This PR adds some typing to several abstract base classes that are used in xarray.

Most of it is working, only one major point I could not figure out:

What is the type of NDArrayMixin.array??? I would appreciate it if someone that has more insight into this would help me.

Several minor open points:

• What is the return value of ExplicitlyIndexed.__getitem__
• What is the return value of ExplicitlyIndexed.transpose
• What is the return value of AbstractArray.data
• Variable.values seems to be able to return scalar values which is incompatible with the AbstractArray definition.

Overall it seems that typing has helped to find some problems again :)

Mypy should fail for tests, I did not adopt them yet, want to solve the outstanding issues first.

This PR adds a utils.parse_dims function for parsing one or more dimensions. Currently every function that accepts multiple dimensions does this by itself.

I decided to first see if it would be useful to centralize the dimension parsing and collect inputs before adding it to other functions.

What happened?

We used Data{set,Array}.rename{_vars}({coord: dim_coord}) to make a coordinate a dimension coordinate (instead of set_index). This results in the coordinate correctly being displayed as a dimension coordinate (with the *) but it does not create an index, such that further operations like sel fail with a strange KeyError.

What did you expect to happen?

I expect one of two things to be true:

1. rename{_vars} does not allow setting dimension coordinates (raises Error and tells you to use set_index)
2. rename{_vars} checks for this occasion and sets the index correctly

Minimal Complete Verifiable Example

```python import xarray as xr

data = xr.DataArray([5, 6, 7], coords={"c": ("x", [1, 2, 3])}, dims="x")

<xarray.DataArray (x: 3)>

array([5, 6, 7])

Coordinates:

c (x) int64 1 2 3

Dimensions without coordinates: x

data_renamed = data.rename({"c": "x"})

<xarray.DataArray (x: 3)>

array([5, 6, 7])

Coordinates:

* x (x) int64 1 2 3

data_renamed.indexes

Empty

data_renamed.sel(x=2)

KeyError: 'no index found for coordinate x'

if we use set_index it works

data_indexed = data.set_index({"x": "c"})

looks the same as data_renamed!

<xarray.DataArray (x: 3)>

array([1, 2, 3])

Coordinates:

* x (x) int64 1 2 3

data_indexed.indexes

x: Int64Index([1, 2, 3], dtype='int64', name='x')

```

Relevant log output

No response

Anything else we need to know?

No response

Environment

INSTALLED VERSIONS

commit: None python: 3.9.1 (default, Jan 13 2021, 15:21:08) [GCC 4.8.5 20150623 (Red Hat 4.8.5-44)] python-bits: 64 OS: Linux OS-release: 3.10.0-1160.49.1.el7.x86_64 machine: x86_64 processor: x86_64 byteorder: little LC_ALL: None LANG: en_US.UTF-8 LOCALE: ('en_US', 'UTF-8') libhdf5: 1.12.0 libnetcdf: 4.7.4

xarray: 0.20.2 pandas: 1.3.5 numpy: 1.21.5 scipy: 1.7.3 netCDF4: 1.5.8 pydap: None h5netcdf: None h5py: None Nio: None zarr: None cftime: 1.5.1.1 nc_time_axis: None PseudoNetCDF: None rasterio: None cfgrib: None iris: None bottleneck: None dask: None distributed: None matplotlib: 3.5.1 cartopy: None seaborn: None numbagg: None fsspec: None cupy: None pint: None sparse: None setuptools: 49.2.1 pip: 22.0.2 conda: None pytest: 6.2.5 IPython: 8.0.0 sphinx: None

Is your feature request related to a problem? Please describe. I have a dataset where I do not know which of two dimensions (lets call them a and b) exists in this dataset (So either it has dims ("a", "other") or ("b", "other")). I would like to make sure that this dimension is first using transpose, but currently this is only possible using if or try statements. Just using ds.transpose("a", "b", "other") raises a ValueError arguments to transpose XXX must be permuted dataset dimensions YYY.

Describe the solution you'd like It would be nice if I could just use ds.transpose("a", "b", "other", missing_dims="ignore") similar to how DataArray.transpose handles it.

Describe alternatives you've considered Currently I'm also using ds.map(lambda x: x.transpose("a", "b", "other", missing_dims="ignore")), which could (maybe?) replace the current implementation of the transpose.

While at it, transpose_coords could also be exposed to Dataset.transpose.