{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:37:59Z","timestamp":1753889879334,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T00:00:00Z","timestamp":1581552000000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T00:00:00Z","timestamp":1581552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,2,13]],"date-time":"2020-02-13T00:00:00Z","timestamp":1581552000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["704111"],"award-info":[{"award-number":["704111"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,4,1]]},"abstract":"<jats:p>We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the &amp;quot;limits&amp;quot; of infinite reduction sequences. This may be seen as a refinement and generalization of the notion of productivity in term rewriting to a setting with higher-order functions and with data specified by nested higher-order inductive and coinductive definitions. Intuitively, we interpret lazy data structures in a higher-order functional language by potentially infinite terms corresponding to their complete unfoldings.   We prove an approximation theorem which essentially states that if a term reduces to an arbitrarily large finite approximation of an infinite object in the interpretation of a coinductive type, then it infinitarily (i.e. in the &amp;quot;limit&amp;quot;) reduces to an infinite object in the interpretation of this type. We introduce a sufficient syntactic correctness criterion, in the form of a type system, for finite terms decorated with type information. Using the approximation theorem, we show that each well-typed term has a well-defined interpretation in our semantics.<\/jats:p>","DOI":"10.23638\/lmcs-16(1:11)2020","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:38:36Z","timestamp":1743701916000},"source":"Crossref","is-referenced-by-count":0,"title":["An operational interpretation of coinductive types"],"prefix":"10.23638","volume":"Volume 16, Issue 1","author":[{"given":"\u0141ukasz","family":"Czajka","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2020,2,13]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1808.05059v5","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1808.05059v5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:38:36Z","timestamp":1743701916000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/4758"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,13]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-16(1:11)2020","relation":{"has-preprint":[{"id-type":"arxiv","id":"1808.05059v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1808.05059v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1808.05059v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1808.05059","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1808.05059","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2020,2,13]]},"article-number":"4758"}}