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  • Cited by 29
  • Cited by
    Crossref Citations
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Scalas, Alceste and Yoshida, Nobuko 2019. Less is more: multiparty session types revisited. Proceedings of the ACM on Programming Languages, Vol. 3, Issue. POPL, p. 1.
    Carbone, Marco Montesi, Fabrizio and Schürmann, Carsten 2018. Choreographies, logically. Distributed Computing, Vol. 31, Issue. 1, p. 51.
    Toninho, Bernardo and Yoshida, Nobuko 2018. Programming Languages and Systems. Vol. 10801, Issue. , p. 827.
    Demangeon, Romain and Yoshida, Nobuko 2018. Causal Computational Complexity of Distributed Processes. p. 344.
    Scalas, Alceste and Yoshida, Nobuko 2018. Multiparty session types, beyond duality. Journal of Logical and Algebraic Methods in Programming, Vol. 97, Issue. , p. 55.
    Crafa, Silvia and Padovani, Luca 2017. The Chemical Approach to Typestate-Oriented Programming. ACM Transactions on Programming Languages and Systems, Vol. 39, Issue. 3, p. 1.
    PADOVANI, LUCA 2017. A simple library implementation of binary sessions. Journal of Functional Programming, Vol. 27, Issue. ,
    Bartoletti, Massimo Murgia, Maurizio Scalas, Alceste and Zunino, Roberto 2017. Verifiable abstractions for contract-oriented systems. Journal of Logical and Algebraic Methods in Programming, Vol. 86, Issue. 1, p. 159.
    Dragoni, Nicola Giallorenzo, Saverio Lafuente, Alberto Lluch Mazzara, Manuel Montesi, Fabrizio Mustafin, Ruslan and Safina, Larisa 2017. Present and Ulterior Software Engineering. p. 195.
    Padovani, Luca 2017. Programming Languages and Systems. Vol. 10201, Issue. , p. 804.
    Atkey, Robert 2017. Programming Languages and Systems. Vol. 10201, Issue. , p. 56.
    Tassarotti, Joseph Jung, Ralf and Harper, Robert 2017. Programming Languages and Systems. Vol. 10201, Issue. , p. 909.
    Carbone, Marco Montesi, Fabrizio Schürmann, Carsten and Yoshida, Nobuko 2017. Multiparty session types as coherence proofs. Acta Informatica, Vol. 54, Issue. 3, p. 243.
    Caires, Luís and Pérez, Jorge A. 2016. Formal Techniques for Distributed Objects, Components, and Systems. Vol. 9688, Issue. , p. 74.
    Lindley, Sam and Morris, J. Garrett 2016. Talking bananas: structural recursion for session types. ACM SIGPLAN Notices, Vol. 51, Issue. 9, p. 434.
    Thiemann, Peter and Vasconcelos, Vasco T. 2016. Context-free session types. ACM SIGPLAN Notices, Vol. 51, Issue. 9, p. 462.
    Lindley, Sam and Morris, J. Garrett 2016. Embedding session types in Haskell. p. 133.
    Lindley, Sam and Morris, J. Garrett 2016. Embedding session types in Haskell. ACM SIGPLAN Notices, Vol. 51, Issue. 12, p. 133.
    Morris, J. Garrett 2016. The best of both worlds: linear functional programming without compromise. ACM SIGPLAN Notices, Vol. 51, Issue. 9, p. 448.
    Thiemann, Peter and Vasconcelos, Vasco T. 2016. Context-free session types. p. 462.
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Propositions as sessions*

  • PHILIP WADLER (a1)
Abstract

Continuing a line of work by Abramsky (1994), Bellin and Scott (1994), and Caires and Pfenning (2010), among others, this paper presents CP, a calculus, in which propositions of classical linear logic correspond to session types. Continuing a line of work by Honda (1993), Honda et al. (1998), and Gay & Vasconcelos (2010), among others, this paper presents GV, a linear functional language with session types, and a translation from GV into CP. The translation formalises for the first time a connection between a standard presentation of session types and linear logic, and shows how a modification to the standard presentation yields a language free from races and deadlock, where race and deadlock freedom follows from the correspondence to linear logic.

