Related papers: An Extensible Ad Hoc Interface between Lean and Ma…

Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages…

Enabling large language models to scale and reliably use hundreds of tools is critical for real-world applications, yet challenging due to the inefficiency and error accumulation inherent in flat tool-calling architectures. To address this,…

Hybrid systems verification is quite important for developing correct controllers for physical systems, but is also challenging. Verification engineers, thus, need to be empowered with ways of guiding hybrid systems verification while…

Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime…

Text documents, including programs, typically have human-readable semantic structure. Historically, programmatic access to these semantics has required explicit in-document tagging. Especially in systems where the text has an execution…

Software tools of Automated Reasoning are too sophisticated for general use in mathematics education and respective reasoning, while Lucas-Interpretation provides a general concept for integrating such tools into educational software with…

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…

Machine learning methods can be a valuable aid in the scientific process, but they need to face challenging settings where data come from inhomogeneous experimental conditions. Recent meta-learning methods have made significant progress in…

As large language model (LLM) assistants become increasingly integrated into enterprise workflows, their ability to generate accurate, semantically aligned, and executable outputs is critical. However, current conversational business…

This article is about the formalization of synthetic differential geometry with the Lean proof assistant and the mathematical library mathlib. The main result we prove and formalize is a Taylor theorem for functions of several variables,…

We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result. The unusual feature of the use of computers here was that a computer generated but human…

Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we…

A MATLAB toolbox is presented, with the goal of checking occurrences of design errors typically found in fixed-point digital systems, considering finite word-length effects. In particular, the present toolbox works as a front-end to a…

Numerical and symbolic methods for optimization are used extensively in engineering, industry, and finance. Various methods are used to reduce problems of interest to ones that are amenable to solution by such software. We develop a…

Large Language Models (LLMs) achieve impressive performance in a wide range of tasks, even if they are often trained with the only objective of chatting fluently with users. Among other skills, LLMs show emergent abilities in mathematical…

Large language models (LLMs) have recently been applied in software engineering to perform tasks such as translating code between programming languages, generating code from natural language, and autocompleting code as it is being written.…

This paper deals with improving querying large language models (LLMs). It is well-known that without relevant contextual information, LLMs can provide poor quality responses or tend to hallucinate. Several initiatives have proposed…

Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…

Dependently typed lambda calculi such as the Logical Framework (LF) can encode relationships between terms in types and can naturally capture correspondences between formulas and their proofs. Such calculi can also be given a logic…

Hybrid systems are characterized by the hybrid evolution of their state: A part of the state changes discretely, the other part changes continuously over time. Typically, modern control applications belong to this class of systems, where a…