src/HOL/Option.thy
author webertj
Fri, 19 Oct 2012 15:12:52 +0200
changeset 49962 a8cc904a6820
parent 49189 3f85cd15a0cc
child 51096 60e4b75fefe1
permissions -rw-r--r--
Renamed {left,right}_distrib to distrib_{right,left}.
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
     1
(*  Title:      HOL/Option.thy
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
     2
    Author:     Folklore
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
     3
*)
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
     4
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
     5
header {* Datatype option *}
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
     6
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
     7
theory Option
35719
99b6152aedf5 split off theory Big_Operators from theory Finite_Set
haftmann
parents: 34886
diff changeset
     8
imports Datatype
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
     9
begin
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    10
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    11
datatype 'a option = None | Some 'a
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    12
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    13
lemma not_None_eq [iff]: "(x ~= None) = (EX y. x = Some y)"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    14
  by (induct x) auto
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    15
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    16
lemma not_Some_eq [iff]: "(ALL y. x ~= Some y) = (x = None)"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    17
  by (induct x) auto
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    18
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    19
text{*Although it may appear that both of these equalities are helpful
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    20
only when applied to assumptions, in practice it seems better to give
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    21
them the uniform iff attribute. *}
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    22
31080
21ffc770ebc0 lemmas by Andreas Lochbihler
nipkow
parents: 30327
diff changeset
    23
lemma inj_Some [simp]: "inj_on Some A"
21ffc770ebc0 lemmas by Andreas Lochbihler
nipkow
parents: 30327
diff changeset
    24
by (rule inj_onI) simp
21ffc770ebc0 lemmas by Andreas Lochbihler
nipkow
parents: 30327
diff changeset
    25
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    26
lemma option_caseE:
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    27
  assumes c: "(case x of None => P | Some y => Q y)"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    28
  obtains
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    29
    (None) "x = None" and P
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    30
  | (Some) y where "x = Some y" and "Q y"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    31
  using c by (cases x) simp_all
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    32
31080
21ffc770ebc0 lemmas by Andreas Lochbihler
nipkow
parents: 30327
diff changeset
    33
lemma UNIV_option_conv: "UNIV = insert None (range Some)"
21ffc770ebc0 lemmas by Andreas Lochbihler
nipkow
parents: 30327
diff changeset
    34
by(auto intro: classical)
21ffc770ebc0 lemmas by Andreas Lochbihler
nipkow
parents: 30327
diff changeset
    35
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    36
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    37
subsubsection {* Operations *}
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    38
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    39
primrec the :: "'a option => 'a" where
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    40
"the (Some x) = x"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    41
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    42
primrec set :: "'a option => 'a set" where
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    43
"set None = {}" |
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    44
"set (Some x) = {x}"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    45
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    46
lemma ospec [dest]: "(ALL x:set A. P x) ==> A = Some x ==> P x"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    47
  by simp
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    48
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    49
declaration {* fn _ =>
39159
0dec18004e75 more antiquotations;
wenzelm
parents: 39150
diff changeset
    50
  Classical.map_cs (fn cs => cs addSD2 ("ospec", @{thm ospec}))
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    51
*}
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    52
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    53
lemma elem_set [iff]: "(x : set xo) = (xo = Some x)"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    54
  by (cases xo) auto
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    55
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    56
lemma set_empty_eq [simp]: "(set xo = {}) = (xo = None)"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    57
  by (cases xo) auto
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    58
31154
f919b8e67413 preprocessing must consider eq
haftmann
parents: 31080
diff changeset
    59
definition map :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a option \<Rightarrow> 'b option" where
f919b8e67413 preprocessing must consider eq
haftmann
parents: 31080
diff changeset
    60
  "map = (%f y. case y of None => None | Some x => Some (f x))"
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    61
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    62
lemma option_map_None [simp, code]: "map f None = None"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    63
  by (simp add: map_def)
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    64
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    65
lemma option_map_Some [simp, code]: "map f (Some x) = Some (f x)"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    66
  by (simp add: map_def)
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    67
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    68
lemma option_map_is_None [iff]:
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    69
    "(map f opt = None) = (opt = None)"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    70
  by (simp add: map_def split add: option.split)
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    71
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    72
lemma option_map_eq_Some [iff]:
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    73
    "(map f xo = Some y) = (EX z. xo = Some z & f z = y)"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    74
