Computer Science 3675
Section 001
Fall 2006
Programming Assignment 2

Overview of assignment

For this assignment, you will write the inc, sum and product functions in a functional style instead of an imperative style. You should find them fairly short and simple.

Language

The language that you will use is Cinnameg. Chapters 15 and 16 give some examples written in Cinnameg, and Appendix A tells some more. There is also an overview and a manual available.

Cinnameg is not a purely functional language, and it allows you to use other styles. For this assignment, stay within the functional subset for writing the arithmetic functions. Do not use Relet. Do not use loops, or anything that changes something once you have already created it.

See the end of this page for more on how to write and run your program.

Representing integers

A nonnegative integer can be represented in binary as a list of zeros and ones. The most convenient way to do so is to put the least significant bit first. For example, the binary number 1101₂ (13 decimal) would be represented by the list [1,0,1,1].

Of course, list [1,0,1,1,0] also represents 13. Leading zeros in the standard representation (as in 01101) are ignored, and they become trailing zeros in the list representation. Say that a list is normalized if it does not end on 0. So [1,0,1,1] is normalized, but [1,0,1,1,0] is not. Note that list [0] is not normalized, but [] is.

The empty list is a representation of 0.

The assignment

Your assignment is to write functions inc, sum, and product that work on lists as representations of binary numbers.

1. inc(x) produces x + 1 (as a normalized list);

2. sum(x,y) produces x + y (as a normalized list);

3. product(x,y) produces the product x * y (as a normalized list)

For example inc([1,1,0,1,0,1]) = [0,0,1,1,0,1], and sum([1,1], [1,1]) = [0,1,1]. The result list of each function should be normalized even if the parameter lists are not. For example, inc([1,0,0,0]) = [0,1].

You can handle normalizion as follows. An example for inc should suffice. First, write an implementation of inc that does not worry about normalizing its result. You might call it inc_a, for example. Now define inc as follows.

   Define inc ?x = normalize(inc_a x).

More on writing and running the program

Write one package that defines and exports your definitions. Do not export the helper functions that do not normalize their results. See here for a skeleton of this module. Copy and paste this into a file called arithmetic.cmg.

Please include at least one example with each function. I have written inc for you. You will need to provide sum and product.

To test your functions, use a separate module. See here for a skeleton of a testing module. Add a few tests in addition to the examples in the implementation module.

You can use either a Windows or Unix implementation of Cinnameg.

Unix version in lab

To comple your packages in Unix, use the following commands (assuming your packages are called arithmetic.cmg and arithtest.cmg.)

   cmgc arithmetic
   cmgc arithest

   cmgr arithtest

Note. The compiler and interpreter are /usr/local/bin/cmgc and /usr/local/bin/cmgr. You need to be sure that /usr/local/bin is in your path.

Note. If you do not want to get a listing, use option -l (dash lower-case-ell). For example, use command

  cmgc -l arithmetic

Windows version

A Windows version is available here. That page contains instructions on how to install it. Read the instructions. See here for instructions on how to use the Windows implementation, once it is installed.

Submitting your work

When you are ready to turn in your work, use command

   ~karl/3675/bin/submit 2 arithmetic.cmg arithtest.cmg

Be sure to include your name in the program.