Coapplicative functors in Haskell

coapplicative.hs

-- Because of the type of 'from', 'Coaplicative' must correspond to "non-empty containers", for the usual hand-wavy definition of "container".
class Functor f => Coapplicative f where
  from :: f a -> a
  separate :: f (Either a b) -> Either (f a) (f b)

instance Coapplicative Identity where
  from (Identity a) = a
  separate (Identity (Left a))  = Left  (Identity a)
  separate (Identity (Right b)) = Right (Identity b)

-- Silly Haskell having no nontrivial comonoids.
class Coapplicative f => Coalternative f where
  full :: f a -> ()
  full _ = ()

  split :: f a -> f (a, a)
  split = fmap (\a -> (a,a))