## Paper: Light Types for Polynomial Time Computation in Lambda-Calculus (at LICS 2004)

**Patrick Baillot Kazushige Terui**

### 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. Finally we establish that as LAL, DLAL allows to represent all polytime functions.

### BibTeX

@InProceedings{BaillotTerui-LightTypesforPolyno, author = {Patrick Baillot and Kazushige Terui}, title = {Light Types for Polynomial Time Computation in Lambda-Calculus}, booktitle = {Proceedings of the Nineteenth Annual IEEE Symposium on Logic in Computer Science (LICS 2004)}, year = {2004}, month = {July}, pages = {266--275}, location = {Turku, Finland}, publisher = {IEEE Computer Society Press} }