#!/usr/bin/env python

 # -*- coding:utf-8 -*-

 def make_sum(a, b):

     return ['+', a, b]

 def make_prod(a, b):

     return ['*', a, b]

 def make_diff(a, b):

     return ['-', a, b]

 def make_div(a, b):

     return ['/', a, b]

 def is_basic_exp(a):

     return not isinstance(a, list)

 def is_number(x):

     return (isinstance(x, int) or isinstance(x, float) or isinstance(x, complex))

 #表达式计算

 def eval_exp(e, values):

     if is_basic_exp(e):

         #如果e位于字典里则返回键对应的值，否则直接返回e

         if e in values.keys():

             return values[e]

         else:

             return e

     op, a, b = e[0], eval_exp(e[1], values), eval_exp(e[2], values)

     if op=='+':

         return eval_sum(a, b)

     elif op=='-':

         return eval_diff(a, b)

     elif op=='*':

         return eval_prod(a, b)

     elif op=='/':

         return eval_div(a, b)

     else:

         raise ValueError("Unknown operator:", op)

 #加法

 def eval_sum(a, b):

     if is_number(a) and is_number(b):

         return a+b

     if is_number(a) and a==0:

         return b

     if is_number(b) and b==0:

         return a

     return make_sum(a, b)

 #减法

 def eval_diff(a, b):

     if is_number(a) and is_number(b):

         return a - b

     if is_number(a) and a==0:

         return -b

     if is_number(b) and b==0:

         return a

     return make_diff(a, b)

 #乘法

 def eval_prod(a, b):

     if is_number(a) and is_number(b):

         return a * b

     if is_number(a) and a==0:

         return 0

     if is_number(b) and b==0:

         return 0

     return make_prod(a, b)

 #除法

 def eval_div(a, b):

     if is_number(a) and is_number(b):

         return a / b

     if is_number(a) and a==0:

         return 0

     if is_number(b) and b==1:

         return a

     if is_number(b) and b==0:

         raise ZeroDivisionError

     return make_div(a, b)

 #取出表达式里所有变量的集合

 var_list = []  #这里使用全局变量

 def varibles(exp):

     for i in range(1,3):

         if is_basic_exp(exp[i]):

             var_list.append(exp[i])

         else:

             varibles(exp[i])

     return var_list

 if __name__=='__main__':

     e1 = make_prod(make_sum('a',3), make_sum('b',make_sum(4,6)))

     print(e1)

     print("变量集合：",varibles(e1))

     values = {}

     values['a'] = 3

     values['b'] = 4

     print(values)

     print(eval_exp(e1, values))