Scala Streams demo

	package streams
	import scala.util.Random
	/**
	* The class Stream implements lazy lists where elements are only evaluated when they are needed.
	* The Stream class also employs memoization such that previously computed values are converted
	* from Stream elements to concrete values of type A.
	*
	* So a Stream needs an initial object and a function to compute the rest of the objects
	*/
	object StreamDemo {
	/**
	* a stream of all positive integers
	*/
	def naturalnumbers: Stream[Int] = Stream.from(1)
	/**
	* A stream of factorials. There are multiple ways to compute this stream but I particularly like
	* this implementation as it maps another stream to the desired stream. Let this one sink in for a bit,
	* it took me more than 1 minute to come up with this solution :)
	*
	*/
	def factorials: Stream[Int] = 1 #:: Stream.from(2).map((x:Int) => x * factorials(x-2))
	/**
	factorials(0) returns first element which is 1 (not lazy evaluated)
	next starts our Stream.from(2) --> {value} which we map to x * factorials(x-2)
	The reason why it has to be factorials(x-2) is because our stream starts at 2 and factorials(2-2)
	returns the first factorial number.
	factorials(1) returns {2} * factorials(2-2) = {2} * 1 = 2
	factorials(2) returns {3} * factorials(3-2) = {3} * 2 = 6
	factorials(3) returns {4} * factorials(4-2) = {4} * 6 = 24
	**/
	sealed trait CoinFlip {
	val outcome: String
	override def toString = outcome
	}
	object Head extends { val outcome = "HEAD" } with CoinFlip
	object Tail extends { val outcome = "TAIL" } with CoinFlip
	val outcomes = List(Head, Tail)
	def flip: CoinFlip = Random.shuffle(outcomes).apply(0)
	def coinflips: Stream[CoinFlip] = flip #:: coinflips
	def main(args: Array[String]): Unit = {
	println(naturalnumbers.take(5).mkString("first 5 natural numbers: [", ",", "]"))
	println(factorials.take(5).mkString("first 5 factorial numbers: [", ",", "]"))
	println(coinflips.take(10).mkString("first 10 coinflips : [", ",", "]"))
	}
	/**
	* This will print:
	* first 5 natural numbers: [1,2,3,4,5]
	* first 5 factorial numbers: [1,2,6,24,120]
	* first 10 coinflips : [TAIL,TAIL,HEAD,TAIL,HEAD,TAIL,HEAD,TAIL,TAIL,TAIL]
	*/
	}

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