Scala's Stream and StackOverflowError - scala

Question

Consider this code (taken from "Functional programming principles in Scala" course by Martin Odersky):
def sieve(s: Stream[Int]): Stream[Int] = {
s.head #:: sieve(s.tail.filter(_ % s.head != 0))
}
val primes = sieve(Stream.from(2))
primes.take(1000).toList
It works just fine. Notice that sieve is in fact NOT tail recursive (or is it?), even though Stream's tail is lazy.
But this code:
def sieve(n: Int): Stream[Int] = {
n #:: sieve(n + 1).filter(_ % n != 0)
}
val primes = sieve(2)
primes.take(1000).toList
throws StackOverflowError.
What is the problem with the second example? I guess filter messes things up, but I can't understand why. It returns a Stream, so it souldn't make evaluation eager (am I right?)

Answer 1

You can highlight the problem with a bit of tracking code:
var counter1, counter2 = 0
def sieve1(s: Stream[Int]): Stream[Int] = {
counter1 += 1
s.head #:: sieve1(s.tail.filter(_ % s.head != 0))
}
def sieve2(n: Int): Stream[Int] = {
counter2 += 1
n #:: sieve2(n + 1).filter(_ % n != 0)
}
sieve1(Stream.from(2)).take(100).toList
sieve2(2).take(100).toList
We can run this and check the counters:
scala> counter1
res2: Int = 100
scala> counter2
res3: Int = 540
So in the first case the depth of the call stack is the number of primes, and in the second it's the largest prime itself (well, minus one).

Answer 2

Neither one of these are tail recursive.
Using the tailrec annotation will tell you whether or not a function is tail recursive.
Adding #tailrec to the two functions above gives:
import scala.annotation.tailrec
#tailrec
def sieve(s: Stream[Int]): Stream[Int] = {
s.head #:: sieve(s.tail.filter(_ % s.head != 0))
}
#tailrec
def sieve(n: Int): Stream[Int] = {
n #:: sieve(n + 1).filter(_ % n != 0)
}
Loading this shows that both definitions are not tail recursive:
<console>:10: error: could not optimize #tailrec annotated method sieve: it contains a recursive call not in tail position
s.head #:: sieve(s.tail.filter(_ % s.head != 0))
^
<console>:10: error: could not optimize #tailrec annotated method sieve: it contains a recursive call not in tail position
n #:: sieve(n + 1).filter(_ % n != 0)