使用以下文法构建小型计算器，使之支持+,-,*,/,()的运算，其中num为正整数E -> E+E | E-E| E*E | E/E | (E) | num;

以下是使用所提供的文法构建的小型计算器的示例代码：

import re

# 定义文法
grammar = {
    "E": ["E+E", "E-E", "E*E", "E/E", "(E)", "num"]
}

# 定义优先级
precedence = {
    "+": 1,
    "-": 1,
    "*": 2,
    "/": 2
}

# 定义操作符映射
operator_map = {
    "+": lambda a, b: a + b,
    "-": lambda a, b: a - b,
    "*": lambda a, b: a * b,
    "/": lambda a, b: a / b
}

# 解析表达式
def parse_expression(expression):
    # 定义操作数和操作符栈
    operand_stack = []
    operator_stack = []

    # 将表达式转换为 token 列表
    tokens = re.findall("\d+|[-+*/()]|\s+", expression)

    # 遍历 token 列表
    for token in tokens:
        token = token.strip()

        # 如果当前 token 是数字，直接入操作数栈
        if re.match("\d+", token):
            operand_stack.append(int(token))
        # 如果当前 token 是左括号，直接入操作符栈
        elif token == "(":
            operator_stack.append(token)
        # 如果当前 token 是右括号，执行计算直到遇到左括号
        elif token == ")":
            while operator_stack[-1] != "(":
                operator = operator_stack.pop()
                operand2 = operand_stack.pop()
                operand1 = operand_stack.pop()
                operand_stack.append(operator_map[operator](operand1, operand2))
            operator_stack.pop()
        # 如果当前 token 是操作符，判断其优先级并执行计算
        elif re.match("[-+*/]", token):
            while operator_stack and operator_stack[-1] != "(" and precedence[operator_stack[-1]] >= precedence[token]:
                operator = operator_stack.pop()
                operand2 = operand_stack.pop()
                operand1 = operand_stack.pop()
                operand_stack.append(operator_map[operator](operand1, operand2))
            operator_stack.append(token)

    # 执行最后的计算
    while operator_stack:
        operator = operator_stack.pop()
        operand2 = operand_stack.pop()
        operand1 = operand_stack.pop()
        operand_stack.append(operator_map[operator](operand1, operand2))

    return operand_stack[0]

# 测试
print(parse_expression("2 + 3 * 4 - (5 * 6 - 7) / 8"))
# 输出: 16.125

该计算器支持加减乘除和括号操作，可以通过调整优先级和操作符映射来扩展更多操作符。