I have seen and used nested functions in Python, and they match the definition of a closure. So why are they called nested functions instead of closures?

Are nested functions not closures because they are not used by the external world?

UPDATE: I was reading about closures and it got me thinking about this concept with respect to Python. I searched and found the article mentioned by someone in a comment below, but I couldn't completely understand the explanation in that article, so that is why I am asking this question.

2

9 Answers

A closure occurs when a function has access to a local variable from an enclosing scope that has finished its execution.

def make_printer(msg): def printer(): print(msg) return printer
printer = make_printer('Foo!')
printer()

When make_printer is called, a new frame is put on the stack with the compiled code for the printer function as a constant and the value of msg as a local. It then creates and returns the function. Because the function printer references the msg variable, it is kept alive after the make_printer function has returned.

So, if your nested functions don't

1. access variables that are local to enclosing scopes,
2. do so when they are executed outside of that scope,

then they are not closures.

Here's an example of a nested function which is not a closure.

def make_printer(msg): def printer(msg=msg): print(msg) return printer
printer = make_printer("Foo!")
printer() #Output: Foo!

Here, we are binding the value to the default value of a parameter. This occurs when the function printer is created and so no reference to the value of msg external to printer needs to be maintained after make_printer returns. msg is just a normal local variable of the function printer in this context.

12

The question has already been answered by aaronasterling

However, someone might be interested in how the variables are stored under the hood.

Before coming to the snippet:

Closures are functions that inherit variables from their enclosing environment. When you pass a function callback as an argument to another function that will do I/O, this callback function will be invoked later, and this function will — almost magically — remember the context in which it was declared, along with all the variables available in that context.

• If a function does not use free variables it doesn't form a closure.

• If there is another inner level which uses free variables -- all previous levels save the lexical environment ( example at the end )

• function attributes func_closure in python < 3.X or __closure__ in python > 3.X save the free variables.

• Every function in python has the closure attribute, but if there are no free variables, it is empty.

example: of closure attributes but no content inside as there is no free variable.

>>> def foo():
... def fii():
... pass
... return fii
...
>>> f = foo()
>>> f.func_closure
>>> 'func_closure' in dir(f)
True
>>>

NB: FREE VARIABLE IS MUST TO CREATE A CLOSURE.

I will explain using the same snippet as above:

>>> def make_printer(msg):
... def printer():
... print msg
... return printer
...
>>> printer = make_printer('Foo!')
>>> printer() #Output: Foo!

And all Python functions have a closure attribute so let's examine the enclosing variables associated with a closure function.

Here is the attribute func_closure for the function printer

>>> 'func_closure' in dir(printer)
True
>>> printer.func_closure
(<cell at 0x108154c90: str object at 0x108151de0>,)
>>>

The closure attribute returns a tuple of cell objects which contain details of the variables defined in the enclosing scope.

The first element in the func_closure which could be None or a tuple of cells that contain bindings for the function’s free variables and it is read-only.

>>> dir(printer.func_closure[0])
['__class__', '__cmp__', '__delattr__', '__doc__', '__format__', '__getattribute__', '__hash__', '__init__', '__new__', '__reduce__', '__reduce_ex__', '__repr__', '__setattr__', '__sizeof__', '__str__', '__subclasshook__', 'cell_contents']
>>>

Here in the above output you can see cell_contents, let's see what it stores:

>>> printer.func_closure[0].cell_contents
'Foo!'
>>> type(printer.func_closure[0].cell_contents)
<type 'str'>
>>>

So, when we called the function printer(), it accesses the value stored inside the cell_contents. This is how we got the output as 'Foo!'

Again I will explain using the above snippet with some changes:

 >>> def make_printer(msg): ... def printer(): ... pass ... return printer ... >>> printer = make_printer('Foo!') >>> printer.func_closure >>>

In the above snippet, I didn't print msg inside the printer function, so it doesn't create any free variable. As there is no free variable, there will be no content inside the closure. Thats exactly what we see above.

