{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:21:05Z","timestamp":1777645265717,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2019,10,19]],"date-time":"2019-10-19T00:00:00Z","timestamp":1571443200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2019,10,19]]},"abstract":"<jats:p>In this article, we introduce Moschovakis higher-order type theory of acyclic recursion [Formula: see text]. We present the potentials of [Formula: see text] for incorporating different reduction systems in [Formula: see text], with corresponding reduction calculi. At first, we introduce the original reduction calculus of [Formula: see text], which reduces [Formula: see text]-terms to their canonical forms. This reduction calculus determines the relation of referential, i.e., algorithmic, synonymy between [Formula: see text]-terms with respect to a chosen semantic structure. Our contribution is the definition of a ( \u03b3) rule and extending the reduction calculus of [Formula: see text] and its referential synonymy to \u03b3-reduction and \u03b3-synonymy, respectively. The \u03b3-reduction is very useful for simplification of terms in canonical forms, by reducing subterms having superfluous \u03bb-abstraction and corresponding functional applications. Typically, such extra \u03bb abstractions can be introduced by the \u03bb-rule of the reduction calculus of [Formula: see text].<\/jats:p>","DOI":"10.3233\/fi-2019-1867","type":"journal-article","created":{"date-parts":[[2019,10,23]],"date-time":"2019-10-23T11:21:41Z","timestamp":1571829701000},"page":"367-411","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":10,"title":["Gamma-Reduction in Type Theory of Acyclic Recursion"],"prefix":"10.1177","volume":"170","author":[{"given":"Roussanka","family":"Loukanova","sequence":"first","affiliation":[{"name":"Department of Mathematics, Stockholm University, Stockholm, Sweden."}]}],"member":"179","published-online":{"date-parts":[[2019,10,19]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2019-1867","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2019-1867","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:48Z","timestamp":1777444308000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2019-1867"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,19]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,10,19]]}},"alternative-id":["10.3233\/FI-2019-1867"],"URL":"https:\/\/doi.org\/10.3233\/fi-2019-1867","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,19]]}}}