A Pragmatic, Scalable Approach to Correct-by-Construction Process Composition Using Classical Linear Logic Inference

  • Petros PapapanagiotouEmail author
  • Jacques Fleuriot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11408)


The need for rigorous process composition is encountered in many situations pertaining to the development and analysis of complex systems. We discuss the use of Classical Linear Logic (CLL) for correct-by-construction resource-based process composition, with guaranteed deadlock freedom, systematic resource accounting, and concurrent execution. We introduce algorithms to automate the necessary inference steps for binary compositions of processes in parallel, conditionally, and in sequence. We combine decision procedures and heuristics to achieve intuitive and practically useful compositions in an applied setting.


Process modelling Composition Correct by construction Workflow Linear logic 



This work was supported by the “DigiFlow: Digitizing Industrial Workflow, Monitoring and Optimization” Innovation Activity funded by EIT Digital. We would like to thank the attendants of the LOPSTR conference, 4–6 September 2018, in Frankfurt, Germany for their insightful comments that helped improve this paper.


  1. 1.
    Van der Aalst, W.M.: The application of petri nets to workflow management. J. Circ. Syst. Comput. 8(01), 21–66 (1998)CrossRefGoogle Scholar
  2. 2.
    Abramsky, S.: Proofs as processes. Theoret. Comput. Sci. 135(1), 5–9 (1994)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Acay, C., Pfenning, F.: Refinements for session typed concurrency (2016)Google Scholar
  4. 4.
    Bellin, G., Scott, P.: On the \(\pi \)-calculus and linear logic. TCS 135(1), 11–65 (1994)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Caires, L., Pfenning, F.: Session types as intuitionistic linear propositions. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 222–236. Springer, Heidelberg (2010). Scholar
  6. 6.
    Christensen, E., Curbera, F., Meredith, G., Weerawarana, S.: Web services description language (WSDL) 1.1 (2001)Google Scholar
  7. 7.
    Dardha, O., Gay, S.J.: A new linear logic for deadlock-free session-typed processes. In: Baier, C., Dal Lago, U. (eds.) FoSSaCS 2018. LNCS, vol. 10803, pp. 91–109. Springer, Cham (2018). Scholar
  8. 8.
    Dardha, O., Pérez, J.A.: Comparing deadlock-free session typed processes. In: Proceedings of the 22th International Workshop on Expressiveness in Concurrency EXPRESS/SOS, pp. 1–15 (2015)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Girard, J.Y.: Linear logic: its syntax and semantics. In: Girard, J.Y., Lafont, Y., Regnier, L. (eds.) Advances in Linear Logic. No. 222 in London Mathematical Society Lecture Notes. Cambridge University Press, Cambridge (1995)Google Scholar
  10. 10.
    Gooch, P., Roudsari, A.: Computerization of workflows, guidelines and care pathways: a review of implementation challenges for process-oriented health information systems. J. Am. Med. Inform. Assoc. 18(6), 738–748 (2011)CrossRefGoogle Scholar
  11. 11.
    Harrison, J.: HOL light: a tutorial introduction. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 265–269. Springer, Heidelberg (1996). Scholar
  12. 12.
    Kezadri Hamiaz, M., Pantel, M., Thirioux, X., Combemale, B.: Correct-by-construction model driven engineering composition operators. Formal Aspects Comput. 28(3), 409–440 (2016)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Laurent, O.: Etude de la polarisation en logique. Ph.D. thesis, Université de la Méditerranée-Aix-Marseille II (2002)Google Scholar
  14. 14.
    Lincoln, P., Mitchell, J., Scedrov, A., Shankar, N.: Decision problems for propositional linear logic. Ann. Pure Appl. Logic 56(1), 239–311 (1992)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Manataki, A., Fleuriot, J., Papapanagiotou, P.: A workflow-driven formal methods approach to the generation of structured checklists for intrahospital patient transfers. J. Biomed. Health Inform. 21(4), 1156–1162 (2017)CrossRefGoogle Scholar
  16. 16.
    Martin, D., et al.: OWL-S: Semantic markup for web services (2004)Google Scholar
  17. 17.
    McDermott, D., et al.: PDDL-the planning domain definition language (1998)Google Scholar
  18. 18.
    Milner, R.: Communicating and Mobile Systems: The \(\pi \)-calculus. Cambridge University Press, Cambridge (1999)Google Scholar
  19. 19.
    OASIS: Web Services Business Process Execution Language, version 2.0, OASIS Standard (2007).
  20. 20.
    Object Management Group: Business Process Model and Notation (BPMN), version 2.0 (2011).
  21. 21.
    Papapanagiotou, P., Fleuriot, J.: WorkflowFM: a logic-based framework for formal process specification and composition. In: de Moura, L. (ed.) CADE 2017. LNCS (LNAI), vol. 10395, pp. 357–370. Springer, Cham (2017). Scholar
  22. 22.
    Rao, J., Küngas, P., Matskin, M.: Composition of semantic web services using linear logic theorem proving. Inf. Syst. 31(4–5), 340–360 (2006)CrossRefGoogle Scholar
  23. 23.
    Szpyrka, M., Nalepa, G.J., Ligęza, A., Kluza, K.: Proposal of formal verification of selected BPMN models with Alvis Modeling Language. In: Brazier, F.M.T., Nieuwenhuis, K., Pavlin, G., Warnier, M., Badica, C. (eds.) Intelligent Distributed Computing V. Studies in Computational Intelligence, vol. 382, pp. 249–255. Springer, Heidelberg (2012). Scholar
  24. 24.
    Tammet, T.: Proof strategies in linear logic. J. Autom. Reasoning 12(3), 273–304 (1994)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Toninho, B., Caires, L., Pfenning, F.: Dependent session types via intuitionistic linear type theory. In: 13th International ACM SIGPLAN Symposium on Principles and Practices of Declarative Programming PPDP 2011, pp. 161–172. ACM (2011)Google Scholar
  26. 26.
    Tounsi, I., Hadj Kacem, M., Hadj Kacem, A.: Building correct by construction SOA design patterns: modeling and refinement. In: Drira, K. (ed.) ECSA 2013. LNCS, vol. 7957, pp. 33–44. Springer, Heidelberg (2013). Scholar
  27. 27.
    Troelstra, A.S.: Lectures on Linear Logic. CSLI Lecture Notes 29, Stanford (1992)Google Scholar
  28. 28.
    Wadler, P.: Propositions as sessions. In: Proceedings of the 17th ACM SIGPLAN International Conference on Functional Programming, pp. 273–286. ACM (2012)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of InformaticsUniversity of EdinburghEdinburghUK

Personalised recommendations