CS 331 Spring 2013
Assignment 6

Assignment 6 is due at 5 p.m. Tuesday, May 7. It is worth 20 points.

Procedures

E-mail answers to the exercises below to ggchappell@alaska.edu, using the subject “PA6”.

• Your answers should consist of two files: ex6a.scm, from Exercise A, and ex6b.fs, from Exercise B. These files (or an archive file containing them) should be attached to your e-mail message.
• Be sure to include your name in your e-mail.
• I may not read your homework e-mail immediately. If you wish to discuss the assignment (or anything else) with me, send me a separate message with a different subject line.

Exercises (20 pts total)

Exercise A — Basic Scheme

Purpose

In this exercise, you will write some simple Scheme functions involving lists.

Instructions

Write Scheme code meeting the requirements outlined below. Place all of this in the file ex6a.scm.

The file should define the following.

• Procedure lastitem. This should take a single argument, a list, and return its last item.
  • Here is a sample DrRacket session that uses lastitem.

    [Interactive Scheme]

    > (lastitem '(1 8 2 5 1 6 3))
    3
    > (lastitem '((1 2) 3 (4 5)))
    (4 5)
    > (lastitem '(1))
    1

  • Procedure lastitem may produce an error message if it is given an empty list or an argument that is not a list. (It will probably do this anyway. In other words, you do not need to worry about what lastitem does if it is given something that does not have a last item.)
  • You may not use the standard Scheme function last.
• Procedure evens. This should take a single argument, a list, and return a list containing items 0, 2, 4, etc.
  • Here is a DrRacket session that uses evens.

    [Interactive Scheme]

    > (evens '(1 9 2 4 6 3 8))
    (1 2 6 8)
    > (evens '(2 3))
    (2)
    > (evens '(4))
    (4)
    > (evens '())
    ()
    > (evens '((1 2) (3 4) (5 6) (7 8)))
    ((1 2) (5 6))

  • Procedure evens may produce an error message if it is given an argument that is not a list. It should handle the empty list as above, however.

Other Requirements & Notes

• Your file must be properly commented, with filename, author, date, and purpose, as usual.
• You may define any other symbols you wish.
• Your functions do not need to do any type checking.
• If you use DrRacket, then a line reading “#lang scheme” will be added to your file. You do not need to remove this line (in fact, I would prefer that you leave it in).
• There will be no test program posted. Test your code!

Exercise B — Basic Forth

Purpose

In this exercise, you will write code for a simple Forth word.

Instructions

Write ANSI Forth code meeting the requirements outlined below. Place all of this in the file ex6b.fs.

The file should define the following.

• Word collcount. This should take a single argument, a number, and return a number. If we call the argument \(n\), then the return value should tell how many applications of the Collatz function (see Assignment 4 for details) are required to take \(n\) to \(1\).
  • Here is a sample gForth session that uses collcount.

    [Interactive Forth]

    1 collcount . 0  ok
    2 collcount . 1  ok
    3 collcount . 7  ok
    4 collcount 5 collcount 6 collcount  ok
    .s <3> 2 5 8  ok
    

Other Requirements & Notes

• Your file must be properly commented, with filename, author, date, and purpose, as usual.
• You may define any other words you wish.
• There will be no test program posted. Test your code!