Re: Proposal: Max and Min for Monoid

23 Sep 2010

      Felipe Lessa  writes:
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On Thu, Sep 23, 2010 at 12:58 PM, Jake McArthur  wrote:
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-- | 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)
Why should we prefer this monoid over
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data Max a = Minimum | Max a
             deriving (Eq, Ord, Read, Show)
instance Ord a => Monoid (Max a) where
  mempty = Minimum
  Minimum `mappend` x   = x
  x `mappend` Minimum   = x
  Max a `mappend` Max b = Max (a `max` b)
You're right, the original wouldn't fly because there are unbounded
types (like Integer) that you'd like to be able to use with Max/Min.

Rather than your proposal I would suggest that Max/Min mirror
the existing First/Last, namely:

    newtype Max a = Max { getMax :: Maybe a }
      deriving (Eq, Ord, Read, Show)

    instance (Ord a) => Monoid (Max a) where
        mempty  = Max Nothing
        mappend = max

G
--
Gregory Collins 