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Ok, so you can't (or don't want to) actually back up your claim that OCaml functors have the same meaning as functors in Haskell. Which is to be expected, because it's bogus. I know OCaml fairly well. The reason you can't show me the map from F(A) to F(B) is that it's not there.

If you want to claim a relation between OCaml functors and category-theoretic functors, then you must be able to justify your claims. Saying "functors represent functions from a module to a module. Oh hey, that sounds just like the standard definition of a functor." is just not a convincing argument.

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>The reason you can't show me the map from F(A) to F(B) is that it's not there.

That is literally the functor. Seriously, read the chapter on modules.

> That is literally the functor.

That would be an answer for Haskell (though a proper one would refer to fmap), but it does not work like that in OCaml. You do know some OCaml, right?

But if it's so obvious, then you can say how it works for the following concrete example:

  module type S = sig
    type t
    val f: t -> int
  end
  
  module F = functor (X: S) -> struct
    type s = X.t * X.t
    let g x = X.f x + X.f x
  end
  
  module A : S = struct
    type t = float
    let f x = int_of_float x
  end
  
  module B : S = struct
    type t = int
    let f x = 2*x
  end
  
  module X = F(A)
  module Y = F(B)

How do I get from X to Y by "literally the functor"?

The point is: In the ML module system there is no equivalent to fmap: (A -> B) -> (F A -> F B), i.e. the functor action on morphisms. So, functors in Haskell and OCaml are different things. If you want to claim otherwise, you'll have to make an actual argument for it.

> How do I get from X to Y by "literally the functor"?

NB You only need to get from X to Y in ways that arise from getting from A to B. Since there doesn't seem to be any relevant concept of morphism it's hard to see how ML functors are anything other than trivially category theoretical.

Yes, I know! That's the point I'm trying to make. This whole discussion is about MustardTiger's claim that functors in OCaml have the same meaning as Functor in Haskell. While the latter model functors in the category-theoretic sense, the same cannot be said for the former.

I know you know :) I'm just reinforcing your point.

Seriously, read the book instead of repeating nonsense: https://realworldocaml.org/v1/en/html/functors.html

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