{"id":2057,"date":"2012-05-30T06:54:00","date_gmt":"2012-05-30T06:54:00","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/?p=2057"},"modified":"2013-03-08T05:48:15","modified_gmt":"2013-03-08T05:48:15","slug":"wave-equation-numerical-resolution-a-comprehensive-mechanized-proof-of-a-c-program","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wave-equation-numerical-resolution-a-comprehensive-mechanized-proof-of-a-c-program\/","title":{"rendered":"Wave equation numerical resolution: a comprehensive mechanized proof of a C program"},"content":{"rendered":"<p>Se ha publicado un nuevo art\u00edculo de formalizaci\u00f3n en Coq: <a href=\"http:\/\/www-lipn.univ-paris13.fr\/~mayero\/publis\/JARFOST2012.pdf\">Wave equation numerical resolution: a comprehensive mechanized proof of a C program<\/a>.<\/p>\n<p>Sus autores son Sylvie Boldo, Fran\u00e7ois Cl\u00e9ment, Jean-Christophe Filli\u00e2tre, Micaela Mayero, Guillaume Melquiond y Pierre Weis.<\/p>\n<p>El resumen del art\u00edculo es <\/p>\n<blockquote><p>\nWe formally prove correct a C program that implements a numerical scheme for the resolution of the one-dimensional acoustic wave equation. Such an implementation introduces errors at several levels: the numerical scheme introduces method errors, and floating-point computations lead to round-off errors. We annotate this C program to specify both method error and round-off error. We use Frama-C to generate theorems that guarantee the soundness of the code. We discharge these theorems using SMT solvers, Gappa, and Coq. This involves a large Coq development to prove the adequacy of the C program to the numerical scheme and to bound errors. To our knowledge, this is the first time such a numerical analysis program is fully machine-checked.\n<\/p><\/blockquote>\n<p>El c\u00f3digo correspondiente se encuentra en <a href=\"http:\/\/fost.saclay.inria.fr\/wave_total_error.html\">http:\/\/fost.saclay.inria.fr\/wave_total_error.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Se ha publicado un nuevo art\u00edculo de formalizaci\u00f3n en Coq: Wave equation numerical resolution: a comprehensive mechanized proof of a C program. Sus autores son Sylvie Boldo, Fran\u00e7ois Cl\u00e9ment, Jean-Christophe Filli\u00e2tre, Micaela Mayero, Guillaume Melquiond y Pierre Weis. El resumen del art\u00edculo es We formally prove correct a C program that implements a numerical scheme&#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":[100,1],"tags":[45,285],"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\/2057"}],"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=2057"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/2057\/revisions"}],"predecessor-version":[{"id":2814,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/posts\/2057\/revisions\/2814"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/media?parent=2057"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/categories?post=2057"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/vestigium\/wp-json\/wp\/v2\/tags?post=2057"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}