(#.) :: Coercible b c => (b -> c) -> (a -> b) -> (a -> c) (#.) _ = coerce {-# INLINE (#.) #-} (.#) :: Coercible a b => (b -> c) -> (a -> b) -> (a -> c) (.#) f _ = coerce f {-# INLINE (.#) #-} The first of these is exported from Data.Functor.Util, and used in many places inside of base for efficiency over '.' (compose), However no module in base actually exports these. I have recently been using Data.Coerce more frequently and think it would be useful to go ahead and export these from somewhere in base. For convenience, I will paste the note about (#.) from Data.Functor.Util: "Note [Function coercion] ~~~~~~~~~~~~~~~~~~~~~~~ Several functions here use (#.) instead of (.) to avoid potential efficiency problems relating to #7542. The problem, in a nutshell: If N is a newtype constructor, then N x will always have the same representation as x (something similar applies for a newtype deconstructor). However, if f is a function, N . f = \x -> N (f x) This looks almost the same as f, but the eta expansion lifts it--the lhs could be _|_, but the rhs never is. This can lead to very inefficient code. Thus we steal a technique from Shachaf and Edward Kmett and adapt it to the current (rather clean) setting. Instead of using N . f, we use N #. f, which is just coerce f `asTypeOf` (N . f) That is, we just *pretend* that f has the right type, and thanks to the safety of coerce, the type checker guarantees that nothing really goes wrong. We still have to be a bit careful, though: remember that #. completely ignores the *value* of its left operand. "