Related papers: Maintaining a Library of Formal Mathematics
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…
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 provides the description of a novel, multi-purpose spline library. In accordance with the increasingly diverse modes of usage of splines, it is multi-purpose in the sense that it supports geometry representation, finite element…
Using AI to write formal proofs for mathematical problems is a challenging task that has seen some advancements in recent years. Automated systems such as Lean can verify the correctness of proofs written in formal language, yet writing the…
We introduce the smt toolbox for Matlab. It implements optimized storage and fast arithmetics for circulant and Toeplitz matrices, and is intended to be transparent to the user and easily extensible. It also provides a set of test matrices,…
We present a collection of modular open source C++ libraries for the development of logic synthesis applications. These libraries can be used to develop applications for the design of classical and emerging technologies, as well as for the…
Due to non-experts also developing security relevant applications it is necessary to support them too. Some improvements in the current research may not reach or impact these developers. Nonetheless these developers use security libraries.…
The role of data libraries in Monte Carlo simulation is discussed. A number of data libraries currently in preparation are reviewed; their data are critically examined with respect to the state-of-the-art in the respective fields. Extensive…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…
This paper contains a discussion of a library of formalized mathematics for the proof assistant Coq which the author worked on in 2011-13.
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
Automatic and adaptive approximation, optimization, or integration of functions in a cone with guarantee of accuracy is a relatively new paradigm. Our purpose is to create an open-source MATLAB package, Guaranteed Automatic Integration…
Continual learning enables AI systems to acquire new knowledge while retaining previously learned information. While traditional unimodal methods have made progress, the rise of Multimodal Large Language Models (MLLMs) brings new challenges…
Large Language Models (LLMs) often struggle with code generation tasks involving niche software libraries. Existing code generation techniques with only human-oriented documentation can fail -- even when the LLM has access to web search and…
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…
MATLAB is a numerical computing platform used by scientists, engineers, mathematicians, and students which contains many mathematical functions, including isprime. MATLAB's isprime function determines which elements of an input array are…
As developers of libraries implementing interval arithmetic, we faced the same difficulties when it came to testing our libraries. What must be tested? How can we devise relevant test cases for unit testing? How can we ensure a high (and…
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,…
This paper proposes a set of techniques to develop correctly rounded math libraries for 32-bit float and posit types. It enhances our RLibm approach that frames the problem of generating correctly rounded libraries as a linear programming…
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…