# Re: Make-rational-number-generator

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On Mon, Feb 16, 2015 at 11:29 AM, John Cowan wrote:

Yes, that's the Stern-Brocot tree discussed in the same paper.  The trouble
is that you need to keep around more (indeed, increasingly more) state.
Here's the Haskell version from the paper:

rats :: [Rational]
rats = concat (unfolds infill [(0,1),(1,0)])
unfolds f a = let (b,a') = f a in b : unfolds f a0
infill xs = (map mkRat ys,interleave xs ys)
where ys = zipWith adj xs (tail xs)
interleave (x : xs) ys = x : interleave ys xs
interleave [] [] = []

The implementation I was envisioning only needs small constant space.
The proof is also simpler: completeness is trivial because we order over
all i/j, and uniqueness is guaranteed by skipping non-reduced forms.

(define (make-rational-number-generator)
(let ((diag 1)
(i 0))
(define (next!)
(cond ((<= (+ i 1) diag)
(set! i (+ i 1)))
(else
(set! diag (+ diag 1))
(set! i 1))))
(lambda ()
(let lp ()
(next!)
(let ((res (/ i (+ 1 (- diag i)))))
(if (= i (numerator res))
res
(lp)))))))

--
Alex