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The Lambda-calculus with multiplicities

Gérard Boudol 1
1 MEIJE - Concurrency, Synchronization and Real-time Programming
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We introduce a refinement of the l-calculus, where the argument of a function is a bag of resources, that is a multiset of terms, whose multiplicities indicate how many copies of them are available. We show that this l-calculus with multiplicities has a natural functionality theory, similar to Coppo and Dezani's intersection type discipline. In our functionality theory the conjunction is managed in a multiplicative manner, according to Girard's terminology. We show that this provides an adequate interpretation of the calculus of the calculus, by establishing that a term is convergent if and only if it has a non-trivial functional character.
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https://hal.inria.fr/inria-00074646
Contributor : Rapport de Recherche Inria <>
Submitted on : Wednesday, May 24, 2006 - 3:59:17 PM
Last modification on : Saturday, January 27, 2018 - 1:30:56 AM
Long-term archiving on: : Tuesday, April 12, 2011 - 6:00:32 PM

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  • HAL Id : inria-00074646, version 1

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Gérard Boudol. The Lambda-calculus with multiplicities. [Research Report] RR-2025, INRIA. 1993. ⟨inria-00074646⟩

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