Module Set: 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.
module type OrderedType =
sig
type t
val compare: t -> t -> int
end
-
The input signature of the functor Set.Make.
t is the type of the set elements.
compare is a total ordering function over the set elements.
This is a two-argument function f such that
f e1 e2 is zero if the elements e1 and e2 are equal,
f e1 e2 is strictly negative if e1 is smaller than e2,
and f e1 e2 is strictly positive if e1 is greater than e2.
Example: a suitable ordering function is
the generic structural comparison function compare.
module type S =
sig
type elt
-
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.
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.
val union: t -> t -> t
val inter: t -> t -> t
val diff: t -> t -> t
-
Union, intersection and set difference.
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 order in which the elements of s are presented to f
is unspecified.
val fold: (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.
The order in which elements of s are presented to f is
unspecified.
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 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.
end
module Make(Ord: OrderedType): (S with type elt = Ord.t)
-
Functor building an implementation of the set structure
given a totally ordered type.