Is it possible to use continuations to make foldRight tail recursive?

Question

The following blog article shows how in F# foldBack can be made tail recursive using continuation passing style.

In Scala this would mean that:

Answer 1

Jon, n.m., thank you for your answers. Based on your comments I thought I'd give a try and use trampoline. A bit of research shows Scala has library support for trampolines in TailCalls. Here is what I came up with after a bit of fiddling around:

def foldContTC[T,U](list: List[T], acc: U)(f: (T, U) => U): U = {
  import scala.util.control.TailCalls._
  @annotation.tailrec
  def loop(l: List[T], k: (U) => TailRec[U]): TailRec[U] = {
    l match {
      case x :: xs => loop(xs, (racc => tailcall(k(f(x, racc)))))
      case Nil => k(acc)
    }
  }
  loop(list, u => done(u)).result
} 

I was interested to see how this compares to the solution without the trampoline as well as the default foldLeft and foldRight implementations. Here is the benchmark code and some results:

val size = 1000
val list = List.fill(size)(1)
val warm = 10
val n = 1000
bench("foldContTC", warm, lots(n, foldContTC(list, 0)(_ + _)))
bench("foldCont", warm, lots(n, foldCont(list, 0)(_ + _)))
bench("foldRight", warm, lots(n, list.foldRight(0)(_ + _)))
bench("foldLeft", warm, lots(n, list.foldLeft(0)(_ + _)))
bench("foldLeft.reverse", warm, lots(n, list.reverse.foldLeft(0)(_ + _)))

The timings are:

foldContTC: warming...
Elapsed: 0.094
foldCont: warming...
Elapsed: 0.060
foldRight: warming...
Elapsed: 0.160
foldLeft: warming...
Elapsed: 0.076
foldLeft.reverse: warming...
Elapsed: 0.155

Based on this, it would seem that trampolining is actually yielding pretty good performance. I suspect that the penalty on top of the boxing/unboxing is relatively not that bad.

Edit: as suggested by Jon's comments, here are the timings on 1M items which confirm that performance degrades with larger lists. Also I found out that library List.foldLeft implementation is not overriden, so I timed with the following foldLeft2:

def foldLeft2[T,U](list: List[T], acc: U)(f: (T, U) => U): U = {
  list match {
    case x :: xs => foldLeft2(xs, f(x, acc))(f)
    case Nil => acc
  }
} 

val size = 1000000
val list = List.fill(size)(1)
val warm = 10
val n = 2
bench("foldContTC", warm, lots(n, foldContTC(list, 0)(_ + _)))
bench("foldLeft", warm, lots(n, list.foldLeft(0)(_ + _)))
bench("foldLeft2", warm, lots(n, foldLeft2(list, 0)(_ + _)))
bench("foldLeft.reverse", warm, lots(n, list.reverse.foldLeft(0)(_ + _)))
bench("foldLeft2.reverse", warm, lots(n, foldLeft2(list.reverse, 0)(_ + _)))

yields:

foldContTC: warming...
Elapsed: 0.801
foldLeft: warming...
Elapsed: 0.156
foldLeft2: warming...
Elapsed: 0.054
foldLeft.reverse: warming...
Elapsed: 0.808
foldLeft2.reverse: warming...
Elapsed: 0.221

So foldLeft2.reverse is the winner...