Type annotations for *args and **kwargs

The proper way to do this is using @overload

from typing import overload

@overload
def foo(arg1: int, arg2: int) -> int:
    ...

@overload
def foo(arg: int) -> int:
    ...

def foo(*args):
    try:
        i, j = args
        return i + j
    except ValueError:
        assert len(args) == 1
        i = args[0]
        return i

print(foo(1))
print(foo(1, 2))

Note that you do not add @overload or type annotations to the actual implementation, which must come last.

You'll need a newish version of both typing and mypy to get support for @overload outside of stub files.

You can also use this to vary the returned result in a way that makes explicit which argument types correspond with which return type. e.g.:

from typing import Tuple, overload

@overload
def foo(arg1: int, arg2: int) -> Tuple[int, int]:
    ...

@overload
def foo(arg: int) -> int:
    ...

def foo(*args):
    try:
        i, j = args
        return j, i
    except ValueError:
        assert len(args) == 1
        i = args[0]
        return i

print(foo(1))
print(foo(1, 2))

For variable positional arguments (*args) and variable keyword arguments (**kw) you only need to specify the expected value for one such argument.

From the Arbitrary argument lists and default argument values section of the Type Hints PEP:

Arbitrary argument lists can as well be type annotated, so that the definition:

def foo(*args: str, **kwds: int): ...

is acceptable and it means that, e.g., all of the following represent function calls with valid types of arguments:

foo('a', 'b', 'c')
foo(x=1, y=2)
foo('', z=0)

So you'd want to specify your method like this:

def foo(*args: int):

However, if your function can only accept either one or two integer values, you should not use *args at all, use one explicit positional argument and a second keyword argument:

def foo(first: int, second: Optional[int] = None):

Now your function is actually limited to one or two arguments, and both must be integers if specified. *args always means 0 or more, and can't be limited by type hints to a more specific range.