How to make a Type-constructor part of the Functor typeclass if it has more than one Type-parameter?

Question

I am trying to understand the way the Functor-Typeclass works in Haskell. If you have a function f :: a -> b -> c and you want to partially apply it to the argB to get a function that takes one argument, you can simply do:

f' :: a -> c
f' x = f x argB

and use that. Is it possible to get such behavior when making something part of the Functor-Typeclass with something like this:

instance Functor (MyTypeconstructor _ argB) where
   fmap <implementation of fmap>

I know you can partially apply a Type-constructor to its first type-parameter (standart currying):

instance Functor (MyTypeconstructor argA) where
   fmap <implementation of fmap>

but how can you partially apply it to its second / third / all except one type-parameter, if this is possible?

thank you.

Answer 1

Suppose you have data F a b = ..., define

newtype Fx a = Fx { unFx :: F a X }

to partially apply F to X in the second argument. Now you can use

instance Functor Fx where
    fmap f fa = ...

to define your instance for F _ X.