Triples procedure
Write a procedure
triples
that takes three infinite streams,
S
,
T
, and
U
, and produces the stream of triples
(Si, Tj, Uk)
such that
i ≤ j ≤ k
. Use
triples
to generate the stream of all Pythagorean triples of positive integers, i.e., the triples
(i, j, k)
such that
i ≤ j
and
i² + j² = k²
.
(define (stream-car stream) (car stream))
(define (stream-cdr stream) (force (cdr stream)))
(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 (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 (stream-map proc . list-of-stream)
(if (null? (car list-of-stream))
'()
(cons-stream
(apply proc
(map (lambda (s)
(stream-car s))
list-of-stream))
(apply stream-map
(cons proc (map (lambda (s)
(stream-cdr s))
list-of-stream))))))
(define (add-streams s1 s2)
(stream-map + s1 s2))
(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 ones (cons-stream 1 ones))
(define integers (cons-stream 1 (add-streams ones integers)))
(define s (triples integers integers integers))
(check-equal? (stream-ref s 0) '(1 1 1))
(check-equal? (stream-ref s 1) '(1 1 2))
(check-equal? (stream-ref s 2) '(2 2 2))
(check-equal? (stream-ref s 3) '(1 1 3))
(check-equal? (stream-ref pythagorian-triples 0) '(3 4 5))
(check-equal? (stream-ref pythagorian-triples 1) '(6 8 10))