It turns out that this combinator 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 defines ~@~ combinator, but also some derived combinators that can help us 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: If function on3 existed in base then it could be defined as: Other usage examples and documentation can be found in Data.Function.Between module.