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Reports (Research Report) Year : 1993

The Lambda-calculus with multiplicities


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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inria-00074646 , version 1 (24-05-2006)


  • 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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