{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T20:53:14Z","timestamp":1776891194682,"version":"3.51.2"},"reference-count":5,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"2","license":[{"start":{"date-parts":[[2008,11,7]],"date-time":"2008-11-07T00:00:00Z","timestamp":1226016000000},"content-version":"unspecified","delay-in-days":6064,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Funct. Prog."],"published-print":{"date-parts":[[1992,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    A closed \u03bb-term\n                    <jats:bold>E<\/jats:bold>\n                    is called an\n                    <jats:italic>enumerator<\/jats:italic>\n                    if\n                  <\/jats:p>\n                  <jats:p>\n                    <jats:disp-formula>\n                      <jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0956796800000356eqnU1\"\/>\n                    <\/jats:disp-formula>\n                  <\/jats:p>\n                  <jats:p>\n                    Here \u22c0\n                    <jats:sup>0<\/jats:sup>\n                    is the set of closed \u03bb-terms,. is the set of natural numbers and the \u231c\n                    <jats:italic>n<\/jats:italic>\n                    \u231d are the Church's numerals \u03bb\n                    <jats:italic>fx<\/jats:italic>\n                    .\n                    <jats:italic>f<\/jats:italic>\n                    <jats:sup>\n                      <jats:italic>n<\/jats:italic>\n                    <\/jats:sup>\n                    <jats:italic>x<\/jats:italic>\n                    . Such an\n                    <jats:bold>E<\/jats:bold>\n                    is called\n                    <jats:italic>reducing<\/jats:italic>\n                    if, moreover\n                  <\/jats:p>\n                  <jats:p>\n                    <jats:disp-formula>\n                      <jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0956796800000356eqnU2\"\/>\n                    <\/jats:disp-formula>\n                  <\/jats:p>\n                  <jats:p>An ingenious recursion theoretic proof by Statman will be presented, showing that every enumerator is reducing. I do not know any direct proof.<\/jats:p>","DOI":"10.1017\/s0956796800000356","type":"journal-article","created":{"date-parts":[[2008,11,7]],"date-time":"2008-11-07T11:14:34Z","timestamp":1226056474000},"page":"233-236","source":"Crossref","is-referenced-by-count":2,"title":["<i>Theoretical Pearls<\/i>\n                    Enumerators of lambda terms are reducing"],"prefix":"10.46298","volume":"2","author":[{"given":"Henk","family":"Barendregt","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2008,11,7]]},"reference":[{"key":"S0956796800000356_ref005","unstructured":"Mulder J. C. 1990. Case studies in process specification and verification. PhD thesis, University of Amsterdam."},{"key":"S0956796800000356_ref006","volume-title":"Two recursion theoretic problems in lambda calculus","author":"Statman","year":"1987"},{"key":"S0956796800000356_ref004","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-36-00227-2"},{"key":"S0956796800000356_ref002","unstructured":"Barendregt H. P. 1971. Some extensional term models for lambda calculi and combinatory logics. PhD thesis, Utrecht University."},{"key":"S0956796800000356_ref003","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1017\/S0956796800020062","article-title":"Theoretical pearls: Self-interpretation in lambda calculus","volume":"1","author":"Barendregt","year":"1991","journal-title":"J. Functional Programming"}],"container-title":["Journal of Functional Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0956796800000356","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T20:17:51Z","timestamp":1776889071000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0956796800000356\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,4]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1992,4]]}},"alternative-id":["S0956796800000356"],"URL":"https:\/\/doi.org\/10.1017\/s0956796800000356","relation":{},"ISSN":["0956-7968","1469-7653"],"issn-type":[{"value":"0956-7968","type":"print"},{"value":"1469-7653","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,4]]}}}