# Module `Map.Make`

Functor building an implementation of the map structure given a totally ordered type.

### Parameters

### Signature

`type key`

`= Ord.t`

The type of the map keys.

`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.- before 4.03
Physical equality was not ensured.

`val update : key -> ('a option -> 'a option) -> 'a t -> 'a t`

`update x f m`

returns a map containing the same bindings as`m`

, except for the binding of`x`

. Depending on the value of`y`

where`y`

is`f (find_opt x m)`

, the binding of`x`

is added, removed or updated. If`y`

is`None`

, the binding is removed if it exists; otherwise, if`y`

is`Some z`

then`x`

is associated to`z`

in the resulting map. If`x`

was already bound in`m`

to a value that is physically equal to`z`

,`m`

is returned unchanged (the result of the function is then physically equal to`m`

).- since
- 4.06.0

`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`

).- before 4.03
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`

. In terms of the`find_opt`

operation, we have`find_opt x (merge f m1 m2) = f (find_opt x m1) (find_opt x m2)`

for any key`x`

, provided that`f None None = None`

.- 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. This is a special case of`merge`

:`union f m1 m2`

is equivalent to`merge f' m1 m2`

, where`f' None None = None`

`f' (Some v) None = Some v`

`f' None (Some v) = Some v`

`f' (Some v1) (Some v2) = f v1 v2`

- 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 satisfies 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`

)- since
- 3.12.0

- before 4.03
Physical equality was not ensured.

`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 min_binding_opt : 'a t -> (key * 'a) option`

Return the smallest binding of the given map (with respect to the

`Ord.compare`

ordering), or`None`

if the map is empty.- since
- 4.05

`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 max_binding_opt : 'a t -> (key * 'a) option`

Same as

`Map.S.min_binding_opt`

, but returns the largest binding of the given map.- since
- 4.05

`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 choose_opt : 'a t -> (key * 'a) option`

Return one binding of the given map, or

`None`

if the map is empty. Which binding is chosen is unspecified, but equal bindings will be chosen for equal maps.- since
- 4.05

`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 find_opt : key -> 'a t -> 'a option`

`find_opt x m`

returns`Some v`

if the current binding of`x`

in`m`

is`v`

, or`None`

if no such binding exists.- since
- 4.05

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

`find_first f m`

, where`f`

is a monotonically increasing function, returns the binding of`m`

with the lowest key`k`

such that`f k`

, or raises`Not_found`

if no such key exists.For example,

`find_first (fun k -> Ord.compare k x >= 0) m`

will return the first binding`k, v`

of`m`

where`Ord.compare k x >= 0`

(intuitively:`k >= x`

), or raise`Not_found`

if`x`

is greater than any element of`m`

.- since
- 4.05

`val find_first_opt : (key -> bool) -> 'a t -> (key * 'a) option`

`find_first_opt f m`

, where`f`

is a monotonically increasing function, returns an option containing the binding of`m`

with the lowest key`k`

such that`f k`

, or`None`

if no such key exists.- since
- 4.05

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

`find_last f m`

, where`f`

is a monotonically decreasing function, returns the binding of`m`

with the highest key`k`

such that`f k`

, or raises`Not_found`

if no such key exists.- since
- 4.05

`val find_last_opt : (key -> bool) -> 'a t -> (key * 'a) option`

`find_last_opt f m`

, where`f`

is a monotonically decreasing function, returns an option containing the binding of`m`

with the highest key`k`

such that`f k`

, or`None`

if no such key exists.- since
- 4.05

`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.

###### Iterators

`val to_seq : 'a t -> (key * 'a) Stdlib.Seq.t`

Iterate on the whole map, in ascending order

- since
- 4.07

`val to_seq_from : key -> 'a t -> (key * 'a) Stdlib.Seq.t`

`to_seq_from k m`

iterates on a subset of the bindings of`m`

, in ascending order, from key`k`

or above.- since
- 4.07

`val add_seq : (key * 'a) Stdlib.Seq.t -> 'a t -> 'a t`

Add the given bindings to the map, in order.

- since
- 4.07

`val of_seq : (key * 'a) Stdlib.Seq.t -> 'a t`

Build a map from the given bindings

- since
- 4.07