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Enter an empty expression to stop. Enter expression: 10-2*3 Result: 4.0 Enter expression: (10-2)*3 Result: 24.0 Enter expression: 10/3.5 Result: 2.857142857142857
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Understanding the Parser
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Let s now take a detailed look at Parser. The string containing the expression to be evaluated is referred to by exp. This field is set each time evaluate( ) is called. It is important to remember that the parser evaluates expressions that are contained in standard Java strings. For example, the following strings contain expressions that the parser can evaluate: "10 5" "2 * 3.3 / (3.1416 * 3.3)" The current index into exp is stored in expIdx. When parsing begins execution, expIdx is set to zero. expIdx is incremented as the parser moves through the expression. The token field holds the current token, and tokType contains the token type. The entry point to the parser is through evaluate( ), which must be called with a string containing the expression to be analyzed. The methods evalExp2( ) through evalExp6( ) along with atom( ) form the recursive-descent parser. They implement an enhanced set of the expression production rules discussed earlier. The comments at the top of each method describe the function they perform. In the next version of the parser, a method called evalExp1( ) will also be added. The handleErr( ) method handles syntax errors in the expression. The methods getToken( ) and isDelim( ) dissect the expression into its component parts, as described earlier. The parser uses getToken( ) to obtain tokens from the expression, beginning at the beginning of the expression and working to the end. Based on the type of token obtained, different actions are taken. To understand exactly how the parser evaluates an expression, work through the following expression: 10 3 * 2 When evaluate( ), the entry point into the parser, is called, it gets the first token. If the token is EOE, then evaluate( ) has been called with a null string, and the NOEXP error is generated. However, in this example, the token contains the number 10. Next, evalExp2( ) is called. evalExp2( ) then calls evalExp3( ), and evalExp3( ) calls evalExp4( ), which in turn calls evalExp5( ). Then evalExp5( ) checks whether the token is a unary plus or minus, which in this case, it is not, so evalExp6( ) is called. At this point evalExp6( ) either recursively
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2: A Recursive-Descent Expression Parser
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calls evalExp2( ) (in the case of a parenthesized expression) or atom( ) to find the value of a number. Since the token is not a left parentheses, atom( ) is executed and the value 10 is returned. Next, another token is retrieved, and the methods begin to return up the chain. At this point, the token is , and the methods return up to evalExp2( ). What happens next is very important. Because the token is , it is saved in op. The parser then gets the next token, which is 3, and the descent down the chain begins again. As before, atom( ) is entered. The value 3 is returned in result and the token * is read. This causes a return back up the chain to evalExp3( ), where the final token 2 is read. At this point, the first arithmetic operation occurs the multiplication of 2 and 3. The result is returned to evalExp2( ) and the subtraction is performed. The subtraction yields the answer 4. Although the process may at first seem complicated, work through some other examples to verify that it functions correctly every time. If an error occurs while parsing, the handleErr( ) method is called. This method throws a ParserException that describes the error. This exception is thrown out of evalutate( ) and must be handled by code that uses the parser. This parser would be suitable for use by a simple desktop calculator, as is illustrated by the previous program. Before it could be used in a computer language, a database, or in a sophisticated calculator, it needs the ability to handle variables. This is the subject of the next section.
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