  by (simp add: map_def split add: option.split)
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    75
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    76
lemma option_map_comp:
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    77
    "map f (map g opt) = map (f o g) opt"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    78
  by (simp add: map_def split add: option.split)
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    79
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    80
lemma option_map_o_sum_case [simp]:
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    81
    "map f o sum_case g h = sum_case (map f o g) (map f o h)"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    82
  by (rule ext) (simp split: sum.split)
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
    83
46526
c4cf9d03c352 added congruence rules for Option.{map|bind}
krauss
parents: 41505
diff changeset
    84
lemma map_cong: "x = y \<Longrightarrow> (\<And>a. y = Some a \<Longrightarrow> f a = g a) \<Longrightarrow> map f x = map g y"
c4cf9d03c352 added congruence rules for Option.{map|bind}
krauss
parents: 41505
diff changeset
    85
by (cases x) auto
c4cf9d03c352 added congruence rules for Option.{map|bind}
krauss
parents: 41505
diff changeset
    86
41505
6d19301074cf "enriched_type" replaces less specific "type_lifting"
haftmann
parents: 41372
diff changeset
    87
enriched_type map: Option.map proof -
41372
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
    88
  fix f g
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
    89
  show "Option.map f \<circ> Option.map g = Option.map (f \<circ> g)"
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
    90
  proof
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
    91
    fix x
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
    92
    show "(Option.map f \<circ> Option.map g) x= Option.map (f \<circ> g) x"
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
    93
      by (cases x) simp_all
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
    94
  qed
40609
efb0d7878538 mapper for option type
haftmann
parents: 39272
diff changeset
    95
next
41372
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
    96
  show "Option.map id = id"
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
    97
  proof
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
    98
    fix x
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
    99
    show "Option.map id x = id x"
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
   100
      by (cases x) simp_all
551eb49a6e91 tuned type_lifting declarations
haftmann
parents: 40968
diff changeset
   101
  qed
40609
efb0d7878538 mapper for option type
haftmann
parents: 39272
diff changeset
   102
qed
efb0d7878538 mapper for option type
haftmann
parents: 39272
diff changeset
   103
39149
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   104
primrec bind :: "'a option \<Rightarrow> ('a \<Rightarrow> 'b option) \<Rightarrow> 'b option" where
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   105
bind_lzero: "bind None f = None" |
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   106
bind_lunit: "bind (Some x) f = f x"
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   107
39149
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   108
lemma bind_runit[simp]: "bind x Some = x"
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   109
by (cases x) auto
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   110
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   111
lemma bind_assoc[simp]: "bind (bind x f) g = bind x (\<lambda>y. bind (f y) g)"
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   112
by (cases x) auto
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   113
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   114
lemma bind_rzero[simp]: "bind x (\<lambda>x. None) = None"
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   115
by (cases x) auto
aabd6d4a5c3a added Option.bind
krauss
parents: 38857
diff changeset
   116
46526
c4cf9d03c352 added congruence rules for Option.{map|bind}
krauss
parents: 41505
diff changeset
   117
lemma bind_cong: "x = y \<Longrightarrow> (\<And>a. y = Some a \<Longrightarrow> f a = g a) \<Longrightarrow> bind x f = bind y g"
c4cf9d03c352 added congruence rules for Option.{map|bind}
krauss
parents: 41505
diff changeset
   118
by (cases x) auto
c4cf9d03c352 added congruence rules for Option.{map|bind}
krauss
parents: 41505
diff changeset
   119
49189
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   120
definition these :: "'a option set \<Rightarrow> 'a set"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   121
where
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   122
  "these A = the ` {x \<in> A. x \<noteq> None}"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   123
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   124
lemma these_empty [simp]:
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   125
  "these {} = {}"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   126
  by (simp add: these_def)
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   127
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   128
lemma these_insert_None [simp]:
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   129
  "these (insert None A) = these A"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   130
  by (auto simp add: these_def)
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   131
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   132
lemma these_insert_Some [simp]:
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   133
  "these (insert (Some x) A) = insert x (these A)"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   134
proof -
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   135
  have "{y \<in> insert (Some x) A. y \<noteq> None} = insert (Some x) {y \<in> A. y \<noteq> None}"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   136
    by auto
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   137
  then show ?thesis by (simp add: these_def)
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   138
qed
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   139
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   140
lemma in_these_eq:
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   141
  "x \<in> these A \<longleftrightarrow> Some x \<in> A"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   142
proof
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   143
  assume "Some x \<in> A"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   144
  then obtain B where "A = insert (Some x) B" by auto
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   145
