{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:07:40Z","timestamp":1763467660072},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2004,8,5]],"date-time":"2004-08-05T00:00:00Z","timestamp":1091664000000},"content-version":"unspecified","delay-in-days":4,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2004,8]]},"abstract":"<jats:p>A purely syntactic and untyped variant of Normalisation by Evaluation for the <jats:inline-formula id=\"ffm001\">$\\lambda$<\/jats:inline-formula>-calculus is presented in the framework of a two-level <jats:inline-formula id=\"ffm002\">$\\lambda$<\/jats:inline-formula>-calculus with rewrite rules to model the inverse of the evaluation functional. Among its operational properties there is a standardisation theorem that formally establishes the adequacy of implementation in functional programming languages. An example implementation in Haskell is provided. The relation to the usual type-directed Normalisation by Evaluation is highlighted, using a short analysis of <jats:inline-formula id=\"ffm003\">$\\eta$<\/jats:inline-formula>-expansion that leads to a perspicuous strong normalisation and confluence proof for <jats:inline-formula id=\"ffm004\">$\\beta\\eta\\!\\up$<\/jats:inline-formula>-reduction as a byproduct.<\/jats:p>","DOI":"10.1017\/s096012950400427x","type":"journal-article","created":{"date-parts":[[2004,10,13]],"date-time":"2004-10-13T17:31:27Z","timestamp":1097688687000},"page":"587-611","source":"Crossref","is-referenced-by-count":22,"title":["Operational aspects of untyped Normalisation by Evaluation"],"prefix":"10.1017","volume":"14","author":[{"given":"KLAUS","family":"AEHLIG","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FELIX","family":"JOACHIMSKI","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2004,8,5]]},"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S096012950400427X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,31]],"date-time":"2019-03-31T18:53:22Z","timestamp":1554058402000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S096012950400427X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,8]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,8]]}},"alternative-id":["S096012950400427X"],"URL":"https:\/\/doi.org\/10.1017\/s096012950400427x","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,8]]}}}