I want a convenient way to generate an Iterable, given a initial object and a function to produce the next object from the current one, that consumes O(1) memory (i.e., it doesn't cache old results; if you want to iterate a second time, the function has to be applied again).

It doesn't seem like there's library support for this. In Scala 2.8, the method scala.collection.Iterable.iterate has signature

def iterate [A] (start: A, len: Int)(f: (A) ⇒ A) : Iterable[A]

so it requires that you specify how many iterated function applications you're interested in ahead of time, and my understanding of the documentation is that Iterable.iterate actually computes all these values immediately. On the other hand, the method scala.collection.Iterator.iterate has signature

def iterate [T] (start: T)(f: (T) ⇒ T) : Iterator[T]

which looks great, but we only get an Iterator which doesn't offer all the convenience of map, filter and friends.

Is there a convenient library method to produce what I want?

and if not,

Can someone suggest the 'colloquial' Scala code for doing this?

To summarise, given an initial object a: A, and a function f: A => A, I'd like a TraversableLike (e.g., probably an Iterable) that generates a, f(a), f(f(a)), ..., and uses O(1) memory, with map, filter etc. functions that also return something that is O(1) in memory.

Iterator.iterate demo with filter:

object I {
  def main(args:Array[String]) {
    val mb = 1024 * 1024
    val gen = Iterator.iterate(new Array[Int](10 * mb)){arr =>
      val res = new Array[Int](10 * mb)
      arr.copyToArray(res)
      println("allocated 10mb")
      res(0) = arr(0) + 1 // store iteration count in first elem of new array
      res
    }
    // take 1 out of 100
    val gen2 = gen filter (arr => arr(0) % 100 == 0)
    // print first 10 filtered
    gen2.take(10).foreach { arr => println("filtered " + arr(0)) }
  }
}

(this may not work in the REPL as the PRINT step may mess up with memory management)

JAVA_OPTS="-Xmx128m" scala -cp classes I will show that the filtering works and is lazy. If it wasn't done in constant memory that would cause a heap error (since it's allocating something like 900*10mb).

Use JAVA_OPTS="-Xmx128m -verbose:gc" scala -cp classes I to see the garbage collection events.

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