Related papers: Bootstrapping LCF Declarative Proofs
We present StepFun-Prover Preview, a large language model designed for formal theorem proving through tool-integrated reasoning. Using a reinforcement learning pipeline that incorporates tool-based interactions, StepFun-Prover can achieve…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
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…
A focused proof system provides a normal form to cut-free proofs that structures the application of invertible and non-invertible inference rules. The focused proof system of Andreoli for linear logic has been applied to both the proof…
In this work, we present an approach towards constructing executable specifications of existing filesystems and verifying their functional properties in a theorem proving environment. We detail an application of this approach to the FAT32…
Fact verification requires validating a claim in the context of evidence. We show, however, that in the popular FEVER dataset this might not necessarily be the case. Claim-only classifiers perform competitively with top evidence-aware…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
Proving mathematical theorems using computer-verifiable formal languages like Lean significantly impacts mathematical reasoning. One approach to formal theorem proving involves generating complete proofs using Large Language Models (LLMs)…
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,…
Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…
This paper tackles the problem of formulating and proving the completeness of focused-like proof systems in an automated fashion. Focusing is a discipline on proofs which structures them into phases in order to reduce proof search…
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
We show that including degrees of a particular kind of provability in the search target for any theorem-prover in sufficiently powerful formal systems over finite-sized statements preserves well-definition and a sufficient consistency while…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
We describe an extension to the TLA+ specification language with constructs for writing proofs and a proof environment, called the Proof Manager (PM), to checks those proofs. The language and the PM support the incremental development and…
We introduce a theorem proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search. Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts.…
Traditional language model-based theorem proving assumes that by training on a sufficient amount of formal proof data, a model will learn to prove theorems. Our key observation is that a wealth of informal information that is not present in…
Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…