Hostname: page-component-76c49bb84f-s7zp8 Total loading time: 0 Render date: 2025-07-02T00:51:48.751Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear logic propositions as session types

Published online by Cambridge University Press:  10 November 2014

LUÍS CAIRES ,
FRANK PFENNING  and
BERNARDO TONINHO
LUÍS CAIRES
Affiliation:
Faculdade de Ciências e Tecnologia and CITI, Universidade Nova de Lisboa, Lisboa, Portugal Emails: btoninho@gmail.com and luis.caires@fct.unl.pt
FRANK PFENNING
Affiliation:
Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA Email: fp@cs.cmu.edu
BERNARDO TONINHO
Affiliation:
Faculdade de Ciências e Tecnologia and CITI, Universidade Nova de Lisboa, Lisboa, Portugal Emails: btoninho@gmail.com and luis.caires@fct.unl.pt Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA Email: fp@cs.cmu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Throughout the years, several typing disciplines for the π-calculus have been proposed. Arguably, the most widespread of these typing disciplines consists of session types. Session types describe the input/output behaviour of processes and traditionally provide strong guarantees about this behaviour (i.e. deadlock-freedom and fidelity). While these systems exploit a fundamental notion of linearity, the precise connection between linear logic and session types has not been well understood.

This paper proposes a type system for the π-calculus that corresponds to a standard sequent calculus presentation of intuitionistic linear logic, interpreting linear propositions as session types and thus providing a purely logical account of all key features and properties of session types. We show the deep correspondence between linear logic and session types by exhibiting a tight operational correspondence between cut-elimination steps and process reductions. We also discuss an alternative presentation of linear session types based on classical linear logic, and compare our development with other more traditional session type systems.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 26 , Special Issue 3: Special Issue: Behavioural Types Part 2 , March 2016 , pp. 367 - 423
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Abramsky, S. (1993) Computational interpretations of linear logic. Theoretical Computer Science 111 (1–2) 3–57.Google Scholar
Andreoli, J.-M. (1992) Logic programming with focusing proofs in linear logic. Journal of Logic and Computation 2 (3) 197–347.Google Scholar
Barber, A. (1997) Dual intuitionistic linear logic, Technical Report LFCS-96-347, University of Edinburgh.Google Scholar
Beffara, E. (2006) A concurrent model for linear logic. Electronic Notes in Theoretical Computer Science 155 147–168.Google Scholar
Bellin, G. and Scott, P. (1994) On the π-calculus and linear logic. Theoretical Computer Science 135 11–65.CrossRefGoogle Scholar
Bonelli, E., Compagnoni, A. and Gunter, E. L. (2005) Correspondence assertions for process synchronization in concurrent communications. Journal of Functional Programming 15 (2) 219–247.Google Scholar
Boreale, M. (1998) On the expressiveness of internal mobility in name-passing calculi. Theoretical Computer Science 195 (2) 205–226.Google Scholar
Caires, L. (2007) Logical semantics of types for concurrency. In: Proceedings of the International Conference on Algebra and Coalgebra in Computer Science (CALCO'07). Springer Lecture Notes in Computer Science 4624 16–35.Google Scholar
Caires, L., Pérez, J. A., Pfenning, F. and Toninho, B. (2012) Relational parametricity for polymorphic session types, Technical Report CMU-CS-12-108, Carnegie Mellon University.Google Scholar
Caires, L. and Pfenning, F. (2010) Session types as intuitionistic linear propositions. In: Proceedings of the 21st International Conference on Concurrency Theory, CONCUR'10. Springer Lecture Notes in Computer Science 6269 222–236.CrossRefGoogle Scholar
Carbone, M. and Debois, S. (2010) A graphical approach to progress for structured communication in web services. In: Proceedings of the 3rd Interaction and Concurrency Experience: Guaranteed Interaction (ICE'10). Electronic Proceedings in Theoretical Computer Science 38 13–27.CrossRefGoogle Scholar
Cervesato, I. and Pfenning, F. (2002) A linear logical framework. Information and Computation 179 (1) 19–75.Google Scholar
