Python递归的问题？

Question

import time

def outer(F):
    def wrapper(x):
        start = time.time()
        F(x)
        end = time.time()
        print(end - start)
    return wrapper


@outer
def func2(a):
    if a == 1:
        return 1
    else:
        return a * func2(a-1)




func2(7)

上面是一段python递归实现阶乘的代码，但是在加上装饰器之后就报错了，想请大家看下问题出在哪里？为什么调用的时候不用 @outer这种方式，而用原始的 outer(func2)(7)就没问题了？
报错如下：

[root@yang python]# python3 test.py 
7.152557373046875e-07
Traceback (most recent call last):
  File "test.py", line 22, in <module>
    func2(7)
  File "test.py", line 6, in wrapper
    F(x)
  File "test.py", line 17, in func2
    return a * func2(a-1)
  File "test.py", line 6, in wrapper
    F(x)
  File "test.py", line 17, in func2
    return a * func2(a-1)
  File "test.py", line 6, in wrapper
    F(x)
  File "test.py", line 17, in func2
    return a * func2(a-1)
  File "test.py", line 6, in wrapper
    F(x)
  File "test.py", line 17, in func2
    return a * func2(a-1)
  File "test.py", line 6, in wrapper
    F(x)
  File "test.py", line 17, in func2
    return a * func2(a-1)
  File "test.py", line 6, in wrapper
    F(x)
  File "test.py", line 17, in func2
    return a * func2(a-1)
TypeError: unsupported operand type(s) for *: 'int' and 'NoneType'

Answer 1

内层应该有返回值

def outer(F):
    def wrapper(x):
        start = time.time()
        ret=F(x)
        end = time.time()
        print(end - start)
        return ret # 内层应该有返回值        
    return wrapper

>>> func2(7)
0.0
0.015625
0.015625
0.03125
0.03125
0.03125
0.046875
5040

Answer 2

你好，
装饰以前的outer(func2)(7)和装饰以后的func2(7)当然不一样。
outer(func2) = 新的函数。outer只一次运行。
func2(7) = outer(func2(7)) = outer(func2(outer(func2(6))))。。。每一次func2运行，outer也运行。
对不起，我的中文真不好，希望你能明白。