Comux - Haskell

Is there a way to prove this class can't be implemented:

class Profunctor p => Comux p
  where
  comux :: p (a, b) (c, d) -> (p a c, p b d)

@Asad Saeeduddin I guess there isn't:

newtype ConstId a b = ConstId b deriving Show

instance Profunctor ConstId where
  dimap _ f (ConstId c) = ConstId $ f c

instance Comux ConstId where
  comux (ConstId (c, d)) = (ConstId c, ConstId d)

Good thinking! I suppose that means it works for data Joker f a b = Joker (f b) as well

when f is Alternative, is Joker f a Category?

Hmm, the left-most morphism will always have to win, so I guess it would be lawful?

I think it can be a semigroupoid but not a category

For the same reason data Const a b = a can't be a monoid

Why Const isn't monoid?

well, the semigroup works like this: x <> _ = x

What if I used Monoid a constraint instead?

basically like Identity instance

yes, it would work then. unfortunately we can't pull the same trick for Category, because it needs to be parametric in a and b

Ah, I see