Typing a Core Binary Field Arithmetic in a Light Logic

TL;DR

This paper develops a library for binary field arithmetic within a light logic framework, ensuring polynomial-time evaluation and a core API fully developed in a restricted linear logic system.

Contribution

It introduces a core API for binary field arithmetic in DLAL extended with a fixpoint, guaranteeing polynomial complexity for functional programs.

Findings

Library for binary field arithmetic in DLAL

Core API developed with polynomial evaluation cost

Ensures complexity bounds through logical restrictions

Abstract

We design a library for binary field arithmetic and we supply a core API which is completely developed in DLAL, extended with a fix point formula. Since DLAL is a restriction of linear logic where only functional programs with polynomial evaluation cost can be typed, we obtain the core of a functional programming setting for binary field arithmetic with built-in polynomial complexity.