{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T01:27:24Z","timestamp":1772242044395,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T00:00:00Z","timestamp":1580428800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T00:00:00Z","timestamp":1580428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T00:00:00Z","timestamp":1580428800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"National Science Foundation","award":["1453796"],"award-info":[{"award-number":["1453796"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,4,1]]},"abstract":"<jats:p>We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to new judgments for gradual type and term dynamism, which were developed in blame calculi and to state the &amp;quot;gradual guarantee&amp;quot; theorem of gradual typing. Combined with the ordinary extensionality ($\\eta$) principles that type theory provides, we show that most of the standard operational behavior of casts is uniquely determined by the gradual guarantee. This provides a semantic justification for the definitions of casts, and shows that non-standard definitions of casts must violate these principles. Our type theory is the internal language of a certain class of preorder categories called equipments. We give a general construction of an equipment interpreting gradual type theory from a 2-category representing non-gradual types and programs, which is a semantic analogue of Findler and Felleisen's definitions of contracts, and use it to build some concrete domain-theoretic models of gradual typing.<\/jats:p>","DOI":"10.23638\/lmcs-16(1:7)2020","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T13:43:30Z","timestamp":1743687810000},"source":"Crossref","is-referenced-by-count":0,"title":["Call-by-name Gradual Type Theory"],"prefix":"10.23638","volume":"Volume 16, Issue 1","author":[{"given":"Max S.","family":"New","sequence":"first","affiliation":[]},{"given":"Daniel R.","family":"Licata","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2020,1,31]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1802.00061v6","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1802.00061v6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T13:43:30Z","timestamp":1743687810000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/5154"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,31]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-16(1:7)2020","relation":{"has-preprint":[{"id-type":"arxiv","id":"1802.00061v5","asserted-by":"subject"},{"id-type":"arxiv","id":"1802.00061v4","asserted-by":"subject"},{"id-type":"arxiv","id":"1802.00061v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1802.00061","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1802.00061","asserted-by":"subject"}],"is-cited-by":[{"id-type":"doi","id":"10.1145\/3485485","asserted-by":"object"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,31]]},"article-number":"5154"}}