Skim Chapter 3 and read Chapter 4 in Scott. Do all of the exercises marked "Check Your Understanding" in a social setting with classmates or friends, but do not turn these in.

Submit solutions on paper for all but the Hana code, but make sure everything is in your CVS repository. You'll have at least

    /homework/cmsi488/hw2.tex
    /homework/cmsi488/scratch/src/main/javacc/Polynomial.jj
    /homework/cmsi488/scratch/src/test/java/edu/lmu/cs/your-id/PolynomialTest.java
    /homework/cmsi488/hana/

1. Write a grammar (using the notation introduced in this class) that is amenable to LL(1) parsing for polynomials whose sole variable is x and for which all coefficients are integers, and all exponents are non-negative integers. The following strings must be accepted.
   • 2x
   • 2x^3+7x+5
   • 3x^8 - x + x^2
   • 3 x - x ^ 3 +2
   • -9x ^ 5 - 0 + 4x^100
   • -3x^1 + 8 x ^ 0
2. Write a command-line application, using JavaCC, that evaluates polynomials from the language you defined above. The first argument should be the polynomial and the second is the value at which to evaluate the polynomial. Here are some example runs:

   $ eval "2x" 10
       20.000000
   $ eval "2x^3+7x+5" 2
       35.000000
   $ eval "3x^8-x+x^2" 1
       3.000000
   $ eval " 3 x - x ^ 3   +2"  0
       2.000000
   

   Make sure to do a good job on this one — you'll get differentiation on the midterm.

3. Write a unit test for the polynomial evaluator in the last problem. This means that if you already did the last problem, and you crammed a lot of logic into a main() method that you did something wrong. Make sure your evaluator is architected as a class which contains a method that returns (as a double) the evaluation of a polynomial (given as a string) at a given value (a double). The main() method should call that evaluate() method, and your unit test should test said evaluate() method.
4. Begin a project for a Hana compiler. Base it on the one for Carlos that was discussed in class. For this assignment, you should build the project structure, implement the semantic classes leaving the semantic analysis methods as stubs, and write a complete abstract syntax tree generator.