[Haskell-cafe] Have you seen this functor/contrafunctor combo?

newtype Q p a = Q (p a -> a)

instance ContraFunctor p => Functor (Q p) where fmap h (Q w) = Q (h . w . cmap h)

using "cmap" for contravariant map. For instance, p a = u -> a.

instance ContraFunctor p => Applicative (Q p) where pure a = Q (pure a) Q fs <*> Q as = Q (\ r -> let f = fs (cmap ($ a) r) a = as (cmap (f $) r) in f a)

I've checked the functor laws but not the applicative laws, and I haven't looked for a Monad instance. Or extend to a more symmetric definition adding a (covariant) functor f to the contravariant functor p.

newtype Q' p f a = Q' (p a -> f a)

A (law-abiding) Functor instance is easy, but I don't know about an Applicative instance. Have you seen Q or Q' before? They look like they ought to be something familiar & useful. -- Conal