TYP: Many typing constructs are invariant
Indexes and columns can be of any hashable type: we often have functions accepting a list/dict/callables of hashable types.

Unfortunately, List/Dict/Mapping/Callable are all invariant in their (first) argument, which leads to unintuitive behavior:

```py
from typing import Hashable

def test(x: list[Hashable]) -> None:
    ...

x1: list[str] = ["a"]  # str is Hashable
test(x1)  # but this still errors

x2: list[Hashable] = ["a"]
test(x2)  # works
```

One (honestly not well-promotet) use case of TypeVars is to allow sub-classes in these cases:

```py
from typing import Hashable, TypeVar

HashableT = TypeVar("HashableT", bound=Hashable)

def test(x: list[HashableT]) -> None:
    ...

x1: list[str] = ["a"]  # str is Hashable
test(x1)  # works :)

x2: list[Hashable] = ["a"]
test(x2)  # still works
```

If we had type tests, we would have noticed this earlier - Thanks to @Dr-Irv for finding this!

xref https://github.com/pandas-dev/pandas/pull/46428#discussion_r835795663

It might be worth preventing Hashable being the first argument to the above typing containers by enforcing that in pandas-dev-flaker
> The issue seems to be how mypy is interpreting the type of `dt` and that inferred type is not compatible with the `Dict` that uses `HashableT` as its key.

In this case it semes to be an issue with the values, not the keys:

> error: Argument "dtype" to "read_csv" has incompatible type "Dict[str, object]"; expected "Optional[Union[Union[ExtensionDtype, Union[str, dtype[Any], Type[str], Type[float], Type[int], Type[complex], Type[bool], Type[object]]], Dict[Any, Union[ExtensionDtype, Union[str, dtype[Any], Type[str], Type[float], Type[int], Type[complex], Type[bool], Type[object]]]]]]"  [arg-type]

```py
NpDtype = Union[str, np.dtype, type_t[Union[str, float, int, complex, bool, object]]]
Dtype = Union["ExtensionDtype", NpDtype]
DtypeArg = Union[Dtype, Dict[HashableT, Dtype]]
```

But there will be issue when multiple HashableT are used within the same function:

```py
from typing import Hashable, TypeVar, List, Dict

HashableT = TypeVar("HashableT", bound=Hashable)

def test(a: Dict[HashableT, str], b:  List[HashableT]) -> None:
    ...

a: Dict[str, str] = {}
b: List[int] = []

test(a, b)  # error
```

If TypeVar is a way to get covariant behavior with these typing containers, then we might need many TypeVars: `HashableT1,, HashableT2, ...` Honestly, I would be inclined to wait until we have type tests, then we know empirically how many we need. > If TypeVar is a way to get covariant behavior with these typing containers, then we might need many TypeVars: `HashableT1,, HashableT2, ...` Honestly, I would be inclined to wait until we have type tests, then we know empirically how many we need.

Based on the discussions that happened as a result of me raising the issue with `mypy`, I don't think that `TypeVar` is the way to get the covariant behavior.  I think we need to use `Sequence[sometype]` instead of `List[sometype]`, where `sometype` is a `Union` or parent of multiple types (e.g., `Hashable`), as that will be covariant.  `List[str]` is OK, but replace `List[str|int]` with `Sequence[str|int]` and replace `List[Hashable]` with `Sequence[Hashable]` .  For `Mapping` and `Dict`, we can't use `Hashable` or `HashableT` as a key - have to switch to `Any`.  I think `Hashable` is OK as the value of a `Mapping` and `Dict` > I think we need to use `Sequence[sometype]` instead of `List[sometype]`

I agree, this is definitely the better option if the implementation actually works with any Sequence (tuples are often handles very differently than lists in pandas).

> For `Mapping` and `Dict`, we can't use `Hashable` or `HashableT` as a key - have to switch to `Any`.

I have not yet understood why we cannot use a TypeVar for keys. As far as I understand, it is the only way to achieve covariant keys (assuming that the TypeVar is used once in the definition). Introducing many Anys in the code base reduces the benefit of  type checking the pandas code itself.

I didn't test this: can Protocols be used as dict keys - might be another why to deal with this.

edit: Hashable is a protocol :( https://github.com/python/typeshed/blob/e8fe316a74b49fae43efe36859c294888160d399/stdlib/typing.pyi#L666 > I have not yet understood why we cannot use a TypeVar for keys. As far as I understand, it is the only way to achieve covariant keys (assuming that the TypeVar is used once in the definition). Introducing many Anys in the code base reduces the benefit of type checking the pandas code itself.

I don't fully understand it either, but here's another way to look at it.

A dictionary or mapping key _must_ be hashable.  For example, you cannot create a `dict` that has keys that are lists.  So if we think of the universe as consisting of distinct sets of types `Hashable` and `NonHashable` types, and all those together correspond to `Any`, then it is impossible to create a `dict` object that has keys that are of type `NonHashable` .  So if a method expects an argument that is a `dict` with keys that are `Hashable`, and we declare that type `dict[Any, Hashable]`, then the typing is doing what it is supposed to do (allow a `dict` with any valid type for the keys) because it is impossible to have a non-hashable key.

Where things get harder is where you want to restrict the keys to be a union of 2 types, e.g., `dict[int | str, str]` .  I think a `TypeVar` _might_ work there (more testing would be required), but `Hashable` is so special that we're better off not using it as the type of a key in a `dict` or `Mapping` .
 > A dictionary or mapping key must be hashable.

That works for dict, but Mapping doesn't seem to have this requirement based on typeshed.

I'll close this PR. I think we need to address this on a case to case basis and test what works and what doesn't.