{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:05Z","timestamp":1753894385493,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2022,2,3]],"date-time":"2022-02-03T00:00:00Z","timestamp":1643846400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Cubical type theory provides a constructive justification of homotopy type\ntheory. A crucial ingredient of cubical type theory is a path lifting operation\nwhich is explained computationally by induction on the type involving several\nnon-canonical choices. We present in this article two canonicity results, both\nproved by a sconing argument: a homotopy canonicity result, every natural\nnumber is path equal to a numeral, even if we take away the equations defining\nthe lifting operation on the type structure, and a canonicity result, which\nuses these equations in a crucial way. Both proofs are done internally in a\npresheaf model.<\/jats:p>","DOI":"10.46298\/lmcs-18(1:28)2022","type":"journal-article","created":{"date-parts":[[2022,2,3]],"date-time":"2022-02-03T19:49:40Z","timestamp":1643917780000},"source":"Crossref","is-referenced-by-count":0,"title":["Canonicity and homotopy canonicity for cubical type theory"],"prefix":"10.46298","volume":"Volume 18, Issue 1","author":[{"given":"Thierry","family":"Coquand","sequence":"first","affiliation":[]},{"given":"Simon","family":"Huber","sequence":"additional","affiliation":[]},{"given":"Christian","family":"Sattler","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2022,2,3]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/9043\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/9043\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:17:45Z","timestamp":1687292265000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/6309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,3]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-18(1:28)2022","relation":{"has-preprint":[{"id-type":"arxiv","id":"1902.06572v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1902.06572v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1902.06572","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1902.06572","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2022,2,3]]},"article-number":"6309"}}