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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.
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https://hal.archives-ouvertes.fr/hal-00012752
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Submitted on : Thursday, October 27, 2005 - 2:54:13 PM
Last modification on : Saturday, February 15, 2020 - 2:04:38 AM

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Patrick Baillot, Kazushige Terui. Light types for polynomial time computation in lambda-calculus. 2004. ⟨hal-00012752⟩

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