Maximum and Minimum monoids

[Michael Snoyman]

On Thu, Dec 27, 2012 at 8:45 PM, Gabriel Gonzalez <gabriel439 at gmail.com>wrote:

> I don't know if this has been brought up before or not, but would it be
> possible to add the Maximum and Minimum monoids to Data.Monoid?  The
> following implementations extend the traditional semigroups using Maybe.
>
> ******
>
> newtype Maximum a = Maximum { getMaximum :: Maybe a }
>
> instance (Ord a) => Monoid (Maximum a) where
>     mempty = Maximum Nothing
>
>     mappend (Maximum Nothing) m2 = m2
>     mappend m1 (Maximum Nothing) = m1
>     mappend (Maximum (Just a1)) (Maximum (Just a2)) = Maximum (Just (max
> a1 a2))
>
> newtype Minimum a = Minimum { getMinimum :: Maybe a }
>
> instance (Ord a) => Monoid (Minimum a) where
>     mempty = Minimum Nothing
>
>     mappend (Minimum Nothing) m2 = m2
>     mappend m1 (Minimum Nothing) = m1
>     mappend (Minimum (Just a1)) (Minimum (Just a2)) = Minimum (Just (min
> a1 a2))
>
> ******
>
> These also give the correct behavior when folding empty structures by
> returning Nothing.
>
> The reason I'm asking is that my `pipes` library uses `WriterT` to
> implement folds and having the above monoids lets me implement minimum and
> maximum folds elegantly.  I can always provide these monoids myself, but I
> feel like they belong in Data.Monoid.
>
>
+1, I've had to implement at least one of these in the past. In my case, I
think I ended up doing it something like:

newtype Maximum a = Maximum { getMaximum :: a }
instance (Ord a, Bounded a) => Monoid (Maximum a) where
    mempty = Maximum minBound
    mappend (Maximum x) (Maximum y) = Maximum (max x y)

It made sense in my specific use case, but I think Gabriel's version is
better as the general approach.

Michael
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