$\Delta$-Nets: Interaction-Based System for Optimal Parallel $\lambda$-Reduction

TL;DR

This paper introduces $ abla$-Nets, a novel universal parallel computation model for $ abla$-calculus, providing an optimal parallel $ abla$-reduction algorithm and enabling more efficient parallel programming and architecture design.

Contribution

It presents $ abla$-Nets as a new model for universal parallel computation and a method to translate $ abla$-terms into this model for optimal reduction.

Findings

Provides a translation method between $ abla$-terms and $ abla$-Nets.

Establishes an algorithm for optimal parallel $ abla$-reduction.

Suggests new avenues for parallel programming languages and architectures.

Abstract

I present a model of universal parallel computation called $\Delta$-Nets, and a method to translate $\lambda$-terms into $\Delta$-nets and back. Together, the model and the method constitute an algorithm for optimal parallel $\lambda$-reduction, solving the longstanding enigma with groundbreaking clarity. I show that the $\lambda$-calculus can be understood as a projection of $\Delta$-Nets$-$one that severely restricts the structure of sharing, among other drawbacks. Unhindered by these restrictions, the $\Delta$-Nets model opens the door to new parallel programming language implementations and computer architectures that are more efficient and performant than previously possible.