Primitive recursion in finiteness spaces
Résumé
We study iteration and recursion operators in the multiset relational model of linear logic and prove them finitary in the sense of the finiteness spaces recently introduced by Ehrhard. This provides a denotational semantics of Gödel's system T and paves the way for a systematic study of a large class of algorithms, following the ideas of Girard's quantitative semantics in a standard algebraic setting.
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