{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:06Z","timestamp":1753894386309,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2022,3,22]],"date-time":"2022-03-22T00:00:00Z","timestamp":1647907200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100014013","name":"UK Research and Innovation","doi-asserted-by":"crossref","award":["EP\/M023974\/1"],"award-info":[{"award-number":["EP\/M023974\/1"]}],"id":[{"id":"10.13039\/100014013","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["864202"],"award-info":[{"award-number":["864202"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["895827"],"award-info":[{"award-number":["895827"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We present semantic correctness proofs of automatic differentiation (AD). We\nconsider a forward-mode AD method on a higher order language with algebraic\ndata types, and we characterise it as the unique structure preserving macro\ngiven a choice of derivatives for basic operations. We describe a rich\nsemantics for differentiable programming, based on diffeological spaces. We\nshow that it interprets our language, and we phrase what it means for the AD\nmethod to be correct with respect to this semantics. We show that our\ncharacterisation of AD gives rise to an elegant semantic proof of its\ncorrectness based on a gluing construction on diffeological spaces. We explain\nhow this is, in essence, a logical relations argument. Throughout, we show how\nthe analysis extends to AD methods for computing higher order derivatives using\na Taylor approximation.<\/jats:p>","DOI":"10.46298\/lmcs-18(1:41)2022","type":"journal-article","created":{"date-parts":[[2022,3,23]],"date-time":"2022-03-23T08:11:00Z","timestamp":1648023060000},"source":"Crossref","is-referenced-by-count":3,"title":["Higher Order Automatic Differentiation of Higher Order Functions"],"prefix":"10.46298","volume":"Volume 18, Issue 1","author":[{"given":"Mathieu","family":"Huot","sequence":"first","affiliation":[]},{"given":"Sam","family":"Staton","sequence":"additional","affiliation":[]},{"given":"Matthijs","family":"V\u00e1k\u00e1r","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2022,3,22]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/9239\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/9239\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:19:31Z","timestamp":1687292371000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/7106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,22]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-18(1:41)2022","relation":{"has-preprint":[{"id-type":"arxiv","id":"2101.06757v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2101.06757v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2101.06757v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2101.06757","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2101.06757","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2022,3,22]]},"article-number":"7106"}}