{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:33:07Z","timestamp":1777645987000,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"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":[[2011,7]]},"abstract":"<jats:p>The \u03bb-theory \u210b is obtained from \u03b2-conversion by identifying all closed unsolvable terms (or, equivalently, terms without head normal form). The range problem for the theory \u210b asks whether a closed term has always (up to equality in \u210b) either an infinite range or a singleton range (that is, it is a constant function). Here we give a solution to a natural version of this problem, giving a positive answer for the theory \u210b restricted to Combinatory Logic. The method of proof applies also to the Lazy \u03bb-Calculus.<\/jats:p>","DOI":"10.3233\/fi-2011-560","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T23:47:12Z","timestamp":1575330432000},"page":"203-222","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Solution to the Range Problem for Combinatory Logic"],"prefix":"10.1177","volume":"111","author":[{"given":"Benedetto","family":"Intrigila","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Roma \u201cTor Vergata\u201d, Rome, Italy. intrigil@mat.uniroma2.it"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Richard","family":"Statman","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Carnegie-Mellon University, Pittsburgh, PA, USA. rs31@andrew.cmu.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2011,1,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2011-560","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2011-560","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:33:59Z","timestamp":1777444439000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2011-560"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,1]]},"references-count":0,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,7]]}},"alternative-id":["10.3233\/FI-2011-560"],"URL":"https:\/\/doi.org\/10.3233\/fi-2011-560","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,1,1]]}}}