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.


今天中午午休的时候想了很久想不出来，后来看了下网上另一个人的解释，如下

(define (inc x y)
  (new-if (= x y)
          0
          (inc (+ x 1) y)))
(inc 1 5)

我开始的时候想的是，第一次是展开成

(new-if (= 1 5)
          0
          (inc 2 5))

然后这个expression的结果我想成了是(inc 2 5)，把new-if当成了if，按这样想下去，应该到(inc 5 5)的时候就该停止了，呵呵 其实是应该展开成上面的表达式后，会继续去eval ，(inc 2 5)，然后遇到new-if，在去(inc 3 5),最后就栈溢出了，看来还是脑子太久没转了，