[Submitted on 22 May 2025 (v1), last revised 22 Jul 2026 (this version, v4)]

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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.

Submission history

From: Daniel Augusto Rizzi Salvadori [view email]
[v1] Thu, 22 May 2025 22:23:59 UTC (19 KB)
[v2] Wed, 28 May 2025 18:23:01 UTC (19 KB)
[v3] Fri, 20 Jun 2025 19:06:56 UTC (18 KB)
[v4] Wed, 22 Jul 2026 18:48:33 UTC (18 KB)