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Logic Journal of IGPL Advance Access originally published online on July 4, 2009
Logic Journal of IGPL 2009 17(5):499-530; doi:10.1093/jigpal/jzp019
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

This article appears in the following Logic Journal of the IGPL issue: Special Issue: Logical and Semantical Frameworks with Applications [View the issue table of contents]

From light logics to type assignments: a case study

Marco Gaboardi

Dipartimento di Informatica, Università degli Studi di Torino. Corso Svizzera 185, 10149 Torino, Italy. E-mail: gaboardi{at}di.unito.it

Simona Ronchi Della Rocca

Dipartimento di Informatica, Universitàa degli Studi di Torino. Corso Svizzera 185, 10149 Torino, Italy. E-mail: ronchi{at}di.unito.it


  Abstract

Using Soft Linear Logic (SLL) as case study, we analyze a method for transforming a light logic into a type assignment system for the {lambda}-calculus, inheriting the complexity properties of the logics. Namely the typing assures the strong normalization in a number of steps polynomial in the size of the term, and moreover all polynomial functions can be computed by {lambda}-terms that can be typed in the system. The proposed method is general enough to be used also for other light logics.

Key Words: type assignment • implicit computational complexity • lambda calculus • polynomial time

Received for publication 11 May 2008.
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