sicp exercise 3.67

;; Exercise 3.67.  Modify the pairs procedure so that (pairs integers integers) will produce the stream of all pairs of integers (i,j) (without the condition i < j). Hint: You will need to mix in an additional stream.


(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))
    (interleave
     (stream-map (lambda(x)(list x (stream-car t)))
                 (stream-cdr s))
     (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 20)

;; Answer:
;Loading "sicp_prob_03.67.scm"...
;(1 1)
;(1 2)
;(2 1)
;(1 3)
;(2 2)
;(1 4)
;(3 1)
;(1 5)
;(2 3)
;(1 6)
;(4 1)
;(1 7)
;(3 2)
;(1 8)
;(5 1)
;(1 9)
;(2 4)
;(1 10)
;(6 1)
;(1 11)
;(3 3)
;... done