Related papers: The Lean mathematical library
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…
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.…
We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving (with moderate training). Prove-It uses a…
We report on a formalization of the change of variables formula in integrals, in the mathlib library for Lean. Our version of this theorem is extremely general, and builds on developments in linear algebra, analysis, measure theory and…
The Mizar Mathematical Library (MML) is a large corpus of formalised mathematical knowledge. It has been constructed over the course of many years by a large number of authors and maintainers. Yet the legal status of these efforts of the…
This paper describes the autofeat Python library, which provides scikit-learn style linear regression and classification models with automated feature engineering and selection capabilities. Complex non-linear machine learning models, such…
To build a large library of mathematics, it seems more efficient to take advantage of the inherent structure of mathematical theories. Various theory presentation combinators have been proposed, and some have been implemented, in both…
mlpack is an open-source C++ machine learning library with an emphasis on speed and flexibility. Since its original inception in 2007, it has grown to be a large project implementing a wide variety of machine learning algorithms, from…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
Large language models (LLMs) have been explored in a variety of reasoning tasks including solving of mathematical problems. Each math dataset typically includes its own specially designed evaluation script, which, while suitable for its…
Today, there are millions of professionals worldwide acting as a designer, architect or engineer in the design, realization, and implementation of information systems. At this moment there is no well established and clearly identified body…
Nowadays the analysis of dynamics of and on networks represents a hot topic in the Social Network Analysis playground. To support students, teachers, developers and researchers in this work we introduce a novel framework, namely NDlib, an…
Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…
Automated formalization of mathematics enables mechanical verification but remains limited to isolated theorems and short snippets. Scaling to textbooks and research papers is largely unaddressed, as it requires managing cross-file…
Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…
Designing algorithms with provable guarantees that also work well in practice remains difficult, requiring both mathematical reasoning and careful implementation. Existing approaches that bridge worst-case theory and empirical performance,…
As the concept and implementation of cutting-edge technologies like artificial intelligence and machine learning has become relevant, academics, researchers and information professionals involve research in this area. The objective of this…
Braidlab is a Matlab package for analyzing data using braids. It was designed to be fast, so it can be used on relatively large problems. It uses the object-oriented features of Matlab to provide a class for braids on punctured disks and a…
The Agda Universal Algebra Library (UALib) is a library of types and programs (theorems and proofs) we developed to formalize the foundations of universal algebra in dependent type theory using the Agda programming language and proof…
Machine learning (ML) in medicine has transitioned from research to concrete applications aimed at supporting several medical purposes like therapy selection, monitoring and treatment. Acceptance and effective adoption by clinicians and…