中缀算术表达式定义

Question

如何定义中缀算术表达式的语法？我有一个中缀＆＃39;计算器的代码，但我需要知道如何定义语法的单词或某些类型的例子。 代码：

import java.util.Stack;
import java.util.StringTokenizer;

public class Infix
{

    public double infix(String expression)
    {
        expression=expression.replaceAll("[\t\n ]", "")+"=";
        String operator="*/+-=";
        StringTokenizer tokenizer=new StringTokenizer(expression, operator, true);
        Stack operatorStack=new Stack();
        Stack valueStack=new Stack();
        while(tokenizer.hasMoreTokens())
        {
            String token=tokenizer.nextToken();
            if(operator.indexOf(token)<0)
                valueStack.push(token);
            else
                operatorStack.push(token);
            resolve(valueStack, operatorStack);
        }
        String lastOne=(String)valueStack.pop();
        return Double.parseDouble(lastOne);   
    }

    public int getPriority(String op)
    {
        if(op.equals("*") || op.equals("/"))
            return 1;
        else if(op.equals("+") || op.equals("-"))
            return 2;
        else if(op.equals("="))
            return 3;
        else
            return Integer.MIN_VALUE;
    }

    public void resolve(Stack values, Stack operators)
    {
        while(operators.size()>=2)
        {
            String first=(String)operators.pop();
            String second=(String)operators.pop();
            if(getPriority(first)<getPriority(second))
            {
                operators.push(second);
                operators.push(first);
                return;
            }
            else
            {
                String firstValue=(String)values.pop();
                String secondValue=(String)values.pop();
                values.push(getResults(secondValue, second, firstValue));
                operators.push(first);
            }
        }
    }

    public String getResults(String operand1, String operator, String operand2)
    {
        System.out.println("Performing "+
                operand1+operator+operand2);
        double op1=Double.parseDouble(operand1);
        double op2=Double.parseDouble(operand2);
        if(operator.equals("*"))
            return ""+(op1*op2);
        else if(operator.equals("/"))
            return ""+(op1/op2);
        else if(operator.equals("+"))
            return ""+(op1+op2);
        else if(operator.equals("-"))
            return ""+(op1-op2);
        else
            return null;
    }

    public static void main(String[] args)
    {
        Infix fix=new Infix();
        String expression="5-3*2*1/2+2";
        System.out.println(expression+"="+fix.infix(expression));
    }
}

此外，如果您不介意，是否有更好，更容易理解的编码方式？ （这不像语法定义那么重要）我希望你理解我的要求:)