This module explores the concept of contravariant functors in Haskell, contrasting them with the more common covariant functors. It uses the MakeString newtype as a concrete example.

From Covariance, contravariance, and positive and negative position and What is a contravariant functor?

The implementation of the function-result fmap and the function-argument contramap are almost exactly the same thing: just function composition (the . operator). The only difference is on which side you compose the adapter function.

fmap :: (r -> s) -> (a -> r) -> (a -> s)
fmap adapter f = adapter . f
fmap adapter = (adapter .)
fmap = (.)

contramap' :: (b -> a) -> (a -> r) -> (b -> r)
contramap' adapter f = f . adapter
contramap' adapter = (. adapter)
contramap' = flip (.)

Note that contramap' is not the same as contramap from Contravariant. You cannot make '(->) r' an actual instance of Contravariant in Haskell code simply because the a is not the last type parameter of (->). Conceptually it works perfectly well, and you can always use a newtype wrapper to swap the type parameters and make that an instance (the contravariant package defines the Op type for exactly this purpose).