DatetimeLike annotation does not appear to work with dates

[gandhis1]

This example is bdate_range, but I suspect this issue is spread more widely.

    import pandas as pd
    from typing import Optional
    from datetime import date
    a: Optional[date] = date(2022, 1, 1)
    b: Optional[date] = date(2022, 1, 10)
    dr = pd.bdate_range(a, b, freq="d")

error: Argument 2 to "bdate_range" has incompatible type "Optional[date]"; expected "Union[str, Union[datetime, datetime64, Timestamp], None]" [arg-type]

Tagging @bashtage as I think he's done some work around this recently. It seems to me that we may have made an assumption somewhere that date is a subset of datetime (it's actually the opposite).

[bashtage]

The issue was that date is not datetime-like in the sense that some pandas functions that lise datetime-like do not accept date. What is needed is a new type DateAndDatetimeLike that includes DateTimeLike + date, but this needs to be thoroughly tested.

[gandhis1]

I am actually surprised that some functions don't accept date. Do you have any examples? I'm wondering if it's more of an oversight than an actual incompatibility. Or is it just that the docs don't say that it accepts a date when it does?

I don't have any hard facts, but I suspect that more of the pandas time series API accepts a date than doesn't. If you agree with that, can we just revert the change?

[bashtage]

It was one of the functions in #351. I tried all of the datetime-like in the type alias and date raised. Basically, it seem there is no consistent definition of what is "datetime like" in pandas.

We shouldn't revert the change since that will result in too broad static typing. All functions that take DatetimeLike should be tested wtih date, and if they pass they should use a new type (e.g. DateAndDatetimeLike).

[bashtage]

The function was interval_range