This question isn't meant as flame-bait! As it might be apparent, I've been looking at Scalaz recently. I'm trying to understand why I need some of the functionality that the library provides. Here's something:

import scalaz._
import Scalaz._
type NEL[A] = NonEmptyList[A]
val NEL = NonEmptyList

I put some println statements in my functions to see what was going on (aside: what would I have done if I was trying to avoid side effects like that?). My functions are:

val f: NEL[Int] => String    = (l: NEL[Int]) => {println("f: " + l); l.toString |+| "X" }
val g: NEL[String] => BigInt = (l: NEL[String]) => {println("g: " + l);  BigInt(l.map(_.length).sum) }

Then I combine them via a cokleisli and pass in a NEL[Int]

val k = cokleisli(f) =>= cokleisli(g)
println("RES: "  + k( NEL(1, 2, 3) ))

What does this print?

f: NonEmptyList(1, 2, 3)
f: NonEmptyList(2, 3)
f: NonEmptyList(3)
g: NonEmptyList(NonEmptyList(1, 2, 3)X, NonEmptyList(2, 3)X, NonEmptyList(3)X)
RES: 57

The RES value is the character count of the (String) elements in the final NEL. Two things occur to me:

1. How could I have known that my NEL was going to be reduced in this manner from the method signatures involved? (I wasn't expecting the result at all)
2. What is the point of this? Can a reasonably simple and easy-to-follow use case be distilled for me?

This question is a thinly-veiled plea for some lovely person like retronym to explain how this powerful library actually works.