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COPYRIGHT: © Cambridge University Press 2014 
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The online version of this paper uses colour to highlight the relation of types to terms and source to target.

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References
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Abramsky, S. (1993) Computational interpretations of linear logic. Theor. Comput. Sci. 111 (1&2), 3–57.
Abramsky, S. (1994) Proofs as processes. Theor. Comput. Sci. 135 (1), 5–9.
Abramsky, S., Gay, S. J. & Nagarajan, R. (1996) Interaction categories and the foundations of typed concurrent programming. In Deductive Program Design: Proceedings of the 1994 Marktoberdorf Summer School, NATO ASI Series F, pp. 35–113.
Bellin, G. & Scott, P. J. (1994) On the pi-calculus and linear logic. Theor. Comput. Sci. 135 (1), 11–65.
Benton, N. & Wadler, P. (1996) Linear logic, monads and the lambda calculus. In Logic in Computer Science (LICS), pp. 420–431.
Berger, M., Honda, K. & Yoshida, N. (2005) Genericity and the pi-calculus. Acta Inform. 42 (2–3), 83–141.
Caires, L., Pérez, J. A., Pfenning, F. & Toninho, B. (2013) Behavioral polymorphism and parametricity in session-based communication. In European Symposium on Programming (ESOP), Lecture Notes in Computer Science, vol. 7792. Berlin, Germany: Springer, pp. 330–349.
Caires, L. & Pfenning, F. (2010) Session types as intuitionistic linear propositions. In 21st International Conference on Concurrency Theory (CONCUR 2010), Paris, France, pp. 222–236.
Caires, L., Pfenning, F. & Toninho, B. (January 2012a) Towards concurrent type theory. In Types in Language Design and Implementation (TLDI), pp. 1–12.
Caires, L., Pfenning, F. & Toninho, B. (2013) Linear logic propositions as session types. Mathematical Structures in Computer Science. To appear in Special Issue on Behavioural Types.
Carbone, M. & Debois, S. (2010) A graphical approach to progress for structured communication in web services. In Interaction and Concurrency Experience (ICE), pp. 13–27.
Fähndrich, M., Aiken, M., Hawblitzel, C., Hodson, O., Hunt, G. C., Larus, J. R. & Levi, S. (2006) Language support for fast and reliable message-based communication in singularity OS. In European Conference on Computer Systems (EuroSys), pp. 177–190.
Gallier, J. H. (1990) On Girard's “Candidats de Reducibilité”. Academic Press, pp. 123–204.
Gay, S. J. & Hole, M. (2005) Subtyping for session types in the pi calculus. Acta Inform., 42 (2–3), 191–225.
Gay, S. J. & Vasconcelos, V. T. (2010) Linear type theory for asynchronous session types. J. Funct. Program. 20 (1), 19–50.
Girard, J.-Y. (1987) Linear logic. Theor. Comput. Sci. 50, 1–102.
Girard, J.-Y. (1991) A new constructive logic: Classical logic. Math. Struct. Comput. Sci. 1 (3), 255–296.
Girard, J.-Y., Lafont, Y. & Taylor, P. (1989) Proofs and Types, Cambridge Tracts in Theoretical Computer Science, vol. 7. Cambridge, UK: Cambridge University Press.
Herbelin, H. (2005) On the degeneracy of sigma-types in presence of computational classical logic. In Typed Lambda Calculi and Applications (TLCA), pp. 209–220.
Honda, K. (1993) Types for dyadic interaction. In Proceedings of the 4th International Conference on Concurrency Theory (CONCUR 1993), Hildesheim, Germany, pp. 509–523.
Honda, K., Vasconcelos, V. T. & Kubo, M. (1998) Language primitives and type discipline for structured communication-based programming. In European Symposium on Programming (ESOP), pp. 122–138.
