{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T04:10:54Z","timestamp":1751429454518,"version":"3.41.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","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":[[2011,2]]},"abstract":"<jats:p> We use the technique of interactive theorem proving to develop the theory and an enumeration technique for finite idempotent relations. Starting from a short mathematical characterization of finite idempotents defined and proved in Isabelle\/HOL, we derive first an iterative procedure to generate all instances of idempotents over a finite set. From there, we develop a more precise theoretical characterization giving rise to an efficient predicate that can be executed in the programming language ML. Idempotent relations represent a very basic, general mathematical concept but the steps taken to develop their theory with the help of Isabelle\/HOL are representative for developing algorithms from a mathematical specification. <\/jats:p>","DOI":"10.3233\/fi-2011-392","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T04:33:30Z","timestamp":1575347610000},"page":"43-65","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Mechanical Analysis of Finite Idempotent Relations"],"prefix":"10.1177","volume":"107","author":[{"given":"Florian","family":"Kamm\u00fcller","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Softwaretechnik und Theoretische Informatik, Technische Universit\u00e4t Berlin, and Middlesex University, The Borroughs, NW4 4BT, London UK. flokam@cs.tu-berlin.de"}]}],"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-2011-392","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2011-392","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:52:18Z","timestamp":1751367138000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2011-392"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,2]]}},"alternative-id":["10.3233\/FI-2011-392"],"URL":"https:\/\/doi.org\/10.3233\/fi-2011-392","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"type":"print","value":"0169-2968"},{"type":"electronic","value":"1875-8681"}],"subject":[],"published":{"date-parts":[[2011,1,1]]}}}