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

Conal Elliott conal at conal.net
Wed Jun 6 03:54:26 CEST 2012

> 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
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