# Write a procedure stream-limit that finds

From SICP:

Exercise 3.64. Write a procedure stream-limit that takes as arguments a stream and a number (the tolerance). It should examine the stream until it finds two successive elements that differ in absolute value by less than the tolerance, and return the second of the two elements. Using this, we could compute square roots up to a given tolerance by

(define (sqrt x tolerance)
(stream-limit (sqrt-stream x) tolerance))


I wrote this answer:

(define (stream-limit s tol)
(if (stream-null? s)
(error "End of stream found before limit reached:" tol)
(let* ((a (stream-car s))
(b (stream-car (stream-cdr s)))
(diff (abs (- a b))))
(if (> tol diff) b (stream-limit (stream-cdr s) tol)))))


Can it be improved?

Looks fine to me. I would only suggest changing (> tol diff) to (< diff tol) because it reads more like the problem specification and is easier to understand.
• Why do you use let* here? Isn't let enough?
• You could define stream-cadr.
• The initializer for diff uses the values of a and b. Since let doesn't create the variable bindings until after evaluating all of the initializer expressions, it won't work here. Commented Dec 4, 2012 at 23:44