Light Logics and Optimal Reduction: Completeness and Complexity
Logic in Computer Science
2007-05-23 v1 Programming Languages
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 of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial (elementary, resp.) bound; on the other hand these terms can also be evaluated by optimal reduction using the abstract version of Lamping's algorithm. The first reduction is global while the second one is local and asynchronous. We prove that for LAL (EAL, resp.) typed terms, Lamping's abstract algorithm also admits a polynomial (elementary, resp.) bound. We also show its soundness and completeness (for EAL and LAL with type fixpoints), by using a simple geometry of interaction model (context semantics).
Cite
@article{arxiv.0704.2448,
title = {Light Logics and Optimal Reduction: Completeness and Complexity},
author = {Patrick Baillot and Paolo Coppola and Ugo Dal Lago},
journal= {arXiv preprint arXiv:0704.2448},
year = {2007}
}