# CS 3520 Homework 1 - Due August 27

This homework is due August 27, 11:59 PM. Place all of the requested functions in a single file, `hw1.txt`, and submit it with `submit` for `hw1`, e.g.: submit 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:`f(x) = (x - x) (4 + f(5))`

` h(z) = (g(z) - z) g(y) = (y + 1) 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>`.`f(x) = x g(z) = y (1 - 1)`

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

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: Tuesday, August 27th, 2002mflatt@cs.utah.edu |