Honda, K., Yoshida, N. & Carbone, M. (2008) Multiparty asynchronous session types. In Symposium on Principles of Programming Languages (POPL 2008), pp. 273–284.
Kobayashi, N. (2002) Type systems for concurrent programs. In Proceedings of the 10th Anniversary Colloquium of UNU/IIST, LNCS, vol. 2757. Berlin, Germany: Springer-Verlag, pp. 439–453.
Kobayashi, N., Pierce, B. C. & Turner, D. N. (1996) Linearity and the pi-calculus. In Principles of Programming Languages Symposium (POPL 1996), St. Petersburg Beach, FL, pp. 358–371.
Kobayashi, N. & Yonezawa, A. (1993) ACL – A concurrent linear logic programming paradigm. In International Logic Programming Symposium (ILPS), pp. 279–294.
Kobayashi, N. & Yonezawa, A. (1994) Higher-order concurrent linear logic programming. In Theory and Practice of Parallel Programming, LNCS, vol. 907. Berlin, Germany: Springer-Verlag, pp. 137–166.
Kobayashi, N. & Yonezawa, A. (1995) Asynchronous communication model based on linear logic. Form. Asp. Comput. 7 (2), 113–149.
Mazurak, K. & Zdancewic, S. (2010) Lolliproc: To concurrency from classical linear logic via Curry–Howard and control. In International Conference on Functional Programming (ICFP 2010), pp. 39–50.
Merro, M. & Sangiorgi, D. (2004) On asynchrony in name-passing calculi. Math. Struct. Comput. Sci. 14 (5), 715–767.
Miller, D.. (1992) The pi-calculus as a theory in linear logic: Preliminary results. In Extensions to Logic Programming, LNCS, vol. 660. Berlin, Germany: Springer-Verlag, pp. 242–264.
Milner, R., Parrow, J. & Walker, D. (1992) A calculus of mobile processes, i. Inf. Comput. 100 (1), 1–40.
Pérez, J., Caires, L., Pfenning, F. & Toninho, B. (2012) Linear logical relations for session-based concurrency. In European Symposium on Programming (ESOP), pp. 539–558.
Pfenning, F., Caires, L. & Toninho, B. (2011) Proof-carrying code in a session-typed process calculus. In Certified Programs and Proofs (CPP), pp. 21–36.
Pierce, B. C. & Sangiorgi, D. (2000) Behavioral equivalence in the polymorphic pi-calculus. J. ACM 47 (3), 531–584.
Pierce, B. C. & Turner, D. N. (2000) Pict: A programming language based on the pi-calculus. In Proof, Language, and Interaction, Essays in Honour of Robin Milner, Plotkin, G. D., Stirling, C. and Tofte, M. (eds). Cambridge, MA: MIT Press, pp. 455–494. ISBN: 978-0-262-16188-6.
Pitts, A. M. (2011) Structural recursion with locally scoped names. J. Funct. Program. 21 (3), 235–286.
Sumii, E. & Kobayashi, N. (1998) A generalized deadlock-free process calculus. (High-Level Concurrent Languages (HLCL), 1998). Electron. Notes Theor. Comput. Sci. 16 (3), 225–247.
Takeuchi, K., Honda, K. & Kubo, M. (1994) An interaction-based language and its typing system. In Proceedings of the 6th International PARLE Conference, Athens, Greece, Halatsis, C., Maritsas, D. G., Philokyprou, G. and Theodoridis, S. (eds), LNCS, vol. 817. Berlin, Germany: Springer-Verlag, pp. 398–413.
Toninho, B., Caires, L. & Pfenning, F. (2012) Functions as session-typed processes. In Foundations of Software Science and Computation (FoSSaCS), pp. 346–360.
Toninho, B., Caires, L. & Pfenning, F. (2013) Higher-order processes, functions, and sessions: A monadic integration. In 22nd European Symposium on Programming (ESOP'13), Lecture Notes in Computer Science, vol. 7792. New York, NY: Springer, pp. 350–369.
Turner, D. N. (1995) The Polymorphic Pi-Calculus: Theory and Implementation, PhD thesis, University of Edinburgh, Edinburgh, UK.
