Related papers: Maintaining a Library of Formal Mathematics
In recent months, large language models (LLMs) have made significant progress in mathematical proof generation, but further advancement is hindered by the lack of a large-scale, high-quality dataset of human-evaluated proofs. While…
This is a user guide for the first version of our developed Maple library, named Singularity. The first version here is designed for the qualitative study of local real zeros of scalar smooth maps. This library will be extended for symbolic…
We formalize Hall's Marriage Theorem in the Lean theorem prover for inclusion in mathlib, which is a community-driven effort to build a unified mathematics library for Lean. One goal of the mathlib project is to contain all of the topics of…
Terms are one of the fundamental mathematical concepts in computing. E.g. every expression characterisable by a context free grammar is a term. We developed a thread-safe Term Library. The biggest challenge is to implement hyper-efficient…
One of the most promising applications of mathematical knowledge management is search: Even if we restrict attention to the tiny fragment of mathematics that has been formalized, the amount exceeds the comprehension of an individual human.…
We present a new package for Mathematica system, called Libra. Its purpose is to provide convenient tools for the transformation of the first-order differential systems $\partial_i \boldsymbol j = M_i \boldsymbol j$ for one or several…
While Large Language Models (LLMs) demonstrate impressive performance in mathematics, existing math benchmarks come with significant limitations. Many focus on problems with fixed ground-truth answers, and are often saturated due to problem…
This paper introduces Paraconsistent-Lib, an open-source, easy-to-use Python library for building PAL2v algorithms in reasoning and decision-making systems. Paraconsistent-Lib is designed as a general-purpose library of PAL2v standard…
Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…
This document defines the mathematical backbone of the Statebox programming language. In the simplest way possible, Statebox can be seen as a clever way to tie together different theoretical structures to maximize their benefits and limit…
Verification of real-time systems involving hard timing constraints and concurrency is of utmost importance. Parametric timed model checking allows for formal verification in the presence of unknown timing constants or uncertainty (e.g.…
Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research…
We observe today a large diversity of proof systems. This diversity has the negative consequence that a lot of theorems are proved many times. Unlike programming languages, it is difficult for these systems to co-operate because they do not…
With the growing complexity of computational and experimental facilities, many scientific researchers are turning to machine learning (ML) techniques to analyze large scale ensemble data. With complexities such as multi-component workflows,…
Current evaluations of mathematical reasoning in large language models (LLMs) are dominated by static benchmarks, either derived from competition-style problems or curated through costly expert effort, resulting in limited coverage of…
How many times have you tried to re-implement a past CAV tool paper, and failed? Reliably reproducing published scientific discoveries has been acknowledged as a barrier to scientific progress for some time but there remains only a small…
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.…
Digital libraries must reach out to users from all walks of life, serving information needs at all levels. To do this, they must attain high standards of usability over an extremely broad audience. This paper details the evolution of one…
Although Rust primarily intends to be a safe programming language that excludes undefined behaviour, it provides its users with the escape hatch of unsafe Rust, allowing them to circumvent some of its strong compile-time checks. This…
Despite the effort put into the detection of academic plagiarism, it continues to be a ubiquitous problem spanning all disciplines. Various tools have been developed to assist human inspectors by automatically identifying suspicious…