I propose to add Functor, Applicative, Monad, Foldable, and Traversable and maybe even MonadFix instances to wrapper newtypes in the Data.Monoid module. The same way as in the semigroups package, e.g. https://hackage.haskell.org/package/semigroups-0.16.1/docs/Data-Semigroup.ht... https://hackage.haskell.org/package/semigroups-0.16.1/docs/Data-Semigroup.ht... Basically: instance Functor Sum where fmap f (Sum x) = Sum (f x) instance Foldable Sum where foldMap f (Sum a) = f a instance Traversable Sum where traverse f (Sum a) = Sum <$> f a instance Applicative Sum where pure = Sum a <* _ = a _ *> a = a Sum f <*> Sum x = Sum (f x) instance Monad Sum where return = Sum _ >> a = a Sum a >>= f = f a instance MonadFix Sum where mfix f = fix (f . getSum)