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

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.