Light types for polynomial time computation in lambda-calculus

TL;DR

This paper introduces Dual Light Affine Logic (DLAL), a new type system for lambda-calculus that guarantees polynomial-time execution of well-typed programs, with a simple type language and properties ensuring computational bounds.

Contribution

DLAL is a novel type system that ensures polynomial-time computation, improves on Light Affine Logic by guaranteeing subject reduction, and supports type inference for propositional cases.

Findings

DLAL guarantees polynomial bounds on lambda-term reductions.

DLAL can represent all polynomial-time functions.

A type inference procedure for propositional DLAL is provided.

Abstract

We propose a new type system for lambda-calculus ensuring that well-typed programs can be executed in polynomial time: Dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one modality. It corresponds to a fragment of Light affine logic (LAL). We show that contrarily to LAL, DLAL ensures good properties on lambda-terms: subject reduction is satisfied and a well-typed term admits a polynomial bound on the reduction by any strategy. We establish that as LAL, DLAL allows to represent all polytime functions. Finally we give a type inference procedure for propositional DLAL.