The deep connection between session-typed concurrency and linear logic is embodied in the language SILL that integrates functional and message-passing concurrent programming. The exacting nature of linear typing provides strong guarantees, such as global progress, absence of deadlock, and race freedom, but it also requires explicit resource management by the programmer. This burden is alleviated in an affine type system where resources need not be used, relying on a simple form of garbage collection.

In this paper we show how to effectively support both linear and affine typing in a single language, in addition to the already present unrestricted (intuitionistic) types. The approach, based on Benton’s adjoint construction, suggests that the usual distinction between synchronous and asynchronous communication can be viewed through the lens of modal logic. We show how polarizing the propositions into positive and negative connectives allows us to elegantly express synchronization in the type instead of encoding it by extra-logical means.


Operational Semantic Garbage Collection Linear Logic Process Expression Asynchronous Communication 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Andreoli, J.M.: Logic programming with focusing proofs in linear logic. Journal of Logic and Computation 2(3), 197–347 (1992)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Barber, A.: Dual intuitionistic linear logic. Tech. Rep. ECS-LFCS-96-347, Department of Computer Science, University of Edinburgh (September 1996)Google Scholar
  3. 3.
    Benton, N.: A mixed linear and non-linear logic: Proofs, terms and models. In: Pacholski, L., Tiuryn, J. (eds.) CSL 1994. LNCS, vol. 933, pp. 121–135. Springer, Heidelberg (1995), an extended version appears as Technical Report UCAM-CL-TR-352, University of Cambridge CrossRefGoogle Scholar
  4. 4.
    Caires, L., Pérez, J.A., Pfenning, F., Toninho, B.: Behavioral polymorphism and parametricity in session-based communication. In: Felleisen, M., Gardner, P. (eds.) ESOP 2013. LNCS, vol. 7792, pp. 330–349. Springer, Heidelberg (2013)CrossRefGoogle 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)CrossRefGoogle Scholar
  6. 6.
    Caires, L., Pfenning, F., Toninho, B.: Linear logic propositions as session types. Mathematical Structures in Computer Science (2013) (to appear ) Special Issue on Behavioural TypesGoogle Scholar
  7. 7.
    Cervesato, I., Scedrov, A.: Relating state-based and process-based concurrency through linear logic. Information and Computation 207(10), 1044–1077 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Chang, B.Y.E., Chaudhuri, K., Pfenning, F.: A judgmental analysis of linear logic. Tech. Rep. CMU-CS-03-131R, Carnegie Mellon University, Department of Computer Science (December 2003)Google Scholar
  9. 9.
    DeYoung, H., Caires, L., Pfenning, F., Toninho, B.: Cut reduction in linear logic as asynchronous session-typed communication. In: Cégielski, P., Durand, A. (eds.) Proceedings of the 21st Conference on Computer Science Logic, CSL 2012, Leibniz International Proceedings in Informatics, Fontainebleau, France, pp. 228–242 (September 2012)Google Scholar
  10. 10.
    Gay, S.J., Hole, M.: Subtyping for session types in the π-calculus. Acta Informatica 42(2-3), 191–225 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Gay, S.J., Vasconcelos, V.T.: Linear type theory for asynchronous session types. Journal of Functional Programming 20(1), 19–50 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    Girard, J.Y.: Linear logic. Theoretical Computer Science 50, 1–102 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Honda, K.: Types for dyadic interaction. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 509–523. Springer, Heidelberg (1993)Google Scholar
  14. 14.
    Honda, K., Vasconcelos, V.T., Kubo, M.: Language primitives and type discipline for structured communication-based programming. In: Hankin, C. (ed.) ESOP 1998. LNCS, vol. 1381, pp. 122–138. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  15. 15.
    Laurent, O.: Polarized proof-nets: Proof-nets for LC. In: Girard, J.-Y. (ed.) TLCA 1999. LNCS, vol. 1581, pp. 213–227. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  16. 16.
    Mostrous, D., Vasconcelos, V.: Affine sessions. In: Kühn, E., Pugliese, R. (eds.) COORDINATION 2014. LNCS, vol. 8459, pp. 115–130. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  17. 17.
    Pérez, J.A., Caires, L., Pfenning, F., Toninho, B.: Linear logical relations and observational equivalences for session-based concurrency. Information and Computation 239, 254–302 (2014)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Reed, J.: A judgmental deconstruction of modal logic (2009) (unpublished manuscript)Google Scholar
  19. 19.
    Simmons, R.J.: Substructural Logical Specifications. Ph.D. thesis, Carnegie Mellon University, available as Technical Report CMU-CS-12-142 (November 2012)Google Scholar
  20. 20.
    Toninho, B.: A Logical Foundation for Session-based Concurrent Computation. Ph.D. thesis, Carnegie Mellon University and New University of Lisbon (2015) (in preparation)Google Scholar
  21. 21.
    Toninho, B., Caires, L., Pfenning, F.: Higher-order processes, functions, and sessions: A monadic integration. In: Felleisen, M., Gardner, P. (eds.) ESOP 2013. LNCS, vol. 7792, pp. 350–369. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  22. 22.
    Toninho, B., Caires, L., Pfenning, F.: Corecursion and non-divergence in session-typed processes. In: Proceedings of the 9th International Symposium on Trustworthy Global Computing (TGC 2014), Rome, Italy (September 2014) (to appear)Google Scholar
  23. 23.
    Vasconcelos, V.T.: Fundamentals of session types. Information and Computation 217, 52–70 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Wadler, P.: Propositions as sessions. In: Proceedings of the 17th International Conference on Functional Programming, ICFP 2012, pp. 273–286. ACM Press, Copenhagen (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Carnegie Mellon UniversityPittsburghUSA
  2. 2.University of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations