Wie analysiert man arithmetische Ausdrücke mit ANTLR: Eine Schritt-für-Schritt-Anleitung?

grammar Exp;

eval returns [double value]
    :    exp=additionExp {$value = $exp.value;}
    ;

additionExp returns [double value]
    :    m1=multiplyExp       {$value =  $m1.value;} 
         ( '+' m2=multiplyExp {$value += $m2.value;} 
         | '-' m2=multiplyExp {$value -= $m2.value;}
         )* 
    ;

multiplyExp returns [double value]
    :    a1=atomExp       {$value =  $a1.value;}
         ( '*' a2=atomExp {$value *= $a2.value;} 
         | '/' a2=atomExp {$value /= $a2.value;}
         )* 
    ;

atomExp returns [double value]
    :    n=Number                {$value = Double.parseDouble($n.text);}
    |    '(' exp=additionExp ')' {$value = $exp.value;}
    ;

Number
    :    ('0'..'9')+ ('.' ('0'..'9')+)?
    ;

java -cp antlr-3.2.jar org.antlr.Tool Exp.g

import org.antlr.runtime.*;

public class ANTLRDemo {
    public static void main(String[] args) throws Exception {
        ANTLRInputStream in = new ANTLRInputStream("12*(5-6)");
        ExpLexer lexer = new ExpLexer(in);
        CommonTokenStream tokens = new CommonTokenStream(lexer);
        ExpParser parser = new ExpParser(tokens);
        System.out.println(parser.eval().value); 
    }
}

// Recompile
javac -cp .:antlr-3.2.jar ANTLRDemo.java

// Run
java -cp .:antlr-3.2.jar ANTLRDemo