CSci 658: Software Language Engineering

Fall 2013
Assignment #1
Due 11:49 p.m., 19 September 2013
(Extended by 2 days)

Complete the following programming tasks by the due date. The program you develop should use functional programming techniques. That is, your program can create data structures and initialize them, but it should not change the values of the data structure once initialized.

1. Modify and extend one of the three functional implementations of the Arithmetic Expression Tree skeleton program on the Lecture Notes page in the following ways:

1. Add the following new kinds of nodes: Sub, Prod, and Div for subtraction, multiplication, and division of numbers, respectively; Neg for negating a value, and Sin and Cos for the sine and cosine trigonometric functions, respectively.
2. Extend functions eval, derive, and valToString to support these new node types. (For differentiation, you may want to look up the formulas in a Calculus textbook to remind yourself of the more complex rules.)
3. Add a new operation simplify that takes an expression tree (as extended in the previous tasks), simplifies it by "evaluating" all subexpressions involving only constants (not evaluating variables), and returns the new expression. For example, Add(Const(1),Const(3)) can be simplified to Const(4).
4. Challenge: Extend the simplifications in other ways. For example, you could take advantage of mathematical properties such as identity elements (x * 1 = x), zeros (x * 0 = 0), associativity ((x + y) + z = x + (y + z), and commutativity ( x + 1 = 1 + x).

2. Design appropriate tests for your program and test the program thoroughly.

3. Document your program appropriately.

4. Submit the source code and documentation for your program and test driver, any needed instructions on how to run the program, and appropriate test output to Blackboard. Also provide your instructor with a paper copy. Be sure to identify yourself in the materials turned in.

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