Verification of Ptime Reducibility for system F Terms: Type Inference in Dual Light Affine Logic

Abstract

In a previous work Baillot and Terui introduced Dual light affine logic (DLAL) 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 by beta reduction 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, determines whether it is typable in DLAL and outputs a concrete typing if there exists any. We show that our procedure can be run in time polynomial in the size of the original Church typed system F term.

Keywords

• computer science - logic in computer science
• computer science - computational complexity
• f.4.1
• f.2.2
• d.1.1