The "official" way to do expression evaluation involves parse trees and reverse Polish notation, but I found a simpler more practical approach: Repeatedly process your list of tokens, making it one step simpler each time by applying a series of rules: 1. If you see the sequence '(', 'number', ')', replace it with just 'number'. 2. For each operator in decreasing precedence, look for the sequence 'number', 'operator', 'number' and replace it with the result of the operation. If you end up with a single number, that's your answer. Anything else indicates a syntax error in the input expression.

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