HW7: Scheme Tracing
Due: Monday 4/6/2009

You should do this by yourself. This is not a group project. If you want you can program these into the JScheme interpreter and see if your final answer is correct...

Trace the evolution of the following Scheme programs:

1. (+ (* 2 (+ 3 (* 4 5) 6) 7) 8)
   

2. (define (sq x) (* x x))
   (define (f L) (sqrt (+ (sq (first L)) (sq (second L)))))
   (f '(3 4))
   

3. (define (g L n)
     (if (null? L) n
         (if (even? (first L))
             (g (rest L) n)
             (g (rest L) (+ n (first L))))))
   (g '(1 2 3 4 5) 0)
   

4. (define (h x y z)
     (if (< x 1) z (h (- x 1) y (* y z))))
   (h 5 2 1)
   

5. (define (f x y) (if (= x 0) y (f (- x 1) (+ y 1))))
   (f 2 5)
   (f -2 7)
   

6. (define (p x y z)
     (if (= x 0) z
         (if (even? x) 
             (p (/ x 2) (* y y) z)
             (p (- x 1) y (* y z))
         )))
   (p 5 2 1)