Library
Module
Module type
Parameter
Class
Class type
val empty : t
The empty set.
add x s
returns a set containing all elements of s
, plus x
. If x
was already in s
, s
is returned unchanged (the result of the function is then physically equal to s
).
val singleton : float -> t
singleton x
returns the one-element set containing only x
.
remove x s
returns a set containing all elements of s
, except x
. If x
was not in s
, s
is returned unchanged (the result of the function is then physically equal to s
).
val cardinal : t -> int
Return the number of elements of a set.
val elements : t -> float 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 -> float
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 min_elt_opt : t -> float option
Return the smallest element of the given set (with respect to the Ord.compare
ordering), or None
if the set is empty.
val max_elt_opt : t -> float option
Same as min_elt_opt
, but returns the largest element of the given set.
val choose : t -> float
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 choose_opt : t -> float option
Return one element of the given set, or None
if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets.
val find : float -> t -> float
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 find_opt : float -> t -> float option
find_opt x s
returns the element of s
equal to x
(according to Ord.compare
), or None
if no such element exists.
val find_first : (float -> bool) -> t -> float
find_first f s
, where f
is a monotonically increasing function, returns the lowest element e
of s
such that f e
, or raises Not_found
if no such element exists.
For example, find_first (fun e -> Ord.compare e x >= 0) s
will return the first element e
of s
where Ord.compare e x >= 0
(intuitively: e >= x
), or raise Not_found
if x
is greater than any element of s
.
val find_first_opt : (float -> bool) -> t -> float option
find_first_opt f s
, where f
is a monotonically increasing function, returns an option containing the lowest element e
of s
such that f e
, or None
if no such element exists.
val find_last : (float -> bool) -> t -> float
find_last f s
, where f
is a monotonically decreasing function, returns the highest element e
of s
such that f e
, or raises Not_found
if no such element exists.
val find_last_opt : (float -> bool) -> t -> float option
find_last_opt f s
, where f
is a monotonically decreasing function, returns an option containing the highest element e
of s
such that f e
, or None
if no such element exists.
val iter : (float -> 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 : (float -> 'acc -> 'acc) -> t -> 'acc -> 'acc
fold f s init
computes (f xN ... (f x2 (f x1 init))...)
, where x1 ... xN
are the elements of s
, in increasing order.
map f s
is the set whose elements are f a0
,f a1
... f
aN
, where a0
,a1
...aN
are the elements of s
.
The elements are passed to f
in increasing order with respect to the ordering over the type of the elements.
If no element of s
is changed by f
, s
is returned unchanged. (If each output of f
is physically equal to its input, the returned set is physically equal to s
.)
filter f s
returns the set of all elements in s
that satisfy predicate f
. If f
satisfies every element in s
, s
is returned unchanged (the result of the function is then physically equal to s
).
filter_map f s
returns the set of all v
such that f x = Some v
for some element x
of s
.
For example,
filter_map (fun n -> if n mod 2 = 0 then Some (n / 2) else None) s
is the set of halves of the even elements of s
.
If no element of s
is changed or dropped by f
(if f x = Some x
for each element x
), then s
is returned unchanged: the result of the function is then physically equal to s
.
partition f s
returns a pair of sets (s1, s2)
, where s1
is the set of all the elements of s
that satisfy the predicate f
, and s2
is the set of all the elements of s
that do not satisfy f
.
split x s
returns a triple (l, present, r)
, where l
is the set of elements of s
that are strictly less than x
; r
is the set of elements of s
that are strictly greater than x
; present
is false
if s
contains no element equal to x
, or true
if s
contains an element equal to x
.
val is_empty : t -> bool
Test whether a set is empty or not.
val mem : float -> t -> bool
mem x s
tests whether x
belongs to the set s
.
equal s1 s2
tests whether the sets s1
and s2
are equal, that is, contain equal elements.
Total ordering between sets. Can be used as the ordering function for doing sets of sets.
val for_all : (float -> bool) -> t -> bool
for_all f s
checks if all elements of the set satisfy the predicate f
.
val exists : (float -> bool) -> t -> bool
exists f s
checks if at least one element of the set satisfies the predicate f
.
val of_list : float 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.
to_seq_from x s
iterates on a subset of the elements of s
in ascending order, from x
or above.