{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:41:12Z","timestamp":1753890072289,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2020,2,20]],"date-time":"2020-02-20T00:00:00Z","timestamp":1582156800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,2,20]],"date-time":"2020-02-20T00:00:00Z","timestamp":1582156800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,2,20]],"date-time":"2020-02-20T00:00:00Z","timestamp":1582156800000},"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":["731143"],"award-info":[{"award-number":["731143"]}],"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 give a new proof of the well-known fact that all functions $(\\mathbb{N} \\to \\mathbb{N}) \\to \\mathbb{N}$ which are definable in G\\&amp;quot;odel's System T are continuous via a syntactic approach. Differing from the usual syntactic method, we firstly perform a translation of System T into itself in which natural numbers are translated to functions $(\\mathbb{N} \\to \\mathbb{N}) \\to \\mathbb{N}$. Then we inductively define a continuity predicate on the translated elements and show that the translation of any term in System T satisfies the continuity predicate. We obtain the desired result by relating terms and their translations via a parametrized logical relation. Our constructions and proofs have been formalized in the Agda proof assistant. Because Agda is also a programming language, we can execute our proof to compute moduli of continuity of T-definable functions.<\/jats:p>","DOI":"10.23638\/lmcs-16(1:22)2020","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:45:30Z","timestamp":1743702330000},"source":"Crossref","is-referenced-by-count":0,"title":["A syntactic approach to continuity of T-definable functionals"],"prefix":"10.23638","volume":"Volume 16, Issue 1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6838-4221","authenticated-orcid":false,"given":"Chuangjie","family":"Xu","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2020,2,20]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1904.09794v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1904.09794v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:45:30Z","timestamp":1743702330000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/5394"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,20]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-16(1:22)2020","relation":{"has-preprint":[{"id-type":"arxiv","id":"1904.09794v3","asserted-by":"subject"},{"id-type":"arxiv","id":"1904.09794v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1904.09794","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1904.09794","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2020,2,20]]},"article-number":"5394"}}