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arXiv:2505.20314cs.LO

$Δ$-Nets: Interaction-Based System for Optimal Parallel $λ$-Reduction

Daniel Augusto Rizzi Salvadori

Abstract

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

arXiv comments
Journal reference
DOI
Subjects
cs.LOLogic in Computer Science cs.ARHardware Architecture cs.DCDistributed, Parallel, and Cluster Computing cs.PLProgramming Languages

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Linked by 5 identifiable commenters in 5 comments across 2 threads, from Nov 2025 to Dec 2025.

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Discussed in comments2 threads

  1. Interactive λ-Reduction 4 comments

    • What the hell is this? The linked paper: https://arxiv.org/pdf/2505.20314 claims the squiggles they introduce are apparently a model to solve Levy-optimal parallel reduction of lambda terms. But the author has no affiliation, it's very weird they're calling this…

      qsortView on HNParent context

    • The annihilating interaction between abstraction and application nodes is well-known in the area of interaction net research to ~correspond to β-reduction, as is also explained in the associated research paper [1]. α-conversion is not required in interaction nets. η-reduction is…

      marvinbornerView on HNParent context

    • I don't know much about any of this, and I'm far from an expert on the lambda calculus. But I skimmed paper by OP, which is informative: https://arxiv.org/abs/2505.20314 The lambda calculus is an alternate model of computation created by Alonzo Church in the 1930s. It's…

      csenseView on HNParent context

    • I'm the author of the research paper (https://arxiv.org/abs/2505.20314) and owner of that GitHub account. Please see my comment here: https://news.ycombinator.com/item?id=46069564

      danaugrsView on HNParent context

  2. Lambda Calculus – Animated Beta Reduction of Lambda Diagrams 1 comment

    • > there's an easy way to translate LC to IN While easy, it sadly doesn't preserve semantics. Specifically, when you duplicate a term that ends up duplicating itself, results will diverge. There exist more involved semantics preserving translations, using so-called croissants and…

      trompView on HNParent context

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