1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(** Module implementing basic combinators for OCaml option type.
It tries follow closely the style of OCaml standard library.
Actually, some operations have the same name as [List] ones:
they actually are similar considering ['a option] as a type
of lists with at most one element. *)
(** [has_some x] is [true] if [x] is of the form [Some y] and [false]
otherwise. *)
let has_some = function
| None -> false
| _ -> true
let is_empty = function
| None -> true
| Some _ -> false
(** Lifting equality onto option types. *)
let equal f x y = match x, y with
| None, None -> true
| Some x, Some y -> f x y
| _, _ -> false
let compare f x y = match x, y with
| None, None -> 0
| Some x, Some y -> f x y
| None, Some _ -> -1
| Some _, None -> 1
let hash f = function
| None -> 0
| Some x -> f x
exception IsNone
(** [get x] returns [y] where [x] is [Some y].
@raise [IsNone] if [x] equals [None]. *)
let get = function
| Some y -> y
| _ -> raise IsNone
(** [make x] returns [Some x]. *)
let make x = Some x
(** [init b x] returns [Some x] if [b] is [true] and [None] otherwise. *)
let init b x =
if b then
Some x
else
None
(** [flatten x] is [Some y] if [x] is [Some (Some y)] and [None] otherwise. *)
let flatten = function
| Some (Some y) -> Some y
| _ -> None
(** [append x y] is the first element of the concatenation of [x] and
[y] seen as lists. *)
let append o1 o2 =
match o1 with
| Some _ -> o1
| None -> o2
(** {6 "Iterators"} ***)
(** [iter f x] executes [f y] if [x] equals [Some y]. It does nothing
otherwise. *)
let iter f = function
| Some y -> f y
| _ -> ()
exception Heterogeneous
(** [iter2 f x y] executes [f z w] if [x] equals [Some z] and [y] equals
[Some w]. It does nothing if both [x] and [y] are [None]. And raises
[Heterogeneous] otherwise. *)
let iter2 f x y =
match x,y with
| Some z, Some w -> f z w
| None,None -> ()
| _,_ -> raise Heterogeneous
(** [map f x] is [None] if [x] is [None] and [Some (f y)] if [x] is [Some y]. *)
let map f = function
| Some y -> Some (f y)
| _ -> None
(** [smartmap f x] does the same as [map f x] except that it tries to share
some memory. *)
let smartmap f = function
| Some y as x -> let y' = f y in if y' == y then x else Some y'
| _ -> None
(** [fold_left f a x] is [f a y] if [x] is [Some y], and [a] otherwise. *)
let fold_left f a = function
| Some y -> f a y
| _ -> a
(** [fold_left2 f a x y] is [f z w] if [x] is [Some z] and [y] is [Some w].
It is [a] if both [x] and [y] are [None]. Otherwise it raises
[Heterogeneous]. *)
let fold_left2 f a x y =
match x,y with
| Some x, Some y -> f a x y
| None, None -> a
| _ -> raise Heterogeneous
(** [fold_right f x a] is [f y a] if [x] is [Some y], and [a] otherwise. *)
let fold_right f x a =
match x with
| Some y -> f y a
| _ -> a
(** [fold_left_map f a x] is [a, f y] if [x] is [Some y], and [a] otherwise. *)
let fold_left_map f a x =
match x with
| Some y -> let a, z = f a y in a, Some z
| _ -> a, None
let fold_right_map f x a =
match x with
| Some y -> let z, a = f y a in Some z, a
| _ -> None, a
let fold_map = fold_left_map
(** [cata f a x] is [a] if [x] is [None] and [f y] if [x] is [Some y]. *)
let cata f a = function
| Some c -> f c
| None -> a
(** {6 More Specific operations} ***)
(** [default a x] is [y] if [x] is [Some y] and [a] otherwise. *)
let default a = function
| Some y -> y
| _ -> a
(** [lift f x] is the same as [map f x]. *)
let lift = map
(** [lift_right f a x] is [Some (f a y)] if [x] is [Some y], and
[None] otherwise. *)
let lift_right f a = function
| Some y -> Some (f a y)
| _ -> None
(** [lift_left f x a] is [Some (f y a)] if [x] is [Some y], and
[None] otherwise. *)
let lift_left f x a =
match x with
| Some y -> Some (f y a)
| _ -> None
(** [lift2 f x y] is [Some (f z w)] if [x] equals [Some z] and [y] equals
[Some w]. It is [None] otherwise. *)
let lift2 f x y =
match x,y with
| Some z, Some w -> Some (f z w)
| _,_ -> None
(** {6 Operations with Lists} *)
module List =
struct
(** [List.cons x l] equals [y::l] if [x] is [Some y] and [l] otherwise. *)
let cons x l =
match x with
| Some y -> y::l
| _ -> l
(** [List.flatten l] is the list of all the [y]s such that [l] contains
[Some y] (in the same order). *)
let rec flatten = function
| x::l -> cons x (flatten l)
| [] -> []
let rec find f = function
| [] -> None
| h :: t -> match f h with
| None -> find f t
| x -> x
let map f l =
let rec aux f l = match l with
| [] -> []
| x :: l ->
match f x with
| None -> raise Exit
| Some y -> y :: aux f l
in
try Some (aux f l) with Exit -> None
end
|
