{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T09:01:57Z","timestamp":1775466117452,"version":"3.50.1"},"reference-count":4,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":17025,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1967,8]]},"abstract":"<jats:p>In combinatory logic there is a system of objects which intuitively represent functions, and a binary relation between these objects, which represents the process of evaluating the result of applying a function to an argument. (This is explained fully in [1].) From this relation called <jats:italic>weak reduction<\/jats:italic>, \u201c\u2265,\u201d an equivalence relation is defined by saying that <jats:italic>X<\/jats:italic> is <jats:italic>weakly equivalent<\/jats:italic> to <jats:italic>Y<\/jats:italic> if and only if there exist <jats:italic>n<\/jats:italic> (with 0 \u2264 <jats:italic>n<\/jats:italic>) and <jats:italic>X<jats:sub>0<\/jats:sub>,\u2026,X<jats:sub>\u03b7<\/jats:sub><\/jats:italic> such that\n<jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S002248120011388X_eqnU1\"\/><\/jats:disp-formula><\/jats:p><jats:p>It turns out that equivalent objects represent the same function, but two objects representing the same function need not be equivalent.<\/jats:p>","DOI":"10.2307\/2271660","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T16:39:49Z","timestamp":1146933589000},"page":"224-236","source":"Crossref","is-referenced-by-count":8,"title":["Axioms for strong reduction in combinatory logic"],"prefix":"10.1017","volume":"32","author":[{"given":"Roger","family":"Hindley","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120011388X_ref004","first-page":"237","volume":"32","author":"Lercher","year":"1967","journal-title":"The decidability of Hindley's axioms for strong reduction"},{"key":"S002248120011388X_ref001","volume-title":"Combinatory logic","volume":"1","author":"Curry","year":"1958"},{"key":"S002248120011388X_ref003","unstructured":"Lercher B. , Strong reduction and recursion in combinatory logic, Doctoral thesis, Pennsylvania State University, 1963."},{"key":"S002248120011388X_ref002","unstructured":"Sanchis L. E. , Normal combinations and the theory of types, Doctoral thesis, Pennsylvania State University, 1963; Notre Dame journal of formal logic, vol. 5 (1964), p. 161."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120011388X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T15:57:17Z","timestamp":1559491037000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120011388X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1967,8]]},"references-count":4,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1967,8]]}},"alternative-id":["S002248120011388X"],"URL":"https:\/\/doi.org\/10.2307\/2271660","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1967,8]]}}}