sicp exercise 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.


; Answer:
;  (A 1 10)  => 1024
;  (A 2  4)  => 65536
;  (A 3  3)  => 65336

;  (define (f n) (A 0 n))    => computes 2n
;  (define (g n) (A 1 n))    => computes 2^n
;  (define (h n) (A 2 n))    => computes 2^2^2^2... n times
;  (define (k n) (* 5 n n))