Related papers: Premise Selection for a Lean Hammer
Vampire has been for a long time the strongest first-order automatic theorem prover, widely used for hammer-style proof automation in ITPs such as Mizar, Isabelle, HOL, and Coq. In this work, we considerably improve the performance of…
Hammers are tools that provide general purpose automation for formal proof assistants. Despite the gaining popularity of the more advanced versions of type theory, there are no hammers for such systems. We present an extension of the…
We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…
While large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, current benchmarks fail to adequately measure library-grounded abstraction -- the ability to reason with high-level interfaces and…
MerLean-Prover is an end-to-end Lean4 theorem prover that replaces sorry declarations with kernel-checkable proofs. It is built from three agent types (Planning, Check, and Lean) composed by a recursive outer loop whose unit of revision is…
Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…
Automated proof generation for formal software verification remains largely unresolved despite advances in large language models (LLMs). While LLMs perform well in NLP, vision, and code generation, formal verification still requires…
Lean processes focus on doing only necessery things in an efficient way. Artificial intelligence and Machine Learning offer new opportunities to optimizing processes. The presented approach demonstrates an improvement of the test process by…
Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers…
General-purpose Large Language Models (LLMs) have achieved remarkable success in intelligence, performing comparably to human experts on complex reasoning tasks such as coding and mathematical reasoning. However, generating formal proofs in…
Lean is an increasingly popular proof assistant based on dependent type theory. Despite its success, it still lacks important automation features present in more seasoned proof assistants, such as the Sledgehammer tactic in Isabelle/HOL. A…
Spatial-temporal reasoning is a challenging task in Artificial Intelligence (AI) due to its demanding but unique nature: a theoretic requirement on representing and reasoning based on spatial-temporal knowledge in mind, and an applied…
This paper introduces PRIMETIME, a synthetic generator that supports both benchmarking and fine-tuning of two primitive operations underlying temporal reasoning in Large Language Models (LLMs): parsing and arithmetic on datetimes. Existing…
Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…
AI-driven autoformalization of mathematics is advancing rapidly. However, the type checker of a proof assistant guarantees only the logical correctness of proofs; it does not verify whether propositions and definitions faithfully capture…
Neural theorem proving has advanced rapidly in the past year, reaching IMO gold-medalist capabilities and producing formal proofs that span thousands of lines. Although such proofs are mechanically verified by formal systems like Lean,…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Recent advances have shown that optimizing prompts for Large Language Models (LLMs) can significantly improve task performance, yet many optimization techniques rely on heuristics or manual exploration. We present LatentPrompt, a…
Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct…
Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…