# Set

## Module Set

To make a set of strings:

`# module SS = Set.Make(String);;`

module SS :
sig
type elt = String.t
type t = Set.Make(String).t
val empty : t
val is_empty : t -> bool
val mem : elt -> t -> bool
val add : elt -> t -> t
val singleton : elt -> t
val remove : elt -> t -> t
val union : t -> t -> t
val inter : t -> t -> t
val diff : t -> t -> t
val compare : t -> t -> int
val equal : t -> t -> bool
val subset : t -> t -> bool
val iter : (elt -> unit) -> t -> unit
val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a
val for_all : (elt -> bool) -> t -> bool
val exists : (elt -> bool) -> t -> bool
val filter : (elt -> bool) -> t -> t
val partition : (elt -> bool) -> t -> t * t
val cardinal : t -> int
val elements : t -> elt list
val min_elt : t -> elt
val max_elt : t -> elt
val choose : t -> elt
val split : elt -> t -> t * bool * t
val find : elt -> t -> elt
end

To create a set you need to start somewhere so here is the empty set:

`# let s = SS.empty;;`

val s : SS.t = <abstr>

Alternatively if we know an element to start with we can create a set like

`# let s = SS.singleton "hello";;`

val s : SS.t = <abstr>

To add some elements to the the set we can do.

```
# let s =
List.fold_right SS.add ["hello"; "world"; "community"; "manager";
"stuff"; "blue"; "green"] s;;
```

val s : SS.t = <abstr>

Now if we are playing around with sets we will probably want to see what is in the set that we have created. To do this we can write a function that will print the set out.

```
# (* Prints a new line "\n" after each string is printed *)
let print_set s =
SS.iter print_endline s;;
```

val print_set : SS.t -> unit = <fun>

If we want to remove a specific element of a set there is a remove function. However if we want to remove several elements at once we could think of it as doing a 'filter'. Let's filter out all words that are longer than 5 characters.

This can be written as:

```
# let my_filter str =
String.length str <= 5;;
```

val my_filter : string -> bool = <fun>
# let s2 = SS.filter my_filter s;;

val s2 : SS.t = <abstr>

or using an anonymous function:

`# let s2 = SS.filter (fun str -> String.length str <= 5) s;;`

val s2 : SS.t = <abstr>

If we want to check and see if an element is in the set it might look like this.

`# SS.mem "hello" s2;;`

- : bool = true

The Set module also provides the set theoretic operations union, intersection and difference. For example, the difference of the original set and the set with short strings (≤ 5 characters) is the set of long strings:

`# print_set (SS.diff s s2);;`

community
manager
- : unit = ()

Note that the Set module provides a purely functional data structure: removing an element from a set does not alter that set but, rather, returns a new set that is very similar to (and shares much of its internals with) the original set.