# The discriminating power of multiplicities in the $\lambda$-calculus

1 MEIJE - Concurrency, Synchronization and Real-time Programming
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The $\lambda$-calculus with multiplicities is a refinement of the lazy $\lambda$-calculus where the argument in an application comes with a multiplicity, which is an upper bound to the number of its uses. This introduces potential deadlocks in the evaluation. We study the discriminating power of this calculus over the usual $\lambda$-terms. We prove in particular that the observational equivalence induced by contexts with multiplicities coincides with the equality of Lévy-Longo trees associated with $\lambda$-terms. This is a consequence of the characterization we give of the corresponding observational precongruence, as an intensional preorder involving $\eta$-expansion, namely Ong's lazy Plotkin-Scott-Engeler preorder.
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Type de document :
Rapport
[Research Report] RR-2441, INRIA. 1994
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https://hal.inria.fr/inria-00074234
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Soumis le : mercredi 24 mai 2006 - 14:49:53
Dernière modification le : samedi 27 janvier 2018 - 01:31:00
Document(s) archivé(s) le : dimanche 4 avril 2010 - 21:25:49

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• HAL Id : inria-00074234, version 1

### Citation

Gérard Boudol, Laneve Cosimo. The discriminating power of multiplicities in the $\lambda$-calculus. [Research Report] RR-2441, INRIA. 1994. 〈inria-00074234〉

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