Abstract
Continuing a line of work by Abramsky (1994), by Bellin and Scott (1994), and by 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), by Honda, Kubo, and Vasconcelos (1998), and by Gay and Vasconcelos (2010), among others, this paper presents GV, a linear functional language with session types, and presents 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 yield a language free from deadlock, where deadlock freedom follows from the correspondence to linear logic.
- Samson Abramsky. Computational interpretations of linear logic. Theoretical Computer Science, 111 (1&2): 3--57, 1993. Google Scholar
Digital Library
- Samson Abramsky. Proofs as processes. Theoretical Computer Science, 135 (1): 5--9, 1994. Google Scholar
Digital Library
- Samson Abramsky, Simon J. Gay, and Rajagopal Nagarajan. Interaction categories and the foundations of typed concurrent programming. In Deductive Program Design, Marktoberdorf, pages 35--113, 1996. Google Scholar
Digital Library
- Gianluigi Bellin and Philip J. Scott. On the pi-calculus and linear logic. Theoretical Computer Science, 135 (1): 11--65, 1994. Google Scholar
Digital Library
- Nick Benton and Philip Wadler. Linear logic, monads and the lambda calculus. In Logic in Computer Science (LICS), pages 420--431, 1996. Google Scholar
Digital Library
- Martin Berger, Kohei Honda, and Nobuko Yoshida. Genericity and the pi-calculus. Acta Inf., 42 (2-3): 83--141, 2005. Google Scholar
Digital Library
- Luís Caires and Frank Pfenning. Session types as intuitionistic linear propositions. In CONCUR, pages 222--236, 2010. Google Scholar
Digital Library
- Luís Caires, Frank Pfenning, and Bernardo Toninho. Towards concurrent type theory. In Types in Language Design and Implementation (TLDI), January 2012. Google Scholar
Digital Library
- LuísCaires, Frank Pfenning, and Bernardo Toninho. Linear logic propositions as session types. Mathematical Structures in Computer Science, 2012. Submitted.Google Scholar
- Marco Carbone and Søren Debois. A graphical approach to progress for structured communication in web services. In Interaction and Concurrency Experience (ICE), pages 13--27, 2010.Google Scholar
Cross Ref
- Manuel Fähndrich, Mark Aiken, Chris Hawblitzel, Orion Hodson, Galen C. Hunt, James R. Larus, and Steven Levi. Language support for fast and reliable message-based communication in Singularity OS. In European Conference on Computer Systems (EuroSys), pages 177--190, 2006. Google Scholar
Digital Library
- Jean H. Gallier. On Girard's "Candidats de Reducibilité", pages 123--204. Academic Press, 1990.Google Scholar
- Simon J. Gay and Malcolm Hole. Subtyping for session types in the pi calculus. Acta Informatica, 42 (2-3): 191--225, 2005. Google Scholar
Digital Library
- Simon J. Gay and Vasco T. Vasconcelos. Linear type theory for asynchronous session types. Journal of Functional Programming, 20 (1): 19--50, 2010. Google Scholar
Digital Library
- Jean-Yves Girard. Linear logic. Theoretical Computer Science, 50: 1--102, 1987. Google Scholar
Digital Library
- Jean-Yves Girard. A new constructive logic: Classical logic. Mathematical Structures in Computer Science, 1 (3): 255--296, 1991.Google Scholar
Cross Ref
- Jean-Yves Girard, Yves Lafont, and Paul Taylor. Proofs and Types, volume 7 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1989. Google Scholar
Digital Library
- Hugo Herbelin. On the degeneracy of sigma-types in presence of computational classical logic. In Typed Lambda Calculi and Applications (TLCA), pages 209--220, 2005. Google Scholar
Digital Library
- Kohei Honda. Types for dyadic interaction. In CONCUR, pages 509--523, 1993. Google Scholar
Digital Library
- Kohei Honda, Vasco T. Vasconcelos, and Makoto Kubo. Language primitives and type discipline for structured communication-based programming. In European Symposium on Programming (ESOP), pages 122--138, 1998. Google Scholar
Digital Library
- Naoki Kobayashi. Type systems for concurrent programs. In 10th Anniversary Colloquium of UNU/IIST, LNCS 2757, pages 439--453, 2002.Google Scholar
- Naoki Kobayashi and Akinori Yonezawa. Acl - a concurrent linear logic programming paradigm. In International Logic Programming Symposium (ILPS), pages 279--294, 1993. Google Scholar
Digital Library
- Naoki Kobayashi and Akinori Yonezawa. Higher-order concurrent linear logic programming. In Theory and Practice of Parallel Programming, LNCS 907, pages 137--166, 1994. Google Scholar
