theory Inductive 
haftmann@24915
     9
imports Lattices Sum_Type
haftmann@16417
    10
uses
wenzelm@10402
    11
  ("Tools/inductive_package.ML")
haftmann@24625
    12
  "Tools/dseq.ML"
berghofe@12437
    13
  ("Tools/inductive_codegen.ML")
wenzelm@10402
    14
  ("Tools/datatype_aux.ML")
wenzelm@10402
    15
  ("Tools/datatype_prop.ML")
wenzelm@10402
    16
  ("Tools/datatype_rep_proofs.ML")
wenzelm@10402
    17
  ("Tools/datatype_abs_proofs.ML")
berghofe@22783
    18
  ("Tools/datatype_case.ML")
wenzelm@10402
    19
  ("Tools/datatype_package.ML")
haftmann@25557
    20
  ("Tools/old_primrec_package.ML")
nipkow@15131
    21
  ("Tools/primrec_package.ML")
haftmann@25534
    22
  ("Tools/datatype_codegen.ML")
nipkow@15131
    23
begin
wenzelm@10727
    24
haftmann@24915
    25
subsection {* Least and greatest fixed points *}
haftmann@24915
    26
haftmann@26013
    27
context complete_lattice
haftmann@26013
    28
begin
haftmann@26013
    29
haftmann@24915
    30
definition
haftmann@26013
    31
  lfp :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a" where
haftmann@24915
    32
  "lfp f = Inf {u. f u \<le> u}"    --{*least fixed point*}
haftmann@24915
    33
haftmann@24915
    34
definition
haftmann@26013
    35
  gfp :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a" where
haftmann@24915
    36
  "gfp f = Sup {u. u \<le> f u}"    --{*greatest fixed point*}
haftmann@24915
    37
haftmann@24915
    38
haftmann@24915
    39
subsection{* Proof of Knaster-Tarski Theorem using @{term lfp} *}
haftmann@24915
    40
haftmann@24915
    41
text{*@{term "lfp f"} is the least upper bound of 
haftmann@24915
    42
      the set @{term "{u. f(u) \<le> u}"} *}
haftmann@24915
    43
haftmann@24915
    44
lemma lfp_lowerbound: "f A \<le> A ==> lfp f \<le> A"
haftmann@24915
    45
  by (auto simp add: lfp_def intro: Inf_lower)
haftmann@24915
    46
haftmann@24915
    47
lemma lfp_greatest: "(!!u. f u \<le> u ==> A \<le> u) ==> A \<le> lfp f"
haftmann@24915
    48
  by (auto simp add: lfp_def intro: Inf_greatest)
haftmann@24915
    49
haftmann@26013
    50
end
haftmann@26013
    51
haftmann@24915
    52
lemma lfp_lemma2: "mono f ==> f (lfp f) \<le> lfp f"
haftmann@24915
    53
  by (iprover intro: lfp_greatest order_trans monoD lfp_lowerbound)
haftmann@24915
    54
haftmann@24915
    55
lemma lfp_lemma3: "mono f ==> lfp f \<le> f (lfp f)"
haftmann@24915
    56
  by (iprover intro: lfp_lemma2 monoD lfp_lowerbound)
haftmann@24915
    57
haftmann@24915
    58
lemma lfp_unfold: "mono f ==> lfp f = f (lfp f)"
haftmann@24915
    59
  by (iprover intro: order_antisym lfp_lemma2 lfp_lemma3)
haftmann@24915
    60
haftmann@24915
    61
lemma lfp_const: "lfp (\<lambda>x. t) = t"
haftmann@24915
    62
  by (rule lfp_unfold) (simp add:mono_def)
haftmann@24915
    63
haftmann@24915
    64
haftmann@24915
    65
subsection {* General induction rules for least fixed points *}
haftmann@24915
    66
haftmann@24915
    67
theorem lfp_induct:
haftmann@24915
    68
  assumes mono: "mono f" and ind: "f (inf (lfp f) P) <= P"
haftmann@24915
    69
  shows "lfp f <= P"
haftmann@24915
    70
proof -
haftmann@24915
    71
  have "inf (lfp f) P <= lfp f" by (rule inf_le1)
haftmann@24915
    72
  with mono have "f (inf (lfp f) P) <= f (lfp f)" ..
