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We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and…
Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the…
LLM-based coding agents are increasingly used to generate code, tests, and documentation. Still, their outputs can be plausible yet misaligned with developer intent and provide limited evidence for review in evolving projects. This limits…
The construction of high-quality parallel corpora for translation research has increasingly evolved from simple sentence alignment to complex, multi-layered annotation tasks. This methodological shift presents significant challenges for…
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
In mathematics, LaTeX is the de facto standard to prepare documents, e.g., scientific publications. While some formulae are still developed using pen and paper, more complicated mathematical expressions used more and more often with…
In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs…
Large language models have recently demonstrated advanced capabilities in solving IMO and Putnam problems; yet their role in research mathematics has remained fairly limited. The key difficulty is verification: suggested proofs may look…
Proof assistants are getting more widespread use in research and industry to provide certified and independently checkable guarantees about theories, designs, systems and implementations. However, proof assistant implementations themselves…
We introduce CSLib, an open-source framework for proving computer-science-related theorems and writing formally verified code in the Lean proof assistant. CSLib aims to be for computer science what Lean's Mathlib is for mathematics. Mathlib…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
Among formal methods, the deductive verification approach allows establishing the strongest possible formal guarantees on critical software. The downside is the cost in terms of human effort required to design adequate formal specifications…
There is a vast gap in the quality of IDE tooling between static languages like Java and dynamic languages like Python or JavaScript. Modern frameworks and libraries in these languages heavily use their dynamic capabilities to achieve the…
Large Language Models (LLMs) acquire extensive knowledge and remarkable abilities from extensive text corpora, making them powerful tools for various applications. To make LLMs more usable, aligning them with human preferences is essential.…
We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
Mechanical proofs by logical relations often involve tedious reasoning about substitution. In this paper, we show that this is not necessarily the case, by developing, in Agda, a proof that all simply typed lambda calculus expressions…
Noisy data, non-convex objectives, model misspecification, and numerical instability can all cause undesired behaviors in machine learning systems. As a result, detecting actual implementation errors can be extremely difficult. We…
Implementing a complex concept as an executable model in a strongly typed, purely functional language hits a sweet spot between mere simulation and formal specification. For research and education it is often desirable to enrich the…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…