Digital Library
- Naoki Kobayashi and Akinori Yonezawa. Asynchronous communication model based on linear logic. Formal Aspects of Computing, 7 (2): 113--149, 1995.Google Scholar
Digital Library
- Naoki Kobayashi, Benjamin C. Pierce, and David N. Turner. Linearity and the pi-calculus. In POPL, pages 358--371, 1996. Google Scholar
Digital Library
- Karl Mazurak and Steve Zdancewic. Lolliproc: to concurrency from classical linear logic via curry-howard and control. In International Conference on Functional Programming (ICFP), pages 39--50, 2010. Google Scholar
Digital Library
- Massimo Merro and Davide Sangiorgi. On asynchrony in name-passing calculi. Mathematical Structures in Computer Science, 14 (5): 715--767, 2004. Google Scholar
Digital Library
- Dale Miller. The pi-calculus as a theory in linear logic: Preliminary results. In Extensions to Logic Programming, LNCS 660, pages 242--264, 1992. Google Scholar
Digital Library
- Robin Milner, Joachim Parrow, and David Walker. A calculus of mobile processes, i. Information and Computation, 100 (1): 1--40, 1992. Google Scholar
Digital Library
- Jorge Pérez, Luís Caires, Frank Pfenning, and Bernardo Toninho. Termination in session-based concurrency via linear logical relations. In European Symposium on Programming (ESOP), 2012.Google Scholar
- Frank Pfenning, Luís Caires, and Bernardo Toninho. Proof-carrying code in a session-typed process calculus. In Certified Programs and Proofs (CPP), pages 21--36, 2011. Google Scholar
Digital Library
- Benjamin C. Pierce and Davide Sangiorgi. Behavioral equivalence in the polymorphic pi-calculus. Journal of the ACM, 47 (3): 531--584, 2000. Google Scholar
Digital Library
- Benjamin C. Pierce and David N. Turner. Pict: a programming language based on the pi-calculus. In Gordon D. Plotkin, Colin Stirling, and Mads Tofte, editors, Proof, Language, and Interaction, Essays in Honour of Robin Milner, pages 455--494. The MIT Press, 2000. ISBN 978-0-262-16188-6. Google Scholar
Digital Library
- Andrew M. Pitts. Structural recursion with locally scoped names. J. Funct. Program., 21 (3): 235--286, 2011. Google Scholar
Digital Library
- Eijiro Sumii and Naoki Kobayashi. A generalized deadlock-free process calculus. In High-Level Concurrent Languages (HLCL), 1998. ENTCS 16(3):225--247, 1998.Google Scholar
Cross Ref
- Kaku Takeuchi, Kohei Honda, and Makoto Kubo. An interaction-based language and its typing system. In C. Halatsis, D. G. Maritsas, G. Philokyprou, and S. Theodoridis, editors, PARLE, LNCS 817, pages 398--413, 1994. Google Scholar
Digital Library
- Bernardo Toninho, Luís Caires, and Frank Pfenning. Functions as session-typed processes. In Foundations of Software Science and Computation (FoSSaCS), 2012. Google Scholar
Digital Library
- David N. Turner. The Polymorphic Pi-calculus: Theory and Implementation. PhD thesis, University of Edinburgh, 1995.Google Scholar
- Vasco T. Vasconcelos. Sessions, from types to programming languages. Bulletin of the European Association for Theoretical Computer Science, 103: 53--73, 2011.Google Scholar
- Nobuko Yoshida and Vasco T. Vasconcelos. Language primitives and type discipline for structured communication-based programming revisited: Two systems for higher-order session communication. Electronic Notes in Theoretical Computer Science, 171 (4): 73--93, 2007. Google Scholar
Digital Library
Index Terms
Propositions as sessions
Recommendations
Propositions as sessions
ICFP '12: Proceedings of the 17th ACM SIGPLAN international conference on Functional programmingContinuing a line of work by Abramsky (1994), by Bellin and Scott (1994), and by 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 ...
Linear lambda calculus with non-linear first-class continuations
ICSCA '17: Proceedings of the 6th International Conference on Software and Computer ApplicationsThe Curry-Howard isomorphism is the correspondence between propositions and types, proofs and lambda-terms, and proof normalization and evaluation. In Curry-Howard isomorphism, we find a duality between values and continuations in pure functional ...
Proofs, tests and continuation passing style
The concept of syntactical duality is central in logic. In particular, the duality defined by classical negation, or more syntactically by left and right in sequents, has been widely used to relate logic and computations. We study the proof/test duality ...







Comments