Related papers: GATlab: Modeling and Programming with Generalized …
Algebraic specification has a long tradition in bridging the gap between specification and programming by making specifications executable. Building on extensive experience in designing, implementing and using specification formalisms that…
This article is intended to an introductory lecture in material physics, in which the modern computational group theory and the electronic structure calculation are in collaboration. The effort of mathematicians in field of the group…
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…
This paper proposes a functional foundation for model driven engineering that unifies model construction, metamodels, templates, and transformations under a single formalism: the model expression algebra. In this algebra, models are values,…
Generalised algebraic theories (GATs) allow multiple sorts indexed over each other. For example, the theories of categories or Martin-L{\"o}f type theories form GATs. Categories have two sorts, objects and morphisms, and the latter are…
We present programming techniques to illustrate the facilities and principles of C++ generic programming using concepts. Concepts are C++'s way to express constraints on generic code. As an initial example, we provide a simple type system…
Automata learning is a popular technique used to automatically construct an automaton model from queries. Much research went into devising ad hoc adaptations of algorithms for different types of automata. The CALF project seeks to unify…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
A long and lasting problem in agent research has been to close the gap between agent logics and agent programming frameworks. The main reason for this problem of establishing a link between agent logics and agent programming frameworks is…
Qualitative reasoning involves expressing and deriving knowledge based on qualitative terms such as natural language expressions, rather than strict mathematical quantities. Well over 40 qualitative calculi have been proposed so far, mostly…
We introduce Graphical Algebraic Geometry (GAG), a family of diagrammatic languages extending the Graphical Linear Algebra programme. We construct several languages within this family and prove that they are universal and complete for the…
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definitions. This results in a steep learning curve for new users…
This article serves as a preliminary introduction to the design of a new, open-source applied and computational category theory framework, named Categorica, built on top of the Wolfram Language. Categorica allows one to configure and…
Recently there has been significant interest in using causal modelling techniques to understand the structure of physical theories. However, the notion of `causation' is limiting - insisting that a physical theory must involve causal…
This paper introduces the Token Space framework, a novel mathematical construct designed to enhance the interpretability and effectiveness of deep learning models through the application of category theory. By establishing a categorical…
We present a library for generic programming in OCaml, adapting some techniques borrowed from other functional languages. The library makes use of three recent additions to OCaml: generalised abstract datatypes are essential to reflect…
Linear Software Models is a systematic effort to formulate a theory of software systems neatly based upon standard mathematics, viz. linear algebra. It has appeared in a series of papers dealing with various aspects of the theory. But one…
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within the Julia framework as they work within the Python…
In various subjects including mathematics, one can hope to use mathematical thinking well when the right kinds of algebraic structure to consider can be discovered or spotted. Therefore, it would help to understand kinds of algebraic…
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…