Amiguet Matthieu writes:
I'm wondering if there has been any work in formalizing statecharts [1] in categorical terms.
Currently John Power and myself are involved in providing an algebraic foundation (in category-theoretic terms) of higraphs, the "visual formalism" [1] which underlie Statecharts. On this basis, we are adding more features in an attempt to study a large subset of the Statecharts language. In brief, our approach is to regard higraphs as graphs in Poset, the category of partially ordered sets and monotone functions. Our main results so far pertain to operations underpinning the semantics of Statecharts and the concept of zooming described by Harel in [1]. Technical details will appear soon in my web page: http://www.dcs.ed.ac.uk/~kxt More generally, our interests are in studying domain-specific programming and specification languages which have a strong diagrammatic component. Statecharts present a most interesting case for study, as they contain a multitude of interacting diagrammatic features and support practically important operations such as zooming. Part of our objective is to evaluate how the different features blend together, in an attempt to research good design principles for the kind of diagrammatic languages used in computing.
If not, do you know of an other algebraic description of this specification language?
I know of a paper by Uselton and Smolka, but which does not use categories: "A Compositional Semantics for Statecharts using Labeled Transition Systems", by A. Uselton, S. Smolka, available online at: http://www.di.ufpe.br/~lrl/statecharts_js.html
Also, it seems to me that the operationnal semantic STATEMATE of Statecharts as described in [2] is very coalgebraic in nature. Did anybody write something about this?
I'm afraid I do not know of any such work. However, your view of STATEMATE semantics seems most interesting. Please feel free to email me (kxt@dcs.ed.ac.uk) or John (ajp@dcs.ed.ac.uk) for a more detailed techical discussion on this subject or any of the above. [1] D. Harel, On Visual Formalisms, Communications of the ACM, 31(5), 1988. -- Konstantinos Tourlas Tel. : 0131-650-5162 Rm 1404, JCMB, The University of Edinburgh, e-mail : kxt@dcs.ed.ac.uk King's Buildings, Edinburgh, EH9 3JZ UK