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

Authors: 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}
  }