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2 Journal of Applied Mathematics and Computational Mechanics

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Coalgebras for modelling observable behaviour of programs

Steingartner W., Novitzka V.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 2

145--157

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.

Some properties of coalgebras and their role in computer science

Steingartner W., Radakovic D., Valkosak F., Macko P.

Journal of Applied Mathematics and Computational Mechanics

2016

Vol. 15, nr 4

145-156

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.