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The λ-calculus in the π-calculus†

Published online by Cambridge University Press:  19 May 2011

XIAOJUAN CAI  and
YUXI FU
XIAOJUAN CAI
Affiliation:
BASICS, Department of Computer Science and MOE-MS Key Laboratory for Intelligent Computing and Intelligent Systems, Shanghai Jiaotong University, Shanghai 200240, China Email: cxj@cs.sjtu.edu.cn; fu-yx@cs.sjtu.edu.cn
YUXI FU
Affiliation:
BASICS, Department of Computer Science and MOE-MS Key Laboratory for Intelligent Computing and Intelligent Systems, Shanghai Jiaotong University, Shanghai 200240, China Email: cxj@cs.sjtu.edu.cn; fu-yx@cs.sjtu.edu.cn
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Abstract

A general approach is proposed for transforming objects to methods on the fly in the framework of the π-calculus. The power of the approach is demonstrated by applying it to generate an encoding of the full lambda calculus in the π-calculus. The encoding is proved to preserve and reflect beta reduction, and is shown to be fully abstract with respect to Abramsky's applicative bisimilarity.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 21 , Issue 5 , October 2011 , pp. 943 - 996
Copyright
Copyright © Cambridge University Press 2011

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References

Abadi, M. and Gordon, A. (1999) A Calculus for Cryptographic Protocols: The Spi Calculus. Information and Computation 148 (1)1–70.CrossRefGoogle Scholar
Abramsky, S. (1990) The Lazy Lambda Calculus. Research Topics in Functional Programming 65–116.Google Scholar
Amadio, R. and Prasad, S. (2000) Modelling IP Mobility. Formal Methods in System Design 17 (1)61–99.CrossRefGoogle Scholar
Baldamus, M., Parrow, J. and Victor, B. (2004) Spi Calculus Translated to π-calculus Preserving May-Tests. In: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LICS'04), IEEE Computer Society 22–31.CrossRefGoogle Scholar
Barendregt, H. (1984) The Lambda Calculus: its Syntax and Semantics, North Holland.Google Scholar
Boudol, G. (1992) Asynchrony and the π-calculus. Technical Report 1702, INRIA Sophia-Antipolis.Google Scholar
Fu, Y. (1997) A Proof Theoretical Approach to Communication. In: Degano, P.Gorrieri, R. and Marchetti-Spaccamela, A. (eds.) Automata, Languages and Programming: Proceedings of the 24th International Colloquium, ICALP'97. Springer-Verlag Lecture Notes in Computer Science 1256 325–335.CrossRefGoogle Scholar
Fu, Y. (1999) Variations on Mobile Processes. Theoretical Computer Science 221 327–368.CrossRefGoogle Scholar
Fu, Y. (2010a) Theory of Interaction. Working Paper.Google Scholar
Fu, Y. (2010b) The Value-Passing Calculus. Working Paper.Google Scholar
Fu, Y and Lu, H. (2010) On the Expressiveness of Interaction. Theoretical Computer Science 411 1387–1451.CrossRefGoogle Scholar
Fu, Y. and Zhu, H. (2010) The Name-Passing Calculus. Working Paper.Google Scholar
Honda, K. and Tokoro, M. (1991) An Object Calculus for Asynchronous Communications. In: America, P. (ed.) Proceedings ECOOP '91: European Conference on Object-Oriented Programming. Springer-Verlag Lecture Notes in Computer Science 512 133–147.CrossRefGoogle Scholar
Honda, K. and Tokoro, M. (1991) On Asynchronous Communication Semantics. In: Madsen, O. L. (ed.) Proceedings ECOOP '92: European Conference on Object-Oriented Programming. Springer-Verlag Lecture Notes in Computer Science 615 21–51.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)119–146.CrossRefGoogle Scholar
Milner, R. (1997) The Polyadic π-calculus: a Tutorial. Theoretical Computer Science 198 239–249.Google Scholar
Milner, R., Parrow, J. and Walker, D. (1992) A Calculus of Mobile Processes, Part I and Part II. Information and Computation 100 (1)1–77.CrossRefGoogle Scholar
Milner, R. and Sangiorgi, D. (1992) Barbed Bisimulation. In: Kuich, W. (ed.) Automata, Languages and Programming, Proceedings 19th International Colloquium ICALP'92. Springer-Verlag Lecture Notes in Computer Science 623 685–695.CrossRefGoogle Scholar
Nestmann, U. and Pierce, B. (2000) Decoding Choice Encodings. Information and Computation 163 (1)1–59.CrossRefGoogle Scholar
Palamidessi, C. (2003) Comparing the Expressive Power of the Synchronous and Asynchronous π-calculi. Mathematical Structures in Computer Science 13 (5)685–719.CrossRefGoogle Scholar
Parrow, J. and Victor, B. (1997) The Update Calculus. In: Johnson, M. (ed.) Algebraic Methodology and Software Technology, Proceedings 6th International Conference, AMAST'97. Springer-Verlag Lecture Notes in Computer Science 1349 409–423.CrossRefGoogle Scholar
Parrow, J. and Sangiorgi, D. (1995) Algebraic Theories for Name-Passing Calculi. Information and Computation 120 174–197.CrossRefGoogle Scholar
Plotkin, G. (1975) Call-by-Name, Call-by-Value and the λ-calculus. Theoretical Computer Science 1 (2)125–159.CrossRefGoogle Scholar
Sangiorgi, D. (1993a) Expressing Mobility in Process Algebras: First-Order and Higher-Order Paradigms, Ph.D. thesis, University of Edinburgh.Google Scholar
Sangiorgi, D. (1993b) From π-calculus to Higher-Order π-calculus – and Back. In: Gaudel, M.-C. and Jouannaud, J.-P. (eds.) Proceedings TAPSOFT '93: Theory and Practice of Software Development. Springer-Verlag Lecture Notes in Computer Science 668 151–166.CrossRefGoogle Scholar
Sangiorgi, D. (1994) The Lazy λ-calculus in a Concurrency Scenario. Information and Computation 111 120–153.CrossRefGoogle Scholar
Sangiorgi, D. (1995) Lazy Functions and Mobile Processes. Technical Report 2515, INRIA Sophia-Antipolis.Google Scholar
Sangiorgi, D. (1996) π-calculus, Internal Mobility, and Agent-Passing Clculi. Theoretical Computer Science 167 (1–2)235–274.CrossRefGoogle Scholar
Sangiorgi, D. and Walker, D. (2001) The π Calculus: A Theory of Mobile Processes, Cambridge University Press.Google Scholar
Thomsen, B. (1993) Plain CHOCS – A Second Generation Calculus for Higher Order Processes. Acta Informatica 30 (1)1–59.CrossRefGoogle Scholar
Thomsen, B. (1995) A Theory of Higher Order Communicating Systems. Information and Computation 116 (1)38–57.CrossRefGoogle Scholar
Walker, D. (1991) π-calculus Semantics for Object-Oriented Programming Languages. In: Ito, T. and Meyer, A. R. (eds.) Theoretical Aspects of Computer Software: Proceedings International Conference TACS '91. Springer-Verlag Lecture Notes in Computer Science 526 532–547.CrossRefGoogle Scholar
Walker, D. (1995) Objects in the π-calculus. Information and Computation 116 (2)253–271.CrossRefGoogle Scholar