module type S_Basic_Compare =sig
..end
Standard operations on sets. This signature does not assume any
particular property on the compare
function used to compare elements,
except that it implements a total order. These are the functions that
make sense for an usage of Set
where only the algorithmic complexity is
interesting to the user.
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 intersection.
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 elements of s
are presented to f
in increasing order
with respect to the ordering over the type of the elements.
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
, in increasing order.
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 Set.Make
.
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 find : elt ->
t -> elt
find x s
returns the element of s
equal to x
(according
to Ord.compare
), or raise Not_found
if no such element
exists.
val of_list : elt list -> t
of_list l
creates a set from a list of elements.
This is usually more efficient than folding add
over the list,
except perhaps for lists with many duplicated elements.