Chang, B.-Y. E., Chaudhuri, K. and Pfenning, F. (2003) A judgmental analysis of linear logic, Technical Report CMU-CS-03-131R, Carnegie Mellon University.Google Scholar
Dezani-Ciancaglini, M. and de' Liguoro, U. (2010) Sessions and session types: An overview. In: 6th International Workshop on Web Services and Formal Methods (WS-FM'09). Springer-Verlag Lecture Notes in Computer Science 6194 1–28.Google Scholar
Dezani-Ciancaglini, M., de' Liguoro, U. and Yoshida, N. (2008) On progress for structured communications. In: Proceedings of the 3th Symposium Trustworthy Global Computing (TGC'07). Springer Lecture Notes in Computer Science 4912 257–275.Google Scholar
Gay, S. and Hole, M. (2005) Subtyping for session types in the Pi calculus. Acta Informatica 42 (2–3) 191–225.CrossRefGoogle Scholar
Girard, J.-Y. (1987) Linear logic. Theoretical Computer Science 50 1–102.CrossRefGoogle Scholar
Girard, J.-Y. and Lafont, Y. (1987) Linear logic and lazy computation. In: Theory and Practice of Software Development (TAPSOFT'87). Springer Lecture Notes in Computer Science 250 52–66.CrossRefGoogle Scholar
Giunti, M. and Vasconcelos, V. T. (2010) A linear account of session types in the Pi-calculus. In: Proceedings of the 21st International Conference on Concurrency Theorym (CONCUR'10). Springer Lecture Notes in Computer Science 6269 432–446.CrossRefGoogle Scholar
Honda, K. (1993) Types for dyadic interaction. In:4th International Conference on Concurrency Theory (CONCUR'93). Springer Lecture Notes in Computer Science 715 509–523.CrossRefGoogle Scholar
Honda, K. and Laurent, O. (2010) An exact correspondence between a typed pi-calculus and polarised proof-nets. Theoretical Computer Science 411 2223–2238.Google Scholar
Honda, K., Vasconcelos, V. T. and Kubo, M. (1998) Language primitives and type discipline for structured communication-based programming. In: European Symposium on Programming (ESOP'98). Springer Lecture Notes in Computer Science 1381 122–138.Google Scholar
Hyland, J. M. E. and Ong, C.-H. L. (1995) Pi-calculus, dialogue games and PCF. In: WG2.8 Conference on Functional Programming Languages 96–107.Google Scholar
Kobayashi, N. (1998) A partially deadlock-free typed process calculus. ACM Transactions on Programming Languages and Systems 20 (2) 436–482.Google Scholar
Kobayashi, N., Pierce, B. C. and Turner, D. N. (1996) Linearity and the pi-calculus. In: 23rd Symposium on Principles of Programming Languages (POPL'96), ACM 358–371.Google Scholar
Merro, M. and Sangiorgi, D. (2004) On asynchrony in name-passing calculi. Mathematical Structures in Computer Science 14 (5) 715–767.CrossRefGoogle Scholar
Milner, R. (1992) Functions as processes. Mathematical Structures in Computer Science 2 (2) 119–141.Google Scholar
Pérez, J. A., Caires, L., Pfenning, F. and Toninho, B. (2012) Termination in session-based concurrency via linear logical relations. In: 22nd European Symposium on Programming (ESOP'12) 539–558.Google Scholar
Pfenning, F., Caires, L. and Toninho, B. (2011) Proof-carrying code in a session-typed process calculus. Certified Programs and Proofs (CPP'11) 21–36.Google Scholar
Sangiorgi, D. (1996) Pi-calculus, internal mobility, and agent passing calculi. Theoretical Computer Science 167 (1–2) 235–274.Google Scholar
Sangiorgi, D. and Walker, D. (2001) The π-Calculus: A Theory of Mobile Processes, Cambridge University Press.Google Scholar
Toninho, B., Caires, L. and Pfenning, F. (2011) Dependent session types via intuitionistic linear type theory. In: Principles and Practice of Declarative Programming (PPDP'11), 161–172.Google Scholar
Toninho, B., Caires, L. and Pfenning, F. (2012) Functions as session-typed processes. In: 15th International Conference on Foundations of Software Science and Computation Structures (FoSSaCS'12) 346–360.Google Scholar
Wadler, P. (2012) Propositions as sessions. In: Proceedings of the 17th International Conference on Functional Programming, ICFP'12 273–286.Google Scholar
Watkins, K., Cervesato, I., Pfenning, F. and Walker, D. (2004) Specifying properties of concurrent computations in CLF. In: Schürmann, C. (ed.) 4th International Workshop on Logical Frameworks and Meta-Languages (LFM'04). Electronic Notes in Theoretical Computer Science 199 67–87.CrossRefGoogle Scholar
Yoshida, N., Honda, K. and Berger, M. (2007) Linearity and bisimulation. Journal of Logic and Algebraic Programming 72 (2) 207–238.CrossRefGoogle Scholar