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

TL;DR

This paper presents a polynomial-time procedure for determining whether system F lambda-terms can be typed in dual light affine logic (DLAL), ensuring polynomial-time evaluability and representation of Ptime functions.

Contribution

It introduces a polynomial-time method to decide DLAL typability for system F terms, bridging type inference with complexity guarantees.

Findings

Procedure runs in polynomial time relative to input size.

Successfully determines DLAL typability for system F terms.

Enables polynomial-time evaluation and representation of Ptime functions.

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.