The ‘Min’ and ‘Max’ newtypes from ‘Data.Semigroup’ require a ‘Bounded’ constraint for their ‘Monoid’ instances, because they wrap a value of type ‘a’ rather than ‘Maybe a’. The latter is something I’ve needed a few times lately for types that cannot be bounded (or just don’t want to be), and it seems base-worthy to me. So if it hasn’t been proposed and dismissed already (or if it has been proposed, but just got backburnered), I’d like to suggest adding the following new types, and at least the following instances, to either ‘Data.Semigroup’ or ‘Data.Monoid’: newtype Minimum a = Minimum { getMinimum :: Maybe a } deriving (Eq, Ord, Monoid, Semigroup) via (Down (Maybe (Down (Max a)))) newtype Maximum a = Maximum { getMaximum :: Maybe a } deriving (Eq, Ord, Monoid, Semigroup) via (Maybe (Max a)) These instances could be specified explicitly instead of with ‘DerivingVia’, but the essential notion here is that ‘Maximum’ uses its empty value ‘Nothing’ as a “negative infinity”, less than all other ‘Just’ values, while ‘Minimum’ reverses that to use ‘Nothing’ as the corresponding “positive infinity”. I assume these would also want more or less the same array of instances as for the existing ‘Min’ and ‘Max’, and there is the usual opportunity to bikeshed about the naming and how these instances ought to relate to one another. I figure that at least the ‘Ord’ instance should match the ordering that the ‘Semigroup’ instance uses, to avoid some potential for confusion/bugs. As for use cases, I tend to reach for these things either in configuration records with many fields that I’m combining by semigroup append (Max, Any, set union, and so on) or when I have a possibly-empty container and don’t want to write e.g. ‘maximum (0 : xs)’ to avoid partiality. For example, ‘foldMap (Minimum . Just &&& Maximum . Just)’ computes the minimum and maximum in a single pass, returning Nothing for a null input. Any thoughts, critiques, questions, rebuttals, edge cases, use cases, &c. are most welcome!