haftmann@24915
    73
  also from mono have "f (lfp f) = lfp f" by (rule lfp_unfold [symmetric])
haftmann@24915
    74
  finally have "f (inf (lfp f) P) <= lfp f" .
haftmann@24915
    75
  from this and ind have "f (inf (lfp f) P) <= inf (lfp f) P" by (rule le_infI)
haftmann@24915
    76
  hence "lfp f <= inf (lfp f) P" by (rule lfp_lowerbound)
haftmann@24915
    77
  also have "inf (lfp f) P <= P" by (rule inf_le2)
haftmann@24915
    78
  finally show ?thesis .
haftmann@24915
    79
qed
haftmann@24915
    80
haftmann@24915
    81
lemma lfp_induct_set:
haftmann@24915
    82
  assumes lfp: "a: lfp(f)"
haftmann@24915
    83
      and mono: "mono(f)"
haftmann@24915
    84
      and indhyp: "!!x. [| x: f(lfp(f) Int {x. P(x)}) |] ==> P(x)"
haftmann@24915
    85
  shows "P(a)"
haftmann@24915
    86
  by (rule lfp_induct [THEN subsetD, THEN CollectD, OF mono _ lfp])
haftmann@24915
    87
    (auto simp: inf_set_eq intro: indhyp)
haftmann@24915
    88
haftmann@26013
    89
lemma lfp_ordinal_induct:
haftmann@26013
    90
  fixes f :: "'a\<Colon>complete_lattice \<Rightarrow> 'a"
haftmann@26013
    91
  assumes mono: "mono f"
haftmann@26013
    92
  and P_f: "\<And>S. P S \<Longrightarrow> P (f S)"
haftmann@26013
    93
  and P_Union: "\<And>M. \<forall>S\<in>M. P S \<Longrightarrow> P (Sup M)"
haftmann@26013
    94
  shows "P (lfp f)"
haftmann@26013
    95
proof -
haftmann@26013
    96
  let ?M = "{S. S \<le> lfp f \<and> P S}"
haftmann@26013
    97
  have "P (Sup ?M)" using P_Union by simp
haftmann@26013
    98
  also have "Sup ?M = lfp f"
haftmann@26013
    99
  proof (rule antisym)
haftmann@26013
   100
    show "Sup ?M \<le> lfp f" by (blast intro: Sup_least)
haftmann@26013
   101
    hence "f (Sup ?M) \<le> f (lfp f)" by (rule mono [THEN monoD])
haftmann@26013
   102
    hence "f (Sup ?M) \<le> lfp f" using mono [THEN lfp_unfold] by simp
haftmann@26013
   103
    hence "f (Sup ?M) \<in> ?M" using P_f P_Union by simp
haftmann@26013
   104
    hence "f (Sup ?M) \<le> Sup ?M" by (rule Sup_upper)
haftmann@26013
   105
    thus "lfp f \<le> Sup ?M" by (rule lfp_lowerbound)
haftmann@26013
   106
  qed
haftmann@26013
   107
  finally show ?thesis .
haftmann@26013
   108
qed 
haftmann@26013
   109
haftmann@26013
   110
lemma lfp_ordinal_induct_set: 
haftmann@24915
   111
  assumes mono: "mono f"
haftmann@24915
   112
  and P_f: "!!S. P S ==> P(f S)"
haftmann@24915
   113
  and P_Union: "!!M. !S:M. P S ==> P(Union M)"
haftmann@24915
   114
  shows "P(lfp f)"
haftmann@26013
   115
  using assms unfolding Sup_set_def [symmetric]
haftmann@26013
   116
  by (rule lfp_ordinal_induct) 
haftmann@24915
   117
haftmann@24915
   118
haftmann@24915
   119
text{*Definition forms of @{text lfp_unfold} and @{text lfp_induct}, 
haftmann@24915
   120
    to control unfolding*}
haftmann@24915
   121
haftmann@24915
   122
lemma def_lfp_unfold: "[| h==lfp(f);  mono(f) |] ==> h = f(h)"
haftmann@24915
   123
by (auto intro!: lfp_unfold)
haftmann@24915
   124
haftmann@24915
   125
lemma def_lfp_induct: 
haftmann@24915
   126
    "[| A == lfp(f); mono(f);
haftmann@24915
   127
        f (inf A P) \<le> P
haftmann@24915
   128
     |] ==> A \<le> P"
haftmann@24915
   129
