Wrong Signature for singledispatch'ed functions/methods

An example:

$ cat -n spam.py 
     1  from __future__ import annotations
     2  from functools import singledispatch
     3  
     4  @singledispatch
     5  def foo(x: int) -> int:
     6      return x + 1
     7  
     8  @foo.register
     9  def _(x: str) -> str:
    10      return "Hello, " + x
$ python
Python 3.11.1+ (heads/3.11:ba88628808, Jan 14 2023, 08:40:06) [GCC 10.2.1 20210110] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import inspect, spam
>>> inspect.signature(spam.foo)
<Signature (x: 'int') -> 'int'>

I would expect here something like <Signature (x: int | str) -> int | str> (i.e. union of types for returned value, same for argument) or an exception.

I'm not sure that the first option is on the table: more accurately this situation fits to case of multiple function signatures (like we have in the stdlib e.g. for the min/max). But the current signature() output is misleading.

UPD: In fact, the Signature must be like <Signature (x: int | str, /) -> int | str>, because:

>>> spam.foo(x=1)
Traceback (most recent call last):
  ...
TypeError: foo requires at least 1 positional argument

Or we can make singledispatch'ed function to be with a positional-only argument iff argument names for different overloaded implementations are different.

PS: Inspired by https://discuss.python.org/t/signatures-a-call-to-action/23580

functools.singledispatch と inspect.signature を使って例を再現し、報告に示されている位置引数の挙動も含めます。意図されているシグネチャのセマンティクスを決定し、そのうえで合意した結果を示すリグレッションカバレッジを追加します。singledispatch のシグネチャが基底実装だけを誤解を招く形で表さなくなった時点で issue は完了です。