CS 3520 Homework 1 - Due August 28

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

   handin cs3520 hw1 hw1.txt

The questions below refer to the language of algebra defined in class.

Exercise 1.1, Evaluations

Show a complete sequence of evaluation steps for the following programs:

(1 + (2 - 3))

f(x) = (x + x) f((4 + 5))

g(y) = (y - 1) h(z) = (z + g(z)) h(17)

A "complete sequence of evaluation steps" is a sequence of <prog> elements separated by ->, where the final element has a number expression after the definitions. You do not have to identify the rule used in each step, since it's obvious enough for now.

Exercise 1.2, Membership Proofs

Which of the following are programs? For each program, provide a proof tree showing that it is an element of <prog>.

(1 + 2)

1 + 2

f(x) = f(x) f(x)

f(x) = 1 (1 + 1) g(x) = 2 (2 + 2)

f(x) = 1 g(x) = 1 (1 - 1)

Here's an example showing how to type a proof tree in a text file:

                        n in <id>
                       -----------
p in <id>  n in <id>   n in <expr>
----------------------------------
      p(n) = n  in  <defn>

but your trees will alayws have something in <prog> at the bottom. Your answer doesn't have to be pretty, but it must be readable.

Last update: Thursday, August 23rd, 2001

mflatt@cs.utah.edu