{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T14:16:06Z","timestamp":1754144166750,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,5,1]]},"abstract":"<jats:p>In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of clauses is enough to ensure reversibility. The language allows to represent any Primitive Recursive Function. We then give a Curry-Howard correspondence with the logic $\u03bc$MALL: linear logic extended with least fixed points allowing inductive statements. The critical part of our work is to show how primitive recursion yields circular proofs that satisfy $\u03bc$MALL validity criterion and how the language simulates the cut-elimination procedure of $\u03bc$MALL.<\/jats:p>","DOI":"10.46298\/lmcs-21(3:4)2025","type":"journal-article","created":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T09:35:07Z","timestamp":1752572107000},"source":"Crossref","is-referenced-by-count":0,"title":["A Curry-Howard Correspondence for Linear, Reversible Computation"],"prefix":"10.46298","volume":"Volume 21, Issue 3","author":[{"given":"Kostia","family":"Chardonnet","sequence":"first","affiliation":[]},{"given":"Alexis","family":"Saurin","sequence":"additional","affiliation":[]},{"given":"Beno\u00eet","family":"Valiron","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2025,7,15]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2302.11887v10","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2302.11887v10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T09:35:07Z","timestamp":1752572107000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/11679"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,15]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(3:4)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2302.11887v8","asserted-by":"subject"},{"id-type":"arxiv","id":"2302.11887v7","asserted-by":"subject"},{"id-type":"arxiv","id":"2302.11887v5","asserted-by":"subject"},{"id-type":"arxiv","id":"2302.11887v4","asserted-by":"subject"},{"id-type":"arxiv","id":"2302.11887v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2302.11887v2","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2302.11887","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2302.11887","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2025,7,15]]},"article-number":"11679"}}