Monoid instance for IO

[Anthony Cowley]

+1

I use a newtype for this, and it's a nuisance.

Anthony

> On Nov 13, 2014, at 10:13 AM, Gabriel Gonzalez <gabriel439 at gmail.com> wrote:
> 
> 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
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