CS 3520 Homework 1 - Due August 27This 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.txtThe questions below refer to the language of algebra defined in class.
Exercise 1.1, EvaluationsShow a complete sequence of evaluation steps for the following programs:
- f(x) = (x - x) (4 + f(5))
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.
- h(z) = (g(z) - z) g(y) = (y + 1) h(17)
Exercise 1.2, Membership ProofsWhich 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)
Here's an example showing how to type a proof tree in a text file:
- f(x) = 1 f(1) g(x) = 2 g(2 + 2)
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.
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