Module type Extset.S

module type S = sig .. end

Output signature of the functor Extset.Make.


module M: Extmap.S 

The module of association tables over elt.

type elt = M.key 

The type of set elements.

type t = unit M.t 

The type of sets of type elt.

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 returns true if s contains x, and false otherwise.

val add : elt -> t -> t

add x s returns a set containing the same elements as s, plus x.

val singleton : elt -> t

singleton x returns the one-element set that contains x.

val remove : elt -> t -> t

remove x s returns a set containing the same elements as s, except for x.

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

merge f s1 s2 computes a set whose elts is a subset of elts of s1 and of s2. The presence of each such element is determined with the function f.

val compare : t -> t -> int

Total ordering between sets.

val equal : t -> t -> bool

equal s1 s2 tests whether the sets s1 and s2 are equal.

val subset : t -> t -> bool

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

val disjoint : t -> t -> bool

disjoint s1 s2 tests whether the sets s1 and s2 are disjoint.

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

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

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

fold f s a computes (f eN ... (f e1 a)...), where e1 ... eN are the element of s in increasing order.

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

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

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

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

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

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

val partition : (elt -> bool) -> t -> t * t

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

val cardinal : t -> int

Return the number of elements in 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.

val min_elt : t -> elt

Return the smallest element of the given set or raise Not_found if the set is empty.

val max_elt : t -> elt

Return the largest element of the given set or raise Not_found if the set is empty.

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, mem, r), where l is the set with all the elements of s that are strictly less than x; r is the set with all the elements of s that are strictly greater than x; mem is true if x belongs to s and false otherwise.

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

change f x s returns a set containing the same elements as s, except x which is added to s if f (mem x s) returns true and removed otherwise.

val union : t -> t -> t

union f s1 s2 computes the union of two sets

val inter : t -> t -> t

inter f s1 s2 computes the intersection of two sets

val diff : t -> t -> t

diff f s1 s2 computes the difference of two sets

val fold_left : ('b -> elt -> 'b) -> 'b -> t -> 'b

same as Extset.S.fold but in the order of List.fold_left

val fold2_inter : (elt -> 'a -> 'a) -> t -> t -> 'a -> 'a

fold2_inter f s1 s2 a computes (f eN ... (f e1 a) ...), where e1 ... eN are the elements of inter s1 s2 in increasing order.

val fold2_union : (elt -> 'a -> 'a) -> t -> t -> 'a -> 'a

fold2_union f s1 s2 a computes (f eN ... (f e1 a) ...), where e1 ... eN are the elements of union s1 s2 in increasing order.

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

translate f s translates the elements in the set s by the function f. f must be strictly monotone on the elements of s. Otherwise it raises Invalid_arg.

val add_new : exn -> elt -> t -> t

add_new e x s adds x to s if s does not contain x, and raises e otherwise.

val is_num_elt : int -> t -> bool

check if the map has the given number of elements

val of_list : elt list -> t

construct a set from a list of elements

val contains : t -> elt -> bool

contains s x is the same as mem x s.

val add_left : t -> elt -> t

add_left s x is the same as add x s.

val remove_left : t -> elt -> t

remove_left s x is the same as remove x s.

val print : (Format.formatter -> elt -> unit) ->
Format.formatter -> t -> unit