[taliesinb]

Thanks for highlighting XArray in your other comments. Yup, XArray is great. As are Dex and the various libraries for named axis DL programming within PyTorch and Jax. I never said these things don't exist -- I even mention them in the linked blog series!

But I do think it's fair to say they are in their infancy, and there is a missing theoretical framework to explain what is going on.

I anticipate name-free array programming will eventually be considered a historical curiosity for most purposes, and everyone will wonder how we put up without it for so long.

[WCSTombs]

Thanks for pointing that out, and sorry for being redundant. I skimmed the blog but missed that.

Overall, I agree with your larger point. I think this it's a natural progression and pretty analogous to assembly language leading to higher-level languages with a much better developer experience. In that case we went from fixed registers to developer-named variables, and now we can go from fixed numerically-indexed array axes to ones indexed by developer-chosen names.

[taliesinb]

No worries! Yes, exactly. It's also similar to doing arithmetic with and without units. Sure, you can do arithmetic without units, but when you are actually working with real-world quantities, but you easily get yourself into a muddle. Unit-carrying quantities and algebraic systems built on them prevent you from doing silly things, and in fact guide you to getting what you want.