Exercise 1.9

 

Exercise 1.9 写道

Exercise 1.9. Each of the following two procedures defines a method for adding two positive integers in
terms of the procedures inc, which increments its argument by 1, and dec, which decrements its
argument by 1

 

(define (+ a b)
  (if (= a 0)
      b
    (inc (+ (dec a) b))))
(define (+ a b)
  (if (= a 0)
      b
    (+ (dec a) (inc b))))

 

写道

Using the substitution model, illustrate the process generated by each procedure in evaluating (+ 4 5).
Are these processes iterative or recursive?

 

这两个函数，分别使用两个用于自增(inc)和自减(dec)变量的方法组成，使用substitution model来展开它们计算(+ 4 5)的过程，并且指出他们的过程是迭代还是递归。

 

严格的按照过程展开即可

第一个：

(+ 4 5)
(inc (+ (dec 4) 5))
(inc (+ 3 5))
(inc (inc (+ (dec 3) 5)))
(inc (inc (+ 2 5)))
(inc (inc (inc (+ 1 5))))
(inc (inc (inc (inc (+ 0 5)))))
(inc (inc (inc (inc 5))))
(inc (inc (inc 6)))
(inc (inc 7))
(inc 8)
9

 这个是一个递归过程

 

第二个方法：

 

(define (+ a b)
  (if (= a 0)
      b
    (+ (dec a) (inc b))))
(+ 4 5)
(+ 3 6)
(+ 2 7)
(+ 1 8)
(+ 0 9)
9

 这个显然是迭代。