CSE 341 -- Scheme Mini-Exercises

1. Write a Scheme expression to compute 3*x+y+10. (Assume that the variables x and y are properly bound.)

2. What is the result of evaluating the following expressions?
   (car '(a b c))

   (cdr '(a b c))

   (car (cdr '(a b c)))

   (number? (cdr '(1 2)))

   (cons 1 ())

   (list 1 ())

3. Suppose we evaluate
   

   (define x 3)
   (define y 10)
   

   Then what is the result of evaluating
   (+ 3 x y)

   (list x y)

   (list 'x 'y)

   (and (= x 3) (> y 1))

   (and (= x 1) (= y (/ 1 0)))

4. Define a function to compute the cube of a number.

5. Joe Hacker states loudly that there is no reason or in Scheme needs to be special -- it can just be defined by the programmer, like this:

   (define (or x y)
     (if x #t y))
   

   Is Joe right?

6. Given the following definitions

   (define x 100)
   (define y 200)
   (define (test x)
      (frog x))
   (define (frog y)
      (+ x y))
   

   what is the result of evaluating
   (frog 10)

   (test 5)
   

7. Define a recursive function that takes a list of numbers and returns a list of their square roots. Thus (sqrts 1.0 2.0 4.0) should return (1.0 1.41421 2.0). (Hint: the answer to the question you were about to ask is sqrt.) What recursion pattern does this function use?

8. Define a function that takes a list of numbers (nested to any depth) and returns the sum of the numbers. In other words, the argument can be a number, a list of lists of lists of numbers, etc. Thus (sum '(1 (2) ((3 4)) 5)) should return 15. What recursion pattern does this function use?

9. Give a different (non-recursive) definition of the sqrts function using map.