Light types for polynomial time computation in lambda calculus

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• 作者：Patrick Baillot ; Kazushige Terui
• 关键词：Linear logic ; Light linear logic ; Lambda calculus ; Type system ; Implicit computational complexity ; Polynomial time complexity
• 刊名：Information and Computation
• 出版年：2009
• 出版时间：January 2009
• 年：2009
• 卷：207
• 期：1
• 页码：41-62
• 全文大小：495 K

文摘

We present a polymorphic 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 (and not only on proof-nets): subject reduction is satisfied and a well-typed term admits a polynomial bound on the length of any of its beta reduction sequences. We also give a translation of LAL into DLAL and deduce from it that all polynomial time functions can be represented in DLAL.