How do I use sets in OCaml?

The Set.S is a module type not a module. You can open only modules. In fact module Set contains three elements:

• module type OrderedType that is a type of modules that implement ordered types;
• module type S that is a type of modules that implement Set data structures;
• functor Make that takes a module of type OrderedType and returns a module of type S.

For example, to create a module, that implements a set for integers, you can do the following:

 module Int = struct 
   type t = int 
   (* use Pervasives compare *)
   let compare = compare
 end

 module Ints = Set.Make(Int)

Other libraries, like Janestreet's Core library, provide sets out of box, for example, Core library has an Int module that is already charged with sets, maps, hashtables, so it can be accessed without any functors:

open Core.Std

let nil = Int.Set.empty

Or, in the modern (2018-2019) version of Janestreet Core or Base libraries, you can use polymorphic sets/maps, which require you to specify the module for keys only when a new set or map is created, e.g., like this

open Base (* or Core, or Core_kernel *)

let nil = Set.empty (module Int)
let one = Set.add nil 1
let two = Set.singleton (module Int) 2

You have to Make a set module from the Set functor.

module SI = Set.Make(struct type t = int let compare = compare end)

Then you can have a set of ints:

# let myset = SI.add 3 SI.empty;;
val myset : SI.t = <abstr>
# SI.elements myset;;
- : SI.elt list = [3]