CS 3520 Homework 1 - Due August 28

This homework is due August 28, 11:59 PM. Implement all of the requested functions in a single file, hw1.scm, and submit it with handin for hw1, e.g.:

   handin cs3520 hw1 hw1.scm

In the exercises below, underlined Scheme text corresponds to displayed values, and other Scheme text corresponds to evaluable expressions. Italics indicate meta-variables.

Exercise 1.1, Scheme warm-up

Implement the following functions (to be graded purely on input-output correctness):

square : takes a number x and returns x²

poly : takes a number x and returns 3x²+7x+42

xor : takes two booleans and returns their exclusive or

sign : takes a number and returns 1 if it's positive, -1 if it's negative, and 0 otherwise

sum-pair : takes a pair of numbers (x . y) and returns x+y

flip : takes a pair (x . y) and returns the pair (y . x) for any x and y.

pair->list : takes a pair (x . y) and returns the list (x y)

sym-in-pair? : takes a symbol and a pair and returns #t if either element of the pair is the given symbol, #f otherwise

two-elem-list? : takes an arbitrary value and returns #t if it is a list of two elements, #f otherwise; for example, the result should be #t for (1 hello), but #f for 7 or (1 . hello)

make-five-list : takes no arguments and returns a list of five elements: 1, 2, 3, 4, and 5

make-identity-list : takes no arguments and returns a list of three elements: lambda, a list containing only x, and x

Exercise 1.2, Expressions vs. displayed values

Which of the following equivalences are true?

1 = 1
'hello = 'hello
'hello = hello
''hello = 'hello
'(1 2 . 3) = (1 2 . 3)
(cons 1 2) = (1 . 2)
(list 1 2) = (1 . 2)
(cons 1 2) = (1 2)
(list 1 2) = (1 2)
(list 'lambda '() 10) = (lambda () 10)
(cons 'lambda (cons '() 10)) = (lambda () 10)
(cons 'lambda (cons '() (cons 10 '()))) = (lambda () 10)

Express your answer as a function answer-for-1.2 that takes no arguments and returns a list of twelve booleans. For example, if the first five equivalences are true and the last seven are false, your function should produce (#t #t #t #t #t #f #f #f #f #f #f #f).

Exercise 1.3, Scheme evaluation

On paper (not handed in), work out all the steps showing how the expression

(((lambda (x) (lambda (y) (- x y))) 2) 1)

reduces to 1.

Then, write a function step (to be handed in) that takes a number n from 0 to 3 and returns a Scheme value representing the nth step of the evaluation of the above expression. Examples:

(step 0) = (((lambda (x) (lambda (y) (- x y))) 2) 1)
(step 3) = 1

Of course, step is not an evaluator in any interesting sense; it merely reports the constant expressions that you worked out on paper.

Last update: Thursday, September 21st, 2000

mflatt@cs.utah.edu