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Asynchronous \(\pi \)-calculus at Work: The Call-by-Need Strategy

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The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11760))

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Abstract

In a well-known and influential paper [17] Palamidessi has shown that the expressive power of the Asynchronous \(\pi \)-calculus is strictly less than that of the full (synchronous) \(\pi \)-calculus. This gap in expressiveness has a correspondence, however, in sharper semantic properties for the former calculus, notably concerning algebraic laws. This paper substantiates this, taking, as a case study, the encoding of call-by-need \(\lambda \)-calculus into the \(\pi \)-calculus. We actually adopt the Local Asynchronous \(\pi \)-calculus, that has even sharper semantic properties. We exploit such properties to prove some instances of validity of \(\beta \)-reduction (meaning that the source and target terms of a \(\beta \)-reduction are mapped onto behaviourally equivalent processes). Nearly all results would fail in the ordinary synchronous \(\pi \)-calculus. We show that however the full \(\beta \)-reduction is not valid. We also consider a refined encoding in which some further instances of \(\beta \)-validity hold. We conclude with a few questions for future work.

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Acknowledgments

Thanks to the reviewers for their careful reading of the paper and their suggestions. Research partly supported by the H2020-MSCA-RISE project ID 778233 “Behavioural Application Program Interfaces (BEHAPI)”.

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Authors and Affiliations

  1. Focus Team, University of Bologna and Inria, Bologna, Italy

    Davide Sangiorgi

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  1. Davide Sangiorgi
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Correspondence to Davide Sangiorgi .

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Editors and Affiliations

  1. Universidade Federal de Minas Gerais, Belo Horizonte, Brazil

    Mário S. Alvim

  2. University of Athens, Athens, Greece

    Kostas Chatzikokolakis

  3. Federal University of Rio Grande do Norte - UFRN, Natal, Brazil

    Carlos Olarte

  4. CNRS & University Javeriana Cali, Palaiseau, France

    Frank Valencia

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Sangiorgi, D. (2019). Asynchronous \(\pi \)-calculus at Work: The Call-by-Need Strategy. In: Alvim, M., Chatzikokolakis, K., Olarte, C., Valencia, F. (eds) The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy. Lecture Notes in Computer Science(), vol 11760. Springer, Cham. https://doi.org/10.1007/978-3-030-31175-9_3

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  • DOI: https://doi.org/10.1007/978-3-030-31175-9_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-31174-2

  • Online ISBN: 978-3-030-31175-9

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