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 <[EMAIL PROTECTED]> 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
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