  then show "x \<in> these A" by (auto simp add: these_def intro!: image_eqI)
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   146
next
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   147
  assume "x \<in> these A"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   148
  then show "Some x \<in> A" by (auto simp add: these_def)
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   149
qed
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   150
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   151
lemma these_image_Some_eq [simp]:
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   152
  "these (Some ` A) = A"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   153
  by (auto simp add: these_def intro!: image_eqI)
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   154
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   155
lemma Some_image_these_eq:
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   156
  "Some ` these A = {x\<in>A. x \<noteq> None}"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   157
  by (auto simp add: these_def image_image intro!: image_eqI)
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   158
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   159
lemma these_empty_eq:
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   160
  "these B = {} \<longleftrightarrow> B = {} \<or> B = {None}"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   161
  by (auto simp add: these_def)
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   162
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   163
lemma these_not_empty_eq:
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   164
  "these B \<noteq> {} \<longleftrightarrow> B \<noteq> {} \<and> B \<noteq> {None}"
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   165
  by (auto simp add: these_empty_eq)
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   166
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   167
hide_const (open) set map bind these
46526
c4cf9d03c352 added congruence rules for Option.{map|bind}
krauss
parents: 41505
diff changeset
   168
hide_fact (open) map_cong bind_cong
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   169
49189
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   170
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   171
subsubsection {* Code generator setup *}
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   172
31154
f919b8e67413 preprocessing must consider eq
haftmann
parents: 31080
diff changeset
   173
definition is_none :: "'a option \<Rightarrow> bool" where
31998
2c7a24f74db9 code attributes use common underscore convention
haftmann
parents: 31154
diff changeset
   174
  [code_post]: "is_none x \<longleftrightarrow> x = None"
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   175
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   176
lemma is_none_code [code]:
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   177
  shows "is_none None \<longleftrightarrow> True"
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   178
    and "is_none (Some x) \<longleftrightarrow> False"
31154
f919b8e67413 preprocessing must consider eq
haftmann
parents: 31080
diff changeset
   179
  unfolding is_none_def by simp_all
f919b8e67413 preprocessing must consider eq
haftmann
parents: 31080
diff changeset
   180
32069
6d28bbd33e2c prefer code_inline over code_unfold; use code_unfold_post where appropriate
haftmann
parents: 31998
diff changeset
   181
lemma [code_unfold]:
38857
97775f3e8722 renamed class/constant eq to equal; tuned some instantiations
haftmann
parents: 37880
diff changeset
   182
  "HOL.equal x None \<longleftrightarrow> is_none x"
39150
c4ff5fd8db99 removed duplicate lemma
krauss
parents: 39149
diff changeset
   183
  by (simp add: equal is_none_def)
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   184
36176
3fe7e97ccca8 replaced generic 'hide' command by more conventional 'hide_class', 'hide_type', 'hide_const', 'hide_fact' -- frees some popular keywords;
wenzelm
parents: 35719
diff changeset
   185
hide_const (open) is_none
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   186
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   187
code_type option
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   188
  (SML "_ option")
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   189
  (OCaml "_ option")
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   190
  (Haskell "Maybe _")
34886
873c31d9f10d some syntax setup for Scala
haftmann
parents: 32069
diff changeset
   191
  (Scala "!Option[(_)]")
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   192
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   193
code_const None and Some
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   194
  (SML "NONE" and "SOME")
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   195
  (OCaml "None" and "Some _")
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   196
  (Haskell "Nothing" and "Just")
37880
3b9ca8d2c5fb Scala: subtle difference in printing strings vs. complex mixfix syntax
haftmann
parents: 36176
diff changeset
   197
  (Scala "!None" and "Some")
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   198
38857
97775f3e8722 renamed class/constant eq to equal; tuned some instantiations
haftmann
parents: 37880
diff changeset
   199
code_instance option :: equal
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   200
  (Haskell -)
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   201
38857
97775f3e8722 renamed class/constant eq to equal; tuned some instantiations
haftmann
parents: 37880
diff changeset
   202
code_const "HOL.equal \<Colon> 'a option \<Rightarrow> 'a option \<Rightarrow> bool"
39272
0b61951d2682 Haskell == is infix, not infixl
haftmann
parents: 39159
diff changeset
   203
  (Haskell infix 4 "==")
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   204
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   205
code_reserved SML
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   206
  option NONE SOME
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   207
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   208
code_reserved OCaml
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   209
  option None Some
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   210
34886
873c31d9f10d some syntax setup for Scala
haftmann
parents: 32069
diff changeset
   211
code_reserved Scala
873c31d9f10d some syntax setup for Scala
haftmann
parents: 32069
diff changeset
   212
  Option None Some
873c31d9f10d some syntax setup for Scala
haftmann
parents: 32069
diff changeset
   213
30246
8253519dfc90 Option.thy
nipkow
parents:
diff changeset
   214
end
49189
3f85cd15a0cc combinator Option.these
haftmann
parents: 46526
diff changeset
   215