1MoreLabels.Set.S(3) OCaml library MoreLabels.Set.S(3)
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6 MoreLabels.Set.S - Output signature of the functor MoreLabels.Set.Make.
7
9 Module type MoreLabels.Set.S
10
12 Module type S
13 = sig end
14 Output signature of the functor MoreLabels.Set.Make .
17 type elt
23 The type of the set elements.
26 type t
29 The type of sets.
32 val empty : t
36 The empty set.
38 val is_empty : t -> bool
42 Test whether a set is empty or not.
44 val mem : elt -> t -> bool
48 mem x s tests whether x belongs to the set s .
51 val add : elt -> t -> t
55 add x s returns a set containing all elements of s , plus x . If x was
58 already in s , s is returned unchanged (the result of the function is
59 then physically equal to s ).
60 Before4.03 Physical equality was not ensured.
63 val singleton : elt -> t
68 singleton x returns the one-element set containing only x .
71 val remove : elt -> t -> t
75 remove x s returns a set containing all elements of s , except x . If x
78 was not in s , s is returned unchanged (the result of the function is
79 then physically equal to s ).
80 Before4.03 Physical equality was not ensured.
83 val union : t -> t -> t
88 Set union.
90 val inter : t -> t -> t
94 Set intersection.
96 val disjoint : t -> t -> bool
100 Test if two sets are disjoint.
102 Since 4.08.0
105 val diff : t -> t -> t
109 Set difference: diff s1 s2 contains the elements of s1 that are not in
111 s2 .
112 val compare : t -> t -> int
116 Total ordering between sets. Can be used as the ordering function for
118 doing sets of sets.
119 val equal : t -> t -> bool
123 equal s1 s2 tests whether the sets s1 and s2 are equal, that is, con‐
126 tain equal elements.
127 val subset : t -> t -> bool
131 subset s1 s2 tests whether the set s1 is a subset of the set s2 .
134 val iter : f:(elt -> unit) -> t -> unit
138 iter ~f s applies f in turn to all elements of s . The elements of s
141 are presented to f in increasing order with respect to the ordering
142 over the type of the elements.
143 val map : f:(elt -> elt) -> t -> t
147 map ~f s is the set whose elements are f a0 , f a1 ... f
150 aN , where a0 , a1 ... aN are the elements of s .
151 The elements are passed to f in increasing order with respect to the
153 ordering over the type of the elements.
154 If no element of s is changed by f , s is returned unchanged. (If each
156 output of f is physically equal to its input, the returned set is phys‐
157 ically equal to s .)
158 Since 4.04.0
161 val fold : f:(elt -> 'a -> 'a) -> t -> init:'a -> 'a
165 fold ~f s init computes (f xN ... (f x2 (f x1 init))...) , where x1
168 ... xN are the elements of s , in increasing order.
169 val for_all : f:(elt -> bool) -> t -> bool
173 for_all ~f s checks if all elements of the set satisfy the predicate f
176 .
177 val exists : f:(elt -> bool) -> t -> bool
181 exists ~f s checks if at least one element of the set satisfies the
184 predicate f .
185 val filter : f:(elt -> bool) -> t -> t
189 filter ~f s returns the set of all elements in s that satisfy predicate
192 f . If f satisfies every element in s , s is returned unchanged (the
193 result of the function is then physically equal to s ).
194 Before4.03 Physical equality was not ensured.
197 val filter_map : f:(elt -> elt option) -> t -> t
202 filter_map ~f s returns the set of all v such that f x = Some v for
205 some element x of s .
206 For example,
208 filter_map (fun n -> if n mod 2 = 0 then Some (n / 2) else None) s
209 is the set of halves of the even elements of s .
210 If no element of s is changed or dropped by f (if f x = Some x for each
212 element x ), then s is returned unchanged: the result of the function
213 is then physically equal to s .
214 Since 4.11.0
217 val partition : f:(elt -> bool) -> t -> t * t
221 partition ~f s returns a pair of sets (s1, s2) , where s1 is the set of
224 all the elements of s that satisfy the predicate f , and s2 is the set
225 of all the elements of s that do not satisfy f .
