A simple parser implemented in Python.

simple_parser.py

class Parser:
    def __init__(self, infix):
        self.__infix = infix
        self.__postfix = ""
        self.__operators = ['+', '-', '*', '/', '^']

    def parse(self):
        self.__infix_to_postfix()
        return self.__eval_postfix()

    def __infix_to_postfix(self):
        stack = []

        for e in self.__infix:
            # OPERAND
            if e not in self.__operators:
                self.__postfix += e
            # OPERATOR
            else:
                if not stack:
                    stack.append(e)
                else:
                    while stack and Parser.__check_precedence(stack[-1], e):  # e < stack[-1]
                        self.__postfix += stack.pop()

                    stack.append(e)

        while stack:
            self.__postfix += stack.pop()

        return self.__postfix

    def __eval_postfix(self):
        stack = []

        for e in self.__postfix:
            if e not in self.__operators:
                stack.append(e)
            else:
                temp = stack[-1]
                stack.pop()

                retVal = Parser.__operation(stack[-1], temp, e)  # !!! --> tmp --> topStack(Operator)temp
                stack.pop()
                stack.append(retVal)

        return stack[-1]

    @staticmethod
    def __operation(a, b, op):
        a = float(a)
        b = float(b)

        if op == "+":
            return a + b
        if op == "-":
            return a - b
        if op == "*":
            return a * b
        if op == "/":
            return a / b
        if op == "^":
            return a ** b

    @staticmethod
    def __check_precedence(op1, op2):
        if op1 == "^":
            return True

        if (op1 == "*" or op1 == "/") and (op2 == "+" or op2 == "-"):
            return True

        """if (op1 == "+" or op1 == "-") and (op2 == "*" or op2 == "/"):
            return False"""
        return False


def main():
    p = Parser("9+1-4*2")
    print(p.parse())

if __name__ == "__main__":
    main()