Related papers: Point-and-write --- Documenting Formal Mathematics…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
The ForMaRE project applies formal mathematical reasoning to economics. We seek to increase confidence in economics' theoretical results, to aid in discovering new results, and to foster interest in formal methods, i.e. computer-aided…
This position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open…
In mathematics, LaTeX is the de facto standard to prepare documents, e.g., scientific publications. While some formulae are still developed using pen and paper, more complicated mathematical expressions used more and more often with…
Artificial intelligence systems are increasingly integrated into writing processes, challenging traditional notions of authorship, responsibility, and intellectual contribution. Current disclosure practices usually indicate whether AI was…
Formal software specification is known to enable early error detection and explicit invariants, yet it has seen limited industrial adoption due to its high notation overhead and the expertise required to use traditional formal languages.…
In this paper we examine various requirements on the formalisation choices under which self-reference can be adequately formalised in arithmetic. In particular, we study self-referential numberings, which immediately provide a strong notion…
The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering a wide range…
Writing assignments in any mathematics course always present several challenges, particularly in lower-level classes where the students are not expecting to write more than a few words at a time. Developed based on strategies from several…
This paper discusses digital online mathematics examinations -- a discussion ranging from high school to university level examinations. In particular, we consider the nature of mathematical writing, what is distinctive about mathematical…
Reasoning about floating-point arithmetic is notoriously hard. While static and dynamic analysis techniques or program repair have made significant progress, more work is still needed to make them relevant to real-world code. On the…
Passive documents and active programs now widely comingle. Document languages include Turing-complete programming elements, and programming languages include sophisticated document notations. However, there are no formal foundations that…
Floating-point arithmetic (FPA) is a mechanical representation of real arithmetic (RA), where each operation is replaced with a rounded counterpart. Various numerical properties can be verified by using SMT solvers that support the logic of…
This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…
This paper summarizes our experience in communicating the elements of reasoning about correctness, and the central role of formal specifications in reasoning about modular, component-based software using a language and an integrated Web IDE…
Use case driven development methodologies put use cases at the center of the software development process. However, in order to support automated development and analysis, use cases need to be appropriately formalized. This will also help…
Formal methods provide systematic and rigorous techniques for software development. We strongly believe that they must be taught in computer science curricula. In this paper we present the pedagogic rationale and the concrete implementation…
Before we can get the whole potential of employing computers in the process of managing mathematical `knowledge', we have to convert informal knowledge into machine-oriented representations. How exactly to support this process so that it…
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
Autoformalization has emerged as a term referring to the automation of formalization - specifically, the formalization of mathematics using interactive theorem provers (proof assistants). Its rapid development has been driven by progress in…