Vasconcelos, V. T. (2011) Sessions, from types to programming languages. Bull. Eur. Assoc. Theor. Comput. Sci. 103, 53–73.
Wadler, P. (September 2012) Propositions as sessions. In International Conference on Functional Programming (ICFP), pp. 273–286.
Yoshida, N. & Vasconcelos, V. T. (2007) Language primitives and type discipline for structured communication-based programming revisited: Two systems for higher-order session communication. Electron. Notes Theor. Comput. Sci. 171 (4), 73–93.
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  • Cited by 29
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Scalas, Alceste and Yoshida, Nobuko 2019. Less is more: multiparty session types revisited. Proceedings of the ACM on Programming Languages, Vol. 3, Issue. POPL, p. 1.
    Carbone, Marco Montesi, Fabrizio and Schürmann, Carsten 2018. Choreographies, logically. Distributed Computing, Vol. 31, Issue. 1, p. 51.
    Toninho, Bernardo and Yoshida, Nobuko 2018. Programming Languages and Systems. Vol. 10801, Issue. , p. 827.
    Demangeon, Romain and Yoshida, Nobuko 2018. Causal Computational Complexity of Distributed Processes. p. 344.
    Scalas, Alceste and Yoshida, Nobuko 2018. Multiparty session types, beyond duality. Journal of Logical and Algebraic Methods in Programming, Vol. 97, Issue. , p. 55.
    Crafa, Silvia and Padovani, Luca 2017. The Chemical Approach to Typestate-Oriented Programming. ACM Transactions on Programming Languages and Systems, Vol. 39, Issue. 3, p. 1.
    PADOVANI, LUCA 2017. A simple library implementation of binary sessions. Journal of Functional Programming, Vol. 27, Issue. ,
    Bartoletti, Massimo Murgia, Maurizio Scalas, Alceste and Zunino, Roberto 2017. Verifiable abstractions for contract-oriented systems. Journal of Logical and Algebraic Methods in Programming, Vol. 86, Issue. 1, p. 159.
    Dragoni, Nicola Giallorenzo, Saverio Lafuente, Alberto Lluch Mazzara, Manuel Montesi, Fabrizio Mustafin, Ruslan and Safina, Larisa 2017. Present and Ulterior Software Engineering. p. 195.
    Padovani, Luca 2017. Programming Languages and Systems. Vol. 10201, Issue. , p. 804.
    Atkey, Robert 2017. Programming Languages and Systems. Vol. 10201, Issue. , p. 56.
    Tassarotti, Joseph Jung, Ralf and Harper, Robert 2017. Programming Languages and Systems. Vol. 10201, Issue. , p. 909.
    Carbone, Marco Montesi, Fabrizio Schürmann, Carsten and Yoshida, Nobuko 2017. Multiparty session types as coherence proofs. Acta Informatica, Vol. 54, Issue. 3, p. 243.
    Caires, Luís and Pérez, Jorge A. 2016. Formal Techniques for Distributed Objects, Components, and Systems. Vol. 9688, Issue. , p. 74.
    Lindley, Sam and Morris, J. Garrett 2016. Talking bananas: structural recursion for session types. ACM SIGPLAN Notices, Vol. 51, Issue. 9, p. 434.
    Thiemann, Peter and Vasconcelos, Vasco T. 2016. Context-free session types. ACM SIGPLAN Notices, Vol. 51, Issue. 9, p. 462.
    Lindley, Sam and Morris, J. Garrett 2016. Embedding session types in Haskell. p. 133.
    Lindley, Sam and Morris, J. Garrett 2016. Embedding session types in Haskell. ACM SIGPLAN Notices, Vol. 51, Issue. 12, p. 133.
    Morris, J. Garrett 2016. The best of both worlds: linear functional programming without compromise. ACM SIGPLAN Notices, Vol. 51, Issue. 9, p. 448.
    Thiemann, Peter and Vasconcelos, Vasco T. 2016. Context-free session types. p. 462.
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