#lang sicp

(define (stream-car stream) 
  (car stream))
(define (stream-cdr stream) 
  (force (cdr stream)))
(define (display-stream-first-n s n)
  (if (and (not (stream-null? s)) (> n 0))
    (begin 
      (display-line (stream-car s))
      (display-stream-first-n (stream-cdr s) (- n 1)))))
(define (display-line x)
  (newline)
  (display x))

(define (integers-starting-from n)
  (cons-stream 
   n (integers-starting-from (+ n 1))))
(define integers (integers-starting-from 1))
(define (stream-map proc . argstreams)
  (if (stream-null? (car argstreams))
      the-empty-stream
      (cons-stream
       (apply proc (map stream-car argstreams))
       (apply stream-map (cons proc (map stream-cdr argstreams))))))

(define (stream-filter pred stream)
  (cond ((stream-null? stream)
         the-empty-stream)
        ((pred (stream-car stream))
         (cons-stream
          (stream-car stream)
          (stream-filter
           pred
           (stream-cdr stream))))
        (else (stream-filter
               pred
               (stream-cdr stream)))))





(define (square x) (* x x))
(define (negate-series S) (stream-map - S))
(define (add-streams s1 s2)
  (stream-map + s1 s2))
(define (mul-streams s1 s2)
  (stream-map * s1 s2))
(define (scale-stream S m) 
  (stream-map (lambda (x) (* x m)) S))
(define (mul-series s1 s2)
  (add-streams 
    (scale-stream s2 (stream-car s1))
    (cons-stream 0 (mul-series (stream-cdr s1) s2))))
(define (partial-sums s)
  (cons-stream 0
    (add-streams s (partial-sums s))))

(define (stream-ref s n)
  (if (= n 0)
      (stream-car s)
      (stream-ref (stream-cdr s) (- n 1))))



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



(display-stream-first-n 
  (stream-filter (lambda (x) 
    (let ((a (car x))
          (b (cadr x))
          (c (caddr x)))
      (= (+ (square a) (square b)) (square c))))
  (triples integers integers integers)) 3)