{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:39:35Z","timestamp":1753889975495,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2008,4,10]],"date-time":"2008-04-10T00:00:00Z","timestamp":1207785600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Some type-based approaches to termination use sized types: an ordinal bound\nfor the size of a data structure is stored in its type. A recursive function\nover a sized type is accepted if it is visible in the type system that\nrecursive calls occur just at a smaller size. This approach is only sound if\nthe type of the recursive function is admissible, i.e., depends on the size\nindex in a certain way. To explore the space of admissible functions in the\npresence of higher-kinded data types and impredicative polymorphism, a\nsemantics is developed where sized types are interpreted as functions from\nordinals into sets of strongly normalizing terms. It is shown that upper\nsemi-continuity of such functions is a sufficient semantic criterion for\nadmissibility. To provide a syntactical criterion, a calculus for\nsemi-continuous functions is developed.<\/jats:p>","DOI":"10.2168\/lmcs-4(2:3)2008","type":"journal-article","created":{"date-parts":[[2008,6,3]],"date-time":"2008-06-03T13:29:20Z","timestamp":1212499760000},"source":"Crossref","is-referenced-by-count":12,"title":["Semi-continuous Sized Types and Termination"],"prefix":"10.46298","volume":"Volume 4, Issue 2","author":[{"given":"Andreas","family":"Abel","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2008,4,10]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1236\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1236\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:06:18Z","timestamp":1681243578000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,4,10]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2168\/lmcs-4(2:3)2008","relation":{"is-same-as":[{"id-type":"arxiv","id":"0804.0876","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.0804.0876","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"arxiv","id":"1202.3496","asserted-by":"subject"},{"id-type":"doi","id":"10.4204\/eptcs.77.1","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arxiv.1202.3496","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2008,4,10]]},"article-number":"1236"}}