Neural Theorem Proving: Generating and Structuring Proofs for Formal Verification

• URL: http://arxiv.org/abs/2504.17017v1
• Date: Wed, 23 Apr 2025 18:04:38 GMT
• Title: Neural Theorem Proving: Generating and Structuring Proofs for Formal Verification
• Authors: Balaji Rao, William Eiers, Carlo Lipizzi,
• Abstract summary: We introduce a framework that generates whole proofs in a formal language to be used within systems that utilize the power of built-in tactics and off-the-shelf automated theorem provers.<n>To train the LLM, we employ a 2-stage finetuning process, where we first use SFT-based training to enable the model to generate syntactically correct Isabelle code.<n>We validate our framework using the miniF2F-test benchmark and the Isabelle proof assistant and design a use case to verify the correctness of the S3 bucket access policy code.
• Score: 0.4779196219827508
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and mechanistic interpretability. Since the introduction of code-specific models, despite their successes in generating code in Lean4 and Isabelle, the task of generalized theorem proving still remains far from being fully solved and will be a benchmark for reasoning capability in LLMs. In this work, we introduce a framework that generates whole proofs in a formal language to be used within systems that utilize the power of built-in tactics and off-the-shelf automated theorem provers. Our framework includes 3 components: generating natural language statements of the code to be verified, an LLM that generates formal proofs for the given statement, and a module employing heuristics for building the final proof. To train the LLM, we employ a 2-stage fine-tuning process, where we first use SFT-based training to enable the model to generate syntactically correct Isabelle code and then RL-based training that encourages the model to generate proofs verified by a theorem prover. We validate our framework using the miniF2F-test benchmark and the Isabelle proof assistant and design a use case to verify the correctness of the AWS S3 bucket access policy code. We also curate a dataset based on the FVEL\textsubscript{\textnormal{ER}} dataset for future training tasks.

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