{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:25:39Z","timestamp":1761611139683},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[1995,9]]},"abstract":"<jats:p> Nonstandard analysis has been put to use in a theorem-prover, where it assists in the analysis of formulae involving limits. The theorem-prover in question is used in the computer program Mathpert to ensure the correctness of calculations in calculus. Although non-standard analysis is widely viewed as non-constructive, it can alternately be viewed as a method of reducing logical manipulation (of formulae with quantifiers) to computation (with rewrite rules). We give a logical theory of nonstandard analysis which is implemented in Mathpert. We describe a procedure for \u201celimination of infinitesimals\u201d (also implemented in Mathpert) and prove its correctness. <\/jats:p>","DOI":"10.1142\/s0129054195000172","type":"journal-article","created":{"date-parts":[[2004,11,12]],"date-time":"2004-11-12T11:59:25Z","timestamp":1100260765000},"page":"299-338","source":"Crossref","is-referenced-by-count":9,"title":["USING NONSTANDARD ANALYSIS TO ENSURE THE CORRECTNESS OF SYMBOLIC COMPUTATIONS"],"prefix":"10.1142","volume":"06","author":[{"given":"MICHAEL","family":"BEESON","sequence":"first","affiliation":[{"name":"Department of Mathematics, and Computer Science, San Jose State University, San Jose, California 95192, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054195000172","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:44:01Z","timestamp":1565138641000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054195000172"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,9]]},"references-count":0,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1995,9]]}},"alternative-id":["10.1142\/S0129054195000172"],"URL":"https:\/\/doi.org\/10.1142\/s0129054195000172","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,9]]}}}