Chapter

Computer Science Logic

Volume 4207 of the series Lecture Notes in Computer Science pp 150-166

Verification of Ptime Reducibility for System F Terms Via Dual Light Affine Logic

  • Vincent AtassiAffiliated withLIPN, Univ. Paris 13 / CNRS
  • , Patrick BaillotAffiliated withLIPN, Univ. Paris 13 / CNRS
  • , Kazushige TeruiAffiliated withNational Institute of Informatics

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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.