Slightly altered rendition of http://tel.github.io/2014/07/27/calkin-wilf-in-swift/

calkin-wilf-update

struct Tree<A> {
    let val: A
    let left: @autoclosure () -> Tree<A>
    let right: @autoclosure () -> Tree<A>
}

struct Stream<A> {
    let val: A
    let next: @autoclosure () -> Stream<A>
}

func calkin(n: Int, m: Int) -> Tree<(Int, Int)> {
    return Tree(
        val: (n, m),
        left: calkin(n+m, m),
        right: calkin(n, n+m)
    )
}

func interleave<A>(sa: Stream<A>, sb: Stream<A>) -> Stream<A> {
    return Stream(
        val: sa.val,
        next: Stream(
            val: sb.val,
            next: interleave(sa.next(), sb.next())
            )
    )
}

func traverse<A>(t: Tree<A>) -> Stream<A> {
    return Stream(
        val: t.val,
        next: interleave(traverse(t.left()), traverse(t.right()))
    )
}

let rats: Stream<(Int, Int)> = traverse(calkin(1,1))

func takeStream<A>(n: Int)(s: Stream<A>) -> [A] {
    var res: [A] = []
    var s = s
    for i in 0..<n {
        res += [s.val]
        s    = s.next()
    }
    return res
}

println(takeStream(10)(s: rats))