(define (close-enough? v1 v2) (define tolerance 1.e-6) (< (/ (abs (- v1 v2)) v2) tolerance)) (define (iterative-improve improve close-enough?) (lambda (x) (let ((xim (improve x))) (if (close-enough? x xim) xim ((iterative-improve improve close-enough?) xim)) ))) ; (a) rewrite sqrt using iterative-improve (define (sqrt x) ((iterative-improve (lambda (y) (/ (+ (/ x y) y) 2)) close-enough?) 1.0)) ; (b) rewrite fixed-point using iterative-improve (define (fixed-point f first-guess) ((iterative-improve ; improve function is nothing but the ; function f whose fixed point is to be found! f close-enough?) first-guess))

<< Previous exercise (1.45) | Index | Next exercise (2.1) >>