Exercise 1.10 · 习题

Exercise 1.10: The following procedure computes
a mathematical function called Ackermann’s function.

(define (A x y)
(cond ((= y 0) 0)
((= x 0) (* 2 y))
((= y 1) 2)
(else (A (- x 1)
(A x (- y 1))))))

What are the values of the following expressions?

(A 1 10)
(A 2 4)
(A 3 3)

Consider the following procedures, where A is the procedure
defined above:

(define (f n) (A 0 n))
(define (g n) (A 1 n))
(define (h n) (A 2 n))
(define (k n) (* 5 n n))

Give concise mathematical definitions for the functions computed by the
procedures f, g, and h for positive integer values of
n. For example, (k n) computes 5

n

2.

练习 1.10：下面的过程计算一个称为 Ackermann 函数的数学函数。

(define (A x y)
(cond ((= y 0) 0)
((= x 0) (* 2 y))
((= y 1) 2)
(else (A (- x 1)
(A x (- y 1))))))

下面各表达式的值分别是什么？

(A 1 10)
(A 2 4)
(A 3 3)

考虑下面几个过程，其中 A 就是上面定义的过程：

(define (f n) (A 0 n))
(define (g n) (A 1 n))
(define (h n) (A 2 n))
(define (k n) (* 5 n n))

对正整数 n，给出过程 f、g 和 h 所计算函数的简洁数学定义。例如，(k n) 计算的是 5n²。