Include vs. Open

The include and open statements are quite similar, but they have a subtly different effect on a structure. Consider this code:

module M = struct
  let x = 0
end

module N = struct
  include M
  let y = x + 1
end

module O = struct
  open M
  let y = x + 1
end

If we enter that in the toplevel, we get the following response:

module M : sig val x : int end
module N : sig val x : int val y : int end
module O : sig val y : int end

Look closely at the values contained in each structure. N has both an x and y, whereas O has only a y. The reason is that include M causes all the definitions of M to also be included in N, so the definition of x from M is present in N. But open M only made those definitions available in the scope of O; it doesn't actually make them part of the structure. So O does not contain a definition of x, even though x is in scope during the evaluation of O's definition of y.

A metaphor for understanding this difference might be: open M imports definitions from M and makes them available for local consumption, but they aren't exported to the outside world. Whereas include M imports definitions from M, makes them available for local consumption, and additionally exports them to the outside world.