Related papers: Using Category Theory in Modeling Generics in OOP …
This paper proposes a formal cognitive framework for problem solving based on category theory. We introduce cognitive categories, which are categories with exactly one morphism between any two objects. Objects in these categories are…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
We define the concept of a regular object with respect to another object in an arbitrary category. We present basic properties of regular objects and we study this concept in the special cases of abelian categories and locally finitely…
In this paper we give a new foundational, categorical formulation for operations and relations and objects parameterizing them. This generalizes and unifies the theory of operads and all their cousins including but not limited to PROPs,…
Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits…
Category theory is famous for its innovative way of thinking of concepts by their descriptions, in particular by establishing universal properties. Concepts that can be characterized in a universal way receive a certain quality seal, which…
Context-oriented programming (COP) is a new technique for programming that allows changing the context in which commands execute as a program executes. Compared to object-oriented programming (aspect-oriented programming), COP is more…
We present Choral, the first choreographic programming language based on mainstream abstractions. The key idea in Choral is a new notion of data type, which allows for expressing that data is distributed over different roles. We use this…
Dependencies between types in object-oriented software can be viewed as directed graphs, with types as nodes and dependencies as edges. The in-degree and out-degree distributions of such graphs have quite different forms, with the former…
Ordinal data is widely prevalent in clinical and other domains, yet there is a lack of both modern, machine-learning based methods and publicly available software to address it. In this paper, we present a model-agnostic method of ordinal…
This paper is about conceptual modeling of aggregates in software engineering. An aggregate is a cluster of domain objects that can be treated as a single unit. In UML, an aggregation is a type of association in which objects are configured…
Applied category theory has recently developed libraries for computing with morphisms in interesting categories, while machine learning has developed ways of learning programs in interesting languages. Taking the analogy between categories…
Many classification problems require decisions among a large number of competing classes. These tasks, however, are not handled well by general purpose learning methods and are usually addressed in an ad-hoc fashion. We suggest a general…
We provide a detailed example for modular ontology modeling based on ontology design patterns.
We present a simple categorical framework for the treatment of probabilistic theories, with the aim of reconciling the fields of Categorical Quantum Mechanics (CQM) and Operational Probabilistic Theories (OPTs). In recent years, both CQM…
These are expanded lecture notes from lectures given at the Workshop on higher structures at MATRIX Melbourne. These notes give an introduction to Feynman categories and their applications. Feynman categories give a universal categorical…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
Object-oriented programming laws have been proposed in the context of languages that are not combined with a behavioral interface specification language (BISL). The strong dependence between source-code and interface specifications may…
We propose a new unified framework for Thompson-like groups using a well-known device called operads and category theory as language. We discuss examples of operad groups which have appeared in the literature before. As a first application,…
We present OBJS, a new transpiler project featuring the implementation of typified variables and functions call management in Javascript, as well as several new operators and syntax patterns that could make coding more agile and versatile.…