Exercise 1.6 · 习题

Exercise 1.6: Alyssa P. Hacker doesn’t see why
if needs to be provided as a special form. “Why can’t I just define it
as an ordinary procedure in terms of cond?” she asks. Alyssa’s friend
Eva Lu Ator claims this can indeed be done, and she defines a new version of
if:

(define (new-if predicate
then-clause
else-clause)
(cond (predicate then-clause)
(else else-clause)))

Eva demonstrates the program for Alyssa:

(new-if (= 2 3) 0 5)
5

(new-if (= 1 1) 0 5)
0

Delighted, Alyssa uses new-if to rewrite the square-root program:

(define (sqrt-iter guess x)
(new-if (good-enough? guess x)
guess
(sqrt-iter (improve guess x) x)))

What happens when Alyssa attempts to use this to compute square roots?

Explain.

练习 1.6：Alyssa P. Hacker 不明白为什么 if 需要作为特殊形式提供。“为什么我不能直接用 cond 将它定义为一个普通的过程呢？”她问道。Alyssa 的朋友 Eva Lu Ator 声称这确实可以做到，并定义了一个新版本的 if：

(define (new-if predicate
then-clause
else-clause)
(cond (predicate then-clause)
(else else-clause)))

Eva 向 Alyssa 演示了这个程序：

(new-if (= 2 3) 0 5)
5

(new-if (= 1 1) 0 5)
0

受此鼓舞，Alyssa 用 new-if 重写了平方根程序：

(define (sqrt-iter guess x)
(new-if (good-enough? guess x)
guess
(sqrt-iter (improve guess x) x)))

当 Alyssa 试图用这个程序计算平方根时，会发生什么？请解释。