An exact correspondence between a typed pi-calculus and polarised proof-nets

Theoretical Computer Science

Volumn 411, Issue 22-24, 2010, Pages 2223-2238

  Honda, Kohei ^a   Laurent, Olivier ^b  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

^b CNRS   (France)

Author keywords

Concurrency; Determinism; Embedding; Interaction; Linear Logic; Logics; Non determinism; Pi calculus; Polarity; Processes; Proof nets; Proofs; Types

Indexed keywords

GEOMETRIC STRUCTURE; LINEAR LOGIC; NON-DETERMINISM; PI CALCULUS; PROOF NET;

CALCULATIONS;

EID: 77950960618     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2010.01.028     Document Type: Article

References (43)

1. Abramsky S. Computational interpretations of linear logic. Theoretical Computer Science 111 1-2 (1993) 3-57
2. Abramsky S. Proofs as processes. Theoretical Computer Science 135 1 (1994) 5-9
3. Agha G. Actors: A Model of Concurrent Computation in Distributed Systems (1986), MIT Press, Cambridge, MA, USA
4. Abramsky S., Jagadeesan R., and Malacaria P. Full abstraction for PCF. Information and Computation 163 (2000) 409-470
5. Beffara E. A concurrent model for linear logic. In: Escardó M., Jung A., and Mislove M. (Eds). Proceedings of the 21st Conference on Mathematical Foundations of Programming Semantics. MFPS'05. Electronic Notes in Theoretical Computer Science vol. 155 (May 2006), Elsevier 147-168
6. Berger M., Honda K., and Yoshida N. Sequentiality and the π-calculus. In: Abramsky S. (Ed). Typed Lambda Calculi and Applications'01. Lecture Notes in Computer Science vol. 2044 (May 2001), Springer 29-45
7. Berger M., Honda K., and Yoshida N. Genericity and the π-calculus. FoSSaCs'03. Lecture Notes in Computer Science vol. 2620 (2003)
8. Beffara E., and Maurel F. Concurrent nets: A study of prefixing in process calculi. Theoretical Computer Science 356 (2005)
9. Gérard Boudol, Asynchrony and the pi-calculus, Technical Report 1702, INRIA, 1992.
10. Bellin G., and Scott P.J. On the pi-calculus and linear logic. Theoretical Computer Science 135 1 (1994) 11-65
11. Baeten J.C.M., and Peter Weijland W. Process Algebra (1990), Cambridge University Press
12. Curien P.-L., and Faggian C. L-nets, strategies and proof-nets. In: Luke Ong C.-H. (Ed). Computer Science Logic. Lecture Notes in Computer Science vol. 3634 (2005), European Association for Computer Science Logic, Springer 167-183
13. Ehrhard T., and Regnier L. Differential interaction nets. Theoretical Computer Science 364 2 (2006) 166-195
14. Faggian C., and Maurel F. Ludics nets, a game model of concurrent interaction. Proceedings of the Twentieth Annual Symposium on Logic in Computer Science (June 2005), IEEE, IEEE Computer Society Press, Chicago 376-385
15. Girard J.-Y. Linear logic. Theoretical Computer Science 50 (1987) 1-102
16. Jean-Yves Girard, Quantifiers in linear logic II, in: Corsi, Sambin (Eds.), Nuovi problemi della logica e della filosofia della scienza, Bologna, 1991, pp. 79-90, CLUEB.
17. Girard J.-Y. Locus solum: From the rules of logic to the logic of rules. Mathematical Structures in Computer Science 11 3 (2001) 301-506
18. Martin J., Hyland E., and Luke Ong C.H. On full abstraction for PCF. Information and Computation 163 (2000) 285-408
19. Hoare T. Communicating Sequential Processes (1985), Prentice Hall
20. Kohei Honda, Composing processes, in: Proceedings of POPL'96, 1996, pp. 344-357.
21. Kohei Honda, Mario Tokoro, An object calculus for asynchronous communication, in: Proceedings of ECOOP'91, 1991.
22. Honda K., Vasconcelos V.T., and Kubo M. Language primitives and type disciplines for structured communication-based programming. In: Hankin C. (Ed). ESOP'98. Lecture Notes in Computer Science vol. 1381 (1998), Springer 22-138
23. Honda K., and Yoshida N. On reduction-based process semantics. Theoretical Computer Science 151 (1995)
24. Kohei Honda, Nobuko Yoshida, Martin Berger, Control in the π-calculus, in: Fourth ACM-SIGPLAN Continuation Workshop, CW'04, 2004. Online proceedings.
25. Ole Jensen, Robin Milner, Bigraphs and mobile processes (revised), Technical report, Cambridge University Computer Laboratory, 2004.
26. Olivier Laurent, Étude de la polarisation en logique, Ph.D. Thesis, Université Aix-Marseille II, March 2002.
27. Laurent O. Polarized proof-nets and λ μ-calculus. Theoretical Computer Science 290 1 (2003) 161-188
28. Laurent O. Syntax vs. semantics: A polarized approach. Theoretical Computer Science 343 1-2 (2005) 177-206
29. Laneve C., Parrow J., and Victor B. Solo diagrams. Proceedings of the 4th Conference on Theoretical Aspects of Computer Science. TACS'01. Lecture Notes in Computer Science vol. 2215 (2001), Springer 127-144
30. Maurel F. Nondeterministic light logics and NP-time. In: Hofmann M. (Ed). Typed Lambda Calculi and Applications'03. Lecture Notes in Computer Science vol. 2701 (June 2003), Springer 241-255
31. Mazza D. Multiport interaction nets and concurrency. In: Abadi M., and de Alfaro L. (Eds). Proceedings of the 16th International Conference on Concurrency Theory. CONCUR 2005. Lecture Notes in Computer Science vol. 3653 (2005), Springer 21-35
32. Milner R. Communication and Concurrency (1989), Prentice Hall
33. Milner R. Functions as processes. Mathematical Structures in Computer Science 2 2 (1992) 119-141
34. Robin Milner, The polyadic π-calculus: A tutorial, in: Proceedings of the International Summer School on Logic Algebra of Specification, Marktoberdorf, 1992.
35. Milner R., Parrow J., and Walker D. A calculus of mobile processes, I/II. Information and Computation 100 1 (1992) 1-77
36. Pierce B.C., and Sangiorgi D. Behavioral equivalence in the polymorphic pi-calculus. Journal of ACM 47 3 (2000) 531-584
37. Regnier L. Une équivalence sur les lambda-termes. Theoretical Computer Science 126 (1994) 281-292
38. Sangiorgi D. πI: A symmetric calculus based on internal mobility. TAPSOFT'95. Lecture Notes in Computer Science vol. 915 (1995), Springer 172-186
39. Sangiorgi D. The name discipline of uniform receptiveness. ICALP'97. Lecture Notes in Computer Science vol. 1256 (1997), Springer 303-313
40. Takeuchi K., Honda K., and Kubo M. An interaction-based language and its typing system. PARLE'94. Lecture Notes in Computer Science vol. 817 (1994) 398-413
41. David N. Turner, The polymorphic pi-calculus: Theory and implementation, Ph.D. thesis, University of Edinburgh, 1995.
42. Vasconcelos V. Typed concurrent objects. In: Tokoro M., and Pareschi R. (Eds). ECOOP'94. Lecture Notes in Computer Science vol. 821 (1994), Springer 100-117
43. Yoshida N., Berger M., and Honda K. Strong normalisation in the π-calculus. Information and Computation 191 2 (2004) 145-202