Scala Language Streams Infinite Streams via Recursion
Example
Streams can be built that reference themselves and thus become infinitely recursive.
// factorial
val fact: Stream[BigInt] = 1 #:: fact.zipWithIndex.map{case (p,x)=>p*(x+1)}
fact.take(10) // (1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880)
fact(24) // 620448401733239439360000
// the Fibonacci series
val fib: Stream[BigInt] = 0 #:: fib.scan(1:BigInt)(_+_)
fib.take(10) // (0, 1, 1, 2, 3, 5, 8, 13, 21, 34)
fib(124) // 36726740705505779255899443
// random Ints between 10 and 99 (inclusive)
def rndInt: Stream[Int] = (util.Random.nextInt(90)+10) #:: rndInt
rndInt.take(10) // (20, 95, 14, 44, 42, 78, 85, 24, 99, 85)
In this context the difference between Var, Val, and Def is interesting. As a def each element is recalculated every time it is referenced. As a val each element is retained and reused after it's been calculated. This can be demonstrated by creating a side-effect with each calculation.
// def with extra output per calculation
def fact: Stream[Int] = 1 #:: fact.zipWithIndex.map{case (p,x)=>print("!");p*(x+1)}
fact(5) // !!!!!!!!!!!!!!! 120
fact(4) // !!!!!!!!!! 24
fact(7) // !!!!!!!!!!!!!!!!!!!!!!!!!!!! 5040
// now as val
val fact: Stream[Int] = 1 #:: fact.zipWithIndex.map{case (p,x)=>print("!");p*(x+1)}
fact(5) // !!!!! 120
fact(4) // 24
fact(7) // !! 5040
This also explains why the random number Stream doesn't work as a val.
val rndInt: Stream[Int] = (util.Random.nextInt(90)+10) #:: rndInt
rndInt.take(5) // (79, 79, 79, 79, 79)
