FunctionK in Scala 3

In the last section we saw the usage of FunctionK and Id in Cats when we were trying to implement rank N types in Scala 2.

But the actual use of FunctionK is like:

import cats.~>
def tupledOptionToList[B,C](a: (Option[B], Option[C]), fnk: Option ~> List): (List[B], List[C]) =
  (fnk(a._1), fnk(a._2))

Same reason as rank n types, normal function Option[A] => List[A] won't work since A should not be in the same rank with B and C.

So Option ~> List~ When F and G are Functor, FunctionK[F, G] is the natural transformation from F to G, noted F ~> G. hide the A type, means the function only map Kind to other Kind, and leave what ever type A not changed, which is also why is called FunctionK(K for Kind).

While in Scala 3, since we have Rank N Types, a.k.a Polymorphic function types, it is very easy to implement ~>.

Basically you don't even need to implement, just a type alias will do:

// kind: * -> *
// FunctionK: (* -> *) -> (* -> *)
type ~>[F[?],G[?]] = [A] => F[A] => G[A]

Use the ~> in infix position, then you get exactly what Cats FunctionK does:

object Main {
  // rank 2 type (forall a. Option a -> List a)
  val optionToList: Option ~> List = [A] => (a: Option[A]) => a.toList
  
  // forall b c. (Option b, Option c) -> (forall a. Option a -> List a) -> (List b, List c)
  def tupledOptionToList[B,C](a: (Option[B], Option[C]), fnk: Option ~> List): (List[B], List[C]) =
      (fnk(a._1), fnk(a._2))
  
  def main(args: Array[String]): Unit = {
    println(
      tupledOptionToList((Some(1), Some("2")), optionToList)
    )
  }
}

No Cats needed, even better, it's also much easier to define a functionK:

// Cats
val optionToList: Option ~> List = new (Option ~> List) {
  def apply(a: Option[A]): List[A] = a.toList
}
// Scala 3
val optionToList: Option ~> List = [A] => (a: Option[A]) => a.toList

Try the above examples online: https://scastie.scala-lang.org/jcouyang/W5jIXajVTU64g8KZe8V7Kw/9

Or clone and run it locally: https://github.com/jcouyang/meow