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Abstract: Typing of lambda-terms in Elementary and Light Affine Logic EAL, LAL, resp.has been studied for two different reasons: on the one hand the evaluation oftyped terms using LAL EAL, resp. proof-nets admits a guaranteed polynomialelementary, resp. bound; on the other hand these terms can also be evaluatedby optimal reduction using the abstract version of Lampings algorithm. Thefirst reduction is global while the second one is local and asynchronous. Weprove that for LAL EAL, resp. typed terms, Lampings abstract algorithm alsoadmits a polynomial elementary, resp. bound. We also show its soundness andcompleteness for EAL and LAL with type fixpoints, by using a simple geometryof interaction model context semantics.



Author: Patrick Baillot, Paolo Coppola, Ugo Dal Lago

Source: https://arxiv.org/







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