This answer from a Category Theory perspective includes the following statement:
...the truth is that there's no real distinction between co and contravariant functor, because every functor is just a covariant functor.
More in details a contravariant functor F from a category C to a category D is nothing more than a (covariant) functor of type F : Cop→D, from the opposite category of C to the category D.
On the other hand, Haskell's
Contravariant merely require
contramap, respectively, to be defined for an instance. This suggests that, from the perspective of Haskell, there exists objects that are
Contravariant but are not
Functors (and vice versa).
So it seems that in Category Theory "there's no real distinction between co and contravariant functors" while in Haskell there is a distinction between
I suspect that this difference has something to with all implementation in Haskell happening in Hask, but I'm not sure.
I think I understand each of the Category Theory and Haskell perspectives on their own, but I'm struggling to find an intuition that connects the two.
It's for convenience.
One could get by with a more general
Functor class, and define instances for endofunctors on Hask (corresponding to our existing
Functor) and functors from Hask^op to Hask (corresponding to our existing
Contravariant). But this comes at a figurative cognitive cost and a quite literal syntactical cost: one must then rely on type inference or type annotations to select an instance, and there are explicit conversions (named
getOp in the standard library) into and out of Hask^op.
Using the names
contramap relaxes both costs: readers do not need to run Hindley-Milner in their head to decide which instance is being selected when it is unambiguous, and writers do not need to give explicit conversions or type annotations to select an instance in cases where it is ambiguous.
(I am actually rewriting history a little bit here. The real reason is because the language designers thought the specialized
Functor would be useful and hadn't imagined or didn't see a need for a more general
Functor. People came along later and noticed it would be useful, sometimes. But experience with the generalized
Functor class shows that can be tedious, and that specialized classes for the most common cases turns out to be a surprisingly good fit after all, for the reasons described above.)