20 Functors

Functors are "functions" on modules. It's a kind of function that takes in a module as input, and spits out a module as output.

module type X = sig
	val x : int
end

module A : X = struct
	let x = 0
end

module type X = sig val x : int end

module A : X

What if we wanted to create a module that is the same as A, but it's x is one bigger. We can use a functor for this:

module IncX = functor (M : X) -> struct
	let x = M.x + 1
end

module IncX : functor (M : X) -> sig val x : int end

Let's go through this

module means we're using module-level syntax. The functor means that we're creating a functor! The module value that it takes in is locally called M, and has signature X. This yields (->) the struct where x is equal to M.x + 1.

A.x

- : int = 0

module B = IncX(A);;

module B : sig val x : int end

B.x

- : int = 1

Now we've defined B, where B.x is one bigger than A.x. There is also syntactic sugar for the keyword functor:

module IncX(M : X) = struct
	let x = M.x + 1
end

module C = IncX(B);;
C.x;;

module IncX : functor (M : X) -> sig val x : int end

module C : sig val x : int end

- : int = 2

OCaml's type checker requires you to specify the : X in the function definition. It cannot infer this

Note that you also don't need to seal the module to use it with a functor.

Syntax

(note that type annotations are required).

module F (M1 : S1) ... (Mn : Sn) = struct
    ...
end

module F =
    functor (M1 : S1)
    -> ...
    -> functor (Mn : Sn)
    -> struct
    ...
end