SICP

Exercise 2.80. Define a generic predicate =zero? that tests if its argument is zero, and install it in the generic arithmetic package. This operation should work for ordinary numbers, rational numbers, and complex numbers.

要判断一个数是否是 0，那么在不同的 package，我们就可以分别判断相应类型的数字是否是 0：

scheme-number (lambda (x) (= 0 x))
rational (lambda (x) (= 0 (numer x)))
polar (lambda (x) (= 0 (real-part x)))
rectangular (lambda (x) (= 0 (real-part x)))
complex 已经有了 polar 与 rectangular 的判断，所以这里可以直接写为 (lambda (x) (=zero? x))

把以上操作放入相应的包内，并全局定义 =zero? 就可以。

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

借用这个 =zero? 的操作，我们可以定义练习 2.78的 equ?：

(define (equ? x y) (=zero? (sub x y)))

其余不需要变动。

下面是测试：


(load "../testframe.scm")

(asserttrue (=zero? 0))
(asserttrue (=zero? (sub (make-rational 1 12)
                         (make-rational 1 12))))
(asserttrue (=zero? (make-complex-from-mag-ang 0 12)))
(asserttrue (=zero? (make-complex-from-real-imag 0 0)))

(asserttrue (equ? '(scheme-number . 3) '(scheme-number . 3)))
(asserttrue (equ? 3 3))

(asserttrue (equ? (make-rational 12 20) (make-rational 3 5)))

(asserttrue (equ? (make-complex-from-mag-ang 3 4)
                  (make-complex-from-mag-ang 3 4)))

(asserttrue (equ? (make-complex-from-mag-ang 3 4)
                  (make-complex-from-mag-ang 3 4)))

(asserttrue (equ? (make-complex-from-real-imag 1 1)
                  (sub (make-complex-from-real-imag 2 3)
                       (make-complex-from-real-imag 1 2))))

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