CS301 Problem Set 2

This assignment is worth 20 points

Your assignment is to do Exercises 8 in Ramsey & Kamin Chapter 2, and Exercise 1, 3, and 4(a) in Ramsey and Kamin, Chapter 3.

Requirements

Each programming exercise answer should be in a separate file named exn.scm where n is the exercise number. Where the exercise has several parts, separate them with comments. The uScheme interpreter is located at ~gexia/public/CS301/software/bin/uscheme.

Each of the procedures you define should be followed by test cases that are automatically executed when you enter, for example

(use ex1.scm)

Each test case, if successful, should print #t; if unsuccessful, it should print #f.

Each set of test cases must be preceded by a line of the form 'test-cases-for-count so that I can visually separate the tests.

You must supply a full set of test cases, even (especially!) if you weren't able to get the definition working to your satisfaction. "Full set" means test the "corner cases" (extremes of possible input values) as well as normal cases. For "possible" input values, carefully note the restrictions given in the textbook, as well as my comments below on the individual exercises.

Exercises 8 from Chapter 2 is a "paper exercise". You may hand it in on paper, or electronically, but in any case your solution must follow the notation used in the book for operational semantics - probably difficult to do if you don't use LaTeX.

Comments on the exercises

Note that the transcripts from the textbook (including definitions of the basic set operations) are all available in ~gexia/public/CS301/301-code/transcripts. This public directory also contains other helpful resources supplied by Norman Ramsey.

Now that you've seen let and lambda, for the best answer, see if you can make all your helper functions local.

• Exercise 8 in Chapter 2: explain your answer.
• Exercise 3: since the functions you're defining operate on sets, your test cases should not depend on the order of elements in the results. You may assume that set parameters really are lists that properly represent sets.
• Exercise 4: try to use as few appends as possible. You may assume that tree parameters really are lists that represent trees as described in the text. Note that the text doesn't explicitly say what happens when the "tree" is the empty list. Figure out what the examples in the text do, and proceed by analogy. For part (b) you may read ahead and use higher-order functions if you wish; otherwise you'll need mutual recursion and, for the best answer, letrec and lambda.