[WIP] Revamp instances of Arbitrary for Numeric

[jedesah]

• Remove hardcoded Int
• Add instances for shapeless.Nat

[jedesah]

There is still a few things to add. In particular an extra property test, as it stands this will probably decrease coverage, but wanted to open the PR sooner rather than later in order to get feedback and avoid extra work.

[fthomas]

Thanks for the PR, @jedesah. I'll take a deeper look at it later today.

[fthomas]

If min > max greaterArbitraryRange[Refined, Long, Nat._10](min, max) probably doesn't produce any values which seems to be the cause of the failed Travis build.

[jedesah]

Yup, that seems like a reasonable hypothesis. Can probably add a precondition on the outer property.

[jedesah]

Tried that. The filter is still triggering scalacheck to abandon. I think there is a way to increase the ratio of discarded examples without triggering the property to abandon the "proof". Or is there a better way to encode information in the types?

[fthomas]

You could do a runtime check which of min and max is the smaller resp. greater value and then pass the smaller as first arg and the greater as second arg to greaterArbitraryRange.

[fthomas]

The Bounded type class is appealing but it currently doesn't give us an Arbitrary[BigInt Refined Positive], right? One way to "fix" this would be to add a low priority implicit Bound[T] from any nt: Numeric[T] with def maxValue = nt.fromInt(Int.MaxValue) and def minValue = nt.fromInt(Int.MinValue). What do you think?

[jedesah]

I think it might be better to provide a (low priority?) instance for BigInt which is Int.MaxValue or Long.MaxValue. I think it's dangerous to assume that an unknown numeric type will support Int.MaxValue. I would rather the user code get a compile error asking for an instance of the Bounded typeclass than a runtime error because nt.fromInt(Int.MaxValue) throws an exception.

Btw, what are the different types for which I need to create instances? Probably all the types in the standard library that have instances for Numeric?

[fthomas]

If I'm handed a nt: Numeric[T] I would never expect that nt.fromInt(x) throws an exception for any x. You would also not expect that Numeric[T].compare throws exceptions, right? But I'm also fine with just an instance for BigInt.

Yes, we should have instances for all types that have Numeric instances in the std lib. A list of these is http://www.scala-lang.org/api/current/index.html#scala.math.Numeric under "Known Subclasses".

[jedesah]

Ah, I assumed it would throw an exception, but I just tested it out with Short and it overflows, so Numeric[Short].fromInt(Int.MaxValue) == -1. But that does not seem a whole lot better. Arguably it's even worse than throwing an exception as it could fail in silent or hard to diagnose ways.

[fthomas]

I also just learned that fromInt is a cast in disguise. So adding a Bounded[BigInt] instance seems to be the better alternative.