Related papers: Proof Recommendation System for the HOL4 Theorem P…

Suppose we have been sold on the idea that formalised proofs in an LCF system should resemble their written counterparts, and so consist of formulas that only provide signposts for a fully verified proof. To be practical, most of the fully…

Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider…

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding…

Traditional automated theorem provers have relied on manually tuned heuristics to guide how they perform proof search. Recently, however, there has been a surge of interest in the design of learning mechanisms that can be integrated into…

Formalizing mathematical proofs using computerized verification languages like Lean 4 has the potential to significantly impact the field of mathematics, it offers prominent capabilities for advancing mathematical reasoning. However,…

Formal, automated theorem proving has long been viewed as a challenge to artificial intelligence. We introduce here a new approach to computer theorem proving, one that employs specialized language models for Lean4 proof generation combined…

Control systems are an integral part of almost every engineering and physical system and thus their accurate analysis is of utmost importance. Traditionally, control systems are analyzed using paper-and-pencil proof and computer simulation…

Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…

Solving mathematical problems using computer-verifiable languages like Lean has significantly impacted the mathematical and computer science communities. State-of-the-art methods utilize a single Large Language Model (LLM) to generate…

This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…

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…

Formal verification using interactive theorem provers ensures high-quality software. However, writing proof scripts for interactive theorem provers is labor-intensive and requires deep expertise. Recent studies have leveraged deep learning…

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…

We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and…

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…

This paper introduces ProofCloud, a proof retrieval engine for verified proofs in higher order logic. It provides a fast proof searching service for mathematicians and computer scientists for the reuse of proofs and proof packages. In…

Recent advances in Automated Theorem Proving have shown the effectiveness of leveraging a (large) language model that generates tactics (i.e. proof steps) to search through proof states. The current model, while trained solely on successful…

We consider the problem of sequential recommendation, where the current recommendation is made based on past interactions. This recommendation task requires efficient processing of the sequential data and aims to provide recommendations…

Recommender systems present a customized list of items based upon user or item characteristics with the objective of reducing a large number of possible choices to a smaller ranked set most likely to appeal to the user. A variety of…

There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we…