{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T23:05:55Z","timestamp":1779836755468,"version":"3.53.1"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2020,3,30]],"date-time":"2020-03-30T00:00:00Z","timestamp":1585526400000},"content-version":"unspecified","delay-in-days":89,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Funct. Prog."],"published-print":{"date-parts":[[2020]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    From the outset, lambda calculus represented natural numbers through iterated application. The successor hence adds one more application, and the predecessor removes. In effect, the predecessor un-applies a term\u2014which seemed impossible, even to Church. It took Kleene a rather oblique glance to sight a related representation of numbers, with an easier predecessor. Let us see what we can do if we look at this old problem with today\u2019s eyes. We discern the systematic ways to\n                    <jats:italic>derive<\/jats:italic>\n                    more predecessors\u2014smaller, faster, and sharper\u2014while keeping all teeth.\n                  <\/jats:p>","DOI":"10.1017\/s095679682000009x","type":"journal-article","created":{"date-parts":[[2020,3,30]],"date-time":"2020-03-30T04:15:30Z","timestamp":1585541730000},"source":"Crossref","is-referenced-by-count":0,"title":["Many more predecessors: A representation workout"],"prefix":"10.1017","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2570-2186","authenticated-orcid":false,"given":"OLEG","family":"KISELYOV","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2020,3,30]]},"reference":[{"key":"S095679682000009X_ref13","first-page":"276","article-title":"A simple lamda-term representing the predecessor function with respect to church numerials","volume":"50","author":"Urbanek","year":"1993","journal-title":"Bull. EATCS"},{"key":"S095679682000009X_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(79)90007-0"},{"key":"S095679682000009X_ref3","unstructured":"Barendregt, H. & Barendsen, E. (2000) Introduction to Lambda Calculus."},{"key":"S095679682000009X_ref4","volume-title":"The Lambda Calculus: Its Syntax and Semantics","author":"Barendregt","year":"1981"},{"key":"S095679682000009X_ref2","doi-asserted-by":"publisher","DOI":"10.2307\/421013"},{"key":"S095679682000009X_ref1","unstructured":"Abadi, M. , Cardelli, L. & Plotkin, G. D. (1993) Types for the Scott numerals. Available at: http:\/\/lucacardelli.name\/Papers\/Notes\/scott2.pdf."},{"key":"S095679682000009X_ref5","first-page":"321","volume-title":"Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics","author":"Barendregt","year":"1990"},{"key":"S095679682000009X_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(85)90135-5"},{"key":"S095679682000009X_ref6","doi-asserted-by":"publisher","DOI":"10.1145\/62678.62726"},{"key":"S095679682000009X_ref8","first-page":"137","volume-title":"APPSEM 2000: International Summer School on Applied Semantics, Advanced Lectures","author":"Dybjer","year":"2002"},{"key":"S095679682000009X_ref9","unstructured":"Kemp, C. J. M. (2007) Theoretical Foundations for Practical \u2018Totally Functional Programming\u2019. Ph.D. thesis, University of Queensland."},{"key":"S095679682000009X_ref14","volume-title":"Principia Mathematica, Volume I","author":"Whitehead","year":"1910"},{"key":"S095679682000009X_ref11","volume-title":"Types and Programming Languages","author":"Pierce","year":"2002"},{"key":"S095679682000009X_ref10","doi-asserted-by":"publisher","DOI":"10.1017\/S0956796800000423"}],"container-title":["Journal of Functional Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S095679682000009X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,26]],"date-time":"2026-05-26T22:36:50Z","timestamp":1779835010000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S095679682000009X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"references-count":14,"alternative-id":["S095679682000009X"],"URL":"https:\/\/doi.org\/10.1017\/s095679682000009x","relation":{},"ISSN":["0956-7968","1469-7653"],"issn-type":[{"value":"0956-7968","type":"print"},{"value":"1469-7653","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020]]},"article-number":"e7"}}