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Reasoning modulo equivalences is natural for everyone, including mathematicians. Unfortunately, in proof assistants based on type theory, equality is appallingly syntactic and, as a result, exploiting equivalences is cumbersome at best.…
Interoperability is one of the key issues in the current efforts to build the Virtual Observatory. We present here some of the tools which already contribute to the efficient exchange of information between archives, databases, and…
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…
While open source communities attract diverse contributors across the globe, only a few open source software repositories provide essential documentation, such as ReadMe or CONTRIBUTING files, in languages other than English. Recently,…
We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to…
We present an algorithm for converting proofs from the OpenTheory interchange format, which can be translated to and from any of the HOL family of proof languages (HOL4, HOL Light, ProofPower, and Isabelle), into the ZFC-based Metamath…
Libraries of formal proofs are an important part of our mathematical heritage, but their usability and sustainability is poor. Indeed, each library is specific to a proof system, sometimes even to some version of this system. Thus, a…
We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called…
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…
Pronouns are a long-standing challenge in machine translation. We present a study of the performance of a range of rule-based, statistical and neural MT systems on pronoun translation based on an extensive manual evaluation using the…
The Common HOL project aims to facilitate porting source code and proofs between members of the HOL family of theorem provers. At the heart of the project is the Common HOL Platform, which defines a standard HOL theory and API that aims to…
Proof assistants enable users to develop machine-checked proofs regarding software-related properties. Unfortunately, the interactive nature of these proof assistants imposes most of the proof burden on the user, making formal verification…
The adoption of heterogeneous computing systems based on diverse architectures to achieve exascale computing power has worsened the performance portability problem of scientific applications that were designed to run on these platforms. To…
Machine learning is permeating every conceivable domain to promote data-driven decision support. The focus is often on advanced black-box models due to their assumed performance advantages, whereas interpretable models are often associated…
A flexible infrastructure for normative reasoning is outlined. A small-scale demonstrator version of the envisioned system has been implemented in the proof assistant Isabelle/HOL by utilising the first authors universal logical reasoning…
This paper explores the potential of Large Language Models to accurately extract and translate equations from typed student responses into a standard format. This is a useful task as standardized equations can be graded reliably using a…
Open-sourced large language models (LLMs) have demonstrated remarkable efficacy in various tasks with instruction tuning. However, these models can sometimes struggle with tasks that require more specialized knowledge such as translation.…
This paper presents an in-depth study of multimodal machine translation (MMT), examining the prevailing understanding that MMT systems exhibit decreased sensitivity to visual information when text inputs are complete. Instead, we attribute…
The Isabelle/HOL proof assistant has a powerful library for continuous analysis, which provides the foundation for verification of hybrid systems. However, Isabelle lacks automated proof support for continuous artifacts, which means that…
The ever-growing complexity of mathematical proofs makes their manual verification by mathematicians very cognitively demanding. Autoformalization seeks to address this by translating proofs written in natural language into a formal…