Part1 Bulding Abstraction with Procedure

本类blog主要对SICP书中的程序进行说明。

#+STARTUP:** Example:Square Roots by Newton's Method#+BEGIN_SRC scheme#lang racket(define (sqrt-iter guess x)  (if (good-enough? guess x)      guess      (sqrt-iter (improve guess x)                 x)))(define (improve guess x)  (average guess (/ x guess)))(define (average x y)  (/ (+ x y) 2))(define (good-enough? guess x)  (< (abs (- (square guess) x)) 0.000001))(define (abs x)  (cond ((> x 0) x)        ((= x 0) 0)        ((< x 0) (- x))))(define (square x)  (* x x))(define (sqrt x)  (sqrt-iter 1 x))#+END_SRC** Procedures as Arguments#+BEGIN_SRC scheme#lang racket;;Page 60(define (sum term a next b)  (if (> a b)      0      (+ (term a)         (sum term (next a) next b))))(define (inc n) (+ n 1))(define (cube x) (* x x x))(define (sum-cubes a b)  (sum cube a inc b))(define (identity x) x)(define (sum-integers a b)  (sum identity a inc b))(define (integral f a b dx)  (define (add-dx x) (+ x dx))  (* (sum f (+ a (/ dx 2.0)) add-dx b)     dx))#+END_SRC** Finding roots of equations by the half-interval method#+BEGIN_SRC scheme#lang racket;;neg-point pos-point是指这个函数运行后的值是正还是负所对应的点(define (search f neg-point pos-point)  (let ((midpoint (average neg-point pos-point)))    (if (close-enough? neg-point pos-point)        midpoint        (let ((test-value (f midpoint)))          (cond ((> test-value 0)                 (search f neg-point midpoint))                ((< test-value 0)                 (search f midpoint pos-point))                (else midpoint))))))(define (average x y) (/ (+ x y) 2))(define (close-enough? x y)  (< (abs (- x y)) 0.001));;这里针对不同点位的情况进行了分类(define (half-interval-method f a b)  (let ((a-value (f a))        (b-value (f b)))    (cond ((and (< a-value 0) (> b-value 0))          (search f a b))          ((and (> a-value 0) (< b-value 0))           (search f b a))          (else           (error "Values are not of opposite sign" a b)))));;使用lambda表达式的好处就是用一个通用的表达式即可，而不需要反复不断的定义新的变量名字;;如果要使用新的(half-interval-method)过程，可以做如下的定义(half-interval-method (lambda (x) (- (* x x x) (* 2 x) 3)) 1.0 2.0)#+END_SRC

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