How to create Functor definition for Either type

Question

I am new to Haskell, trying to understand Functor. I took following code from Data.Either module (Replaced data Either with Either1). I just updated by removing 'Either1 a' and replaced it with 'Either1' (instance Functor Either1 where).

data Either1 a b = Left1 a | Right1 b

instance Functor Either1 where
    fmap f (Left1 x) = Left1 x
    fmap f (Right1 y) = Right1 (f y)

When i try to load above snippet, I am getting following error.

Prelude> :load Sample.hs
[1 of 1] Compiling Main             ( Sample.hs, interpreted )

Sample.hs:3:18:
    Expecting one more argument to ‘Either1’
    The first argument of ‘Functor’ should have kind ‘* -> *’,
      but ‘Either1’ has kind ‘* -> * -> *’
    In the instance declaration for ‘Functor Either1’
Failed, modules loaded: none.

My question is, Why should I put "Either1 a" while defining fmap function, why can't 'Either1" ?

Answer 1

As noted in the answer to your previous question, functors require a type of kind * -> *. Either1 has kind * -> * -> *; you need to partially apply Either1 to get a type of the proper kind.

> :k Either1
Either1 :: * -> * -> *
> :k Either1 Int
Either1 Int :: * -> *

When defining the Functor instance, it doesn't really matter to the functor what the first type is, so you can just specify an unconstrained type variable instead of a concrete type like Int.

Answer 2

When you implement Functor, you need a type that accepts a single type argument. Either1 accepts two type arguments, a and b, so your definition should look like this:

instance Functor (Either1 a) where
    fmap f (Left1 x) = Left1 x
    fmap f (Right1 y) = Right1 (f y)

(I also fixed a compilation error in the Left1 case; you were missing the f parameter)

The online book, Learn You a Haskell has a great introduction on Functors which talks in depth about the partial application of Either described here.