Related papers: idris-ct: A Library to do Category Theory in Idris
Dependent types allow us to express precisely what a function is intended to do. Recent work on Quantitative Type Theory (QTT) extends dependent type systems with linearity, also allowing precision in expressing when a function can run.…
We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph rewriting. By examples, we show how this paradigm of software development makes it…
We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to…
The concept of category from mathematics happens to be useful to computer programmers in many ways. Unfortunately, all "good" explanations of categories so far have been designed by mathematicians, or at least theoreticians with a strong…
Category theory provides a compact method of encoding mathematical structures in a uniform way, thereby enabling the use of general theorems on, for example, equivalence and universal constructions. In this article we develop the method of…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
Safely integrating third-party code in applications while protecting the confidentiality of information is a long-standing problem. Pure functional programming languages, like Haskell, make it possible to enforce lightweight…
The generality and pervasiness of category theory in modern mathematics makes it a frequent and useful target of formalization. It is however quite challenging to formalize, for a variety of reasons. Agda currently (i.e. in 2020) does not…
Information technology system (ITS), informally, consists of hardware and software infrastructure (e.g., workstations, servers, laptops, installed software packages, databases, LANs, firewalls, etc.), along with physical and logical…
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language,…
We present ICAR, a mathematical framework derived from category theory for representing cybersecurity NIST and MITRE's ontologies. Designed for cybersecurity, ICAR is a category whose objects are cybersecurity knowledge (weakness,…
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…
We explore a quantitative interpretation of 2-dimensional intuitionistic type theory (ITT) in which the identity type is interpreted as a "type of differences". We show that a fragment of ITT, that we call difference type theory (dTT),…
Category Theory provides us with a clear notion of what is an internal structure. This will allow us to focus our attention on a certain type of relationship between context and structure.
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…
We are in this paper discussing conceptualisations of the relationship between IT and organisational issues. To move beyond an IT enables/ constrains position, we argue that it is necessary to take the specifics of an information system…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
We present a new design for an algebraic simplification library structured around concepts from universal algebra: theories, models, homomorphisms, and universal properties of free algebras and free extensions of algebras. The library's…
I propose a notion of theory motivated by Category theory.
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…