Abstract
For structural operational semantics (SOS) of process algebras, various notions of bisimulation have been studied, together with rule formats ensuring that bisimilarity is a congruence. For programming languages, however, SOS generally involves auxiliary entities (e.g. stores) and computed values, and the standard bisimulation and rule formats are not directly applicable.
Here, we first introduce a notion of bisimulation based on the distinction between computations and values, with a corresponding liberal congruence format. We then provide metatheory for a modular variant of SOS (MSOS) which provides a systematic treatment of auxiliary entities. This is based on a higher order form of bisimulation, and we formulate an appropriate congruence format. Finally, we show how algebraic laws can be proved sound for bisimulation with reference only to the (M)SOS rules defining the programming constructs involved in them. Such laws remain sound for languages that involve further constructs.
Chapter PDF
Similar content being viewed by others
Keywords
References
Bernstein, K.L.: A congruence theorem for structured operational semantics of higher-order languages. In: 13th Annual IEEE Symposium on Logic in Computer Science, pp. 153–164. IEEE (1998)
Fokkink, W.: The Tyft/Tyxt Format Reduces to Tree Rules. In: Hagiya, M., Mitchell, J.C. (eds.) TACS 1994. LNCS, vol. 789, pp. 440–453. Springer, Heidelberg (1994)
Groote, J.F., Vaandrager, F.: Structured operational semantics and bisimulation as a congruence. Inf. and Comput. 100(2), 202–260 (1992)
Howe, D.J.: Equality in lazy computation systems. In: Fourth Annual IEEE Symposium on Logic in Computer Science, pp. 198–203. IEEE (1989)
Leroy, X.: The Caml Light system, documentation and user’s guide (1997), http://caml.inria.fr/pub/docs/manual-caml-light/
Levy, P.B.: Call-by-Push-Value: A Subsuming Paradigm. In: Girard, J.-Y. (ed.) TLCA 1999. LNCS, vol. 1581, pp. 228–243. Springer, Heidelberg (1999)
Milner, R.: A Calculus of Communicating Systems. LNCS, vol. 92. Springer, Heidelberg (1980)
Mosses, P.D.: Modular structural operational semantics. J. Log. Algebr. Program. 60-61, 195–228 (2004)
Mosses, P.D.: Component-based semantics. In: Huisman, M. (ed.) Eighth Intl. Workshop on Specification and Verification of Component-Based Systems, pp. 3–10. ACM, New York (2009)
Mosses, P.D., Mousavi, M.R., Reniers, M.A.: Robustness of equations under operational extensions. In: Fröschle, S., Valencia, F.D. (eds.) 17th International Workshop on Expressiveness in Concurrency. EPTCS, arXiv, vol. 41, pp. 106–120 (2010)
Mosses, P.D., New, M.J.: Implicit propagation in structural operational semantics. In: Hennessy, M., Klin, B. (eds.) Fifth Workshop on Structural Operational Semantics. Electr. Notes Theor. Comput. Sci., vol. 229(4), pp. 49–66. Elsevier, Amsterdam (2009)
Mousavi, M.R., Gabbay, M., Reniers, M.: SOS for Higher Order Processes. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 308–322. Springer, Heidelberg (2005)
Mousavi, M.R., Reniers, M.A., Groote, J.F.: Notions of bisimulation and congruence formats for SOS with data. Inf. and Comput. 200(1), 107–147 (2005)
Mousavi, M.R., Reniers, M.A., Groote, J.F.: SOS formats and meta-theory: 20 years after. Theor. Comput. Sci. 373(3), 238–272 (2007)
Park, D.: Concurrency and Automata on Infinite Sequences. In: Proc. 5th GI-Conference on Theoretical Computer Science, pp. 167–183. Springer, London (1981)
Plotkin, G.D.: A structural approach to operational semantics. J. Log. Algebr. Program. 60-61, 17–139 (2004); Originally Tech. Rep. DAIMI FN-19, Dept. of Computer Science, Univ. Aarhus (1981)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Churchill, M., Mosses, P.D. (2013). Modular Bisimulation Theory for Computations and Values. In: Pfenning, F. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2013. Lecture Notes in Computer Science, vol 7794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37075-5_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-37075-5_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37074-8
Online ISBN: 978-3-642-37075-5
eBook Packages: Computer ScienceComputer Science (R0)