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Exercise solution:
A stream that converges to the square root a number

Here is a possible solution:

(define (improve-sqrt-guess guess x)
 (/ (+ guess (/ x guess)) 2))

(define (sqrt-stream x)
    (map-stream (lambda (g) (improve-sqrt-guess g x))
                (sqrt-stream x))))

; Below we reproduce some of the basic stream functions, on which sqrt-stream depends.

(define-syntax cons-stream
  (syntax-rules ()
    ((cons-stream x y)
     (cons x (delay y)))))

(define head car)

(define (tail stream) (force (cdr stream)))

(define empty-stream? null?)

(define the-empty-stream '())

(define (stream-section n stream)
  (cond ((= n 0) '())
        (else (cons (head stream)
                (- n 1)
               (tail stream))))))

(define (map-stream f stream)
  (cond ((empty-stream? stream) the-empty-stream)
        (else (cons-stream (f (head stream)) (map-stream f (tail stream))))))