Abstract
Message Sequence Charts (MSC) and Sequence Diagrams (SD) are graphical models representing the behaviours of distributed and concurrent systems via the scheduling of discrete emission and reception events. So as to exploit them in formal methods, a mathematical semantics is required. In the literature, different kinds of semantics are proposed: denotational semantics, well suited to reason about algebraic properties and operational semantics, well suited to establish verification algorithms. We define an algebraic language to specify so-called interactions, similar to the MSC and SD models. It is equipped with a denotational semantics associating sets of traces (sequences of observed events) to interactions. We then define a structural operational semantics in the style of process algebras and prove the equivalence of the two semantics.
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Notes
- 1.
For a set E, \(\mathcal{P}(E)\) is the set of all subsets of E.
- 2.
The free term \(\mathcal {F}\)-algebra is defined by interpreting symbols of \(\mathcal {F}\) as constructors of new terms: for \(f \in \mathcal {F}\) of arity j, for \(t_1, \ldots t_j \in \mathbb {I}_\varOmega \), \(f(t_1, \ldots t_j)\) is interpreted as itself.
References
Akshay, S., Bollig, B., Gastin, P., Mukund, M., Narayan Kumar, K.: Distributed timed automata with independently evolving clocks. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 82–97. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85361-9_10
Baeten, J.: Process algebra with explicit termination. Computing science reports, Technische Universiteit Eindhoven (2000)
Eichner, C., Fleischhack, H., Meyer, R., Schrimpf, U., Stehno, C.: Compositional semantics for UML 2.0 sequence diagrams using petri nets. In: Prinz, A., Reed, R., Reed, J. (eds.) SDL 2005. LNCS, vol. 3530, pp. 133–148. Springer, Heidelberg (2005). https://doi.org/10.1007/11506843_9
Haddad, S., Khmelnitsky, I.: Dynamic recursive petri nets. In: Janicki, R., Sidorova, N., Chatain, T. (eds.) PETRI NETS 2020. LNCS, vol. 12152, pp. 345–366. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-51831-8_17
Harel, D., Maoz, S.: Assert and negate revisited: modal semantics for UML sequence diagrams. Softw. Syst. Model. 7(2), 237–252 (2008)
Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Hoboken (1985)
Ingólfsdóttir, A., Lin, H.: A symbolic approach to value-passing processes. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 427–478. Elsevier Science, Amsterdam (2001). https://doi.org/10.1016/B978-044482830-9/50025-4
Jacobs, J., Simpson, A.: On a process algebraic representation of sequence diagrams. In: Canal, C., Idani, A. (eds.) SEFM 2014. LNCS, vol. 8938, pp. 71–85. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-15201-1_5
Knapp, A., Mossakowski, T.: UML interactions meet state machines - an institutional approach. In: 7th Conference on Algebra and Coalgebra in Computer Science (CALCO). Leibniz International Proceedings in Informatics (LIPIcs), vol. 72 (2017)
Knapp, A., Wuttke, J.: Model checking of UML 2.0 interactions. In: Kühne, T. (ed.) MODELS 2006. LNCS, vol. 4364, pp. 42–51. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-69489-2_6
Lodaya, K., Weil, P.: Series-parallel languages and the bounded-width property. Theor. Comput. Sci. 237(1–2), 347–380 (2000). https://doi.org/10.1016/S0304-3975(00)00031-1
Lu, L., Kim, D.K.: Required behavior of sequence diagrams: semantics and conformance. ACM Trans. Softw. Eng. Methodol. 23(2), 1–28 (2014). https://doi.org/10.1145/2523108
Mahe, E.: Coq proof for the equivalence of the semantics. erwanm974.github.io/coq_hibou_label_semantics_equivalence/. Accessed 14 Oct 2021
Mahe, E., Bannour, B., Gaston, C., Lapitre, A., Le Gall, P.: A small-step approach to multi-trace checking against interactions. In: Proceedings of the 36th Annual ACM Symposium on Applied Computing, SAC 2021, pp. 1815–1822. Association for Computing Machinery, New York (2021). https://doi.org/10.1145/3412841.3442054
Mahe, E., Gaston, C., Gall, P.L.: Revisiting semantics of interactions for trace validity analysis. In: FASE 2020. LNCS, vol. 12076, pp. 482–501. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45234-6_24
Mauw, S., Reniers, M.A.: Operational semantics for MSC’96. Comput. Netw. 31(17), 1785–1799 (1999). https://doi.org/10.1016/S1389-1286(99)00060-2
Micskei, Z., Waeselynck, H.: The many meanings of UML 2 sequence diagrams: a survey. Softw. Syst. Model. 10(4), 489–514 (2011)
OMG: Unified Modeling Language v2.5.1, December 2017. omg.org/spec/UML/2.5.1/PDF
Parrow, J.: An introduction to the \(\pi \)-calculus. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, pp. 479–543. Elsevier, North-Holland (2001)
Plotkin, G.: A structural approach to operational semantics. J. Log. Algebraic Program. 60–61, 17–139 (2004). https://doi.org/10.1016/j.jlap.2004.05.001
Reniers, M.: Message sequence chart: syntax and semantics. Ph.D. thesis, Mathematics and Computer Science (1999). https://doi.org/10.6100/IR524323
Rensink, A., Wehrheim, H.: Weak sequential composition in process algebras. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836, pp. 226–241. Springer, Heidelberg (1994). https://doi.org/10.1007/978-3-540-48654-1_20
Störrle, H.: Semantics of interactions in UML 2.0. In: 2003 Proceedings of IEEE Symposium on Human Centric Computing Languages and Environments, pp. 129–136, October 2003. https://doi.org/10.1109/HCC.2003.1260216
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Mahe, E., Gaston, C., Gall, P.L. (2022). Equivalence of Denotational and Operational Semantics for Interaction Languages. In: Aït-Ameur, Y., Crăciun, F. (eds) Theoretical Aspects of Software Engineering. TASE 2022. Lecture Notes in Computer Science, vol 13299. Springer, Cham. https://doi.org/10.1007/978-3-031-10363-6_8
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