Functor MakeSet
functor MakeSet (Ord : OrderedType) : SET where type elt = Ord.t = struct ... end
Sets over given 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.
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Input module Ord : OrderedType
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type t
The type of the set elements.
val compare : t -> t -> int
A total ordering function over the set elements.
This is a two-argument function
f such that
f e1 e2 is zero if
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
Pervasives.compare.
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
Set union.
val inter : t -> t -> t
Set interseection.
val diff : t -> t -> t
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 for_all : (elt -> bool) -> t -> bool
for_all p s checks if all elements of the set
satisfy the predicate p.
val exists : (elt -> bool) -> t -> bool
exists p s checks if at least one element of
the set satisfies the predicate p.
val filter : (elt -> bool) -> t -> t
filter p s returns the set of all elements in s
that satisfy predicate p.
val partition : (elt -> bool) -> t -> t * 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 : 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 MakeSet.
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.