Related papers: Recycling Proof Patterns in Coq: Case Studies
Most existing implementations of multiple precision arithmetic demand that the user sets the precision {\em a priori}. Some libraries are said adaptable in the sense that they dynamically change the precision of each intermediate operation…
Human mathematicians are often good at recognizing modular and reusable theorems that make complex mathematical results within reach. In this paper, we propose a novel method called theoREm-from-prooF extrACTOR (REFACTOR) for training…
New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In…
The Lax Logical Framework, LLFP, was introduced, by a team including the last two authors, to provide a conceptual framework for integrating different proof development tools, thus allowing for external evidence and for postponing,…
We present Cobra, a modern proof presentation framework, leveraging cutting-edge presentation technology together with a state of the art interactive theorem prover to present formalized mathematics as active documents. Cobra provides both…
Leveraging outputs from multiple large language models (LLMs) is emerging as a method for harnessing their power across a wide range of tasks while mitigating their capacity for making errors, e.g., hallucinations. However, current…
Modern language models (LMs) have been successfully employed in source code generation and understanding, leading to a significant increase in research focused on learning-based code intelligence, such as automated bug repair, and test case…
Objective: In this study, we aim to replicate an artefact-based study on software testing to address the gap. We focus on (a) providing a step by step guide of the replication, reflecting on challenges when replicating artefact-based…
Large language models (LLMs) have demonstrated remarkable capability to generate fluent responses to a wide variety of user queries. However, this has also raised concerns about the potential misuse of such texts in journalism, education,…
As large language models (LLMs) converge towards similar capabilities, the key to advancing their performance lies in identifying and incorporating valuable new information sources. However, evaluating which text collections are worth the…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
Machine-learned interatomic potentials (MILPs) are rapidly gaining interest for molecular modeling, as they provide a balance between quantum-mechanical level descriptions of atomic interactions and reasonable computational efficiency.…
Despite the dramatic progress in Large Language Model (LLM) development, LLMs often provide seemingly plausible but not factual information, often referred to as hallucinations. Retrieval-augmented LLMs provide a non-parametric approach to…
This paper presents Holbert: a work-in-progress pedagogical proof assistant and online textbook platform, aimed at the educational use-case, specifically for the teaching of programming language theory. Holbert allows proof exercises and…
We advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The…
In this work, we conduct an experiment using state-of-the-art LLMs to translate MiniF2F into Rocq. The translation task focuses on generating a Rocq theorem based on three sources: a natural language description, the Lean formalization, and…
Multimodal large language models (MLLMs) carry the potential to support humans in processing vast amounts of information. While MLLMs are already being used as a fact-checking tool, their abilities and limitations in this regard are…
We present a system that utilizes machine learning for tactic proof search in the Coq Proof Assistant. In a similar vein as the TacticToe project for HOL4, our system predicts appropriate tactics and finds proofs in the form of tactic…
The widely held belief that BQP strictly contains BPP raises fundamental questions: Upcoming generations of quantum computers might already be too large to be simulated classically. Is it possible to experimentally test that these systems…
We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-computational' proofs from the mainstream mathematical…