A function with no side effects fits the pure mathematical abstraction of a function: there are no global changes to variables. If we avoid the global statement, we will almost meet this threshold. To be pure, a function should also avoid changing the state mutable objects.
Here's an example of a pure function:
def m(n: int) -> int: return 2**n-1
This result depends only on the parameter, n. There are no changes to global variables and the function doesn't update any mutable data structures.
Any references to values in the Python global namespace (using a free variable) is something we can rework into a proper parameter. In most cases, it's quite easy. Here is an example that depends on a free variable:
def some_function(a: ...
