(use-modules (srfi srfi-41))



(define base (stream-from 1))



(define (curry f)
    (lambda (x)
        (lambda (y)
            (f x y))))



(define-stream (stream-ordered-diff xstrm ystrm)
    (stream-match xstrm (() '()) ((x . xs)
        (stream-match ystrm (() xstrm) ((y . ys)
            (if (eq? x y)
                (stream-ordered-diff xs ys)
                (stream-cons x (stream-ordered-diff xs ystrm))))))))



(define-stream (stream-merge xstrm ystrm)
    (stream-match xstrm (() ystrm) ((x . xs)
        (stream-match ystrm (() xstrm) ((y . ys)
            (cond ((< x y) (stream-cons x (stream-merge xs ystrm)))
                  ((> x y) (stream-cons y (stream-merge xstrm ys)))
                  ((eq? x y) (stream-cons x (stream-merge xs ys)))))))))



(define (f i j)
    (+ i j (* 2 i j)))



(define-stream (i-stream i)
    (stream-map
        ((curry f) i)
        (stream-from i)))



(define ij-stream
    (stream-let loop ((n 1) (strm (i-stream 1)))
        (let* ((cutoff ((curry >) (stream-car (i-stream n))))
               (next (+ n 1))
               (available (stream-take-while cutoff strm))
               (remainder (stream-drop-while cutoff strm)))
            (stream-append available (loop next (stream-merge remainder (i-stream next)))))))



(define-stream (sieve input)
    (stream-map
        (lambda (x) (+ 1 (* 2 x)))
        (stream-ordered-diff input ij-stream)))



(define sundaram (stream-cons 2 (sieve base)))