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.
Type de document :
[Research Report] RR-2025, INRIA. 1993
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Soumis le : mercredi 24 mai 2006 - 15:59:17
Dernière modification le : samedi 27 janvier 2018 - 01:30:56
Document(s) archivé(s) le : mardi 12 avril 2011 - 18:00:32



  • HAL Id : inria-00074646, version 1



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



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