LLM is very good at programming when there are huge number of guardrails against them. For example, exploit testing is a great usecase because getting a shell is getting a shell.
They kind of acts as a smarter version of infinite monkey that can try and iterate much more efficiently than human does.
On the other hand, in tasks that requires creativity, architecture, and projects without guard rail, they tend to do a terrible job, and often yielding solution that is more convoluted than it needs to be or just plain old incorrect.
I find it is yet another replacement for “pure labor”, where the most unintelligent part of programming, i.e. writing the code, is automated away. While I will still write code from scratch when I am trying to learn, I likely will be able automate some code writing, if I know exactly how to implement it in my head, and I also have access to plenty of testing to gaurentee correctness.
I believe they are higher dimensional string diagrams. Maybe called n-diagrams? They are used in higher homotopy and higher category theory, I believe. But not entirely sure.
https://arxiv.org/pdf/2305.06938
EDIT: Found it! they are called surface diagram, which are generalization of string diagram to 3-categories https://golem.ph.utexas.edu/category/2010/03/modeling_surface_diagrams.html https://ncatlab.org/nlab/show/surface+diagram
Still not sure what the proof is talking about though :(
But from the conclusion it looks like some sort of natruality condition, where the morphisms are slided around except beta.
EDIT AGAIN: got in touch with my string diagram contact. Here is the paper https://arxiv.org/pdf/0807.0658
Note the conclusion at the bottom, the proof on the right and the axiom on the left doesn’t seem to be related.
The proof on the right is Theorem 6; the equality at bottom is in section 3.4, where the proof is omitted because “follows from definition”; the axiom on the left is HM1 and HM2 on page 19.