{"id":7990,"date":"2023-03-29T06:00:41","date_gmt":"2023-03-29T04:00:41","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7990"},"modified":"2023-03-06T13:23:57","modified_gmt":"2023-03-06T11:23:57","slug":"29-mar-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/29-mar-23\/","title":{"rendered":"Universo y grafo de una relaci\u00f3n binaria"},"content":{"rendered":"<p>Usando el <a href=\"https:\/\/bit.ly\/3IVVqOT\">tipo de las relaciones binarias<\/a>, definir las funciones<\/p>\n<pre lang=\"text\">\n   universo :: Eq a => Rel a -> [a]\n   grafo    :: Eq a => ([a],[(a,a)]) -> [(a,a)]\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li><code>universo r<\/code> es el universo de la relaci\u00f3n <code>r<\/code>. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     \u03bb> r = R ([1, 3],[(3, 1), (3, 3)])\n     \u03bb> universo r\n     [1,3]\n<\/pre>\n<ul>\n<li><code>grafo r<\/code> es el grafo de la relaci\u00f3n r. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     \u03bb> grafo r\n     [(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\n\nuniverso :: Eq a => Rel a -> [a]\nuniverso (R (u,_)) = u\n\ngrafo :: Eq a => Rel a -> [(a,a)]\ngrafo (R (_,g)) = g\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\nA = TypeVar('A')\n\nRel = tuple[list[A], list[tuple[A, A]]]\n\ndef universo(r: Rel[A]) -> list[A]:\n    return r[0]\n\ndef grafo(r: Rel[A]) -> list[tuple[A, A]]:\n    return r[1]\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo de las relaciones binarias, definir las funciones universo :: Eq a => Rel a -> [a] grafo :: Eq a => ([a],[(a,a)]) -> [(a,a)] tales que universo r es el universo de la relaci\u00f3n r. Por ejemplo, \u03bb> r = R ([1, 3],[(3, 1), (3, 3)]) \u03bb> universo r [1,3] grafo r&#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\/7990"}],"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=7990"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7990\/revisions"}],"predecessor-version":[{"id":7999,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7990\/revisions\/7999"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7990"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7990"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7990"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}