### Map.S (3)

#### NAME

Map.S - Output signature of the functor Map.Make.#### Module type

Module type Map.S#### Documentation

Module type
**S**

=
**sig end**

Output signature of the functor
**Map.Make**
.

*type key *

The type of the map keys.

*type *
**+'a**
*t *

The type of maps from type
**key**
to type
**'a**
.

*val empty *
:
**'a t**

The empty map.

*val is_empty *
:
**'a t -> bool**

Test whether a map is empty or not.

*val mem *
:
**key -> 'a t -> bool**

**mem x m**
returns
**true**
if
**m**
contains a binding for
**x**
,
and
**false**
otherwise.

*val add *
:
**key -> 'a -> 'a t -> 'a t**

**add x y m**
returns a map containing the same bindings as
**m**
, plus a binding of
**x**
to
**y**
. If
**x**
was already bound
in
**m**
to a value that is physically equal to
**y**
,
**m**
is returned unchanged (the result of the function is
then physically equal to
**m**
). Otherwise, the previous binding
of
**x**
in
**m**
disappears.

**Before4.03**
Physical equality was not ensured.

*val singleton *
:
**key -> 'a -> 'a t**

**singleton x y**
returns the one-element map that contains a binding
**y**
for
**x**
.

**Since**
3.12.0

*val remove *
:
**key -> 'a t -> 'a t**

**remove x m**
returns a map containing the same bindings as
**m**
, except for
**x**
which is unbound in the returned map.
If
**x**
was not in
**m**
,
**m**
is returned unchanged
(the result of the function is then physically equal to
**m**
).

**Before4.03**
Physical equality was not ensured.

*val merge *
:
**(key -> 'a option -> 'b option -> 'c option) ->**
**'a t -> 'b t -> 'c t**

**merge f m1 m2**
computes a map whose keys is a subset of keys of
**m1**
and of
**m2**
. The presence of each such binding, and the corresponding
value, is determined with the function
**f**
.

**Since**
3.12.0

*val union *
:
**(key -> 'a -> 'a -> 'a option) ->**
**'a t -> 'a t -> 'a t**

**union f m1 m2**
computes a map whose keys is the union of keys
of
**m1**
and of
**m2**
. When the same binding is defined in both
arguments, the function
**f**
is used to combine them.

**Since**
4.03.0

*val compare *
:
**('a -> 'a -> int) -> 'a t -> 'a t -> int**

Total ordering between maps. The first argument is a total ordering
used to compare data associated with equal keys in the two maps.

*val equal *
:
**('a -> 'a -> bool) -> 'a t -> 'a t -> bool**

**equal cmp m1 m2**
tests whether the maps
**m1**
and
**m2**
are
equal, that is, contain equal keys and associate them with
equal data.
**cmp**
is the equality predicate used to compare
the data associated with the keys.

*val iter *
:
**(key -> 'a -> unit) -> 'a t -> unit**

**iter f m**
applies
**f**
to all bindings in map
**m**
.
**f**
receives the key as first argument, and the associated value
as second argument. The bindings are passed to
**f**
in increasing
order with respect to the ordering over the type of the keys.

*val fold *
:
**(key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b**

**fold f m a**
computes
**(f kN dN ... (f k1 d1 a)...)**
,
where
**k1 ... kN**
are the keys of all bindings in
**m**
(in increasing order), and
**d1 ... dN**
are the associated data.

*val for_all *
:
**(key -> 'a -> bool) -> 'a t -> bool**

**for_all p m**
checks if all the bindings of the map
satisfy the predicate
**p**
.

**Since**
3.12.0

*val exists *
:
**(key -> 'a -> bool) -> 'a t -> bool**

**exists p m**
checks if at least one binding of the map
satisfy the predicate
**p**
.

**Since**
3.12.0

*val filter *
:
**(key -> 'a -> bool) -> 'a t -> 'a t**

**filter p m**
returns the map with all the bindings in
**m**
that satisfy predicate
**p**
. If
**p**
satisfies every binding in
**m**
,
**m**
is returned unchanged (the result of the function is then
physically equal to
**m**
)

**Before4.03**
Physical equality was not ensured.

**Since**
3.12.0

*val partition *
:
**(key -> 'a -> bool) -> 'a t -> 'a t * 'a t**

**partition p m**
returns a pair of maps
**(m1, m2)**
, where
**m1**
contains all the bindings of
**s**
that satisfy the
predicate
**p**
, and
**m2**
is the map with all the bindings of
**s**
that do not satisfy
**p**
.

**Since**
3.12.0

*val cardinal *
:
**'a t -> int**

Return the number of bindings of a map.

**Since**
3.12.0

*val bindings *
:
**'a t -> (key * 'a) list**

Return the list of all bindings of the given map.
The returned list is sorted in increasing order with respect
to the ordering
**Ord.compare**
, where
**Ord**
is the argument
given to
**Map.Make**
.

**Since**
3.12.0

*val min_binding *
:
**'a t -> key * 'a**

Return the smallest binding of the given map
(with respect to the
**Ord.compare**
ordering), or raise
**Not_found**
if the map is empty.

**Since**
3.12.0

*val max_binding *
:
**'a t -> key * 'a**

Same as
**Map.S.min_binding**
, but returns the largest binding
of the given map.

**Since**
3.12.0

*val choose *
:
**'a t -> key * 'a**

Return one binding of the given map, or raise
**Not_found**
if
the map is empty. Which binding is chosen is unspecified,
but equal bindings will be chosen for equal maps.

**Since**
3.12.0

*val split *
:
**key -> 'a t -> 'a t * 'a option * 'a t**

**split x m**
returns a triple
**(l, data, r)**
, where
**l**
is the map with all the bindings of
**m**
whose key
is strictly less than
**x**
;
**r**
is the map with all the bindings of
**m**
whose key
is strictly greater than
**x**
;
**data**
is
**None**
if
**m**
contains no binding for
**x**
,
or
**Some v**
if
**m**
binds
**v**
to
**x**
.

**Since**
3.12.0

*val find *
:
**key -> 'a t -> 'a**

**find x m**
returns the current binding of
**x**
in
**m**
,
or raises
**Not_found**
if no such binding exists.

*val map *
:
**('a -> 'b) -> 'a t -> 'b t**

**map f m**
returns a map with same domain as
**m**
, where the
associated value
**a**
of all bindings of
**m**
has been
replaced by the result of the application of
**f**
to
**a**
.
The bindings are passed to
**f**
in increasing order
with respect to the ordering over the type of the keys.

*val mapi *
:
**(key -> 'a -> 'b) -> 'a t -> 'b t**

Same as
**Map.S.map**
, but the function receives as arguments both the
key and the associated value for each binding of the map.