  by (blast intro: lfp_induct)
haftmann@24915
   130
haftmann@24915
   131
lemma def_lfp_induct_set: 
haftmann@24915
   132
    "[| A == lfp(f);  mono(f);   a:A;                    
haftmann@24915
   133
        !!x. [| x: f(A Int {x. P(x)}) |] ==> P(x)         
haftmann@24915
   134
     |] ==> P(a)"
haftmann@24915
   135
  by (blast intro: lfp_induct_set)
haftmann@24915
   136
haftmann@24915
   137
(*Monotonicity of lfp!*)
haftmann@24915
   138
lemma lfp_mono: "(!!Z. f Z \<le> g Z) ==> lfp f \<le> lfp g"
haftmann@24915
   139
  by (rule lfp_lowerbound [THEN lfp_greatest], blast intro: order_trans)
haftmann@24915
   140
haftmann@24915
   141
haftmann@24915
   142
subsection {* Proof of Knaster-Tarski Theorem using @{term gfp} *}
haftmann@24915
   143
haftmann@24915
   144
text{*@{term "gfp f"} is the greatest lower bound of 
haftmann@24915
   145
      the set @{term "{u. u \<le> f(u)}"} *}
haftmann@24915
   146
haftmann@24915
   147
lemma gfp_upperbound: "X \<le> f X ==> X \<le> gfp f"
haftmann@24915
   148
  by (auto simp add: gfp_def intro: Sup_upper)
haftmann@24915
   149
haftmann@24915
   150
lemma gfp_least: "(!!u. u \<le> f u ==> u \<le> X) ==> gfp f \<le> X"
haftmann@24915
   151
  by (auto simp add: gfp_def intro: Sup_least)
haftmann@24915
   152
haftmann@24915
   153
lemma gfp_lemma2: "mono f ==> gfp f \<le> f (gfp f)"
haftmann@24915
   154
  by (iprover intro: gfp_least order_trans monoD gfp_upperbound)
haftmann@24915
   155
haftmann@24915
   156
lemma gfp_lemma3: "mono f ==> f (gfp f) \<le> gfp f"
haftmann@24915
   157
  by (iprover intro: gfp_lemma2 monoD gfp_upperbound)
haftmann@24915
   158
haftmann@24915
   159
lemma gfp_unfold: "mono f ==> gfp f = f (gfp f)"
haftmann@24915
   160
  by (iprover intro: order_antisym gfp_lemma2 gfp_lemma3)
haftmann@24915
   161
haftmann@24915
   162
haftmann@24915
   163
subsection {* Coinduction rules for greatest fixed points *}
haftmann@24915
   164
haftmann@24915
   165
text{*weak version*}
haftmann@24915
   166
lemma weak_coinduct: "[| a: X;  X \<subseteq> f(X) |] ==> a : gfp(f)"
haftmann@24915
   167
by (rule gfp_upperbound [THEN subsetD], auto)
haftmann@24915
   168
haftmann@24915
   169
lemma weak_coinduct_image: "!!X. [| a : X; g`X \<subseteq> f (g`X) |] ==> g a : gfp f"
haftmann@24915
   170
apply (erule gfp_upperbound [THEN subsetD])
haftmann@24915
   171
apply (erule imageI)
haftmann@24915
   172
done
haftmann@24915
   173
haftmann@24915
   174
lemma coinduct_lemma:
haftmann@24915
   175
     "[| X \<le> f (sup X (gfp f));  mono f |] ==> sup X (gfp f) \<le> f (sup X (gfp f))"
haftmann@24915
   176
  apply (frule gfp_lemma2)
haftmann@24915
   177
  apply (drule mono_sup)
haftmann@24915
   178
  apply (rule le_supI)
haftmann@24915
   179
  apply assumption
haftmann@24915
   180
  apply (rule order_trans)
haftmann@24915
   181
  apply (rule order_trans)
haftmann@24915
   182
  apply assumption
haftmann@24915
   183
  apply (rule sup_ge2)
haftmann@24915
   184
  apply assumption
haftmann@24915
   185
  done
haftmann@24915
   186
haftmann@24915
   187
text{*strong version, thanks to Coen and Frost*}
haftmann@24915
   188
lemma coinduct_set: "[| mono(f);  a: X;  X \<subseteq> f(X Un gfp(f)) |] ==> a : gfp(f)"
