assign_coords adds coordinates without a new dimension if the value is scalar

Problem

assign_corods correctly disallows creating a new dimension when assigning list-like coords with a name that does not match an existing dimension. However, it does allow this operation if the value is scalar.

MCVE

Consider the following DataArray:

>>> coords = {"fruit": ("x", ["apple", "banana"])}
>>> arr = xr.DataArray([[1, 2, 3], [4, 5, 6]], dims=("x", "y"), coords=coords)
>>> arr
<xarray.DataArray (x: 2, y: 3)>
array([[1, 2, 3],
       [4, 5, 6]])
Coordinates:
    fruit    (x) <U6 'apple' 'banana'
Dimensions without coordinates: x, y

I can assign new coordinates to an existing dimension:

>>> arr.assign_coords(color=("x", ["red", "yellow"]))
<xarray.DataArray (x: 2, y: 3)>
array([[1, 2, 3],
       [4, 5, 6]])
Coordinates:
    fruit    (x) <U6 'apple' 'banana'
    color    (x) <U6 'red' 'yellow'
Dimensions without coordinates: x, y

And I cannot (correctly) assign coordinates to a new (nonexistent) dimension:

>>> arr.assign_coords(color=["red", "yellow"])
...
ValueError: cannot add coordinates with new dimensions to a DataArray

The above fails because Xarray, in the absence of an explicit dimension, tries to assign the new coordinates to a color dimension which does not exist. So far so good. But why does this work?

>>> arr = arr.assign_coords(color="red")
>>> arr
<xarray.DataArray (x: 2, y: 3)>
array([[1, 2, 3],
       [4, 5, 6]])
Coordinates:
    fruit    (x) <U6 'apple' 'banana'
    color    <U3 'red'
Dimensions without coordinates: x, y

I would expect this to fail because color is not a dimension. But these appear to be newly added coordinates without a dimension?

>>> arr.coords
Coordinates:
    fruit    (x) <U6 'apple' 'banana'
    color    <U3 'red'

[gwgundersen]

I see. This is because coordinates are just DataArray objects. So

>>> arr.coords['y'] = range(3)

is equivalent to

>>> new_coords = xr.DataArray(data=range(3))
>>> arr.coords['y'] = new_coords

And the reason this is a ValueError is that new_coords has a default dimension dim_0 that is not on arr. However, this

>>> arr.coords['y'] = 1

is equivalent to…

>>> new_coords = xr.DataArray(data=1, dims=[])
>>> arr.coords['y'] = new_coords

And new_coords has no dimensions that are not on arr.

[shoyer]

This was intentional. array.assign_coords(name=value) should be equivalent to array = array.copy(deep=False); array.coords[name] = value.

You are allowed to add new coordinates to a DataArray if they share existing dimensions. You are not allowed to add coordinates with new dimensions, because it is enforced as an invariant of the DataArray data model that all coordinate dimensions are found on the DataArray variable as well.