Light types for polynomial time computation in lambda-calculus
Abstract
We propose a new type system for lambda-calculus ensuring that well-typed programs can be executed in polynomial time: Dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one modality. It corresponds to a fragment of Light affine logic (LAL). We show that contrarily to LAL, DLAL ensures good properties on lambda-terms: subject reduction is satisfied and a well-typed term admits a polynomial bound on the reduction by any strategy. We establish that as LAL, DLAL allows to represent all polytime functions. Finally we give a type inference procedure for propositional DLAL.
Keywords
Cite
@article{arxiv.cs/0402059,
title = {Light types for polynomial time computation in lambda-calculus},
author = {Patrick Baillot and Kazushige Terui},
journal= {arXiv preprint arXiv:cs/0402059},
year = {2016}
}
Comments
20 pages (including 10 pages of appendix). (revised version; in particular section 5 has been modified). A short version is to appear in the proceedings of the conference LICS 2004 (IEEE Computer Society Press)