Light types for polynomial time computation in lambda-calculus

Details Light types for polynomial time computation in lambda-calculus Light types for polynomial time computation in lambda-calculus

2004-02-26

arxiv.org/abs/cs/0402059v2

Computer Science

Logic in Computer Science

20 pages (including 10 pages of appendix). (revised version; in particular section 5 has been modified). A short version is to

Scientific paper

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.

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