tl;dr Great point @abrudz -- I wish MDAPL went deeper into things like this -- not just the how to but the underlying why

That is a GREAT point. I had not considered that reduce1st was the more fundamental operation than reduce. It's things like this that still stun me about APL. In fact, I would like to offer that I think insights like this are the only short coming of MDAPL -- I feel like there should be a sequel or some additional insights into the deeper thinking behind it.

For instance, in the classic CS curriculum, one of the foundational schools of thought is lambda calculus -- which we are taught is equivalent to a turing machine (aka an infinite length vector) -- and that one of the first things we learn to construct from pure functions is a cons or pair, and then from nesting pairs we learn to make a linked list. We are then taught that associative data structures are made by creating a list of pairs, and "objects" and polymorphism are made from functions that "pass messages" to specially constructed associative lists, an so on. And I've gone on to repeat this to my students as time goes on.

However, I suspect based on my learning of APL that tensors are a mathematically equivalent way to represent general computation. However my first reading of "Mastering Dyalog" felt like a teaser -- that there are many truths and proofs like the one @abrudz just presented -- that are only hinted at.

It also seems like array-oriented programmers are largely partitioned off from the rest of devs so it's hard to bump into that information by accident. So for instance, it's hard to understand what non-trivial day-to-day applications would look like. For instance, writing a web server or parsing a text document -- but it's clearly possible. Not only that, the underlying algorithms for things like the magical inner product function are not treated in MDAPL.

Given the importance of tensors to ML/AI, I am really surprised there is not a lot more research and training invested into array oriented programming. In some of the scientific computing circles we're making efforts to understand tensors better and some early experimental efforts and incorporating APL into the language, but I feel like I'm poking a very elegant and complex machine with a stick to try to understand how it works. Besides MDAPL, I'm not even sure where to go to get deeper insight!

Anyway thanks for listening to my TED talk and all the great work on MDAPL!

Should the book be first-axis oriented? #16

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