Julia's burgeoning popularity has renewed my interest in dynamic dispatch.  It seems to me that many methods that have been written as a giant switch on types can more clearly be written using dynamic dispatch.  It was prettty exciting to see that Python already has single dispatch built in, and that it supports type annotations!

Would it be possible and desirable to extend it slightly to support Union types?

---

In [1]: from functools import singledispatch

In [3]: from typing import Any, Union

In [4]: @singledispatch

   ...: def a(x: Any):

   ...:     print("a")

   ...: 

In [5]: class X: pass

In [6]: class Y: pass

In [7]: @a.register

   ...: def _(x: Union[X, Y]):

   ...:     print("b")

   ...: 

---------------------------------------------------------------------------

TypeError                                 Traceback (most recent call last)

<ipython-input-7-b6a194bcade0> in <module>

      1 @a.register

----> 2 def _(x: Union[X, Y]):

      3     print("b")

      4 

~/.pyenv/versions/3.8.5/lib/python3.8/functools.py in register(cls, func)

    858             argname, cls = next(iter(get_type_hints(func).items()))

    859             if not isinstance(cls, type):

--> 860                 raise TypeError(

    861                     f"Invalid annotation for {argname!r}. "

    862                     f"{cls!r} is not a class."

TypeError: Invalid annotation for 'x'. typing.Union[__main__.X, __main__.Y] is not a class.