{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:38:16Z","timestamp":1753889896226,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2008,12,25]],"date-time":"2008-12-25T00:00:00Z","timestamp":1230163200000},"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>We discuss the treatment of initial datatypes and final process types in the\nwide-spectrum language HasCASL. In particular, we present specifications that\nillustrate how datatypes and process types arise as bootstrapped concepts using\nHasCASL's type class mechanism, and we describe constructions of types of\nfinite and infinite trees that establish the conservativity of datatype and\nprocess type declarations adhering to certain reasonable formats. The latter\namounts to modifying known constructions from HOL to avoid unique choice; in\ncategorical terminology, this means that we establish that quasitoposes with an\ninternal natural numbers object support initial algebras and final coalgebras\nfor a range of polynomial functors, thereby partially generalising\ncorresponding results from topos theory. Moreover, we present similar\nconstructions in categories of internal complete partial orders in\nquasitoposes.<\/jats:p>","DOI":"10.2168\/lmcs-4(4:17)2008","type":"journal-article","created":{"date-parts":[[2009,1,9]],"date-time":"2009-01-09T10:25:55Z","timestamp":1231496755000},"source":"Crossref","is-referenced-by-count":2,"title":["Bootstrapping Inductive and Coinductive Types in HasCASL"],"prefix":"10.46298","volume":"Volume 4, Issue 4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3146-5906","authenticated-orcid":false,"given":"Lutz","family":"Schr\u00f6der","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2008,12,25]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1166\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1166\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:05:24Z","timestamp":1681243524000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1166"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,12,25]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2168\/lmcs-4(4:17)2008","relation":{"is-same-as":[{"id-type":"arxiv","id":"0812.3836","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.0812.3836","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2008,12,25]]},"article-number":"1166"}}