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Verification of Ptime reducibility for system F terms via Dual Light Affine Logic

Vincent Atassi·Patrick Baillot·Kazushige Terui
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Abstract

In a previous work we introduced Dual Light Affine Logic (DLAL) ([BaillotTerui04]) as a variant of Light Linear Logic suitable for guaranteeing complexity properties on lambda-calculus terms: all typable terms can be evaluated in polynomial time and all Ptime functions can be represented. In the present work we address the problem of typing lambda-terms in second-order DLAL. For that we give a procedure which, starting with a term typed in system F, finds all possible ways to decorate it into a DLAL typed term. We show that our procedure can be run in time polynomial in the size of the original Church typed system F term.

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Vincent Atassi, Patrick Baillot, Kazushige Terui. 2006-03-27. Verification of Ptime reducibility for system F terms via Dual Light Affine Logic. https://arxiv.org/abs/cs/0603104

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