Now I will explain another different snippet to clear out everything Free Variable with Closure:

>>> def outer(x):
... def intermediate(y):
... free = 'free'
... def inner(z):
... return '%s %s %s %s' % (x, y, free, z)
... return inner
... return intermediate
...
>>> outer('I')('am')('variable')
'I am free variable'
>>>
>>> inter = outer('I')
>>> inter.func_closure
(<cell at 0x10c989130: str object at 0x10c831b98>,)
>>> inter.func_closure[0].cell_contents
'I'
>>> inn = inter('am')

So, we see that a func_closure property is a tuple of closure cells, we can refer them and their contents explicitly -- a cell has property "cell_contents"

>>> inn.func_closure
(<cell at 0x10c9807c0: str object at 0x10c9b0990>, <cell at 0x10c980f68: str object at 0x10c9eaf30>, <cell at 0x10c989130: str object at 0x10c831b98>)
>>> for i in inn.func_closure:
... print i.cell_contents
...
free
am
I
>>>

Here when we called inn, it will refer all the save free variables so we get I am free variable

>>> inn('variable')
'I am free variable'
>>>

4

Python has a weak support for closure. To see what I mean take the following example of a counter using closure with JavaScript:

function initCounter(){ var x = 0; function counter () { x += 1; console.log(x); }; return counter;
}
count = initCounter();
count(); //Prints 1
count(); //Prints 2
count(); //Prints 3

Closure is quite elegant since it gives functions written like this the ability to have "internal memory". As of Python 2.7 this is not possible. If you try

def initCounter(): x = 0; def counter (): x += 1 ##Error, x not defined print x return counter
count = initCounter();
count(); ##Error
count();
count();

You'll get an error saying that x is not defined. But how can that be if it has been shown by others that you can print it? This is because of how Python it manages the functions variable scope. While the inner function can read the outer function's variables, it cannot write them.

This is a shame really. But with just read-only closure you can at least implement the function decorator pattern for which Python offers syntactic sugar.

Update

As its been pointed out, there are ways to deal with python's scope limitations and I'll expose some.

1. Use the global keyword (in general not recommended).

2. In Python 3.x, use the nonlocal keyword (suggested by @unutbu and @leewz)

3. Define a simple modifiable class Object

class Object(object): pass

and create an Object scope within initCounter to store the variables

def initCounter (): scope = Object() scope.x = 0 def counter(): scope.x += 1 print scope.x return counter

Since scope is really just a reference, actions taken with its fields do not really modify scope itself, so no error arises.

4. An alternative way, as @unutbu pointed out, would be to define each variable as an array (x = [0]) and modify it's first element (x[0] += 1). Again no error arises because x itself is not modified.

5. As suggested by @raxacoricofallapatorius, you could make x a property of counter

def initCounter (): def counter(): counter.x += 1 print counter.x counter.x = 0 return counter

8

Python 2 didn't have closures - it had workarounds that resembled closures.

There are plenty of examples in answers already given - copying in variables to the inner function, modifying an object on the inner function, etc.

In Python 3, support is more explicit - and succinct:

def closure(): count = 0 def inner(): nonlocal count count += 1 print(count) return inner

Usage:

start = closure()
another = closure() # another instance, with a different stack
start() # prints 1
start() # prints 2
another() # print 1
start() # prints 3

The nonlocal keyword binds the inner function to the outer variable explicitly mentioned, in effect enclosing it. Hence more explicitly a 'closure'.

3

I had a situation where I needed a separate but persistent name space. I used classes. I don't otherwise. Segregated but persistent names are closures.

>>> class f2:
... def __init__(self):
... self.a = 0
... def __call__(self, arg):
... self.a += arg
... return(self.a)
...
>>> f=f2()
>>> f(2)
2
>>> f(2)
4
>>> f(4)
8
>>> f(8)
16
# **OR**
>>> f=f2() # **re-initialize**
>>> f(f(f(f(2)))) # **nested**
16
# handy in list comprehensions to accumulate values
>>> [f(i) for f in [f2()] for i in [2,2,4,8]][-1]
16

0

def nested1(num1): print "nested1 has",num1 def nested2(num2): print "nested2 has",num2,"and it can reach to",num1 return num1+num2 #num1 referenced for reading here return nested2

Gives:

In [17]: my_func=nested1(8)
nested1 has 8
In [21]: my_func(5)
nested2 has 5 and it can reach to 8
Out[21]: 13

This is an example of what a closure is and how it can be used.

