by
Gérard Boudol

Citations: | 17 - 2 self |

@MISC{Boudol93thelambda-calculus,

author = {Gérard Boudol},

title = {The Lambda-Calculus with Multiplicities},

year = {1993}

}

We introduce a refinement of the λ-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 "λ-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, by establishing that a term is convergent if and only if it has a non-trivial functional character.

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