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

I present a model of universal parallel computation called $\mathrm{\Delta }$-Nets, and a method to translate $\lambda$-terms into $\mathrm{\Delta }$-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 $\mathrm{\Delta }$-Nets$-$one that severely restricts the structure of sharing, among other drawbacks. Unhindered by these restrictions, the $\mathrm{\Delta }$-Nets model opens the door to new parallel programming language implementations and computer architectures that are more efficient and performant than previously possible.