Summary of Proving Theorems Recursively, by Haiming Wang et al.
Proving Theorems Recursively
by Haiming Wang, Huajian Xin, Zhengying Liu, Wenda Li, Yinya Huang, Jianqiao Lu, Zhicheng Yang, Jing Tang, Jian Yin, Zhenguo Li, Xiaodan Liang
First submitted to arxiv on: 23 May 2024
Categories
- Main: Artificial Intelligence (cs.AI)
- Secondary: None
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A recent advancement in automated theorem proving uses language models to explore expanded search spaces through step-by-step proof generation. However, most approaches rely on short-sighted heuristics like log probability or value function scores that can lead to suboptimal or distracting subgoals, hindering the discovery of longer proofs. To overcome this challenge, the POETRY (PrOvE Theorems RecursivelY) approach proves theorems in a recursive, level-by-level manner within the Isabelle theorem prover. Unlike previous methods, POETRY searches for a verifiable sketch of the proof at each level and focuses on solving the current level’s theorem or conjecture. Intermediate conjectures are temporarily replaced by a placeholder tactic called sorry, deferring their proofs to subsequent levels. This allows the theorem to be tackled incrementally, outlining the overall theorem at the first level and then solving intermediate conjectures at deeper levels. The POETRY approach is evaluated on the miniF2F and PISA datasets, achieving significant performance gains over state-of-the-art methods. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Automated theorem proving uses language models to find longer proofs. However, current approaches use short-sighted heuristics that can lead to incomplete or distracting subgoals. A new method called POETRY proves theorems in a step-by-step manner, focusing on solving each level’s theorem or conjecture. It does this by searching for a sketch of the proof at each level and temporarily replacing intermediate steps with a placeholder tactic. This approach allows the theorem to be solved incrementally, starting with the overall theorem and then filling in the details. The POETRY method is tested on two datasets and finds longer proofs than current methods. |
Keywords
» Artificial intelligence » Probability
