Recursive Streams in Scala

RecursiveStreams.scala

import scala.math.{BigInt, BigDecimal}

object RecursiveStreams
{
  // natural numbers
  lazy val N: Stream[BigInt] = Stream.cons(BigInt(1), N.map(_ + 1))

  // fibonacci series
  lazy val fib: Stream[BigInt] = Stream.cons(BigInt(0), Stream.cons(BigInt(1), fib.zip(fib.tail).map(a => a._1 + a._2)))

  // factorials
  lazy val fac: Stream[BigInt] = Stream.cons(BigInt(1), fac.zip(N).map(a => a._1 * a._2))

  // pi / 4 
  lazy val piOver4: Stream[Double] = Stream.cons(1d, N.map(a => (1 - (a.toDouble % 2) * 2) / (2 * a.toDouble + 1)))

  def estimatePi(n: Int): Double = piOver4.take(n).sum * 4

  def main(args: Array[String]) {
    assert(N(0) == 1)
    assert(fib(0) == 0)
    assert(fac(0) == 1)

    assert(fib(5) == 5)
    assert(fac(5) == 120)

    println("First 10 natural numbers: %s".format(N.take(10).mkString(" ")))
    println("First 10 fibonacci numbers: %s".format(fib.take(10).mkString(" ")))
    println("First 10 factorials: %s".format(fac.take(10).mkString(" ")))

    println("Pi estimate: %s".format(estimatePi(5000)))
  }
}