## On the representation of McCarthy’s ambin the π-calculus (2004)

### BibTeX

@MISC{Carayol04onthe,

author = {Arnaud Carayol and Daniel Hirschkoff and Davide Sangiorgi},

title = {On the representation of McCarthy’s ambin the π-calculus},

year = {2004}

}

### OpenURL

### 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.