Einführung in die Kategorientheorie

Gajdoš

2021

Politehnika (Online)

This work aims to present the software support for teaching in the field of formal semantics of imperative programming languages. The main part focuses on a software tool that provides a visual representation of the individual steps of the calculation in categorical semantics, which can also be referred to as graph semantics. The use of software tools in teaching to visually represent computational steps considerably facilitates understanding by students and can also serve as a good basis for supporting distance learning. Our program works in the standard form: after reading the correct user input, a visual representation of the meaning of the program is generated in the form of a category of states, which is displayed as an oriented graph. For better extensibility, the program is implemented as a web application.

Section: Categories In the Backgroundmentioning

confidence: 99%

The visualization of a graph semantics of imperative languages

Gajdoš

2021

Politehnika (Online)

“…A category = ( , ) is a mathematical structure consisting of a class of objects, e.g. ‫,ܣ‬ ‫,ܤ‬ … and a class of morphisms of the form ݂: ‫ܣ‬ → ‫ܤ‬ between them [12,13]. Every object has its identity morphism ݅݀ : ‫ܣ‬ → ‫ܣ‬ and morphisms are composable.…”

Section: Basic Notionsmentioning

confidence: 99%

Coalgebras for modelling observable behaviour of programs

J. Appl. Math. Comput. Mech.

Novitzká

2017

Abstract. A useful tool for modelling behaviour in theoretical computer science is the concept of coalgebras. Coalgebras enable one to model execution of programs step by step using categorical structures and polynomial endofunctors. In our paper, we start with a short introduction of basic notions and we use this method for modelling structural operational semantics of a simple imperative language.

“…Precisely, a category C is a mathematical structure that consists of a set of objects, e.g. ‫,ܣ‬ ‫,ܤ‬ … and a set of morphisms or arrows of the form ݂ ∶ ‫ܣ‬ → ‫ܤ‬ between them [7,8].…”

Section: Basic Conceptsmentioning

confidence: 99%

Some properties of coalgebras and their rôle in computer science

J. Appl. Math. Comput. Mech.

Radaković

Valkošák

et al. 2016

Abstract. This paper introduces basic theoretical knowledge of coalgebras in computer science. Coalgebras are, specifically in category theory, structures defined according to an endofunctor. For both algebra and coalgebra, a functor is a convenient and general way of defining a signature. We present practical usage of the coalgebras in an example. We observe a behavior of a simple Sequencer developed in SLGeometry framework. We model its behavior with the simple program written in Python, and we describe its behavior within coalgebra of endofunctor. The computation of the values stored in internal states is performed coinductively. Our approach can be used in the teaching process of formal methods for young software engineers.