Computer Science 3675
Fall 1999
Programming Assignment 2

Due: Sep 22, 5:00pm. Revised due date: Oct. 6, 5:00pm.

The assignment

An 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 1101 (13 decimal) would be represented by the list [1,0,1,1]. Of course, list [1,0,1,1,0] also represents the same number. Leading zeros are ignored. The empty list is a representation of 0.

Your assignment is to write two functions, sum and product, that compute the sum and product of two binary numbers, each represented as a list. For example, sum([1,0,1], [0,0,1,1]) = [1,0,0,0,1] (since 5+12=17), and product([1,0,1], [0,1]) = [0,1,0,1] (since (5)(2) = 10).

Write the functions in an equational style in Astarte. Test your functions on at least the same numbers as in programming assignment 1.

Make your functions definitions simple and elegant. Include a comment for each explaining what it does (but not how it works). That is, give a contract for each function.

Keep track of your time, in just the same way as for programming assignment 1.

Hints

Do not start worrying about Astarte syntax until you have a set of equations that you believe are correct and complete, in the sense that every case is covered by at least one equation. When you think you have solid equational definitions, code them up.

Hint 1. Understanding lists as numbers

Think of a list as representing a number. Let N(L) be the number that list L represents. Then N(h::t) = h + 2*N(t). When inspecting equations, see if they make any sense when the lists are thought of as numbers. If you write A = B, then you should expect that N(A) = N(B). For example, one equation that you might write is 
      sum(0::a,0::b) = 0::sum(a,b)
Check this out, keeping in mind that sum(x,y) is supposed to be x+y. The equation says 
      (0 + 2*a) + (0 + 2*b) = (0 + 2*(a+b))
which is easily seen to be true.

Hint 2: inc

You will find some a helper function useful. Write a function inc(x) that adds one to x. That is, if x is a list that represents number n, then inc(x) is a list that represents number n+1. Think about the cases to handle.

  1. What is inc([])?
  2. What is inc(0::x)?
  3. What is inc(1::x)?
Check your answers.

Using Astarte

A manual is available for the Astarte programming language. Please look at that before writing and running your program. The most relevant pages for you are the following. Read only as much of each that appears to be useful. When you get into more esoteric looking material, try writing your program instead of just reading on.
  • Compiling and running programs
  • Note to new users
  • General lexical and syntactic issues
  • Example package
  • Functional programming
    • You might want to consult these.
  • Giving things names
  • Pattern matching
  • Lists
  • Defining functions

    • What to turn in

    Email me the source code of your program. Put it all in one file, including the test code, for simplicity. Send your program as an attachment, not in the body of the message. As a subject, use
    3675 Assn 2 your name
    Be sure to include your name in the program.

    The body of the email message should report your account of time spent, in hours. For example, 

               Learning language: 2.5 hr
           Development:       1 hr
           Debugging/testing: 1 hr
    Of course, the times shown here are only examples, and might not be representative of the times that you use.