Question

I want to use OCaml to generates sets of data and make comparisons between them. I have seen the documentation for Module types like Set.OrderType, Set.Make, etc, but I can’t figure out how to initialize a set or otherwise use them.

Answer 1

Sets are defined using a functorial interface. For any given type, you have to create a Set module for that type using the Set.Make functor. An unfortunate oversight of the standard libraries is that they don’t define Set instances for the built-in types. In most simple cases, it’s sufficient to use Pervasives.compare. Here’s a definition that works for int:

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

The module IntSet will implement the Set.S interface. Now you can operate on sets using the IntSet module:

let s = IntSet.empty ;;
let t = IntSet.add 1 s ;;
let u = IntSet.add 2 s ;;
let tu = IntSet.union t u ;;

Note that you don’t have to explicitly define the input structure for Set.Make as an OrderedType; type inference will do the work for you. Alternatively, you could use the following definition:

module IntOrder : Set.OrderedType = struct
  type t = int
  let compare = Pervasives.compare
end

module IntSet = Set.Make( IntOrder )

This has the advantage that you can re-use the same module to instantiate a Map:

module IntMap = Map.Make( IntOrder )

You lose some genericity in using functors, because the type of the elements is fixed. For example, you won’t be able to define a function that takes a Set of some arbitrary type and performs some operation on it. (Luckily, the Set module itself declares many useful operations on Sets.)