SICP 习题解答 1.10

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$5n^2$.

我的答案：

(A 1 10)  ; 1024
(A 2 4); 65536
(A 3 3); 65536

数学定义，归纳法

1 $f(n)=2n$

2 $g(n)=2^n$

3 $h(n)=2^{h(n-1)}$