{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/d-nets-interaction-based-system-for-optimal","title":"$Δ$-Nets: Interaction-Based System for Optimal Parallel $λ$-Reduction","arxiv_id":"2505.20314","date":"2025-05-22","proceeding":null,"authors":["Daniel Augusto Rizzi Salvadori"],"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.","url_abs":"https://arxiv.org/abs/2505.20314v3","url_pdf":"https://arxiv.org/pdf/2505.20314v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"d-nets-interaction-based-system-for-optimal","repo_url":"https://github.com/danaugrs/deltanets","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}