I think we don't have to make it sounds like there are *that* many types of compatibility: really there is just array organisation (indexing/reshaping) and array arithmetic. These correspond roughly to ShapedLikeNDArray in astropy and NDArrayOperatorMixin in numpy (missing so far is concatenation). The advantage of the ABC classes is that they can supply missing methods (say, size, isscalar, __len__, and ndim given shape; __iter__ given __getitem__, ravel, squeeze, flatten given reshape; etc.).
-- Marten
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