{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T20:33:09Z","timestamp":1693859589235},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2013,9,30]],"date-time":"2013-09-30T00:00:00Z","timestamp":1380499200000},"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":"Terminal coalgebras for a functor serve as semantic domains for state-based\nsystems of various types. For example, behaviors of CCS processes, streams,\ninfinite trees, formal languages and non-well-founded sets form terminal\ncoalgebras. We present a uniform account of the semantics of recursive\ndefinitions in terminal coalgebras by combining two ideas: (1) abstract GSOS\nrules l specify additional algebraic operations on a terminal coalgebra; (2)\nterminal coalgebras are also initial completely iterative algebras (cias). We\nalso show that an abstract GSOS rule leads to new extended cia structures on\nthe terminal coalgebra. Then we formalize recursive function definitions\ninvolving given operations specified by l as recursive program schemes for l,\nand we prove that unique solutions exist in the extended cias. From our results\nit follows that the solutions of recursive (function) definitions in terminal\ncoalgebras may be used in subsequent recursive definitions which still have\nunique solutions. We call this principle modularity. We illustrate our results\nby the five concrete terminal coalgebras mentioned above, e.\\,g., a finite\nstream circuit defines a unique stream function.<\/jats:p>","DOI":"10.2168\/lmcs-9(3:28)2013","type":"journal-article","created":{"date-parts":[[2013,11,29]],"date-time":"2013-11-29T13:44:29Z","timestamp":1385732669000},"source":"Crossref","is-referenced-by-count":10,"title":["Abstract GSOS Rules and a Modular Treatment of Recursive Definitions"],"prefix":"10.46298","volume":"Volume 9, Issue 3","author":[{"given":"Stefan","family":"Milius","sequence":"first","affiliation":[]},{"given":"Lawrence S","family":"Moss","sequence":"additional","affiliation":[]},{"given":"Daniel","family":"Schwencke","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2013,9,30]]},"reference":[{"key":"895:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1180\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1180\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:05:32Z","timestamp":1681243532000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1180"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,30]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-9(3:28)2013","relation":{"is-same-as":[{"id-type":"arxiv","id":"1307.2538","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1307.2538","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"doi","id":"10.1007\/978-3-319-66167-4_1","asserted-by":"subject"},{"id-type":"doi","id":"10.5281\/zenodo.3228083","asserted-by":"subject"},{"id-type":"doi","id":"10.5281\/zenodo.3228084","asserted-by":"subject"},{"id-type":"handle","id":"1871.1\/bda0766d-256c-487b-ba33-935c32a65336","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9,30]]}}}