如何在程序中將中綴表達式轉換為後綴表達式？

import operator
import string

ARITHMETIC_OPERATORS = {
"+": operator.add, "-": operator.sub,
"*": operator.mul, "/": operator.div,
"%": operator.mod, "^": operator.pow,
"//": operator.floordiv,
}

class BadPostfixNotation(Exception):
"""NotImplemented"""
def __init__(self, message):
self._message = "BadPostfixNotation when build:{0}".format(message)

@property
def message(self):
return self._message

def validate_expr(expression):
"""
Validate the expression
"""
pass

def torpn(expr):
"""
A General Infix-to-Postfix Conversion.
The solution assumes that all expression are the right infix expression.
See:
http://interactivepython.org/runestone/static/pythonds/BasicDS/stacks.html
RPN:
Postfix Expressions(http://en.wikipedia.org/wiki/Reverse_Polish_notation)
For example:
A * B + C * D =&> A B * C D * +
( A + B ) * C - ( D - E ) * ( F + G ) =&>A B + C * D E - F G + * -
TODO:
check valid of the expr.
"""

postfixchar = string.letters+string.digits
precedence = {"^": 3, "*": 3, "/": 3, "+": 2, "-": 2, "(": 1}
token_list = expr.split()
postfix_stack, op_stack = [], []
for token in token_list:
if token in postfixchar:
postfix_stack.append(token)
elif token == "(":
op_stack.append(token)
elif token == ")":
tmp_token = op_stack.pop()
while tmp_token != "(":
postfix_stack.append(tmp_token)
tmp_token = op_stack.pop()
else:
while len(op_stack) != 0 and precedence[op_stack[-1]] &>= precedence[token]:
postfix_stack.append(op_stack.pop())
op_stack.append(token)
while len(op_stack) != 0:
postfix_stack.append(op_stack.pop())
return " ".join(postfix_stack)

def postfix(expr, operators=ARITHMETIC_OPERATORS):
"""
Postfix Evaluation
"""
stack = []