{"id":3245,"date":"2013-04-23T04:42:11","date_gmt":"2013-04-23T04:42:11","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=3245"},"modified":"2013-04-25T11:43:08","modified_gmt":"2013-04-25T11:43:08","slug":"resena-formalizing-knuth-bendix-orders-and-knuth-bendix-completion","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/resena-formalizing-knuth-bendix-orders-and-knuth-bendix-completion\/","title":{"rendered":"Rese\u00f1a: Formalizing Knuth-Bendix orders and Knuth-Bendix completion"},"content":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en <a href=\"http:\/\/www.cl.cam.ac.uk\/research\/hvg\/Isabelle\/index.html\">Isabelle\/HOL<\/a> sobre sistemas de reescritura titulado <a href=\"http:\/\/cl-informatik.uibk.ac.at\/users\/griff\/publications\/ST-RTA13.pdf\">Formalizing Knuth-Bendix orders and Knuth-Bendix completion<\/a>.<\/p>\n<p>Sus autores son <a href=\"http:\/\/www.jaist.ac.jp\/~c-sterna\/\">Christian Sternagel<\/a> (del Instituto japon\u00e9s de ciencias y tecnolog\u00eda) y <a href=\"http:\/\/cl-informatik.uibk.ac.at\/users\/thiemann\/\">Ren\u00e9 Thiemann<\/a> (de la Univ. de Innsbruck, Austria).<\/p>\n<p>El trabajo se presentar\u00e1 en junio en la <a href=\"http:\/\/rta2013.few.vu.nl\">RTA 2013<\/a> (24th International Conference<br \/>\non Rewriting Techniques and Applications).<\/p>\n<p>Su resumen es<\/p>\n<blockquote><p>\nWe present extensions of <a href=\"http:\/\/cl-informatik.uibk.ac.at\/software\/ceta\/\">our Isabelle Formalization of Rewriting<\/a> that cover two historically related concepts: the Knuth-Bendix order and the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Knuth%E2%80%93Bendix_completion_algorithm\">Knuth-Bendix completion procedure<\/a>. The former, besides being the first development of its kind in a proof assistant, is based on a generalized version of the Knuth-Bendix order. We compare our version to variants from the literature and show all properties required to certify termination proofs of <a href=\"http:\/\/en.wikipedia.org\/wiki\/Term_rewriting_system\">TRSs<\/a>. The latter comprises the formalization of important facts that are related to completion, like Birkhoff\u2019s theorem, the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Critical_pair_%28logic%29\">critical pair theorem<\/a>, and a soundness proof of completion, showing that the strict encompassment condition is superfluous for finite runs. As a result, we are able to certify completion proofs.\n<\/p><\/blockquote>\n<p>El c\u00f3digo con las correspondientes teor\u00edas Isabelle se encuentra en la versi\u00f3n 2.10 de <a href=\"http:\/\/cl-informatik.uibk.ac.at\/software\/ceta\/\">IsaFoR\/CeTA<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Se ha publicado un art\u00edculo de razonamiento formalizado en Isabelle\/HOL sobre sistemas de reescritura titulado Formalizing Knuth-Bendix orders and Knuth-Bendix completion. Sus autores son Christian Sternagel (del Instituto japon\u00e9s de ciencias y tecnolog\u00eda) y Ren\u00e9 Thiemann (de la Univ. de Innsbruck, Austria). El trabajo se presentar\u00e1 en junio en la RTA 2013 (24th International Conference&#8230;<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[1],"tags":[144,285],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_likes_enabled":false,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/3245"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/comments?post=3245"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/3245\/revisions"}],"predecessor-version":[{"id":3256,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/3245\/revisions\/3256"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=3245"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=3245"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=3245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}