It turns out that this combinator

f ~@~ g = (f .) . (. g)

is a powerful thing. It was abstracted from following (commonly used) pattern f . h . g where f and g are fixed.

This library not only define ~@~ combinator, but also some derived combinators that can help us to easily define a lot of things including lenses. See lens package for detais on what lenses are.

Function Data.Function.on can be implemented using ~@~ as:

on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
on f g = (id ~@~ g ~@~ g) f

If function on3 existed in base then it could be defined as:

on3 :: (b -> b -> b -> d) -> (a -> b) -> a -> a -> a -> d
on3 f g = (id ~@~ g ~@~ g ~@~ g) f

Other usage examples and documentation can be found in Data.Function.Between.

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