Functors in SML

A functor in ML means a "parametrized module". It's an unfortunate choice of words, because "functor" has come to mean something completely different in functional programming. I will discuss that "something completely different" implemented in Standard ML.

In Haskell, the functor class consists of the fmap function and the <$ infix operator. I do not believe the <$ infix operator is necessary. We can then implement this as a signature:

signature FUNCTOR = sig
    type 'a f;
    val fmap : ('a -> 'b) -> 'a f -> 'b f;
end;

There are two constraints to a functor:

1. fmap id = id it preserves the identity function, and
2. fmap (f o g) = (fmap f) o (fmap g) it preserves composition.

• Implicit Functors in OCaml
• Joel Björnson, More type classes which implements functors, monoids, and applicatives in OCaml