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Please read up on the ML module system and its origins.

http://cs.stackexchange.com/questions/9769/what-is-the-relat...

Functors play very different roles in Haskell and OCaml/ML.

In Haskell, the Functor class is there to implement the functoriality of a type. If F is a functor, then one implements maps of type F A -> F B from given A -> B in a functorial way.

In ML, the term functor was chosen because they are not first-class functions, but "a level up" (much like a functor is a level up from the maps in the category that it operates on). However, if F is an ML functor, then there are no "maps" between the modules F(A) and F(B). The morphism part, which is the essence of a Functor in Haskell, is missing in ML. This is why I think that the functor terminology isn't very good in ML.

Not everything that maps one thing to another is a functor.

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>However, if F is an ML functor, then there are no "maps" between the modules F(A) and F(B).

Yes there is, the functor. Just repeating a false statement won't make it come true.

> Yes there is, the functor.

What we have is a functor F, which would be defined as in:

  module F =
    functor (X: S) -> ....

If you have two modules A and B of signature S, then you can form F(A) and F(B) and these are both modules. Now where are the maps from F(A) to F(B)? Just saying "the functor" does not explain this.

> Just repeating a false statement won't make it come true.

Exactly!

I can't teach you ocaml on hn. If you want to learn, try this: https://realworldocaml.org/

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.

>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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