categories: Re: statecharts and categories

[Konstantinos Tourlas <kxt@dcs.ed.ac.uk>]

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