Proposal: Max and Min for Monoid

Gregory Collins greg at gregorycollins.net
Thu Sep 23 13:47:48 EDT 2010

```Felipe Lessa <felipe.lessa at gmail.com> writes:
> On Thu, Sep 23, 2010 at 12:58 PM, Jake McArthur <jake.mcarthur at gmail.com> wrote:
>
>>>    -- | 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
>
>> 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 }