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

To complete 0_'s answer, fibonacci is being instanciated through the apply method of Memo's companion object, generated automatically by the compiler since Memo is a case class.

This means that the following code is generated for you:

object Memo {
  def apply[A, B](f: A => B): Memo[A, B] = new Memo(f)
}

Scala has special handling for the apply method: its name needs not be typed when calling it. The two following calls are strictly equivalent:

Memo((a: Int) => a * 2)

Memo.apply((a: Int) => a * 2)

The case block is known as pattern matching. Under the hood, it generates a partial function - that is, a function that is defined for some of its input parameters, but not necessarily all of them. I'll not go in the details of partial functions as it's beside the point (this is a memo I wrote to myself on that topic, if you're keen), but what it essentially means here is that the case block is in fact an instance of PartialFunction.

If you follow that link, you'll see that PartialFunction extends Function1 - which is the expected argument of Memo.apply.

So what that bit of code actually means, once desugared (if that's a word), is:

lazy val fibonacci: Memo[Int, BigInt] = Memo.apply(new PartialFunction[Int, BigInt] {
  override def apply(v: Int): Int =
    if(v == 0)      0
    else if(v == 1) 1
    else            fibonacci(v - 1) + fibonacci(v - 2)

  override isDefinedAt(v: Int) = true
})

Note that I've vastly simplified the way the pattern matching is handled, but I thought that starting a discussion about unapply and unapplySeq would be off topic and confusing.