Hi Stephan,
I fear my example about thinking about `ndarray.__array_function__` distracted from the gist of my question, which was whether for `__array_function__` implementations *generally* it wouldn't be handier to have all unique types rather than just those that override `__array_function__`. It would seem that for any other implementation than for numpy itself, the presence of __array_function__ is indeed almost irrelevant. As a somewhat random example, why would it, e.g., for DASK be useful to know that another argument is a Quantity, but not that it is a file handle? (Presumably, it cannot handle either...)
In practice, it is of course easy to simply ignore arguments that don’t define __array_function__. But I do think the distinction is important for more than merely ndarray: the value of the types argument tells you the set of types that might have a conflicting implementation.
For example, Dask might be happy to handle any non-arrays as scalars (like NumPy), e.g., it should be fine to make a dask array consisting of a decimal object. Since decimal doesn’t define __array_function__, there’s no need to do anything special to handle it inside dask.array.Array.__array_function__. If decimal appeared in types, then dask would have to be careful to let arbitrary types that don’t define __array_function__ pass through.
In contrast, dask definitely wants to know if another type defines __array_function__, because they might have a conflicting implementation. This is the main reason why we have the types argument in the first place — to make these checks easy. In my experience, it is super common for Python arithmetic methods to be implemented improperly, i.e., never returning NotImplemented. This will hopefully be less common with __array_function__.
More broadly, it is only necessary to reject an argument type at the __array_function__ level if it defines __array_function__ itself, because that’s the only case where it would make a difference to return NotImplemented rather than trying (and failing) to call the overriden function implementation.
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