Static Allocation with Zig

Theoretically infinite memory isn't really the problem with reasoning about Turing-complete programs. In practice, the inability to guarantee that any program will halt still applies to any system with enough memory to do anything more than serve as an interesting toy.

I mean, I think this should be self-evident: our computers already do have finite memory. Giving a program slightly less memory to work with doesn't really change anything; you're still probably giving that statically-allocated program more memory than entire machines had in the 80s, and it's not like the limitations of computers in the 80s made us any better at reasoning about programs in general.

Most applications don’t need to bother the user with things like how much memory they think will be needed upfront. They just allocate how much and when necessary. Most applications today are probably servers that change all the time. You would not know upfront how much memory you’d need as that would keep changing on every release! Static allocation may work in a few domains but it certainly doesn’t work in most.

Knowledge sharing with next generations is one of those very tricky things.

For one thing, how would I know where to find this? What book? What teacher? There are so many books, must I read all of them? What if my coworkers awaren't aware of it, how can they share it with me?

Also, an old saying goes, if you're good at something, never do it for free. This isn't exactly a trade secret, but how many people blog about every advanced technique and trick they know? I blogged about how to create real C function pointers from Lua closures, as a way to advertise for my product, but that could very well have been kept a trade secret (and probably should have, as I got 0 sales from that blog post still). Why would anyone want to share this "tiger style" knowledge with newer generations with no personal benefit? Aren't they incentivized to use it secretly, or maybe write it in a book, or blog about it for advertising?

That "once all the input has been given to the program" is doing a bit of heavy lifting since we have a number of programs where we have either unbounded input, or input modulated by the output itself (e.g., when a human plays a game their inputs are affected by previous outputs, which is the point after all), or other such things. But you can model all programs as their initial contents and all inputs they will ever receive, in principle if not in fact, and then your program is really just a finite state automaton.

Static allocation helps make it more clear, but technically all computers are bounded by their resources anyhow, so it really doesn't change anything. No program is Turing complete.

The reason why we don't think of them this way is several fold, but probably the most important is that the toolkit you get with finite state automata don't apply well in our real universe to real programs. The fact that mathematically, all programs can in fact be proved to halt or not in finite time by simply running them until they either halt or a full state of the system is repeated is not particularly relevant to beings like us who lack access to the requisite exponential space and time resources necessary to run that algorithm for real. The tools that come from modeling our systems as Turing Complete are much more practically relevant to our lives. There's also the fact that if your program never runs out of RAM, never reaches for more memory and gets told "no", it is indistinguishable from running on a system that has infinite RAM.

Technically, nothing in this universe is Turing Complete. We have an informal habit of referring to things that "would be Turing Complete if extended in some reasonably obvious manner to be infinitely large" as simply being Turing Complete even though they aren't. If you really, really push that definition, the "reasonably obvious manner" can spark disagreements, but generally all those disagreements involve things so exponentially large as to be practically irrelevant anyhow and just be philosophy in the end. For example, you can't just load a modern CPU up with more and more RAM, eventually you would get to the point where there simply isn't enough state in the CPU to address more RAM, not even if you hook together all the registers in the entire CPU and all of its cache and everything else it has... but such an amount of RAM is so inconceivably larger than our universe that it isn't going to mean anything practical in this universe. You then get into non-"obvious" ways you might extend it from there, like indirect referencing through other arbitrarily large values in RAM, but it is already well past the point where it has any real-world meaning.