haftmann@24915
   189
by (blast intro: weak_coinduct [OF _ coinduct_lemma, simplified sup_set_eq])
haftmann@24915
   190
haftmann@24915
   191
lemma coinduct: "[| mono(f); X \<le> f (sup X (gfp f)) |] ==> X \<le> gfp(f)"
haftmann@24915
   192
  apply (rule order_trans)
haftmann@24915
   193
  apply (rule sup_ge1)
haftmann@24915
   194
  apply (erule gfp_upperbound [OF coinduct_lemma])
haftmann@24915
   195
  apply assumption
haftmann@24915
   196
  done
haftmann@24915
   197
haftmann@24915
   198
lemma gfp_fun_UnI2: "[| mono(f);  a: gfp(f) |] ==> a: f(X Un gfp(f))"
haftmann@24915
   199
by (blast dest: gfp_lemma2 mono_Un)
haftmann@24915
   200
haftmann@24915
   201
haftmann@24915
   202
subsection {* Even Stronger Coinduction Rule, by Martin Coen *}
haftmann@24915
   203
haftmann@24915
   204
text{* Weakens the condition @{term "X \<subseteq> f(X)"} to one expressed using both
haftmann@24915
   205
  @{term lfp} and @{term gfp}*}
haftmann@24915
   206
haftmann@24915
   207
lemma coinduct3_mono_lemma: "mono(f) ==> mono(%x. f(x) Un X Un B)"
haftmann@24915
   208
by (iprover intro: subset_refl monoI Un_mono monoD)
haftmann@24915
   209
haftmann@24915
   210
lemma coinduct3_lemma:
haftmann@24915
   211
     "[| X \<subseteq> f(lfp(%x. f(x) Un X Un gfp(f)));  mono(f) |]
haftmann@24915
   212
      ==> lfp(%x. f(x) Un X Un gfp(f)) \<subseteq> f(lfp(%x. f(x) Un X Un gfp(f)))"
haftmann@24915
   213
apply (rule subset_trans)
haftmann@24915
   214
apply (erule coinduct3_mono_lemma [THEN lfp_lemma3])
haftmann@24915
   215
apply (rule Un_least [THEN Un_least])
haftmann@24915
   216
apply (rule subset_refl, assumption)
haftmann@24915
   217
apply (rule gfp_unfold [THEN equalityD1, THEN subset_trans], assumption)
haftmann@24915
   218
apply (rule monoD, assumption)
haftmann@24915
   219
apply (subst coinduct3_mono_lemma [THEN lfp_unfold], auto)
haftmann@24915
   220
done
haftmann@24915
   221
haftmann@24915
   222
lemma coinduct3: 
haftmann@24915
   223
  "[| mono(f);  a:X;  X \<subseteq> f(lfp(%x. f(x) Un X Un gfp(f))) |] ==> a : gfp(f)"
haftmann@24915
   224
apply (rule coinduct3_lemma [THEN [2] weak_coinduct])
haftmann@24915
   225
apply (rule coinduct3_mono_lemma [THEN lfp_unfold, THEN ssubst], auto)
haftmann@24915
   226
done
haftmann@24915
   227
haftmann@24915
   228
haftmann@24915
   229
text{*Definition forms of @{text gfp_unfold} and @{text coinduct}, 
haftmann@24915
   230
    to control unfolding*}
haftmann@24915
   231
haftmann@24915
   232
lemma def_gfp_unfold: "[| A==gfp(f);  mono(f) |] ==> A = f(A)"
haftmann@24915
   233
by (auto intro!: gfp_unfold)
haftmann@24915
   234
haftmann@24915
   235
lemma def_coinduct:
haftmann@24915
   236
     "[| A==gfp(f);  mono(f);  X \<le> f(sup X A) |] ==> X \<le> A"
haftmann@24915
   237
by (iprover intro!: coinduct)
haftmann@24915
   238
haftmann@24915
   239
lemma def_coinduct_set:
haftmann@24915
   240
     "[| A==gfp(f);  mono(f);  a:X;  X \<subseteq> f(X Un A) |] ==> a: A"
haftmann@24915
   241
by (auto intro!: coinduct_set)
haftmann@24915
   242
haftmann@24915
   243
(*The version used in the induction/coinduction package*)
haftmann@24915
   244
lemma def_Collect_coinduct:
