Monoid instance for IO

I would like to add the following `Monoid` instance for `IO` to `Data.Monoid`: ``` instance Monoid a => Monoid (IO a) where mempty = pure mempty mappend = liftA2 mappend ``` I describe the benefit of this particular instance in this blog post: http://www.haskellforall.com/2014/07/equational-reasoning-at-scale.html ... and Conal Elliot describes the general trick of recursively lifting `Monoid` instances in his type class morphisms paper: http://conal.net/papers/type-class-morphisms/type-class-morphisms-long.pdf The primary benefit of the `Monoid` instance is that it chains well with other `Monoid` instances in `base` to create derived `Monoid` instances. The following types are examples of useful derived `Monoid` instances: ``` IO () -- Because `()` is a `Monoid` a -> IO () -- Because `a -> r` is a `Monoid` if `r` is a `Monoid` IO (a -> IO ()) -- This comment explains the utility of this instance: http://www.reddit.com/r/haskell/comments/22bn1m/monads_lifting_join_and_sideeffecting_actions/cglhgu0 ``` Here are other alternatives that I considered: **Alternative A)** Define a newtype for the `Monoid` instance, either specialized to `IO`: ``` newtype IOMonoid a = IOMonoid { getIOMonoid :: IO a } deriving (Functor, Applicative, Monad) instance Monoid a => Monoid (IOMonoid a) where mempty = pure mempty mappend = liftA2 mappend ``` ... or generalized to all applicatives: ``` newtype LiftMonoid f a = LiftMonoid ( getLiftMonoid :: f a } instance (Applicative f, Monoid a) => Monoid (LiftMonoid f a) where ... ``` I prefer not to use a newtype because the principle benefit of a `Monoid` instance for `IO` is for the derived instances. Using the example `IO (a -> IO ())` type, suppose that I had two values of that type which I wanted to mappend: ``` m :: IO (a -> IO ()) n :: IO (a -> IO ()) ``` Using newtypes (either one), I'd have to write: ``` getNewtype (Newtype (fmap (fmap Newtype) m) <> Newtype (fmap (fmap Newtype) n)) ``` ... instead of just: ``` m <> n ``` **Alternative B)** Provide a different `Monoid` instance for `IO`, such as one that uses concurrency There are two issues with this approach: 1. There is not a well-defined semantics for non-`STM` concurrency that we could use to prove the `Monoid` laws 2. Even if there were a well-defined semantics, it would be better suited as an `Alternative` instance instead of a `Monoid` instance To clarify the latter point, Peaker convinced me [[ http://www.reddit.com/r/haskell/comments/2guo44/what_is_wrong_with_the_monoid_instance_for_maybe/ckmrcux | here ]] that for certain `Applicative`s it's worth distinguishing the behavior of the `Alternative` instance from the behavior of the `Monoid` instance. The `Monoid` instance can recursively delegate to the `Monoid` instance of the `Applicative`'s type parameter, whereas the `Alternative` instance cannot. I also created a task on phabricator here since I'm used to the Github style of discussing issues on the repository issue tracker: https://phabricator.haskell.org/T55?workflow=create