arXiv:2606.03303v1 Announce Type: new Abstract: Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean. We present LEAP, an agentic framework that enables general-purpose foundation models to achieve state-of-the-art performance on automated formal theorem proving. LEAP leverages foundation model capabilities, such as informal reasoning, instruction following, and iterative self-refinement. By decomposing complex problems into smaller units, the system bridges formal proof construction wi
The continuous development of advanced LLMs and their ongoing limitations in formal reasoning necessitate agentic frameworks to bridge the gap between informal language understanding and rigorous logical proof. This innovation arises from the urgent need to deploy LLMs in high-stakes domains requiring verifiability.
This development significantly enhances LLMs' capabilities in formal mathematics, potentially accelerating research in fields reliant on proofs and precise logical structures, while also laying groundwork for more reliable AI systems. It expands the scope of tasks where AI can autonomously contribute to foundational knowledge.
General-purpose LLMs can now achieve state-of-the-art performance in automated formal theorem proving, moving beyond informal reasoning to mechanically verifiable proofs. This changes the landscape of AI-assisted mathematical discovery and proof generation.
- · AI research labs
- · Formal verification sector
- · Software engineering (for bug proving)
- · Mathematics community
- · Tasks requiring manual formal proof
- · AI developers focused solely on informal reasoning
- · Traditional theorem proving software without agentic integration
LLMs become significantly more capable in formal logic and automated theorem proving.
This improved capability leads to faster development and verification of complex algorithms and software, reducing errors and increasing system reliability.
The acceleration of formal proof generation could lead to breakthroughs in fundamental mathematics and computer science that were previously bottlenecked by the difficulty of human-generated proofs.
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Read at arXiv cs.AI