Exam II, CS 257

I want American computers in space. Don't want Russian computers. Russian computers are like Russian booster rockets ... biggest in world.

- Georgy Grechko, former Soviet cosmonaut

1. What value is printed when you type each of the following to Scheme? (2 points each)

   expression	result
   (define (foo x) (if (= x 0) + *)) ((foo 2) 3 4)
   (and 'a 'b 'c)
   (or 'a 'b 'c)
   (if 'a 'b 'c)
   (define a '(1 2 3)) `(a ,a b ,@a c (,a) (d ,@a a))

2. Write a tail-recursive definition of add-nums, a function that takes a single argument, a list, a returns the sum of all the elements in the list that were numbers. The sum should not include numbers nested within sublists. Hint: use a helper function of two arguments (6 points for being tail recursive, 4 for being correct)

   Examples:

   (add-nums '())                    ; 0
   (add-nums '(a 1 b 2 c 3 d e))     ; 6
   (add-nums '((1) 2 (a 45 b) c 3))  ; 5
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

3. Rewrite the following pseudocode in Scheme, using procedure calls in place of goto and assignment. (10 points)

   foo(i,j)
   {
    L1:
     if (i < j) {
       j = j-i;
       goto L1;
     } else if (j < i) {
       i = i-j;
       goto L1;
     } else
       return i;
   }
   
   
   
   
   
   
   
   
   
   
   
   
   

4. Convert each expression into an equivalent backquote form. (2 points each)

   expression	equivalent using backquote
   (list 'this 'is 'example n 'of m)	`(this is example ,n of ,m)
   (append s1 '(followed by) s2)
   (cons 'foo (append s '(more)))
   (list 'joe (list 'the x) 'saw (car y))
   (cons 'a (car y))
   (append (list (+ a 3) (+ a 4)) '(and more))

5. Extra credit: Given these definitions

   (define (c-car x c) (c (car x)))
   
   (define (c-cdr x c) (c (cdr x)))
   
   (define (c-cons x lis c) (c (cons x lis)))
   
   (define (c-null? x c1 c2) (if (null? x) (c1) (c2)))
   
   (define (foo a b c)
     (c-null? a
   	   (lambda () (c b))
   	   (lambda ()
   	     (c-car a
   		    (lambda (caa)
   		      (c-cdr a
   			     (lambda (cda)
   			       (foo cda b
   				    (lambda (fcdab)
   				      (c-cons caa fcdab c))))))))))
   

   What does (foo '(x y z) '(p d q) (lambda (x) x)) return? (3 points + Scheme self actualization)