{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T05:21:57Z","timestamp":1776316917114,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We introduce a call-by-name lambda-calculus $\\lambda Jn$ with generalized\napplications which is equipped with distant reduction. This allows to unblock\n$\\beta$-redexes without resorting to the standard permutative conversions of\ngeneralized applications used in the original $\\Lambda J$-calculus with\ngeneralized applications of Joachimski and Matthes. We show strong\nnormalization of simply-typed terms, and we then fully characterize strong\nnormalization by means of a quantitative (i.e. non-idempotent intersection)\ntyping system. This characterization uses a non-trivial inductive definition of\nstrong normalization --related to others in the literature--, which is based on\na weak-head normalizing strategy. We also show that our calculus $\\lambda Jn$\nrelates to explicit substitution calculi by means of a faithful translation, in\nthe sense that it preserves strong normalization. Moreover, our calculus\n$\\lambda Jn$ and the original $\\Lambda J$-calculus determine equivalent notions\nof strong normalization. As a consequence, $\\lambda J$ inherits a faithful\ntranslation into explicit substitutions, and its strong normalization can also\nbe characterized by the quantitative typing system designed for $\\lambda Jn$,\ndespite the fact that quantitative subject reduction fails for permutative\nconversions.<\/jats:p>","DOI":"10.46298\/lmcs-20(3:10)2024","type":"journal-article","created":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T19:35:07Z","timestamp":1722281707000},"source":"Crossref","is-referenced-by-count":1,"title":["A Faithful and Quantitative Notion of Distant Reduction for the Lambda-Calculus with Generalized Applications"],"prefix":"10.46298","volume":"Volume 20, Issue 3","author":[{"given":"Jos\u00e9 Esp\u00edrito","family":"Santo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Delia","family":"Kesner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lo\u00efc","family":"Peyrot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2024,7,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/13995\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/13995\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,29]],"date-time":"2024-07-29T19:35:07Z","timestamp":1722281707000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/10901"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(3:10)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2201.04156v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2201.04156v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2201.04156","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2201.04156","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,29]]},"article-number":"10901"}}