Only use annotations of `@overload`ed functions to type check the implementation

Consider the following real-world example of a function. The type of one of the parameters of this function depends on another one:

from typing import *

K = TypeVar("K", bound=Hashable)
V = TypeVar("V")


@overload
def dict_get_factory(dictionary: Dict[K, V], 
                     key: K, 
                     factory: Callable[[], V], 
                     takes_key: Literal[False]) -> V: ...

@overload
def dict_get_factory(dictionary: Dict[K, V], 
                     key: K, 
                     factory: Callable[[K], V], 
                     takes_key: Literal[True]) -> V: ...

def dict_get_factory(dictionary: Dict[K, V], 
                     key: K, 
                     factory: Union[Callable[[], V], Callable[[K], V]], 
                     takes_key: bool=False) -> V:
    """Like dict.setdefault(), but uses a factory

    >>> dict_get_factory(d := {}, "foo", int)
    0
    >>> dict_get_factory(d, "bar", lambda key: len(key), takes_key=True)
    3
    >>> d
    {'foo': 0, 'bar': 3}
    """
    try:
        return dictionary[key]
    except KeyError:
        return dictionary.setdefault(key, 
                factory(key) if takes_key else factory())
                
i1: int = dict_get_factory({"foo": 1}, "bar", lambda: 1, False)   # ok
i2: int = dict_get_factory({"foo": 1}, "bar", lambda s: 1, True)  # ok

It doesn't typecheck as if you only look at the annotations of the implementation, the signature of the factory is ambiguous:

main.py:36: error: Too many arguments
main.py:36: error: Too few arguments

I don't think it's possible to annotate the implementation in such a way that it would typecheck. So it would be nice if mypy used the signatures of the @overloaded methods, and one wouldn't have to annotate the signature of the implementation at all. Even if you could annotate it in such a way that it would typecheck, wouldn't it be redundant?

Beginne mit dem Overload-Beispiel im Issue und untersuche, wie mypy Implementierungssignaturen und Overload-Prüfungen behandelt. Bestimme das erwartete Verhalten für Aufrufe innerhalb der Implementierung, füge anschließend gezielte Regressionstests hinzu und verifiziere, dass das Beispiel nicht mehr über widersprüchliche Factory-Aufruffehler berichtet.