HW6: Tracing the evolution of programs

For this homework you are to trace through the evolution of the following Scheme programs. If the program would go into an infinite loop, then trace it for a while and then state that it loops.

• (define (c t) (+ 32 (/ (* t 9) 5)))
  (c 100)
  (c 37)
  

• (define (s x) (* x x))
  (define (t x y) (+ 1 (* x y)))
  (s (t 3 (s 2)))
  

• For the following, note that % is the remainder operator, so (% 53 7) is 4 and 53/7=7 with a remainder of 4.

  (define (hmmm a b)
    (if (= a 0) b
        (hmmm b (% a b))))
  (hmmm 42 150)
  

• (define (ahha x n p)
    (if (= n 0) p
        (ahha x (- n 1) (* x p))))
  (ahha 2 10 1)
  

• (define (f x y z)
    (if (= x 0) z
        (f (- x 1) y (* z y))))
  (f 8 2 1)
  (f -3 2 1)
  

Note: if your responses were given by a program that I had access to, I could easily create one of these problems that you could not solve by creating a problem that involved your code! As you are human, that trick does not apply!