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# Lambda-Calculus, Multiplicities and the pi-Calculus

1 MEIJE - Concurrency, Synchronization and Real-time Programming
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this paper we study the semantics of the $\lambda$-calculus induced by Milner's encoding into the $\pi$-calculus. We show that the resulting may testing preorder on $\lambda$-terms coincides with the inclusion of Lévy-Longo trees. To establish this result, we use a refinement of the $\lambda$-calculus where the argument of a function may be of limited availability. In our $\lambda$-calculus with multiplicities, evaluation is deterministic, but it may deadlock, due to the lack of resources. We show that this feature is enough to make the $\lambda$-calculus as discriminating as the $\pi$-calculus.
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https://hal.inria.fr/inria-00074103
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Submitted on : Wednesday, May 24, 2006 - 2:31:56 PM
Last modification on : Friday, February 4, 2022 - 3:16:12 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:18:13 PM

### Identifiers

• HAL Id : inria-00074103, version 1

### Citation

Gérard Boudol, Cosimo Laneve. Lambda-Calculus, Multiplicities and the pi-Calculus. [Research Report] RR-2581, INRIA. 1995, pp.33. ⟨inria-00074103⟩

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