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arXiv · 2505.20314

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

Daniel Augusto Rizzi Salvadori
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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.

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Daniel Augusto Rizzi Salvadori. 2025-05-22. $\Delta$-Nets: Interaction-Based System for Optimal Parallel $\lambda$-Reduction. https://arxiv.org/abs/2505.20314

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