Oops -- I wasn't watching this thread. I like Jules's definition, though I'd write it as follows.

-- Standard instance: monad applied to monoid
instance Monoid a => Monoid (IO a) where
mempty = return mempty
mappend = liftM2 mappend

You can replace "IO" with any monad at all, to make similar instances.

Here's the instance i use. It's in Control.Instances in the TypeCompose library. See http://www.haskell.org/haskellwiki/TypeCompose.

-- Standard instance: applicative functor applied to monoid
instance Monoid a => Monoid (IO a) where
mempty = pure mempty
mappend = (*>)

On second thought, I don't really like (*>), since it's easy to accidentally discard a useful value. (I dislike (>>) for the same reason.) Generalizing the "monad applied to monoid" instance above:

-- Standard instance: applicative functor applied to monoid
instance Monoid a => Monoid (IO a) where
mempty = pure mempty
mappend = liftA2 mappend

That will be the definition in the next TypeCompose release.

All of these instances agree for a = (). The first & third are more compelling to me than the second, since they make full use of the Monoid a constraint.

Cheers, - Conal

On 5/16/07, Jules Bean <jules@jellybean.co.uk> wrote:

Tomasz Zielonka wrote:
> On Wed, May 16, 2007 at 09:28:31AM +0100, Jules Bean wrote:
>
>> Tomasz Zielonka wrote:
>>
>>> You mean using the (Monoid b) => Monoid (a -> b) instance ?
>>> I can see that IO () makes a perfect Monoid, but there doesn't seem to
>>> be a standard instance for that.
>>>
>> Indeed, all Monads are Monoids (that is, if m :: * -> * is a Monad, then
>> m a :: * is a Monoid, for any fixed type a) by using >>.
>>
>
> Are you sure that (IO Int) is a monoid with mappend = (>>)? How do you
> define mempty, so it is an identity for mappend?
>
> It would help if type a was a Monoid, then:
>
>     mempty = return mempty
>     mappend mx my = do
>         x <- mx
>         y <- my
>         return (x `mappend` y)
>
> It's easier if a = ().
>

Oops, you're right. I spoke too fast.

It's only a monoid for (). Otherwise you can't hope to have a right
identity.

Jules