{"id":3598,"date":"2018-01-09T06:00:41","date_gmt":"2018-01-09T04:00:41","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3598"},"modified":"2022-03-25T20:09:32","modified_gmt":"2022-03-25T18:09:32","slug":"enumeracion-de-los-numeros-enteros","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/enumeracion-de-los-numeros-enteros\/","title":{"rendered":"Enumeraci\u00f3n de los n\u00fameros enteros"},"content":{"rendered":"<p>Definir la sucesi\u00f3n<\/p>\n<pre lang=\"text\">\n   enteros :: [Int]\n<\/pre>\n<p>tal que sus elementos son los n\u00fameros enteros comenzando en el 0 e intercalando los positivos y los negativos. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   ghci> take 23 enteros\n   [0,1,-1,2,-2,3,-3,4,-4,5,-5,6,-6,7,-7,8,-8,9,-9,10,-10,11,-11]\n<\/pre>\n<p>Comprobar con QuickCheck que el n-\u00e9simo t\u00e9rmino de la sucesi\u00f3n es<br \/>\n<code>(1-(2*n+1)*(-1)^n)\/4<\/code>.<\/p>\n<p>Nota. En la comprobaci\u00f3n usar<\/p>\n<pre lang=\"text\">\n   quickCheckWith (stdArgs {maxSize=7}) prop_enteros\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\nimport Control.Applicative ((<**>))\n\n-- 1\u00aa definici\u00f3n\nenteros :: [Int]\nenteros = 0 : concat [[n,-n] | n <- [1..]]\n\n-- 2\u00aa definici\u00f3n\nenteros2 :: [Int]\nenteros2 = 0 : [y | x <- [1..], y <- [x, -x]]\n\n-- 3\u00aa definici\u00f3n\nenteros3 :: [Int]\nenteros3 = iterate siguiente 0\n  where siguiente i | i > 0     = -i\n                    | otherwise = 1 - i\n\n-- 4\u00aa definici\u00f3n\nenteros4 :: [Int]\nenteros4 = iterate (\\i -> if i > 0 then -i else 1-i) 0\n\n-- 5\u00aa definici\u00f3n\nenteros5 :: [Int]\nenteros5 = 0 : [f x | x <- [1..], f <- [id, negate]]\n\n-- 6\u00aa definici\u00f3n\nenteros6 :: [Int]\nenteros6 = 0 : ([1..] <**> [id, negate])\n\n-- La propiedad es\nprop_enteros :: Int -> Property\nprop_enteros n = \n    n >= 0 ==> enteros !! n == (1-(2*n+1)*(-1)^n) `div` 4\n\n-- La comprobaci\u00f3n es\n--    ghci> quickCheckWith (stdArgs {maxSize=7}) prop_enteros\n--    +++ OK, passed 100 tests.\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la sucesi\u00f3n enteros :: [Int] tal que sus elementos son los n\u00fameros enteros comenzando en el 0 e intercalando los positivos y los negativos. Por ejemplo, ghci> take 23 enteros [0,1,-1,2,-2,3,-3,4,-4,5,-5,6,-6,7,-7,8,-8,9,-9,10,-10,11,-11] Comprobar con QuickCheck que el n-\u00e9simo t\u00e9rmino de la sucesi\u00f3n es (1-(2*n+1)*(-1)^n)\/4. Nota. En la comprobaci\u00f3n usar quickCheckWith (stdArgs {maxSize=7}) prop_enteros Soluciones import&#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":[5],"tags":[8,12,63,50,415,434,11,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3598"}],"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=3598"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3598\/revisions"}],"predecessor-version":[{"id":3783,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3598\/revisions\/3783"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3598"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3598"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3598"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}