We can only have one instance of a class for a particular type, so how do we choose? The module Data.Monoid contains the instance instance Monoid (a -> a) where mempty = id mappend = (.) I want to argue that a more natural instance is the pointwise lifting: instance Monoid b => Monoid (a -> b) where mempty _ = mempty mappend f g x = f x `mappend` g x This instance is compositional, in that it builds instances for complex types (like functions of many arguments) out of instances for simpler ones, and it's consistent with the instances for tuples. It's also Haskell 98. If the second instance were used instead, the first could be replaced with one for data Endo a = Endo { runEndo :: a -> a } That's a bit awkward, but not as much as simulating the pointwise lifting by hand.