SICP 习题1.44 smooth

smooth函数

(define (smooth f)
(lambda (x)
(/ (+ (f (- x dx)) (f x) (f (+ x dx))) 3)))

(define dx 0.001)

(define (compose f g)
(lambda (x) (f (g x))))

(define (repeated f times)
(if (= times 1)
f
(compose f (repeated f (- times 1)))))

(define (n-smooth f n)
(lambda (x)
(((repeated smooth n) f) x)))

(define square
(lambda (x) (* x x)))

(newline)
(display ((n-smooth square 10) 5))