Hey, first author here, and you are right to think that there are a lot of computational processes that can be "cast" into tiny programming languages. This is more apparent with DB queries (and I think there is a long list of papers on this topic) but less for graphics, which is why I found this so exciting to work on. If you peek at the last paragraph in the related works section of the paper, you will see a list of papers that try to do exactly that for a variety of graphics/fabrication domains.

I think good-old fashioned AI is the key here! Lot of the Lean proofs are discharged by a proof-search procedure called "grind". And if "grind" fails, an LLM can read the logs of the failed proof-search and figure out if there are any missing theorems needed.