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

Davide Sangiorgi 1, 2
2 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
Abstract : In a well-known and influential paper [17] Palamidessi has shown that the expressive power of the Asynchronous π-calculus is strictly less than that of the full (synchronous) $π$-calculus. This gap in expres-siveness 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 λ-calculus into the $π$-calculus. We actually adopt the Local Asynchronous π-calculus, that has even sharper semantic properties. We exploit such properties to prove some instances of validity of $β$-reduction (meaning that the source and target terms of a $β$-reduction are mapped onto be-haviourally equivalent processes). Nearly all results would fail in the ordinary synchronous $π$-calculus. We show that however the full $β$-reduction is not valid. We also consider a refined encoding in which some further instances of $β$-validity hold. We conclude with a few questions for future work.
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https://hal.inria.fr/hal-02399695
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Submitted on : Monday, December 9, 2019 - 11:12:33 AM
Last modification on : Friday, October 30, 2020 - 12:04:04 PM
Long-term archiving on: : Tuesday, March 10, 2020 - 3:39:50 PM

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Davide Sangiorgi. Asynchronous pi-calculus at Work: The Call-by-Need Strategy. The Art of Modelling Computational Systems: A Journey from Logic and Concurrency to Security and Privacy, Nov 2019, Paris, France. pp.33-49, ⟨10.1007/978-3-030-31175-9_3⟩. ⟨hal-02399695⟩

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