Typing of lambda-terms in elementary and light affine logic (EAL and LAL, respectively) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, respectively) proof-nets admits a guaranteed polynomial (elementary, respectively) 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, respectively) typed terms, Lamping’s abstract algorithm also admits a polynomial (elementary, respectively) bound. We also give a proof of its soundness and completeness (for EAL and LAL with type fixpoints), by using a simple geometry of interaction model (context semantics).
P. Baillot, P. Coppola, U. Dal Lago (2011). Light Logics and Optimal Reduction: Completeness and Complexity. INFORMATION AND COMPUTATION, 209(2), 118-142 [10.1016/j.ic.2010.10.002].
Light Logics and Optimal Reduction: Completeness and Complexity.
DAL LAGO, UGO
2011
Abstract
Typing of lambda-terms in elementary and light affine logic (EAL and LAL, respectively) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, respectively) proof-nets admits a guaranteed polynomial (elementary, respectively) 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, respectively) typed terms, Lamping’s abstract algorithm also admits a polynomial (elementary, respectively) bound. We also give a proof of its soundness and completeness (for EAL and LAL with type fixpoints), by using a simple geometry of interaction model (context semantics).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
