Getting Started

Download the example implementation of precedence climbing:

PrecedenceClimbingJava.zip

Import it into Eclipse. You should see a project called PrecedenceClimbing.

Your Task

You have two tasks:

Add support for the ^ operator, meaning exponentiation. It should have a higher precedence than the already-supported operators, and should be right-associative. Note that you will need to modify the lexer to recognize ^ as a token.
Allow parentheses to be used to explicitly specify the order of operation. To do this, modify parsePrimary so that if it sees a left parenthesis, it consumes it, calls parse to parse an expression, and then consumes a right parenthesis. Test by entering expressions such as (a + b) * 3 and verify that the parse tree reflects the intended order of operations.

You will need to modify the lexer so that it supports the exponentiation operator (^) and left and right parentheses as terminal symbols:

Modify the definition of LEGAL in Lexer.java to include the ^, (, and ) characters
Modify Symbol.java to define new terminal symbols for exponentiation and left and right parentheses
Modify the definition of the fromCharacter method in Symbol.java to handle ^, (, and ) characters

You will also need to modify the parsePrimary method in the parser class so that it applies the F → ( E ) production when appropriate.