{"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/reverse-ad-at-higher-types-pure-principled","title":"Reverse AD at Higher Types: Pure, Principled and Denotationally Correct","arxiv_id":"2007.05283","date":"2020-07-10","proceeding":null,"authors":["Matthijs Vákár"],"abstract":"We show how to define forward- and reverse-mode automatic differentiation source-code transformations or on a standard higher-order functional language. The transformations generate purely functional code, and they are principled in the sense that their definition arises from a categorical universal property. We give a semantic proof of correctness of the transformations. In their most elegant formulation, the transformations generate code with linear types. However, we demonstrate how the transformations can be implemented in a standard functional language without sacrificing correctness. To do so, we make use of abstract data types to represent the required linear types, e.g. through the use of a basic module system.","url_abs":"https://arxiv.org/abs/2007.05283v2","url_pdf":"https://arxiv.org/pdf/2007.05283v2.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":"reverse-ad-at-higher-types-pure-principled","repo_url":"https://github.com/VMatthijs/CHAD","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2007.05283","atlas_url":"https://app.syntology.ai/?focus=2007.05283","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}