HOL4PSG: AI-Driven Proof Sequence Generation for the HOL4 Theorem Prover
Bibliographic record
Abstract
Interactive theorem proving is an inherently complex and expertise-intensive process, requiring significant user intervention and deep domain knowledge. This complexity often hinders the construction of valid proofs and limits the accessibility of formal verification tools. HOL4, a powerful theorem prover widely used in formal methods, exemplifies these challenges due to the intricate structure of formal proofs and the cognitive burden placed on users. To address these limitations, this paper presents HOL4PSG, an Artificial Intelligence (AI)-driven Proof Sequence Generation framework that enhances both the usability and efficiency of interactive theorem proving by leveraging Large Language Models (LLMs). Specifically, we employ sequence-to-sequence architectures, such as MarianMT and T5 to automatically generate complete proof sequences from given theorem statements. This task is particularly demanding due to the need to capture intricate logical dependencies and ensure proof validity. Our training pipeline includes extensive hyperparameter tuning and performance evaluation to optimize the model’s effectiveness. Experimental results demonstrate that HOL4PSG significantly reduces the cognitive load on users while improving proof construction efficiency, outperforming existing approaches in terms of accuracy and usability.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.021 | 0.008 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".