Module Sette

module Sette: sig .. end

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.

Modified by B. Jeannet to get a generic type and a few additions (like conversions form and to maps and pretty-printing).

type 'a t

The type of sets over elements of type 'a.

type 'a tzz =

`\|`	`Emptyzz`
`\|`	`Nodezz of 'a tzz * 'a * 'a tzz * int`

Meant to be internal, but exporting needed for Mappe.maptoset.

val repr : 'a t -> 'a tzz

val obj : 'a tzz -> 'a t

val splitzz : 'a -> 'a tzz -> 'a tzz * bool * 'a tzz

Meant to be internal, but exporting needed for Mappe.maptoset.

val empty : 'a t

The empty set.

val is_empty : 'a t -> bool

Test whether a set is empty or not.

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

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

val 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.

val singleton : 'a -> 'a t

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

val 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.

val union : 'a t -> 'a t -> 'a t

val inter : 'a t -> 'a t -> 'a t

val diff : 'a t -> 'a t -> 'a t

Union, intersection and set difference.

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

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

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

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

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

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

val iter : ('a -> unit) -> 'a t -> unit

iter f s applies f in turn to all elements of s. The order in which the elements of s are presented to f is unspecified.

val 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. The order in which elements of s are presented to f is unspecified.
Raises Not_found if no fount
Returns the computed accumulator

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

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

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

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

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

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

val 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.

val cardinal : 'a t -> int

Return the number of elements of a set.

val 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 Pervasives.compare.

val 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.

val max_elt : 'a t -> 'a

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

val 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.

val print : ?first:(unit, Format.formatter, unit) Pervasives.format ->
       ?sep:(unit, Format.formatter, unit) Pervasives.format ->
       ?last:(unit, Format.formatter, unit) Pervasives.format ->
       (Format.formatter -> 'a -> unit) -> Format.formatter -> 'a t -> unit

module type S = sig .. end

Output signature of the functor Sette.Make.

module Make: functor (Ord : Set.OrderedType) -> S  with type elt = Ord.t 
				       and module Ord=Ord

Functor building an implementation of the set structure given a totally ordered type.