{"id":8017,"date":"2023-04-06T06:00:33","date_gmt":"2023-04-06T04:00:33","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8017"},"modified":"2023-03-18T20:17:27","modified_gmt":"2023-03-18T18:17:27","slug":"06-abr-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/06-abr-23\/","title":{"rendered":"Relaciones de equivalencia"},"content":{"rendered":"<p>Usando el <a href=\"https:\/\/bit.ly\/3IVVqOT\">tipo de las relaciones binarias<\/a>, definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   esEquivalencia :: Ord a => Rel a -> Bool\n<\/pre>\n<p>tal que <code>esEquivalencia r<\/code> se verifica si la relaci\u00f3n <code>r<\/code> es de equivalencia. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> esEquivalencia (R ([1,3,5],[(1,1),(1,3),(3,1),(3,3),(5,5)]))\n   True\n   \u03bb> esEquivalencia (R ([1,2,3,5],[(1,1),(1,3),(3,1),(3,3),(5,5)]))\n   False\n   \u03bb> esEquivalencia (R ([1,3,5],[(1,1),(1,3),(3,3),(5,5)]))\n   False\n<\/pre>\n<p><b>Soluciones<\/b><\/p>\n<p>A continuaci\u00f3n se muestran las <a href=\"#haskell\">soluciones en Haskell<\/a> y las <a href=\"#python\">soluciones en Python<\/a>.<\/p>\n<p><a name=\"haskell\"><\/a><br \/>\n<b>Soluciones en Haskell<\/b><\/p>\n<pre lang=\"haskell\">\nimport Relaciones_binarias (Rel(R))\nimport Relaciones_reflexivas (reflexiva)\nimport Relaciones_simetricas (simetrica)\nimport Relaciones_transitivas (transitiva)\n\nesEquivalencia :: Ord a => Rel a -> Bool\nesEquivalencia r = reflexiva r && simetrica r && transitiva r\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom typing import TypeVar\n\nfrom src.Relaciones_binarias import Rel, relacionArbitraria\nfrom src.Relaciones_reflexivas import reflexiva\nfrom src.Relaciones_simetricas import simetrica\nfrom src.Relaciones_transitivas import transitiva\n\nA = TypeVar('A')\n\ndef esEquivalencia(r: Rel[A]) -> bool:\n    return reflexiva(r) and simetrica(r) and transitiva(r)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo de las relaciones binarias, definir la funci\u00f3n esEquivalencia :: Ord a => Rel a -> Bool tal que esEquivalencia r se verifica si la relaci\u00f3n r es de equivalencia. Por ejemplo, \u03bb> esEquivalencia (R ([1,3,5],[(1,1),(1,3),(3,1),(3,3),(5,5)])) True \u03bb> esEquivalencia (R ([1,2,3,5],[(1,1),(1,3),(3,1),(3,3),(5,5)])) False \u03bb> esEquivalencia (R ([1,3,5],[(1,1),(1,3),(3,3),(5,5)])) False Soluciones A continuaci\u00f3n se muestran las&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","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":[581],"tags":[576],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8017"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=8017"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8017\/revisions"}],"predecessor-version":[{"id":8018,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8017\/revisions\/8018"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}