Proposal: Max and Min for Monoid (ticket # 1952)

[Ross Paterson]

On Sun, Dec 02, 2007 at 09:57:50AM -0800, Conal Elliott wrote:
> My proposed addition:
> 
> -- | Ordered monoid under 'max'.
> newtype Max a = Max { getMax :: a }
> 	deriving (Eq, Ord, Read, Show, Bounded)
> 
> instance (Ord a, Bounded a) => Monoid (Max a) where
> 	mempty = Max minBound
> 	Max a `mappend` Max b = Max (a `max` b)

Funny, I was thinking of proposing a Max type that adjoined a synthetic
identity, as we did in the finger tree paper:

data Max a = NoMax | Max a
	deriving (Eq, Ord, Read, Show)

instance Ord a => Monoid (Max a) where
	mempty = NoMax
	NoMax `mappend` b = b
	a `mappend` NoMax = a
	Max x `mappend` Max y = Max (x `max` y)

and similarly for Min.  One could even define

	getMax :: Bounded a => Max a -> a
	getMax NoMax = minBound
	getMax (Max x) = x