Pure, or type-free, Linear Logic proof nets are Turing complete once cut-elimination is considered as computation. We introduce modal impredicativity as a new form of impredicativity causing cutelimination to be problematic from a complexity point of view. Modal impredicativity occurs when, during reduction, the conclusion of a residual of a box b interacts with a node that belongs to the proof net inside another residual of b. Technically speaking, superlazy reduction is a new notion of reduction that allows to control modal impredicativity. More specifically, superlazy reduction replicates a box only when all its copies are opened. This makes the overall cost of reducing a proof net finite and predictable. Specifically, superlazy reduction applied to any pure proof nets takes primitive recursive time. Moreover, any primitive recursive function can be computed by a pure proof net via superlazy reduction. © Springer-Verlag Berlin Heidelberg 2009.
CITATION STYLE
Dal Lago, U., Roversi, L., & Vercelli, L. (2009). Taming modal impredicativity: Superlazy reduction. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5407 LNCS, pp. 137–151). https://doi.org/10.1007/978-3-540-92687-0_10
Mendeley helps you to discover research relevant for your work.