Taming Modal Impredicativity: Superlazy Reduction
| dc.creator | Lago, Ugo Dal | |
| dc.creator | Roversi, Luca | |
| dc.creator | Vercelli, Luca | |
| dc.date | 2008-10-16 | |
| dc.date | 2008-10-17 | |
| dc.date.accessioned | 2026-07-07T10:10:39Z | |
| dc.date.available | 2026-07-07T10:10:39Z | |
| dc.description | 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 the complexity of cut-elimination 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. | |
| dc.identifier | https://arxiv.org/abs/0810.2891 | |
| dc.identifier | http://arxiv.org/abs/0810.2891 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171655 | |
| dc.subject | Logic in Computer Science | |
| dc.title | Taming Modal Impredicativity: Superlazy Reduction | |
| dc.type | text |