Let's say I want to have a very generic ListF data type:
{-# LANGUAGE GADTs, DataKinds #-}
data ListF :: * -> * -> * where
Nil :: List a b
Cons :: a -> b -> List a b
Now I can use this data type with Data.Fix to build an f-algebra
import qualified Data.Fix as Fx
instance Functor (ListF a :: * -> *) where
fmap f (Cons x y) = Cons x (f y)
fmap _ Nil = Nil
sumOfNums = Fx.cata f (Fx.Fix $ Cons 2 (Fx.Fix $ Cons 3 (Fx.Fix $ Cons 5 (Fx.Fix Nil))))
where
f (Cons x y) = x + y
f Nil = 0
But how I can use this very generic data type ListF to create what I consider the default Functor instance for recursive lists (mapping over each value in the list)
I guess I could use a Bifunctor (mapping over the first value, traversing the second), but I don't know how that could ever work with Data.Fix.Fix?