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LeanDojoChatGPT reviews and mentions
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'A-Team' of Math Proves a Critical Link Between Addition and Sets
Check out this paper:
https://leandojo.org/
People have already trained models to assist suggestion tactics. They then linked it up to ChatGPT to interactively solve proofs.
In this scenario, ChatGPT asks the model for tactic suggestions, applies it to the proof and uses the feedback from Lean to then proceed with the next step.
FYI, The programmatic interface to Lean was written by an OpenAI employee who was on the Lean team a few years ago.
Also, check out Lean’s roadmap. They aspire to position Lean to becoming a target for LLMs because it has been designed for verification from the ground up.
As math and compsci nerds contribute to mathlib, all of those proofs are also building up a huge corpus that will likely be leveraged for both verification and optimization.
If AI can make verification a lot easier, then we’re likely going to see verification change programming similarly to the way it changed electronics.
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Formalizing 100 Theorems
Good questions!
Nowadays, there is indeed a movement towards interoperability between the various proof assistants, one of these bridge-building projects is called Dedukti: https://deducteam.github.io/ It's a challenging project because the different proof assistants which are currently in use differ in their foundational perspectives and their idioms. The question how to best formalize mathematics is still an open research problem, just as the question how to best develop programs, but we already have quite a good understanding of many important issues in this area.
Also, by now there are attempts to use AI for discovering proofs, see for instance https://leandojo.org/ or https://github.com/lean-dojo/LeanDojoChatGPT.
Stats
lean-dojo/LeanDojoChatGPT is an open source project licensed under MIT License which is an OSI approved license.
The primary programming language of LeanDojoChatGPT is Python.
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