On the representation of McCarthy's amb in the π-calculus

  • Authors:

  • Arnaud Carayol;Daniel Hirschkoff;Davide Sangiorgi

  • Affiliations:

  • IRISA, Campus de Beaulieu, 35042 Rennes, France and LIP, ENS Lyon, 46 allée d'Italie, 69364 Lyon Cedex 7, France;LIP, ENS Lyon, 46 allée d'Italie, 69364 Lyon Cedex 7, France;Dipartimento di Scienze dell'Informazione, Universita di Bologna, Via di Mura Anteo Zamboni 7, 40127 Bologna, Italy

  • Venue:
  • Theoretical Computer Science - Expressiveness in concurrency
  • Year:
  • 2005

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Abstract

We study the encoding of λ, the call-by-name λ-calculus enriched with McCarthy's amb operator, into the π-calculus. Semantically, amb is a challenging operator, for the fairness constraints that it expresses. We prove that, under a certain interpretation of divergence in the λ-calculus (weak divergence), a faithful encoding is impossible. However, with a different interpretation of divergence (strong divergence), the encoding is possible, and for this case we derive results and coinductive proof methods to reason about λ that are similar to those for the encoding of pure λ-calculi. We then use these methods to derive the most important laws concerning amb. We take bisimilarity as behavioural equivalence on the π-calculus, which sheds some light on the relationship between fairness and bisimilarity.