## table of contents

Map.S(3o) | OCaml library | Map.S(3o) |

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

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

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

**update key f m** returns a map containing the same bindings
as **m** , except for the binding of **key** . Depending on the value
of **y** where **y** is **f (find_opt key m)** , the binding of
**key** is added, removed or updated. If **y** is **None** , the
binding is removed if it exists; otherwise, if **y** is **Some z**
then **key** is associated to **z** in the resulting map. If
**key** 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** ).

**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 are a subset of the
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
x (find_opt x m1) (find_opt x m2)** for any key **x** , provided that
**f x 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 are a subset of the
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' _key None None = None**

- **f' _key (Some v) None = Some v**

- **f' _key None (Some v) = Some v**

- **f' key (Some v1) (Some v2) = f key 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 init** computes **(f kN dN ... (f k1 d1
init)...)** , 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 f m** checks if all the bindings of the map satisfy
the predicate **f** .

**Since** 3.12.0

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

**exists f m** checks if at least one binding of the map
satisfies the predicate **f** .

**Since** 3.12.0

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

**filter f m** returns the map with all the bindings in
**m** that satisfy predicate **p** . If every binding in **m**
satisfies **f** , **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 filter_map* : **(key -> 'a -> 'b option) -> 'a
t -> 'b t**

**filter_map f m** applies the function **f** to every
binding of **m** , and builds a map from the results. For each binding
**(k, v)** in the input map:

-if **f k v** is **None** then **k** is not in the
result,

-if **f k v** is **Some v'** then the binding **(k, v')**
is in the output map.

For example, the following function on maps whose values are lists

drops all bindings of

filter_map

(fun _k li -> match li with [] -> None | _::tl -> Some tl)

m

**m**whose value is an empty list, and pops the first element of each value that is non-empty.

**Since** 4.11.0

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

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

**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 of keys 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 binding with the smallest key in a 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 binding with the smallest key in 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 binding with
the largest key in 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 binding
with the largest key in 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 value of **x** in **m**
, or raises **Not_found** if no binding for **x** exists.

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

**find_opt x m** returns **Some v** if the current value of
**x** in **m** is **v** , or **None** if no binding for **x**
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.

## Maps and Sequences¶

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

Iterate on the whole map, in ascending order of keys

**Since** 4.07

*val to_rev_seq* : **'a t -> (key * 'a) Seq.t**

Iterate on the whole map, in descending order of keys

**Since** 4.12

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

**to_seq_from k m** iterates on a subset of the bindings of
**m** , in ascending order of keys, from key **k** or above.

**Since** 4.07

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

Add the given bindings to the map, in order.

**Since** 4.07

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

Build a map from the given bindings

**Since** 4.07

2022-01-19 | OCamldoc |