Polarized Linear Logic with Fixpoints
Résumé
We introduce and study µLLP, which can be viewed both as an extension of Laurent's Polarized Linear Logic, LLP, with least and greatest fixpoints, and as a polarized version of Baelde's Linear Logic with fixpoints (µMALL and µLL). We take advantage of the implicit structural rules of µLLP to introduce a term syntax for this language, in the spirit of the classical lambda-calculus and of system L in the style of Curien, Herbelin and Munch-Maccagnoni. We equip this language with a deterministic reduction semantics as well as a denotational semantics based on the notion of non-uniform totality spaces and the notion of categorical model for linear logic with fixpoint introduced by Ehrhard and Jafarrahmani. We prove an adequacy result for µLLP between these operational and denotational semantics, from which we derive a normalization property for µLLP thanks to the properties of the totality interpretation.
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