Positive integers and non-empty collections

Positive integers and non-empty collections

Hi all. cats implements non-empty collections such as NonEmptyList. I think we might squeeze a little more out of the concept. Wouldn't it be nice to have a type PosInt (for positive integers) and define

def size[A](nel: NonEmptyList[A]): PosInt

Moreover, this would allow us to add safer alternatives to functions which accept Int and produce a List. E. g. replicateA

def replicateA[A](n: PosInt, fa: F[A]): F[NonEmptyList[A]]

The use case I had in mind

Imagine a user who wants to generate random values and estimate their mean. To that end the user defines

type Random[T] = State[Gen, T]
val random: Random[T] = ...
val gen: Gen = ...

def average[T](nel: NonEmptyList[T]) : T = nel.reduce / size(nel)

Here we implicitly assume T is a semigroup and also defines division operator def /(n: PosInt): T.

Now it would make sense to code

average(replicateA(PosInt(100) , random).runA(gen))

I'd appreciate hearing your thoughts.

The issue proposes a PosInt type and safer alternatives involving NonEmptyList, size, and replicateA, but names no files or tests. Start by reviewing those existing APIs and the surrounding Cats design; the work is done only after the proposed types and signatures have an agreed design and corresponding implementation and tests.