【SICP练习】102 练习2.79-2.80

最新推荐文章于 2019-02-02 03:32:20 发布

转载最新推荐文章于 2019-02-02 03:32:20 发布 · 125 阅读

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原文链接：https://my.oschina.net/nomasp/blog/503248

本文详细介绍如何在Scheme语言中实现数值的抽象处理，包括定义等值判断（equ?）和零值判断（=zero?）的通用操作，适用于常规数、有理数及复数。通过构造不同类型数值的包，展示如何利用apply-generic函数实现跨类型操作。

练习2-79

首先需要加载第125页的apply-generic函数，然后添加题中要求的通用型操作equ？。

(define (equ? x y) (apply-generic ‘equ? x y))

题目要求我们能够处理常规的数、有理数和复数。分别列出如下。

常规数：

(define (install-scheme-number-package) (define (tag x) (attach-tag 'scheme-number x)) (put 'make 'scheme-number (lambda (x) (tag x))) (put 'equ? '(scheme-number scheme-number) (lambda (x y) (= x y))) 'done)

(define (make-scheme-number n) ((get 'make 'scheme-number) n))

有理数：

define (install-rational-package)  
    (define (numer x)
        (car x))
    (define (denom x)
        (cdr x))
    (define (make-rat n d)
        (let ((g (gcd n d)))
            (cons (/ n g) (/ d g))))
    (define (tag x)
        (attach-tag 'rational x)) (put 'make 'rational (lambda (n d) (tag (make-rat n d)))) (put 'equ? '(rational rational) (lambda (x y) (and (= (numer x) (numer y)) (= (denom x) (denom y))))) 'done)

(define (make-rational n d)
    ((get 'make 'rational) n d))

复数：

(define (install-complex-package) (define (make-from-real-imag x y) ((get 'make-from-real-imag 'rectangular) x y)) (define (make-from-mag-ang r a) ((get 'make-from-mag-ang 'polar) r a)) (define (tag z) (attach-tag 'complex z)) (put 'make-from-real-imag 'complex (lambda (x y) (tag (make-from-real-imag x y)))) (put 'make-from-mag-ang 'complex (lambda (r a) (tag (make-from-mag-ang r a)))) (put 'equ? '(complex complex) (lambda (x y) (and (= (real-part x) (real-part y)) (= (imag-part x) (imag-part y))))) 'done)
(define (make-complex-from-real-imag x y) ((get 'make-from-real-imag 'complex) x y))
(define (make-complex-from-mag-ang r a) ((get 'make-from-mag-ang 'complex) r a))

练习2-80

和上一题一样，先加载第125页的apply-generic函数，然后添加题中要求的通用型操作=zero?。

(define (=zero? x) (apply-generic ‘=zero? x))

常规数：

(define (install-scheme-number-package) (define (tag x) (attach-tag 'scheme-number x)) (put 'make 'scheme-number (lambda (x) (tag x))) (put '=zero? '(scheme-number) (lambda (value) (= value 0))) 'done)
(define (make-scheme-number n) ((get 'make 'scheme-number) n))

有理数：

(define (install-rational-package) (define (numer x) (car x)) (define (denom x) (cdr x)) (define (make-rat n d) (let ((g (gcd n d))) (cons (/ n g) (/ d g)))) (define (tag x) (attach-tag 'rational x)) (put 'make 'rational (lambda (n d) (tag (make-rat n d)))) (put '=zero? '(rational) (lambda (r) (= 0 (numer r)))) 'done)
(define (make-rational n d) ((get 'make 'rational) n d))

复数：

(define (install-complex-package) (define (make-from-real-imag x y) ((get 'make-from-real-imag 'rectangular) x y)) (define (make-from-mag-ang r a) ((get 'make-from-mag-ang 'polar) r a)) (define (tag z) (attach-tag 'complex z)) (put 'make-from-real-imag 'complex (lambda (x y) (tag (make-from-real-imag x y)))) (put 'make-from-mag-ang 'complex (lambda (r a) (tag (make-from-mag-ang r a)))) (put '=zero? '(complex) (lambda (c) (and (= 0 (real-part c)) (= 0 (imag-part c))))) 'done)
(define (make-complex-from-real-imag x y) ((get 'make-from-real-imag 'complex) x y))
(define (make-complex-from-mag-ang r a) ((get 'make-from-mag-ang 'complex) r a))

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