package cryptodbm

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Module Cryptodbm_internals.SetpSource

Sets over ordered types.

This module implements the set data structure, given a total ordering function over the set elements. All operations over sets are purely applicative (no side-effects). The implementation uses balanced binary trees, and is therefore reasonably efficient: insertion and membership take time logarithmic in the size of the set, for instance.

Sourcetype 'a t
Sourcetype 'a cmp = 'a -> 'a -> int

It is necessary to provide a comparison function to build a new set. * Binary operators on sets check that both arguments use the same comparison function, * otherwise, a failure is raised.

Sourceval empty : 'a cmp -> 'a t

The empty set.

Sourceval is_empty : 'a t -> bool

Test whether a set is empty or not.

Sourceval mem : 'a -> 'a t -> bool

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

Sourceval find : 'a -> 'a t -> 'a

find x s finds an element y in s which is equal to x. raise Not_found if no such element is in the set.

Sourceval add : 'a -> 'a t -> 'a t

add x s returns a set containing all elements of s, plus x. If x was already in s, s is returned unchanged.

Sourceval singleton : 'a cmp -> 'a -> 'a t

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

Sourceval remove : 'a -> 'a t -> 'a t

remove x s returns a set containing all elements of s, except x. If x was not in s, s is returned unchanged.

Sourceval union : 'a t -> 'a t -> 'a t

Set union.

Sourceval inter : 'a t -> 'a t -> 'a t

Set intersection.

Sourceval diff : 'a t -> 'a t -> 'a t

Set difference.

Sourceval compare : 'a t -> 'a t -> int

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

Sourceval equal : 'a t -> 'a t -> bool

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

Sourceval subset : 'a t -> 'a t -> bool

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

Sourceval iter : ('a -> unit) -> 'a 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.

Sourceval fold : ('a -> 'b -> 'b) -> 'a t -> 'b -> 'b

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

Sourceval for_all : ('a -> bool) -> 'a t -> bool

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

Sourceval exists : ('a -> bool) -> 'a t -> bool

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

Sourceval filter : ('a -> bool) -> 'a t -> 'a t

filter p s returns the set of all elements in s that satisfy predicate p.

Sourceval partition : ('a -> bool) -> 'a t -> 'a t * 'a t

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

Sourceval cardinal : 'a t -> int

Return the number of elements of a set.

Sourceval elements : 'a t -> 'a 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 Set.Make.

Sourceval min_elt : 'a t -> 'a

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

Sourceval max_elt : 'a t -> 'a

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

Sourceval choose : 'a t -> 'a

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.

Sourceval split : 'a -> 'a t -> 'a t * bool * 'a 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.

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