sicp exercise 3.66

;; Exercise 3.66.  Examine the stream (pairs integers integers). Can you make any general comments about the order in which the pairs are placed into the stream? For example, about how many pairs precede the pair (1,100)? the pair (99,100)? the pair (100,100)? (If you can make precise mathematical statements here, all the better. But feel free to give more qualitative answers if you find yourself getting bogged down.)

(define (display-line str)
  (display str)
  (newline))

(define (display-stream str num)
  (define (internal index)
    (if (> index num) 'printed
        (begin
          (display-line (stream-ref str index))
          (internal (+ 1 index)))))
  (internal 0))


(define (interleave s1 s2)
  (if (stream-null? s1)
      s2
      (cons-stream (stream-car s1)
                   (interleave s2 (stream-cdr s1)))))

(define (pairs s t)
  (cons-stream
   (list (stream-car s) (stream-car t))
   (interleave
    (stream-map (lambda (x) (list (stream-car s) x))
                (stream-cdr t))
    (pairs (stream-cdr s) (stream-cdr t)))))

(define (integers-from-n n)
  (cons-stream n (integers-from-n (+ 1 n))))

(define integers (integers-from-n 1))

(define int-pairs (pairs integers integers))

(newline)

(display-stream int-pairs 10)

;; Felt bogged down, so ran the program to find the answer
;Loading "sicp_prob_03.66.scm"...
;(1 1)
;(1 2)
;(2 2)
;(1 3)
;(2 3)
;(1 4)
;(3 3)
;(1 5)
;(2 4)
;(1 6)
;(3 4)
;... done