(Apologies if this is a typeshed issue.) When calling min with different types for the iterable and the default, like min(Iterable[T], default=S), min often does not infer the correct type for the result, and gives a confusing error message "Cannot infer type argument 1 of "min". I assumed that meant it couldn't infer the type of argument 1, but I think it actually means it can't infer the first (only) type parameter in the definition:

def min(iterable: Iterable[_T], key: Callable[[_T], Any] = ..., default: _T = ...) -> _T: ...

I would expect the result of min(Iterable[T], default=S) to be:

• The common supertype of S and T (possibly S or T itself), if they share a supertype narrower than Any or object
• Union[S, T] otherwise (Optional[T] in the case S is None)

But maybe that's hard / impossible to express with the type system?

Here's some code that illustrates the problem. Oddly, fixed-length tuples typecheck fine, but variable-length tuples do not. Explicitly specifying the type of the result (which is the same as the type parameter) does not help.

from typing import Tuple, Optional

t1 = (0, 1, 2)          # type: Tuple[int, int, int]        # The inferred type without any type hint
min(t1, default=None)   # typechecks

t2 = (0, 1, 2)          # type: Tuple[int, ...]
min(t2, default=None)   # error: Cannot infer type argument 1 of "min"
min(t2, default=None)   # type: Optional[int]               # Does not help

min([0, 1, 2], default=None)        # error: Cannot infer type argument 1 of "min"
min(iter((0, 1, 2)), default=None)  # error: Cannot infer type argument 1 of "min"

$ python -V ; pip freeze | egrep 'mypy|typing'
Python 3.4.3+
mypy==0.501
typing==3.6.1