{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T11:29:16Z","timestamp":1761823756618,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2014,12,9]],"date-time":"2014-12-09T00:00:00Z","timestamp":1418083200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We examine the relationship between the algebraic lambda-calculus, a fragment\nof the differential lambda-calculus and the linear-algebraic lambda-calculus, a\ncandidate lambda-calculus for quantum computation. Both calculi are algebraic:\neach one is equipped with an additive and a scalar-multiplicative structure,\nand their set of terms is closed under linear combinations. However, the two\nlanguages were built using different approaches: the former is a call-by-name\nlanguage whereas the latter is call-by-value; the former considers algebraic\nequalities whereas the latter approaches them through rewrite rules. In this\npaper, we analyse how these different approaches relate to one another. To this\nend, we propose four canonical languages based on each of the possible choices:\ncall-by-name versus call-by-value, algebraic equality versus algebraic\nrewriting. We show that the various languages simulate one another. Due to\nsubtle interaction between beta-reduction and algebraic rewriting, to make the\nlanguages consistent some additional hypotheses such as confluence or\nnormalisation might be required. We carefully devise the required properties\nfor each proof, making them general enough to be valid for any sub-language\nsatisfying the corresponding properties.<\/jats:p>","DOI":"10.2168\/lmcs-10(4:8)2014","type":"journal-article","created":{"date-parts":[[2015,5,18]],"date-time":"2015-05-18T07:32:47Z","timestamp":1431934367000},"source":"Crossref","is-referenced-by-count":9,"title":["Call-by-value, call-by-name and the vectorial behaviour of the algebraic \\lambda-calculus"],"prefix":"10.46298","volume":"Volume 10, Issue 4","author":[{"given":"Ali","family":"Assaf","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5175-6882","authenticated-orcid":false,"given":"Alejandro","family":"D\u00edaz-Caro","sequence":"additional","affiliation":[]},{"given":"Simon","family":"Perdrix","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8098-9944","authenticated-orcid":false,"given":"Christine","family":"Tasson","sequence":"additional","affiliation":[]},{"given":"Beno\u00ee t","family":"Valiron","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2014,12,9]]},"reference":[{"key":"982:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/927\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/927\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:59:11Z","timestamp":1681243151000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/927"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,9]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-10(4:8)2014","relation":{"is-same-as":[{"id-type":"arxiv","id":"1005.2897","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1005.2897","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2014,12,9]]},"article-number":"927"}}