haftmann@24915
   245
    "[| A == gfp(%w. Collect(P(w)));  mono(%w. Collect(P(w)));   
haftmann@24915
   246
        a: X;  !!z. z: X ==> P (X Un A) z |] ==>  
haftmann@24915
   247
     a : A"
haftmann@24915
   248
apply (erule def_coinduct_set, auto) 
haftmann@24915
   249
done
haftmann@24915
   250
haftmann@24915
   251
lemma def_coinduct3:
haftmann@24915
   252
    "[| A==gfp(f); mono(f);  a:X;  X \<subseteq> f(lfp(%x. f(x) Un X Un A)) |] ==> a: A"
haftmann@24915
   253
by (auto intro!: coinduct3)
haftmann@24915
   254
haftmann@24915
   255
text{*Monotonicity of @{term gfp}!*}
haftmann@24915
   256
lemma gfp_mono: "(!!Z. f Z \<le> g Z) ==> gfp f \<le> gfp g"
haftmann@24915
   257
  by (rule gfp_upperbound [THEN gfp_least], blast intro: order_trans)
haftmann@24915
   258
haftmann@24915
   259
berghofe@23734
   260
subsection {* Inductive predicates and sets *}
wenzelm@11688
   261
wenzelm@11688
   262
text {* Inversion of injective functions. *}
wenzelm@11436
   263
wenzelm@11436
   264
constdefs
wenzelm@11436
   265
  myinv :: "('a => 'b) => ('b => 'a)"
wenzelm@11436
   266
  "myinv (f :: 'a => 'b) == \<lambda>y. THE x. f x = y"
wenzelm@11436
   267
wenzelm@11436
   268
lemma myinv_f_f: "inj f ==> myinv f (f x) = x"
wenzelm@11436
   269
proof -
wenzelm@11436
   270
  assume "inj f"
wenzelm@11436
   271
  hence "(THE x'. f x' = f x) = (THE x'. x' = x)"
wenzelm@11436
   272
    by (simp only: inj_eq)
wenzelm@11436
   273
  also have "... = x" by (rule the_eq_trivial)
wenzelm@11439
   274
  finally show ?thesis by (unfold myinv_def)
wenzelm@11436
   275
qed
wenzelm@11436
   276
wenzelm@11436
   277
lemma f_myinv_f: "inj f ==> y \<in> range f ==> f (myinv f y) = y"
wenzelm@11436
   278
proof (unfold myinv_def)
wenzelm@11436
   279
  assume inj: "inj f"
wenzelm@11436
   280
  assume "y \<in> range f"
wenzelm@11436
   281
  then obtain x where "y = f x" ..
wenzelm@11436
   282
  hence x: "f x = y" ..
wenzelm@11436
   283
  thus "f (THE x. f x = y) = y"
wenzelm@11436
   284
  proof (rule theI)
wenzelm@11436
   285
    fix x' assume "f x' = y"
wenzelm@11436
   286
    with x have "f x' = f x" by simp
wenzelm@11436
   287
    with inj show "x' = x" by (rule injD)
wenzelm@11436
   288
  qed
wenzelm@11436
   289
qed
wenzelm@11436
   290
wenzelm@11436
   291
hide const myinv
wenzelm@11436
   292
wenzelm@11436
   293
wenzelm@11688
   294
text {* Package setup. *}
wenzelm@10402
   295
berghofe@23734
   296
theorems basic_monos =
haftmann@22218
   297
  subset_refl imp_refl disj_mono conj_mono ex_mono all_mono if_bool_eq_conj
wenzelm@11688
   298
  Collect_mono in_mono vimage_mono
wenzelm@11688
   299
  imp_conv_disj not_not de_Morgan_disj de_Morgan_conj
wenzelm@11688
   300
  not_all not_ex
wenzelm@11688
   301
  Ball_def Bex_def
wenzelm@18456
   302
  induct_rulify_fallback
wenzelm@11688
   303
haftmann@24915
   304
ML {*
haftmann@24915
   305
val def_lfp_unfold = @{thm def_lfp_unfold}
haftmann@24915
   306
val def_gfp_unfold = @{thm def_gfp_unfold}
haftmann@24915
   307
val def_lfp_induct = @{thm def_lfp_induct}
haftmann@24915
   308
val def_coinduct = @{thm def_coinduct}
haftmann@25510
   309
val inf_bool_eq = @{thm inf_bool_eq} RS @{thm eq_reflection}
