How do I write recursive anonymous functions?

In my continued effort to learn scala, I'm working through 'Scala by example' by Odersky and on the chapter on first class functions, the section on anonymous function avoids a situation of recursive anonymous function. I have a solution that seems to work. I'm curious if there is a better answer out there.

From the pdf: Code to showcase hig开发者_如何学运维her order functions

def sum(f: Int => Int, a: Int, b: Int): Int =
  if (a > b) 0 else f(a) + sum(f, a + 1, b)

def id(x: Int): Int = x
def square(x: Int): Int = x * x
def powerOfTwo(x: Int): Int = if (x == 0) 1 else 2 * powerOfTwo(x-1)

def sumInts(a: Int, b: Int): Int = sum(id, a, b)
def sumSquares(a: Int, b: Int): Int = sum(square, a, b)
def sumPowersOfTwo(a: Int, b: Int): Int = sum(powerOfTwo, a, b)

scala> sumPowersOfTwo(2,3)
res0: Int = 12

from the pdf: Code to showcase anonymous functions

def sum(f: Int => Int, a: Int, b: Int): Int =
  if (a > b) 0 else f(a) + sum(f, a + 1, b)

def sumInts(a: Int, b: Int): Int = sum((x: Int) => x, a, b)
def sumSquares(a: Int, b: Int): Int = sum((x: Int) => x * x, a, b)
// no sumPowersOfTwo

My code:

def sumPowersOfTwo(a: Int, b: Int): Int = sum((x: Int) => {
   def f(y:Int):Int = if (y==0) 1 else 2 * f(y-1); f(x) }, a, b)

scala> sumPowersOfTwo(2,3)
res0: Int = 12

---

For what it's worth... (the title and "real question" don't quite agree)

Recursive anonymous function-objects can be created through the "long hand" extending of FunctionN and then using this(...) inside apply.

(new Function1[Int,Unit] {
  def apply(x: Int) {
    println("" + x)
    if (x > 1) this(x - 1)
  }
})(10)

However, the amount of icky-ness this generally introduces makes the approach generally less than ideal. Best just use a "name" and have some more descriptive, modular code -- not that the following is a very good argument for such ;-)

val printingCounter: (Int) => Unit = (x: Int) => {
    println("" + x)
    if (x > 1) printingCounter(x - 1)
}
printingCounter(10)

Happy coding.

---

You can generalize this indirect recursion to:

case class Rec[I, O](fn : (I => O, I) => O) extends (I => O) {
  def apply(v : I) = fn(this, v)
}

Now sum can be written using indirect recursion as:

val sum = Rec[Int, Int]((f, v) => if (v == 0) 0 else v + f(v - 1))

The same solution can be used to implement memoization for example.