Scheme (3)

By freeuniverser

Scheme is logical. Maybe this is the charm of functional language ~A program of Scheme:

 1 ;square root 2  3 ;Newton's method 4  5 (define (sqrt x) 6  7     (define (square n) (* n n)) 8  9     (define (average x y)10 11         (/ (+ x y) 2))12 13     ;guess the square root14 15     ;improve the guess-method16 17     (define (improve guess x)18 19         (average guess (/ x guess)))20 21     ;a predetermined tolerance(here is 0.001)22 23     (define (good-enough? guess x)24 25         (< (abs (- (square guess) x)) 0.001))26 27     ;a radicand and guess a value as square root28 29     (define (sqrt-iter guess x)30 31         (if(good-enough? guess x)32 33             guess34 35             (sqrt-iter (improve guess x)36 37                           x)))38 39     ;guess the square root of any number is 1.040 41     (sqrt-iter 1.0 x))42 43 ;Procedural decomposition of the sqrt program.