{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:34:16Z","timestamp":1753889656901,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2006,11,3]],"date-time":"2006-11-03T00:00:00Z","timestamp":1162512000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/assumed-1991-2003"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We present a formalization of a version of Abadi and\n  Plotkin's logic for parametricity for a polymorphic dual\nintuitionistic\/linear type theory with fixed points, and show, following\nPlotkin's suggestions, that it can be used to define a wide collection of\ntypes, including existential types, inductive types, coinductive types and\ngeneral recursive types. We show that the recursive types satisfy a universal\nproperty called dinaturality, and we develop reasoning principles for the\nconstructed types. In the case of recursive types, the reasoning principle is a\nmixed induction\/coinduction principle, with the curious property that\ncoinduction holds for general relations, but induction only for a limited\ncollection of ``admissible'' relations. A similar property was observed in\nPitts' 1995 analysis of recursive types in domain theory. In a future paper we\nwill develop a category theoretic notion of models of the logic presented here,\nand show how the results developed in the logic can be transferred to the\nmodels.<\/jats:p>","DOI":"10.2168\/lmcs-2(5:2)2006","type":"journal-article","created":{"date-parts":[[2006,11,23]],"date-time":"2006-11-23T09:29:44Z","timestamp":1164274184000},"source":"Crossref","is-referenced-by-count":11,"title":["Linear Abadi and Plotkin Logic"],"prefix":"10.46298","volume":"Volume 2, Issue 5","author":[{"given":"Lars","family":"Birkedal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rasmus E.","family":"M\u00f8gelberg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rasmus Lerchedahl","family":"Petersen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2006,11,3]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/2233\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/2233\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:10:14Z","timestamp":1681243814000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/2233"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,11,3]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2168\/lmcs-2(5:2)2006","relation":{"is-same-as":[{"id-type":"arxiv","id":"cs\/0611004","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.cs\/0611004","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2006,11,3]]},"article-number":"2233"}}