Static variable in Python?

The another function-based way of doing this in python is:

def f(arg, static_var=[0]):
    static_var[0] += arg

As the static_var object is initialised at the function definition, and then reused for all the calls, it will act like a static variable. Note that you can't just use an int, as they are immutable.

>>> def f(arg, static_var=[0]):
...         static_var[0] += arg
...         print(static_var[0])
... 
>>> f(1)
1
>>> f(2)
3
>>> f(3)
6

Assuming what you want is "a variable that is initialised only once on first function call", there's no such thing in Python syntax. But there are ways to get a similar result:

1 - Use a global. Note that in Python, 'global' really means 'global to the module', not 'global to the process':

_number_of_times = 0

def yourfunc(x, y):
    global _number_of_times
    for i in range(x):
        for j in range(y):
            _number_of_times += 1

2 - Wrap you code in a class and use a class attribute (ie: an attribute that is shared by all instances). :

class Foo(object):
    _number_of_times = 0

    @classmethod
    def yourfunc(cls, x, y):
        for i in range(x):
            for j in range(y):
                cls._number_of_times += 1

Note that I used a classmethod since this code snippet doesn't need anything from an instance

3 - Wrap you code in a class, use an instance attribute and provide a shortcut for the method:

class Foo(object):
    def __init__(self):
         self._number_of_times = 0

    def yourfunc(self, x, y):
        for i in range(x):
            for j in range(y):
                self._number_of_times += 1

yourfunc = Foo().yourfunc

4 - Write a callable class and provide a shortcut:

class Foo(object):
    def __init__(self):
         self._number_of_times = 0

    def __call__(self, x, y):
        for i in range(x):
            for j in range(y):
                self._number_of_times += 1


yourfunc = Foo()

4 bis - use a class attribute and a metaclass

class Callable(type):
    def __call__(self, *args, **kw):
        return self._call(*args, **kw)

class yourfunc(object):
    __metaclass__ = Callable

    _numer_of_times = 0

    @classmethod
    def _call(cls, x, y):
        for i in range(x):
            for j in range(y):                 
                cls._number_of_time += 1

5 - Make a "creative" use of function's default arguments being instantiated only once on module import:

def yourfunc(x, y, _hack=[0]):
    for i in range(x):
        for j in range(y):
            _hack[0] += 1

There are still some other possible solutions / hacks, but I think you get the big picture now.

EDIT: given the op's clarifications, ie "Lets say you have a recursive function with default parameter but if someone actually tries to give one more argument to your function it could be catastrophic", it looks like what the OP really wants is something like:

# private recursive function using a default param the caller shouldn't set
def _walk(tree, callback, level=0):
    callback(tree, level)
    for child in tree.children:
        _walk(child, callback, level+1):

# public wrapper without the default param
def walk(tree, callback):
    _walk(tree, callback)

Which, BTW, prove we really had Yet Another XY Problem...

Python doesn't have static variables by design. For your example, and use within loop blocks etc. in general, you just use a variable in an outer scope; if that makes it too long-lived, it might be time to consider breaking up that function into smaller ones.

For a variable that continues to exist between calls to a function, that's just reimplementing the basic idea of an object and a method on that object, so you should make one of those instead.

You can create a closure with nonlocal to make them editable (python 3.x only). Here's an example of a recursive function to calculate the length of a list.

def recursive_len(l):
    res = 0
    def inner(l2):
        nonlocal res
        if l2:
            res += 1
            inner(l2[1:])
    inner(l)
    return res

Or, you can assign an attribute to the function itself. Using the trick from here:

def fn(self):
    self.number_of_times += 1
fn.func_defaults = (fn,)
fn.number_of_times = 0

fn()
fn()
fn()
print (fn.number_of_times)