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?

[kailuowang]

Ah for some reason I thought your upper and lower bound isn't order associated, now I have no idea how I got that impression. My bad.

[johnynek]

No problem. In thinking about this more, we probably want this to extend PartialOrder so it can represent the top and bottom of any Lattice, but then maybe indeed these are equivalent to bounded meet and bounded join semi lattices as @edmundnobel suggests.

[izeigerman]

Hi everyone. I've got the following implementation of Enum and Bounded type classes here: https://github.com/izeigerman/scalanum . Is there any chance for it to be included into Cats? Is it missing anything else beside the integration with PartialOrder?

[Michaelt293]

I like the idea of adding these type classes to Cats. Just a couple of ideas, I think the laws could be expressed as minValue <= a and maxValue >= a. The implementation provided by @izeigerman looks good. I just wonder whether using IndexededSeq in EnumIndex is the way to go since it would then be possible to provide an empty sequence to an instance. An exception would then be thrown when using head and tail to the get the min and max values.

[LukaJCB]

Hey @izeigerman are you still interested in getting included into Cats? I'm sorry no one ever got back to you, but I think this is definitely still on the table :)

[izeigerman]

@LukaJCB, yes, I still am! Will create a PR soon.

[LukaJCB]

Awesome, thank you!

[izeigerman]

@LukaJCB Quick question though: I'm having a hard time coming up with laws for Enum typeclass. It doesn't appear that it has any. What makes the matter even worse is that similarly to its Haskell's counterpart, Enum is expected to return a runtime error under certain condition. Can you suggest the best way to handle this in cats?
I was going to place *Bounded typeclasses into the kernel module, but I'm not that sure about Enum.

[LukaJCB]

I think we should start with adding *Bounded first and then discussing the specifics of Enum in the other ticket, #2342. :) If you need any help with setting up the laws and everything, please feel free to reach out in the cats-dev gitter channel!

[LukaJCB]

Closed by #2913