Say I have a map with measurable objects, and I'd like the maximum of their widths, defaulting to 0. The machinery of Foldable (foldMap) and Semigroup (Max) seems perfect, except that I can't seem to introduce the arbitrary lower bound.
data Thing
width :: Thing -> Double
maxWidth :: Map k Thing -> Double
maxWidth things = getMax . foldMap (Max . width) $ things
This rightly complains about the missing Bounded instance for Double, since the Monoid instance of Max a uses mempty = minBound.
I see that the source for Data.Foldable uses a different definition of newtype Max to implement maximum. That variant would do nicely, but it seems to not be exported:
maxWidth things = fromMaybe 0 . getMax . foldMap (Max . Just . width) $ things
You can use the Option monoid to get a monoid instance for any Semigroup. Option a is just a newtype wrapper over Maybe a, but it's Monoid instance only requires Semigroup a rather than Monoid a. So we can use it with Max:
maximumMaybe :: (Ord a, Foldable t) => t a -> Maybe a
maximumMaybe = fmap getMax . getOption . foldMap (Option . Just . Max)
If you want a default value for the empty list case, you can use fromMaybe:
maximumWithDefault :: (Ord a, Foldable t) => a -> t a -> a
maximumWithDefault d = fromMaybe d . maximumMaybe
Another option is to just use maximumMay :: (Ord a, Foldable t) => t a -> Maybe a from the safe package.
If you are using base-4.11.0 or higher, you no longer need the Option a type since the restriction on Monoid (Maybe a) has been lifted to Semigroup a. So as of base-4.11.0, which came with GHC 8.4.1, you can write:
maximumMaybe :: (Ord a, Foldable t) => t a -> Maybe a
maximumMaybe = fmap getMax . foldMap (Just . Max)