Related papers: Formalization and Implementation of Algebraic Meth…
Formal methods are mathematically-based techniques for the rigorous development of software-intensive systems. The railway signaling domain is a field in which formal methods have traditionally been applied, with several success stories.…
We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and…
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…
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
In this paper, we discuss an interaction between complex geometry and integrable systems. Section 1 reviews the classical results on integrable systems. New examples of integrable systems, which have been discovered, are based on the Lax…
Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equations based on the classical theorem of B\'ezout. This was…
Algebraic effects and handlers are a powerful abstraction to build non-local control-flow mechanisms such as resumable exceptions, lightweight threads, co-routines, generators, and asynchronous I/O. All of such features have very evolved…
This is a survey on recent progress in algebraic deformation theory and the application of algebraic operads to its study. We review the classical homotopical tools in the theory of algebraic operads, namely Koszul duality. We give concrete…
Formal methods yet advantageous, face challenges towards wide acceptance and adoption in software development practices. The major reason being presumed complexity. The issue can be addressed by academia with a thoughtful plan of teaching…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
We formalise the basics of the double-pushout approach to graph transformation in the proof assistant Isabelle/HOL and provide associated machine-checked proofs. Specifically, we formalise graphs, graph morphisms and rules, and a definition…
For associative algebras in many different categories, it is possible to develop the machinery of Gr\"obner bases. A Gr\"obner basis of defining relations for an algebra of such a category provides a "monomial replacement" of this algebra.…
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
In this paper we present the first-ever computer formalization of the theory of Gr\"obner bases in reduction rings, which is an important theory in computational commutative algebra, in Theorema. Not only the formalization, but also the…
With the exception of q-hypergeometric summation, the use of computer algebra packages implementing Zeilberger's "holonomic systems approach" in a broader mathematical sense is less common in the field of q-series and basic hypergeometric…
We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
Implicitly described domains are a well established tool in the simulation of time dependent problems, e.g. using level-set methods. In order to solve partial differential equations on such domains, a range of numerical methods was…
The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in…