Related papers: Using Category Theory in Modeling Generics in OOP …
Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics,…
We survey recent generalizations and improvements of the linear programming method that involve semidefinite programming. A general framework using group representations and tools from graph theory is provided.
Generic ontologies were introduced as an extension (Generic DOL) of the Distributed Ontology, Modeling and Specification Language, DOL, with the aim to provide a language for Generic Ontology Design Patterns. In this paper we present a…
The paper describes a mechanism for indirect object representation and access (ORA) in programming languages. The mechanism is based on using a new programming construct which is referred to as concept. Concept consists of one object class…
A paradox of requirements specifications as dominantly practiced in the industry is that they often claim to be object-oriented (OO) but largely rely on procedural (non-OO) techniques. Use cases and user stories describe functional flows,…
Object orientation has become the predominant paradigm for conceptual modeling (e.g., UML), where the notions of class and object form the primitive building blocks of thought. Classes act as templates for objects that have attributes and…
Object-oriented programming (OOP) is aimed at describing the structure and behaviour of objects by hiding the mechanism of their representation and access in primitive references. In this article we describe an approach, called…
We develop foundations for oriented category theory, an extension of $(\infty,\infty)$-category theory obtained by systematic usage of the Gray tensor product, in order to study lax phenomena in higher category theory. As categorical…
We examine the use of classes to formulate several categorical notions. This leads to two proposals: an explicit structure for working with subobjects, and a hierarchy of $k$-classes. We apply the latter to both ordinary and higher…
In this paper we present NLOMJ--a natural language object model in Java with English as the experiment language. This modal describes the grammar elements of any permissible expression in a natural language and their complicated relations…
An empirical study was conducted to analyse design strategies and knowledge used in object-oriented software design. Eight professional programmers experienced with procedural programming languages and either experienced or not experienced…
We present a case study in applied category theory written from the point of view of an applied domain: the formalization of the widely-used property graphs data model in an enterprise setting using elementary constructions from type theory…
In this paper we describe a new approach to programming which generalizes object-oriented programming. It is based on using a new programming construct, called concept, which generalizes classes. Concept is defined as a pair of two classes:…
In this paper we present a new approach to data modelling, called the concept-oriented model (CoM), and describe its main features and characteristics including data semantics and operations. The distinguishing feature of this model is that…
In this survey, we provide an overview of category theory-derived machine learning from four mainstream perspectives: gradient-based learning, probability-based learning, invariance and equivalence-based learning, and topos-based learning.…
Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework…
In category theory, the use of string diagrams is well known to aid in the intuitive understanding of certain concepts, particularly when dealing with adjunctions and monoidal categories. We show that string diagrams are also useful in…
Datatype-generic programming increases program abstraction and reuse by making functions operate uniformly across different types. Many approaches to generic programming have been proposed over the years, most of them for Haskell, but…
This book dwells on mathematical and algorithmic issues of data analysis based on generality order of descriptions and respective precision. To speak of these topics correctly, we have to go some way getting acquainted with the important…
The main goal of concept-oriented programming (COP) is describing how objects are represented and accessed. It makes references (object locations) first-class elements of the program responsible for many important functions which are…