Haskell - 具有递归数据构造函数的仿函数实例

Question

I am having trouble implementing a recursive functor instance. I have tried as follow, but I receive an error that cannot construct the infinite type: b ~ List b

data List a = Hol x a| Hoofd x [List a]
            deriving (Show,Eq,Ord)
instance Functor List where
            fmap f Hol x a = Hol x (f a)
            fmap f (Hoofd x rest) = Hoofd x (fmap f rest)  

Can anyone please suggest me how to fix this and what's my problem? Thanks

Answer 1

The fmap will work on the list, so perform a mapping. This means that you use f:: a -> b to convert a List a -> List b , which will not work: you need another functor mapping, so:

instance Functor List where
    fmap f (Hol x a) = Hol x (f a)
    fmap f (Hoofd x rest) = Hoofd x (fmap (fmap f) rest)

or we can work with a helper function:

instance Functor List where
    fmap f = go
        where go (Hol x a) = Hol x (f a)
              go (Hoofd x rest) = Hoofd x (fmap go rest)

Or we can work with the Compose type to perform a mapping that is two (or more) layers deep:

import Data.Functor.Compose(Compose(getCompose))

instance Functor List where
    fmap f (Hol x a) = Hol x (f a)
    fmap f (Hoofd x xs) = Hoofd x (getCompose (fmap f (Compose xs)))