Related papers: Point-and-write --- Documenting Formal Mathematics…
Increased demands in the field of scientific computation require that algorithms be more efficiently implemented. Maintaining correctness in addition to efficiency is a challenge that software engineers in the field have to face. In this…
The lambda calculus since more than half a century is a model and foundation of functional programming languages. However, lambda expressions can be evaluated with different reduction strategies and thus, there is no fixed cost model nor…
Despite extensive research both on the theoretical and practical fronts, formalising, reasoning about, and implementing languages with variable binding is still a daunting endeavour - repetitive boilerplate and the overly complicated…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
Modeling-Simulation-Optimization workflows play a fundamental role in applied mathematics. The Mathematical Research Data Initiative, MaRDI, responded to this by developing a FAIR and machine-interpretable template for a comprehensive…
Algorithms like those for differentiating functional expressions manipulate the syntactic structure of mathematical expressions in a mathematically meaningful way. A formalization of such an algorithm should include a specification of its…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
Capture calculus has recently been proposed as a solution to effect checking, achieved by tracking the captured references of terms in the types. Boxes, along with the box and unbox operations, are a crucial construct in capture calculus,…
Regular expressions in an Automata Theory and Formal Languages course are mostly treated as a theoretical topic. That is, to some degree their mathematical properties and their role to describe languages is discussed. This approach fails to…
Traditional human-computer interaction takes place through formally-specified systems like structured UIs and programming languages. Recent AI systems promise a new set of informal interactions with computers through natural language and…
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…
While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications,…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
Written language is a useful tool for non-visual creative activities like writing essays and planning searches. This paper investigates the integration of written language in to the visualization design process. We create the idea of a…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
We present the first approach to automatically building resources for academic writing. The aim is to build a writing aid system that automatically edits a text so that it better adheres to the academic style of writing. On top of existing…
Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…
Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today.…