Wow! This is exciting. I have speculated that this would be possible. Since I've been learning about databases and dynamic db query optimization, it struck me as surprising that we didn't have similar things for more of our computational universe. Now that this is here, it makes me wonder what else we can optimize in using the same high level techniques.
The more you know about what you want to do ahead of time, the more optimally you can reorder your sequence of steps to give a better-than-naive solution. It makes me think about all software in terms of these abstract computation graphs and makes me wonder what else we can optimize automatically.
Of course, we do absolutely do need a formal model here, so we know what edits are possible, the same way db engines have relational algebra as their backing model. But this whole thing makes me feel like manual software optimization is soon to fall to AI. And I'm thinking that includes good-old-fashion AI first, not second, to LLM's. But I'm sure LLMs would be useful here too, especially for the formalization.
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.
eigenblake · · focus · HN ↗
The more you know about what you want to do ahead of time, the more optimally you can reorder your sequence of steps to give a better-than-naive solution. It makes me think about all software in terms of these abstract computation graphs and makes me wonder what else we can optimize automatically.
Of course, we do absolutely do need a formal model here, so we know what edits are possible, the same way db engines have relational algebra as their backing model. But this whole thing makes me feel like manual software optimization is soon to fall to AI. And I'm thinking that includes good-old-fashion AI first, not second, to LLM's. But I'm sure LLMs would be useful here too, especially for the formalization.
bhargavkk · · focus · HN ↗
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.