Since LaTeX is Turing Complete it is clearly possible, albeit very inefficient, but would it be remotely feasible as a stunt? Moreover, is it currently being done or has there been a proof of work/concept?
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First of all, LaTeX isn't a language itself, but a set of macros for the TeX language. As TeX is Turing Complete, it can do anything that any other language can do, including, a priori, mine cryptocurrency.
However, it doesn't make any sense at all. It's like using PHP for operating system development. Just for example: although, in principle, TeX can do everything, the LuaLaTeX compiler accepts Lua code to facilitate some things. So TeX isn't suitable even for some typesetting needs.
Finally, the answer is probably no, there's no reason why somebody would be working on this kind of stuff.
Héliton Martins
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1Well, there are some fairly nefarious reasons, a lot of servers host exposed TeX compilers. – Zackkenyon Jan 29 '22 at 21:52
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Yep, but TeX limits the RAM usage by default (what sometimes avoid even some typesetting needs, like generating big figures). – Héliton Martins Feb 02 '22 at 18:45