haftmann@25510
   310
val inf_fun_eq = @{thm inf_fun_eq} RS @{thm eq_reflection}
haftmann@25510
   311
val sup_bool_eq = @{thm sup_bool_eq} RS @{thm eq_reflection}
haftmann@25510
   312
val sup_fun_eq = @{thm sup_fun_eq} RS @{thm eq_reflection}
haftmann@24915
   313
val le_boolI = @{thm le_boolI}
haftmann@24915
   314
val le_boolI' = @{thm le_boolI'}
haftmann@24915
   315
val le_funI = @{thm le_funI}
haftmann@24915
   316
val le_boolE = @{thm le_boolE}
haftmann@24915
   317
val le_funE = @{thm le_funE}
haftmann@24915
   318
val le_boolD = @{thm le_boolD}
haftmann@24915
   319
val le_funD = @{thm le_funD}
haftmann@25510
   320
val le_bool_def = @{thm le_bool_def} RS @{thm eq_reflection}
haftmann@25510
   321
val le_fun_def = @{thm le_fun_def} RS @{thm eq_reflection}
haftmann@24915
   322
*}
haftmann@24915
   323
berghofe@21018
   324
use "Tools/inductive_package.ML"
berghofe@21018
   325
setup InductivePackage.setup
berghofe@21018
   326
berghofe@23734
   327
theorems [mono] =
haftmann@22218
   328
  imp_refl disj_mono conj_mono ex_mono all_mono if_bool_eq_conj
berghofe@21018
   329
  imp_conv_disj not_not de_Morgan_disj de_Morgan_conj
berghofe@21018
   330
  not_all not_ex
berghofe@21018
   331
  Ball_def Bex_def
berghofe@21018
   332
  induct_rulify_fallback
berghofe@21018
   333
wenzelm@11688
   334
wenzelm@12023
   335
subsection {* Inductive datatypes and primitive recursion *}
wenzelm@11688
   336
wenzelm@11825
   337
text {* Package setup. *}
wenzelm@11825
   338
wenzelm@10402
   339
use "Tools/datatype_aux.ML"
wenzelm@10402
   340
use "Tools/datatype_prop.ML"
wenzelm@10402
   341
use "Tools/datatype_rep_proofs.ML"
wenzelm@10402
   342
use "Tools/datatype_abs_proofs.ML"
berghofe@22783
   343
use "Tools/datatype_case.ML"
wenzelm@10402
   344
use "Tools/datatype_package.ML"
wenzelm@7700
   345
setup DatatypePackage.setup
haftmann@25557
   346
use "Tools/old_primrec_package.ML"
haftmann@24699
   347
use "Tools/primrec_package.ML"
berghofe@12437
   348
haftmann@25534
   349
use "Tools/datatype_codegen.ML"
haftmann@25534
   350
setup DatatypeCodegen.setup
haftmann@25534
   351
berghofe@12437
   352
use "Tools/inductive_codegen.ML"
berghofe@12437
   353
setup InductiveCodegen.setup
berghofe@12437
   354
nipkow@23526
   355
text{* Lambda-abstractions with pattern matching: *}
nipkow@23526
   356
nipkow@23526
   357
syntax
nipkow@23529
   358
  "_lam_pats_syntax" :: "cases_syn => 'a => 'b"               ("(%_)" 10)
nipkow@23526
   359
syntax (xsymbols)
nipkow@23529
   360
  "_lam_pats_syntax" :: "cases_syn => 'a => 'b"               ("(\<lambda>_)" 10)
nipkow@23526
   361
nipkow@23529
   362
parse_translation (advanced) {*
nipkow@23529
   363
let
nipkow@23529
   364
  fun fun_tr ctxt [cs] =
nipkow@23529
   365
    let
nipkow@23529
   366
      val x = Free (Name.variant (add_term_free_names (cs, [])) "x", dummyT);
nipkow@24349
   367
      val ft = DatatypeCase.case_tr true DatatypePackage.datatype_of_constr
nipkow@24349
   368
                 ctxt [x, cs]
nipkow@23529
   369
    in lambda x ft end
nipkow@23529
   370
in [("_lam_pats_syntax", fun_tr)] end
nipkow@23526
   371
*}
nipkow@23526
   372
nipkow@23526
   373
end