TraversableF.hs

import Data.Monoid

newtype F a b = F (a -> b)
  deriving (Functor)
  
instance Monoid b => Monoid (F a b) where
  mempty = F mempty
  mappend (F f) (F g) = F (f <> g)

instance (Bounded a, Enum a) => Foldable (F a) where
  foldMap f (F g) = foldMap (f . g) [minBound..maxBound]

instance (Bounded a, Enum a) => Traversable (F a) where
  traverse f (F g) = fmap (F . index) (traverse (f . g) [minBound..maxBound])
    where
      index xs x = xs !! fromEnum x