{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T01:27:25Z","timestamp":1772242045053,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2017,10,23]],"date-time":"2017-10-23T00:00:00Z","timestamp":1508716800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,10,23]],"date-time":"2017-10-23T00:00:00Z","timestamp":1508716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2017,10,23]],"date-time":"2017-10-23T00:00:00Z","timestamp":1508716800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/100014013","name":"UK Research and Innovation","doi-asserted-by":"crossref","award":["EP\/M016951\/1"],"award-info":[{"award-number":["EP\/M016951\/1"]}],"id":[{"id":"10.13039\/100014013","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,3,31]]},"abstract":"<jats:p>We develop normalisation by evaluation (NBE) for dependent types based on presheaf categories. Our construction is formulated in the metalanguage of type theory using quotient inductive types. We use a typed presentation hence there are no preterms or realizers in our construction, and every construction respects the conversion relation. NBE for simple types uses a logical relation between the syntax and the presheaf interpretation. In our construction, we merge the presheaf interpretation and the logical relation into a proof-relevant logical predicate. We prove normalisation, completeness, stability and decidability of definitional equality. Most of the constructions were formalized in Agda.<\/jats:p>","DOI":"10.23638\/lmcs-13(4:1)2017","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T13:29:16Z","timestamp":1743686956000},"source":"Crossref","is-referenced-by-count":8,"title":["Normalisation by Evaluation for Type Theory, in Type Theory"],"prefix":"10.23638","volume":"Volume 13, Issue 4","author":[{"given":"Thorsten","family":"Altenkirch","sequence":"first","affiliation":[]},{"given":"Ambrus","family":"Kaposi","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2017,10,23]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1612.02462v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1612.02462v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T13:29:16Z","timestamp":1743686956000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/2588"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,23]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-13(4:1)2017","relation":{"has-preprint":[{"id-type":"arxiv","id":"1612.02462v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1612.02462v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1612.02462v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1612.02462","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1612.02462","asserted-by":"subject"}],"is-cited-by":[{"id-type":"doi","id":"10.1007\/978-3-030-33636-3_12","asserted-by":"object"},{"id-type":"doi","id":"10.1145\/3158111","asserted-by":"object"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,10,23]]},"article-number":"2588"}}