# Map.S.3o man page

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** . 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** )

**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 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.