Verification of Ptime reductibility for system F terms Via Dual Light Affine Logic

Abstract

In a previous work we introduced Dual Light Affine Logic (DLAL) ([BT04]) 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. © Springer-Verlag Berlin Heidelberg 2006.