OCaml: Set modules

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.)

Answer 2

In addition to Chris's answer, it may be useful to say that some standard library modules already adhere to the OrderedType signature. For example, you can simply do:

module StringSet = Set.Make(String) ;;       (* sets of strings *)
module Int64Set = Set.Make(Int64) ;;         (* sets of int64s *)
module StringSetSet = Set.Make(StringSet) ;; (* sets of sets of strings *)

And so on.

Here's a simple usage example for StringSet; remember that sets are functional data structures, so adding a new element to a set returns a new set:

let set = List.fold_right StringSet.add ["foo";"bar";"baz"] StringSet.empty ;;
StringSet.mem "bar" set ;; (* returns true *)
StringSet.mem "zzz" set ;; (* returns false *)