0704.315 Programming Languages

Due Date

Section 1: Wednesday Sept 19, 18:30

Section 2: Wednesday Sept 19, 12:30

Form of Submission

Homework can submitted via email or printout by deadline.

Assignment

1. What is the difference between the Scheme values '(1 2) and '(1 . 2)?
   [3 pts]
   
   

   The former is a list (a linked list of two pairs), the latter is a (single) pair.

2. From The Schemer's Guide, Question 1 in Problem Set 2 (p.55)
   [1 pt each]
   
   
   1. '((Mozart) Sibelius)
   2. #f
   3. '((Offenbach Bach Weber Strauss) Weber)
   4. '(())
   5. #f
   6. #t
   7. #f
   8. '(Offenbach . Weber)
   9. '((Bach))
   10. '((Percy Grainger) Offenbach Bach Weber Strauss)
   11. 'Weber
   12. '((Weber) Strauss)

3. Write a function list-length, that returns the number of elements in a given list. So:

   	(list-length '(eeny meeny miney mo)) --> 4
           (list-length '())                    --> 0   
   	

   [5 pts]

     (define (list-length li)
       (if (null? li)
   	0
   	(+ 1 (list-length (rest li)))))
        
   

4. Write a function list-append, that takes two lists as arguments, and returns the result of appending the latter to the end of the former. So:

   	(list-append '(mary had a little lamb) '(her fleece was white as snow))
              -> '(mary had a little lamb her fleece was white as snow)
           (list-append '() '(eeny meeny miney mo))
              -> '(eeny meeny miney mo)
           (list-append '(eeny meeny miney mo) '())
              -> '(eeny meeny miney mo)
           (list-append '() '())
              -> '()
   	

   [5 pts]

     (define (list-append a b)
       (if (null? a)
   	b
   	(cons (first a) (list-append (rest a) b))))
        
   

5. Write a function nth, that takes two arguments, an integer (n) and a list, and returns the nth element from the list. If n is larger than the length of the list, return null (the empty list). If n is less than 1, return null. So:

   	(nth 2 '(eeny meeny miney mo)) --> 'meeny
   	(nth 4 '(eeny meeny miney mo)) --> 'mo
   	(nth 5 '(eeny meeny miney mo)) --> '()
   	(nth 0 '(eeny meeny miney mo)) --> '()
   	

   [5 pts]

     (define (nth n li)
       (cond ((null? li) '())
   	  ((< n 1) '())
   	  ((= n 1) (first li))
   	  (else (nth (- n 1) (rest li)))))
        
   

6. Write a function marry, that takes two lists of equal length as arguments, and returns a list of pairs of the first elements, the second elements, etc. Don't worry about the case when the arguments are of unequal length. So:

           (marry '(a b c) '(1 2 3))  --> '((a . 1) (b . 2) (c . 3))
           (marry '() '())  --> '()
   	

   [5 pts]

     (define (marry li1 li2)
       (if (null? li1)
   	'()
   	(cons (cons (first li1) (first li2))
   	      (marry (rest li1) (rest li2)))))
   
   

7. Write a function reverse-list, that takes a list as argument and returns a list of the same elements in reverse order. So:

           (reverse-list '(a b c d)) --> '(d c b a)
           (reverse-list '() '())  --> '()
   	

   Hint: You may need to write a "helper function" for reverse-list to call.
   [5 pts]

     (define (list-reverse li)
       (reverse-helper li '()))
        
     (define (reverse-helper li result)
       (if (null? li)
   	result
   	(reverse-helper (rest li) (cons (first li) result))))