Add Bounded typeclass

[julien-truffaut]

trait Bounded[A] extends Order[A]{
  def minValue: A
  def maxValue: A
}

such as min(a, minValue) == minValue and max(a, maxValue) == maxValue

[kevinmeredith]

Why must Bounded extend Order?

I don't believe that Haskell's Bounded imposes such a constraint:

iPrelude> :i Bounded
class Bounded a where
  minBound :: a
  maxBound :: a

[julien-truffaut]

It is correct but in this case Bounded will be lawless isn't it?

[kevinmeredith]

What laws must a Bounded instance obey?

reference - http://stackoverflow.com/questions/43029076/type-class-w-min/43029124?noredirect=1#comment73326210_43029124

[julien-truffaut]

@kevinmeredith see my first comment (such as ...)

[edmundnoble]

This seems to not be Bounded any more when you add those laws, but BoundedLattice (https://github.com/typelevel/algebra/blob/master/core/src/main/scala/algebra/lattice/BoundedLattice.scala) seeing as < and > can be implemented using meet/join and Eq.

[johnynek]

I'm not crazy about Bounded. Would prefer LowerBounded and UpperBounded. String, for instance is LowerBounded. NonNegative numbers are LowerBounded. There are some examples of only UpperBounded as well.

[julien-truffaut]

I agree with @johnynek it would be more useful to one typeclass for upper and another for lower bound. Here is an example https://github.com/julien-truffaut/newts/blob/master/core/shared/src/main/scala/newts/Min.scala#L35

[kailuowang]

For lawless typeclasses, we might also want to consider adding them to alleycats instead, especially if they are not that "core" and we still intend to keep cats.core lean.

[johnynek]

I don't see how his is lawless when it has an associated Ordering. So, they could extend Order and everything is fine, no?

[kailuowang]

@johnynek I didn't make it clear. I was referring to LowerBounded and UpperBounded.

[johnynek]

trait LowerBounded[A] extends Order[A] {
  // law: compare(minValue, a) <= 0 for all a
  def minValue: A
}

I'm probably missing it, but how is that lawless? Maybe I'm missing context?