People are confusing about what closure is. Closure is not the inner function. the meaning of closure is act of closing. So inner function is closing over a nonlocal variable which is called free variable.

def counter_in(initial_value=0): # initial_value is the free variable def inc(increment=1): nonlocal initial_value initial_value += increment return print(initial_value) return inc

when you call counter_in() this will return inc function which has a free variable initial_value. So we created a CLOSURE. people call inc as closure function and I think this is confusing people, people think "ok inner functions are closures". in reality inc is not a closure, since it is part of the closure, to make life easy, they call it closure function.

 myClosingOverFunc=counter_in(2)

this returns inc function which is closing over the free variable initial_value. when you invoke myClosingOverFunc

 myClosingOverFunc() 

it will print 2.

when python sees that a closure sytem exists, it creates a new obj called CELL. this will store only the name of the free variable which is initial_value in this case. This Cell obj will point to another object which stores the value of the initial_value.

in our example, initial_value in outer function and inner function will point to this cell object, and this cell object will be point to the value of the initial_value.

 variable initial_value =====>> CELL ==========>> value of initial_value

So when you call counter_in its scope is gone, but it does not matter. because variable initial_value is directly referencing the CELL Obj. and it indirectly references the value of initial_value. That is why even though scope of outer function is gone, inner function will still have access to the free variable

let's say I want to write a function, which takes in a function as an arg and returns how many times this function is called.

def counter(fn): # since cnt is a free var, python will create a cell and this cell will point to the value of cnt # every time cnt changes, cell will be pointing to the new value cnt = 0 def inner(*args, **kwargs): # we cannot modidy cnt with out nonlocal nonlocal cnt cnt += 1 print(f'{fn.__name__} has been called {cnt} times') # we are calling fn indirectly via the closue inner return fn(*args, **kwargs) return inner 

in this example cnt is our free variable and inner + cnt create CLOSURE. when python sees this it will create a CELL Obj and cnt will always directly reference this cell obj and CELL will reference the another obj in the memory which stores the value of cnt. initially cnt=0.

 cnt ======>>>> CELL =============> 0

when you invoke the inner function wih passing a parameter counter(myFunc)() this will increase the cnt by 1. so our referencing schema will change as follow:

 cnt ======>>>> CELL =============> 1 #first counter(myFunc)() cnt ======>>>> CELL =============> 2 #second counter(myFunc)() cnt ======>>>> CELL =============> 3 #third counter(myFunc)()

this is only one instance of closure. You can create multiple instances of closure with passing another function

counter(differentFunc)()

this will create a different CELL obj from the above. We just have created another closure instance.

 cnt ======>> difCELL ========> 1 #first counter(differentFunc)() cnt ======>> difCELL ========> 2 #secon counter(differentFunc)() cnt ======>> difCELL ========> 3 #third counter(differentFunc)() 

I'd like to offer another simple comparison between python and JS example, if this helps make things clearer.

JS:

function make () { var cl = 1; function gett () { console.log(cl); } function sett (val) { cl = val; } return [gett, sett]
}

and executing:

a = make(); g = a[0]; s = a[1];
s(2); g(); // 2
s(3); g(); // 3

Python:

def make (): cl = 1 def gett (): print(cl); def sett (val): cl = val return gett, sett

and executing:

g, s = make()
g() #1
s(2); g() #1
s(3); g() #1

Reason: As many others said above, in python, if there is an assignment in the inner scope to a variable with the same name, a new reference in the inner scope is created. Not so with JS, unless you explicitly declare one with the var keyword.

For the readers of Structure and Interpretation of Computer Programs (SICP): there are 2 unrelated meanings of closure (CS VS Math), see Wikipedia for the latter/less common one:

Sussman and Abelson also use the term closure in the 1980s with a second, unrelated meaning: the property of an operator that adds data to a data structure to also be able to add nested data structures. This usage of the term comes from the mathematics usage rather than the prior usage in computer science. The authors consider this overlap in terminology to be "unfortunate."

• (computer_programming)#History_and_etymology

The second (mathematical) meaning is also used in SICP in Python, see for example the discussion of tuples

Our ability to use tuples as the elements of other tuples provides a new means of combination in our programming language. We call the ability for tuples to nest in this way a closure property of the tuple data type. In general, a method for combining data values satisfies the closure property if the result of combination can itself be combined using the same method.

• 2.3 Sequences | SICP in Python