Min & Max without Bounded

Oleg Grenrus oleg.grenrus at iki.fi
Tue Nov 10 21:57:25 UTC 2020

Aren't Min and Max sufficient by themselves:

>>> foldMap (Just . Min &&& Just . Max) [1..10 :: Integer]
(Just (Min {getMin = 1}),Just (Max {getMax = 10}))

- Oleg

On 10.11.2020 23.19, Jon Purdy wrote:
> 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!
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