But the type declaration you provided should be treated as an "or" statement. For example, int | str is regarded by mypy as either int or str. Sorry for being a bit naive, but would you mind explaining a bit more about the expected output you want so that I can help solve the problem for you? Like what's the final result you excepted.

I would like mypy to report that return Hello in incompatible with overload #2: if a is of type str, the body of f does not return a bool.

Something like that:

main.py:14: error: Incompatible return value type in overload 2 (got "str", expected "bool")  [return-value]

This is evidenced in the example by the fact that f("some string") is "Hello" while reveal_type(f("some string")) is bool.

Overload specification does not require any function body checks against overloaded signatures. Overloads are explicitly external to the function itself: foreign callers see them and don't see the implementation signature, while the impl itself is only checked against its own signature.

For reference, PEP 484 says:

The @overload-decorated definitions are for the benefit of the type checker only, since they will be overwritten by the non-@overload-decorated definition, while the latter is used at runtime but should be ignored by a type checker.

(emphasis mine)

I must say I find this underwhelming.