Module Equality.Equality

module Equality: sig .. end

Representation of an equality between a set of elements. The signatures is roughly a subset of Ocaml's Set.S. An equality always contains at least two elements; operations that break this invariant return Trivial.

include Datatype.S

val pair : Equality.elt -> Equality.elt -> t Equality.trivial

The equality between two elements.

val mem : Equality.elt -> t -> bool

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

val add : Equality.elt -> t -> t

add x s returns the equality between all elements of s and x.

val remove : Equality.elt -> t -> t Equality.trivial

remove x s returns the equality between all elements of s, except x.

val union : t -> t -> t

Union.

val inter : t -> t -> t Equality.trivial

Intersection.

val intersects : t -> t -> bool

intersect s s' = true iff the two equalities both involve the same element.

val compare : t -> t -> int

val equal : t -> t -> bool

val subset : t -> t -> bool

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

iter f s applies f in turn to all elements of s.

val fold : (Equality.elt -> 'a -> 'a) -> t -> 'a -> 'a

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

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

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

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

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

val filter : (Equality.elt -> bool) -> t -> t Equality.trivial

filter p s returns the equality between all elements in s that satisfy predicate p.

val cardinal : t -> int

Return the number of elements of the equality.

val choose : t -> Equality.elt

Return the representative of the equality.

val elements : t -> Equality.elt list

Returns the list of all elements of the given set.