{"id":2028,"date":"2016-01-26T06:00:21","date_gmt":"2016-01-26T04:00:21","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2028"},"modified":"2016-02-02T07:03:00","modified_gmt":"2016-02-02T05:03:00","slug":"conjunto-de-funciones","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/conjunto-de-funciones\/","title":{"rendered":"Conjunto de funciones"},"content":{"rendered":"<p>Una funci\u00f3n f entre dos conjuntos A e B se puede representar mediante una lista de pares de AxB tales que para cada elemento a de A existe un \u00fanico elemento b de B tal que (a,b) pertenece a f. Por ejemplo,<\/p>\n<ul>\n<li>[(1,2),(3,6)] es una funci\u00f3n de [1,3] en [2,4,6];<\/li>\n<li>[(1,2)] no es una funci\u00f3n de [1,3] en [2,4,6], porque no tiene ning\u00fan par cuyo primer elemento sea igual a 3;<\/li>\n<li>[(1,2),(3,6),(1,4)] no es una funci\u00f3n porque hay dos pares distintos cuya primer elemento es 1.<\/li>\n<\/ul>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   funciones :: [a] -> [a] -> [[(a,a)]]\n<\/pre>\n<p>tal que (funciones xs ys) es el conjunto de las funciones de xs en ys. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> funciones [] [2,4,6]\n   [[]]\n   \u03bb> funciones [3] [2,4,6]\n   [[(3,2)],[(3,4)],[(3,6)]]\n   \u03bb> funciones [1,3] [2,4,6]\n   [[(1,2),(3,2)], [(1,2),(3,4)], [(1,2),(3,6)], [(1,4),(3,2)], [(1,4),(3,4)],\n    [(1,4),(3,6)], [(1,6),(3,2)], [(1,6),(3,4)], [(1,6),(3,6)]]\n<\/pre>\n<p>Comprobar con QuickCheck que si xs es un conjunto con n elementos e ys un conjunto con m elementos, entonces (funciones xs ys) tiene m^n elementos.<\/p>\n<p>Nota. Al hacer la comprobaci\u00f3n limitar el tama\u00f1o de las pruebas como se indica a continuaci\u00f3n<\/p>\n<pre lang=\"text\">\n   \u03bb> quickCheckWith (stdArgs {maxSize=7}) prop_funciones\n   +++ OK, passed 100 tests.\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\nfunciones :: [a] -> [a] -> [[(a,a)]]\nfunciones [] _      = [[]]\nfunciones (x:xs) ys = [((x,y):f) | y <- ys, f <- fs]\n    where fs = funciones xs ys\n\nprop_funciones :: [Int] -> [Int] -> Bool\nprop_funciones xs ys =\n    length (funciones xs ys) == (length ys)^(length xs)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Una funci\u00f3n f entre dos conjuntos A e B se puede representar mediante una lista de pares de AxB tales que para cada elemento a de A existe un \u00fanico elemento b de B tal que (a,b) pertenece a f. Por ejemplo, [(1,2),(3,6)] es una funci\u00f3n de [1,3] en [2,4,6]; [(1,2)] no es una funci\u00f3n&#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":[4],"tags":[6,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2028"}],"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=2028"}],"version-history":[{"count":7,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2028\/revisions"}],"predecessor-version":[{"id":2071,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2028\/revisions\/2071"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2028"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2028"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2028"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}