Programming Languages -- Spring 1996

Homework One: Basic Scheme

Due Monday, January 15, at 9:00am

Write the function member-twice? that returns true if a particular atom appears at least twice in a list of atoms:

> (member-twice? (quote c) (quote (a b c d d b a)))
#f
> (member-twice? (quote b) (quote (a b c d d b a)))
#t

Write the function rember2 that takes an atom a and a list of atoms ls, and removes the second occurrence of a in ls.
```
> (rember2 (quote a) (quote (a b d a c)))
(a b d c)
> (rember2 (quote a) (quote (a b d c)))
(a b d c)
```
Write the function multtup that takes a list of numbers (a tuple) and multiplies all the numbers in the list together.
```
> (multtup (quote (3 2 4)))
24
> (multtup (quote (6 2 1)))
12
> (multtup (quote ()))
1
```
Write the function list-index that takes an atom a and a list ls, and returns the zero-based index of a in ls. If the atom a does not occur in ls, it should return -1. This is a difficult exercise.
```
> (list-index (quote a) (quote (b a c)))
1
> (list-index (quote d) (quote (b a c)))
-1
```
Write the function tree-mult that takes a possibly deep list of numbers and multiplies all the numbers together.
```
> (tree-mult (quote ((1 2) 3 (((4))))))
24
> (tree-mult (quote ((1) (2 3 4) 5 6)))
720
```
Write the function duplicate that takes a number n and an atom a and returns a list containing only n occurrences of a.
```
> (duplicate 3 'foo)
(foo foo foo)
> (duplicate 0 'foo)
()
```
Write the function compose2 that takes two unary functions f and g, and returns a unary function that is the composition of f and g.
```
> ((compose2 zero? sub1) 2)
#f
> ((compose2 zero? sub1) 1)
#t
```
Write the function assq that takes an atom a and an association list (a list of non-empty lists) als, and returns the first list in als whose car is a. If there are no lists in als whose car is a, assq returns #f.
```
> (assq 'g '((b c) (d f g) (g c 3) (f (g h))))
(g c 3)
> (assq 'g '((b c) (d f g) (f (g h))))
#f
```
Write the function list-ref that takes a number n and a list ls of length at least n+1, and returns the (zero-based) nth element in ls.
```
> (list-ref 3 '(a b c d e f))
d
> (list-ref 0 '(a b c d))
a
```
Write the function snoc that takes a list ls and a datum i, and returns a new list where i has been added to the end of ls.
```
> (snoc '(a b c) '(x y))
(a b c (x y))
> (snoc '() 'a)
(a)
```
Write the function intersection that takes two sets (lists of symbols without duplicates) s0 and s1, and returns a new set containing all elements that are in both s0 and s1.
```
> (intersection '(a b c) '(b c d))
(b c) or (c b)
> (intersection '(a b c) '(d e f))
()
```
Write the function count-parens that takes a possibly deep list ls and returns the number of parentheses in the printed representation of the list.
```
> (count-parens '((a b) (()) c))
8
> (count-parens '())
2
```
Write the function sum-of-squares that takes a tuple (list of numbers) tup and returns the sum of the squares of the numbers.
```
> (sum-of-squares '())
0
> (sum-of-squares '(3))
9
> (sum-of-squares '(3 4))
25
```

Submission

Write your answers to the exercises in a file (with comments, following the proper indentation rules), and send that file to

c311@lakshmi.cs.indiana.edu

with the subject line

01

Assuming you've saved your homework in the file ``one.ss'' in the current directory, one way to submit is with the command:

Mail -s "01" c311@lakshmi.cs.indiana.edu < one.ss

Back to the c311 page

ehilsdal@cs.indiana.edu

Sun Jan 7 23:32:49 EST 1996