{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T03:05:09Z","timestamp":1767927909768,"version":"3.49.0"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T00:00:00Z","timestamp":1648512000000},"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>We present XTT, a version of Cartesian cubical type theory specialized for\nBishop sets \\`a la Coquand, in which every type enjoys a definitional version\nof the uniqueness of identity proofs. Using cubical notions, XTT reconstructs\nmany of the ideas underlying Observational Type Theory, a version of\nintensional type theory that supports function extensionality. We prove the\ncanonicity property of XTT (that every closed boolean is definitionally equal\nto a constant) using Artin gluing.<\/jats:p>","DOI":"10.46298\/lmcs-18(1:43)2022","type":"journal-article","created":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T12:29:53Z","timestamp":1648643393000},"source":"Crossref","is-referenced-by-count":4,"title":["A Cubical Language for Bishop Sets"],"prefix":"10.46298","volume":"Volume 18, Issue 1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0585-5564","authenticated-orcid":false,"given":"Jonathan","family":"Sterling","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9590-3303","authenticated-orcid":false,"given":"Carlo","family":"Angiuli","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1944-0789","authenticated-orcid":false,"given":"Daniel","family":"Gratzer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2022,3,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/9264\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/9264\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:20:44Z","timestamp":1687292444000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/9069"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-18(1:43)2022","relation":{"has-preprint":[{"id-type":"arxiv","id":"2003.01491v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2003.01491","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2003.01491","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,29]]},"article-number":"9069"}}