package logtk

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include Set.S with type elt = int
type elt = int

The type of the set elements.

type t

The type of sets.

val empty : t

The empty set.

val is_empty : t -> bool

Test whether a set is empty or not.

val mem : elt -> t -> bool

mem x s tests whether x belongs to the set s.

val add : elt -> t -> t

add x s returns a set containing all elements of s, plus x. If x was already in s, s is returned unchanged (the result of the function is then physically equal to s).

• before 4.03

Physical equality was not ensured.

val singleton : elt -> t

singleton x returns the one-element set containing only x.

val remove : elt -> t -> t

remove x s returns a set containing all elements of s, except x. If x was not in s, s is returned unchanged (the result of the function is then physically equal to s).

• before 4.03

Physical equality was not ensured.

val union : t -> t -> t

Set union.

val inter : t -> t -> t

Set intersection.

val disjoint : t -> t -> bool

Test if two sets are disjoint.

• since 4.08.0
val diff : t -> t -> t

Set difference: diff s1 s2 contains the elements of s1 that are not in s2.

val compare : t -> t -> int

Total ordering between sets. Can be used as the ordering function for doing sets of sets.

val equal : t -> t -> bool

equal s1 s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements.

val subset : t -> t -> bool

subset s1 s2 tests whether the set s1 is a subset of the set s2.

val iter : (elt -> unit) -> t -> unit

iter f s applies f in turn to all elements of s. The elements of s are presented to f in increasing order with respect to the ordering over the type of the elements.

val map : (elt -> elt) -> t -> t

map f s is the set whose elements are f a0,f a1... f aN, where a0,a1...aN are the elements of s.

The elements are passed to f in increasing order with respect to the ordering over the type of the elements.

If no element of s is changed by f, s is returned unchanged. (If each output of f is physically equal to its input, the returned set is physically equal to s.)

• since 4.04.0
val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a

fold f s init computes (f xN ... (f x2 (f x1 init))...), where x1 ... xN are the elements of s, in increasing order.

val for_all : (elt -> bool) -> t -> bool

for_all f s checks if all elements of the set satisfy the predicate f.

val exists : (elt -> bool) -> t -> bool

exists f s checks if at least one element of the set satisfies the predicate f.

val filter : (elt -> bool) -> t -> t

filter f s returns the set of all elements in s that satisfy predicate f. If f satisfies every element in s, s is returned unchanged (the result of the function is then physically equal to s).

• before 4.03

Physical equality was not ensured.

val filter_map : (elt -> elt option) -> t -> t

filter_map f s returns the set of all v such that f x = Some v for some element x of s.

For example,

filter_map (fun n -> if n mod 2 = 0 then Some (n / 2) else None) s

is the set of halves of the even elements of s.

If no element of s is changed or dropped by f (if f x = Some x for each element x), then s is returned unchanged: the result of the function is then physically equal to s.

• since 4.11.0
val partition : (elt -> bool) -> t -> t * t

partition f s returns a pair of sets (s1, s2), where s1 is the set of all the elements of s that satisfy the predicate f, and s2 is the set of all the elements of s that do not satisfy f.

val cardinal : t -> int

Return the number of elements of a set.

val elements : t -> elt list

Return the list of all elements of the given set. The returned list is sorted in increasing order with respect to the ordering Ord.compare, where Ord is the argument given to Stdlib.Set.Make.

val min_elt : t -> elt

Return the smallest element of the given set (with respect to the Ord.compare ordering), or raise Not_found if the set is empty.

val max_elt : t -> elt

Same as min_elt, but returns the largest element of the given set.

val choose : t -> elt

Return one element of the given set, or raise Not_found if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets.

val split : elt -> t -> t * bool * t

split x s returns a triple (l, present, r), where l is the set of elements of s that are strictly less than x; r is the set of elements of s that are strictly greater than x; present is false if s contains no element equal to x, or true if s contains an element equal to x.

val find : elt -> t -> elt

find x s returns the element of s equal to x (according to Ord.compare), or raise Not_found if no such element exists.

• since 4.01.0

Iterators

val to_seq_from : elt -> t ->

to_seq_from x s iterates on a subset of the elements of s in ascending order, from x or above.

• since 4.07
val to_rev_seq : t ->

Iterate on the whole set, in descending order

• since 4.12
val min_elt_opt : t -> elt option

Safe version of min_elt.

• since 1.5
val max_elt_opt : t -> elt option

Safe version of max_elt.

• since 1.5
val choose_opt : t -> elt option

Safe version of choose.

• since 1.5
val find_opt : elt -> t -> elt option

Safe version of find.

• since 1.5
val find_first : (elt -> bool) -> t -> elt

Find minimum element satisfying predicate.

• since 1.5
val find_first_opt : (elt -> bool) -> t -> elt option

Safe version of find_first.

• since 1.5
val find_last : (elt -> bool) -> t -> elt

Find maximum element satisfying predicate.

• since 1.5
val find_last_opt : (elt -> bool) -> t -> elt option

Safe version of find_last.

• since 1.5
val of_iter : t

Build a set from the given iter of elements.

• since 2.8
val add_iter : t -> t
• since 2.8
val to_iter : t ->

to_iter t converts the set t to a iter of the elements.

• since 2.8
val of_seq : t
val add_seq : t -> t
val to_seq : t ->
val of_list : elt list -> t

Build a set from the given list of elements, added in order using add.

val add_list : t -> elt list -> t
• since 0.14
val to_list : t -> elt list

to_list t converts the set t to a list of the elements.

val to_string : ?start:string -> ?stop:string -> ?sep:string -> (elt -> string) -> t -> string

Print the set in a string

• since 2.7
val pp : ?start:string -> ?stop:string -> ?sep:string ->

Print the set.