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

$Δ$-Nets: Interaction-Based System for Optimal Parallel $λ$-Reduction — mentioned by danaugrs

Tue, 02 Dec 2025 17:26:22 GMT

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

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$Δ$-Nets: Interaction-Based System for Optimal Parallel $λ$-Reduction — mentioned by csense

Sun, 30 Nov 2025 04:31:04 GMT

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 basically a restricted programming language where the only things you can do are define anonymous functions, and apply those anonymous functions to input variables or the output of other functions. The Lambda calculus statement And = λp.λq.p q p is more conventionally notated as And(p, q) = p(q(p)). You can reduce lambda…

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$Δ$-Nets: Interaction-Based System for Optimal Parallel $λ$-Reduction — mentioned by marvinborner

Thu, 27 Nov 2025 12:02:22 GMT

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 an additional rule not typically discussed, but see for example [2]. [1] https://arxiv.org/pdf/2505.20314 [2] https://www.sciencedirect.com/science/article/pii/S030439750...

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$Δ$-Nets: Interaction-Based System for Optimal Parallel $λ$-Reduction — mentioned by qsort

Thu, 27 Nov 2025 09:00:03 GMT

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 "lambda-reduction" and it heavily smells of AI slop? I hope I'm wrong but it doesn't look right. Can anyone with expertise in this field chime in?

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$Δ$-Nets: Interaction-Based System for Optimal Parallel $λ$-Reduction — mentioned by tromp

Mon, 24 Nov 2025 14:16:29 GMT

> 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 brackets, or with the recent rephrased approach of [1]. [1] https://arxiv.org/abs/2505.20314

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