【SICP练习】102 练习2.79-2.80

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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