On the Representation of McCarthy's amb in the pi-calculus

We study the encoding of, 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 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. As a spin-off result, we show that there is no small-step operational semantics for that preserves the branching structure of terms and yields the correct predicates of convergence and (weak) divergence