{"id":8026,"date":"2023-04-12T06:00:27","date_gmt":"2023-04-12T04:00:27","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8026"},"modified":"2023-03-29T16:51:35","modified_gmt":"2023-03-29T14:51:35","slug":"12-abr-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/12-abr-23\/","title":{"rendered":"Clausura reflexiva"},"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   clausuraReflexiva :: Eq a => Rel a -> Rel a\n<\/pre>\n<p>tal que <code>clausuraReflexiva r<\/code> es la clausura reflexiva de <code>r<\/code>; es decir, la menor relaci\u00f3n reflexiva que contiene a r. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> clausuraReflexiva (R ([1,3],[(1,1),(3,1)]))\n   R ([1,3],[(1,1),(3,1),(3,3)])\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 Data.List (union)\nimport Test.QuickCheck (quickCheck)\n\nclausuraReflexiva :: Eq a => Rel a -> Rel a\nclausuraReflexiva (R (u,g)) =\n  R (u, g `union` [(x,x) | x <- u])\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\n\nA = TypeVar('A')\n\ndef clausuraReflexiva(r: Rel[A]) -> Rel[A]:\n    (u, g) = r\n    return (u, list(set(g) | {(x, x) for x in u}))\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo de las relaciones binarias, definir la funci\u00f3n clausuraReflexiva :: Eq a => Rel a -> Rel a tal que clausuraReflexiva r es la clausura reflexiva de r; es decir, la menor relaci\u00f3n reflexiva que contiene a r. Por ejemplo, \u03bb> clausuraReflexiva (R ([1,3],[(1,1),(3,1)])) R ([1,3],[(1,1),(3,1),(3,3)]) Soluciones A continuaci\u00f3n se muestran las soluciones&#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\/8026"}],"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=8026"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8026\/revisions"}],"predecessor-version":[{"id":8027,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8026\/revisions\/8027"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8026"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8026"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8026"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}