226 val cardinal : t -> int
230 Return the number of elements of a set.
232 val elements : t -> elt list
236 Return the list of all elements of the given set. The returned list is
238 sorted in increasing order with respect to the ordering Ord.compare ,
239 where Ord is the argument given to Set.Make .
240 val min_elt : t -> elt
244 Return the smallest element of the given set (with respect to the
246 Ord.compare ordering), or raise Not_found if the set is empty.
247 val min_elt_opt : t -> elt option
251 Return the smallest element of the given set (with respect to the
253 Ord.compare ordering), or None if the set is empty.
254 Since 4.05
257 val max_elt : t -> elt
261 Same as MoreLabels.Set.S.min_elt , but returns the largest element of
263 the given set.
264 val max_elt_opt : t -> elt option
268 Same as MoreLabels.Set.S.min_elt_opt , but returns the largest element
270 of the given set.
271 Since 4.05
274 val choose : t -> elt
278 Return one element of the given set, or raise Not_found if the set is
280 empty. Which element is chosen is unspecified, but equal elements will
281 be chosen for equal sets.
282 val choose_opt : t -> elt option
286 Return one element of the given set, or None if the set is empty. Which
288 element is chosen is unspecified, but equal elements will be chosen for
289 equal sets.
290 Since 4.05
293 val split : elt -> t -> t * bool * t
297 split x s returns a triple (l, present, r) , where l is the set of ele‐
300 ments of s that are strictly less than x ; r is the set of elements of
301 s that are strictly greater than x ; present is false if s contains no
302 element equal to x , or true if s contains an element equal to x .
303 val find : elt -> t -> elt
307 find x s returns the element of s equal to x (according to Ord.compare
310 ), or raise Not_found if no such element exists.
311 Since 4.01.0
314 val find_opt : elt -> t -> elt option
318 find_opt x s returns the element of s equal to x (according to Ord.com‐
321 pare ), or None if no such element exists.
322 Since 4.05
325 val find_first : f:(elt -> bool) -> t -> elt
329 find_first ~f s , where f is a monotonically increasing function, re‐
332 turns the lowest element e of s such that f e , or raises Not_found if
333 no such element exists.
334 For example, find_first (fun e -> Ord.compare e x >= 0) s will return
336 the first element e of s where Ord.compare e x >= 0 (intuitively: e >=
337 x ), or raise Not_found if x is greater than any element of s .
338 Since 4.05
341 val find_first_opt : f:(elt -> bool) -> t -> elt option
345 find_first_opt ~f s , where f is a monotonically increasing function,
348 returns an option containing the lowest element e of s such that f e ,
349 or None if no such element exists.
350 Since 4.05
353 val find_last : f:(elt -> bool) -> t -> elt
357 find_last ~f s , where f is a monotonically decreasing function, re‐
360 turns the highest element e of s such that f e , or raises Not_found if
361 no such element exists.
362 Since 4.05
365 val find_last_opt : f:(elt -> bool) -> t -> elt option
369 find_last_opt ~f s , where f is a monotonically decreasing function,
372 returns an option containing the highest element e of s such that f e ,
373 or None if no such element exists.
374 Since 4.05
377 val of_list : elt list -> t
381 of_list l creates a set from a list of elements. This is usually more
384 efficient than folding add over the list, except perhaps for lists with
385 many duplicated elements.
386 Since 4.02.0
389 Iterators
394 val to_seq_from : elt -> t -> elt Seq.t
395 to_seq_from x s iterates on a subset of the elements of s in ascending
398 order, from x or above.
399 Since 4.07
402 val to_seq : t -> elt Seq.t
406 Iterate on the whole set, in ascending order
408 Since 4.07
411 val to_rev_seq : t -> elt Seq.t
415 Iterate on the whole set, in descending order
417 Since 4.12
420 val add_seq : elt Seq.t -> t -> t
424 Add the given elements to the set, in order.
426 Since 4.07
429 val of_seq : elt Seq.t -> t
433 Build a set from the given bindings
435 Since 4.07
438OCamldoc 2022-07-22 MoreLabels.Set.S(3)