The Microcosm Principle and Compositionality of GSOS-Based Component Calculi
In the previous work by Jacobs, Sokolova and the author, synchronous parallel composition of coalgebras—yielding a coalgebra—and parallel composition of behaviors—yielding a behavior, where behaviors are identified with states of the final coalgebra—were observed to form an instance of the microcosm principle. The microcosm principle, a term by Baez and Dolan, refers to the general phenomenon of nested algebraic structures such as a monoid in a monoidal category. Suitable organization of these two levels of parallel composition led to a general compositionality theorem: the behavior of the composed system relies only on the behaviors of its constituent parts. In the current paper this framework is extended so that it accommodates any process operator—not restricted to parallel composition—whose meaning is specified by means of GSOS rules. This generalizes Turi and Plotkin’s bialgebraic modeling of GSOS, by allowing a process operator to act as a connector between components as coalgebras.
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- 1.Aceto, L., Fokkink, W., Verhoef, C.: Structural operational semantics. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 197–292. Elsevier, Amsterdam (2001)Google Scholar
- 9.Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
- 10.Curien, P.L.: Operads, clones, and distributive laws, preprint, available online (2008)Google Scholar
- 11.Hasuo, I.: Tracing Anonymity with Coalgebras. Ph.D. thesis, Radboud Univ. Nijmegen (2008)Google Scholar
- 12.Hasuo, I.: The microcosm principle and compositionality of GSOS-based component calculi. Extended version with proofs, available online (May 2011)Google Scholar
- 13.Hasuo, I., Jacobs, B., Sokolova, A.: Generic trace semantics via coinduction. Logical Methods in Comp. Sci. 3(4:11) (2007)Google Scholar
- 15.Jacobs, B.: Introduction to coalgebra. Towards mathematics of states and observations, Draft of a book (2005), http://www.cs.ru.nl/B.Jacobs/PAPERS
- 20.Plotkin, G.D.: A structural approach to operational semantics, report DAIMI FN-19, Aarhus Univ. (1981)Google Scholar
- 22.Turi, D., Plotkin, G.: Towards a mathematical operational semantics. In: Logic in Computer Science, pp. 280–291. IEEE, Computer Science Press (1997)Google Scholar