Re: Data.Monoid

On Tue, Sep 13, 2005 at 08:35:39PM -0400, Cale Gibbard wrote:

On 13/09/05, Ross Paterson wrote:

...

(regurgitating http://www.haskell.org/pipermail/libraries/2005-July/004057.html)

I propose to replace the instance

instance Monoid (a -> a) where mempty = id mappend = (.)

with

newtype Endo a = Endo { runEndo :: a -> a }

instance Monoid (Endo a) where mempty = Endo id Endo f `mappend` Endo g = Endo (f . g)

instance Monoid b => Monoid (a -> b) where mempty _ = mempty mappend f g x = f x `mappend` g x

I don't think it's clear which of the two instances is more useful. I would actually probably consider the existing instance more fundamental, and get more use out of it. (It's occasionally quite handy together with WriterT), but who knows - perhaps it's best if they're both wrapped in newtypes for the time being.

The old instance is handy with the writer monad, but it's a dead end; the proposed (pointwise) one lets you lift through a series of function types, just as you can with tuple types. Fiddling with the Endo newtype will be some bother, but simulating the pointwise lifting by hand is much more awkward.