$Δ$-Nets: Interaction-Based System for Optimal Parallel $λ$-Reduction
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918066627018752 |
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| author | Salvadori, Daniel Augusto Rizzi |
| author_facet | Salvadori, Daniel Augusto Rizzi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20314 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $Δ$-Nets: Interaction-Based System for Optimal Parallel $λ$-Reduction Salvadori, Daniel Augusto Rizzi Logic in Computer Science Hardware Architecture Distributed, Parallel, and Cluster Computing Programming Languages 68Q04 (Primary) 68Q85, 68Q06 (Secondary) F.0; F.1.1 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. |
| title | $Δ$-Nets: Interaction-Based System for Optimal Parallel $λ$-Reduction |
| topic | Logic in Computer Science Hardware Architecture Distributed, Parallel, and Cluster Computing Programming Languages 68Q04 (Primary) 68Q85, 68Q06 (Secondary) F.0; F.1.1 |
| url | https://arxiv.org/abs/2505.20314 |