In Scala, what does “extends (A => B)” on a case class mean?

Question

In researching how to do Memoization in Scala, I\'ve found some code I didn\'t grok. I\'ve tried to look this particular \"thing\" up, but don\'t know by what to call it; i.

Answer 1

This answer is a synthesis of the partial answers provided by both 0__ and Nicolas Rinaudo.

Summary:

There are many convenient (but also highly intertwined) assumptions being made by the Scala compiler.

1. Scala treats extends (A => B) as synonymous with extends Function1[A, B] (ScalaDoc for Function1[+T1, -R])
2. A concrete implementation of Function1's inherited abstract method apply(x: A): B must be provided; def apply(x: A): B = cache.getOrElseUpdate(x, f(x))
3. Scala assumes an implied match for the code block starting with = Memo {
4. Scala passes the content between {} started in item 3 as a parameter to the Memo case class constructor
5. Scala assumes an implied type between {} started in item 3 as PartialFunction[Int, BigInt] and the compiler uses the "match" code block as the override for the PartialFunction method's apply() and then provides an additional override for the PartialFunction's method isDefinedAt().

Details:

The first code block defining the case class Memo can be written more verbosely as such:

case class Memo[A,B](f: A => B) extends Function1[A, B] {    //replaced (A => B) with what it's translated to mean by the Scala compiler
  private val cache = mutable.Map.empty[A, B]
  def apply(x: A): B = cache.getOrElseUpdate(x, f(x))  //concrete implementation of unimplemented method defined in parent class, Function1
}

The second code block defining the val fibanocci can be written more verbosely as such:

lazy val fibonacci: Memo[Int, BigInt] = {
  Memo.apply(
    new PartialFunction[Int, BigInt] {
      override def apply(x: Int): BigInt = {
        x match {
          case 0 => 0
          case 1 => 1
          case n => fibonacci(n-1) + fibonacci(n-2)
        }
      }
      override def isDefinedAt(x: Int): Boolean = true
    }
  )
}

Had to add lazy to the second code block's val in order to deal with a self-referential problem in the line case n => fibonacci(n-1) + fibonacci(n-2).

And finally, an example usage of fibonacci is:

val x:BigInt = fibonacci(20) //returns 6765 (almost instantly)