function is lacking a `__signature__` attribute

PEP-362 specifies that in order to cache the signature of any function, it is possible for the user to set its __signature__ attribute.

Actual

This attribute is not set in the builtins module over at https://github.com/python/typeshed/blob/main/stdlib/builtins.pyi#L1009

As a result a typechecker might reject the following piece of code

from inspect import signature


def main():

    def f():
        pass

    f.__signature__ = signature(f)


if __name__ == "__main__":
    main()

e.g. with pyright I have a false positive

/Users/leogermond/Lab/python/signature/main.py
  /Users/leogermond/Lab/python/signature/main.py:9:7 - error: Cannot assign to attribute "__signature__" for class "function"
    Attribute "__signature__" is unknown (reportFunctionMemberAccess)
1 error, 0 warnings, 0 informations

Expected

I would the __signature__ attribute to be specified in the function class (with a special marker indicating it's optional?) of the builtins module. A type checker such as pyright could then infer that setting this attribute is possible and accept the piece of code given in example.

Start at stdlib/builtins.pyi around line 1009 and inspect how the function class is declared. Compare the requested optional signature support with PEP 362 and the provided assignment example, then verify that a type checker such as pyright accepts it when the stub change is complete.