相关论文: Designing a Theorem Prover

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,…

The large language models (LLMs) might produce a persuasive argument within mathematical and logical fields, although such argument often includes some minor missteps, including the entire omission of side conditions, invalid inference…

Large language models (LLMs) have shown increasing competence in solving mathematical reasoning problems. However, many open-source LLMs still struggle with errors in calculation and semantic understanding during intermediate reasoning…

As the name suggests, type-logical grammars are a grammar formalism based on logic and type theory. From the prespective of grammar design, type-logical grammars develop the syntactic and semantic aspects of linguistic phenomena…

Theorem provers are important tools for people working in formal verification. There are a myriad of interactive systems available today, with varying features and approaches motivating their development. These design choices impact their…

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…

We define the concept of collaborative theorem proving and outline our plan to make it a reality. We believe that a successful implementation of collaborative theorem proving is a necessary prerequisite for the formal verification of large…

We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…

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…

The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…

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,…

Theorem proving is a fundamental task in mathematics. With the advent of large language models (LLMs) and interactive theorem provers (ITPs) like Lean, there has been growing interest in integrating LLMs and ITPs to automate theorem…

To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem…

We describe a general method for verifying inequalities between real-valued expressions, especially the kinds of straightforward inferences that arise in interactive theorem proving. In contrast to approaches that aim to be complete with…

Large language models (LLMs) have demonstrated significant potential in formal theorem proving, yet state-of-the-art performance often necessitates prohibitive test-time compute via massive roll-outs or extended context windows. In this…

The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…

Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in a pure and simple setting.…

Large Language Models (LLMs) have emerged as powerful tools in mathematical theorem proving, particularly when utilizing formal languages such as LEAN. A prevalent proof method involves the LLM prover iteratively constructing the proof…

Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…

Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…