{"id":7783,"date":"2023-01-16T06:00:09","date_gmt":"2023-01-16T04:00:09","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7783"},"modified":"2022-12-30T18:56:50","modified_gmt":"2022-12-30T16:56:50","slug":"16-ene-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/16-ene-23\/","title":{"rendered":"Expresiones aritm\u00e9ticas reducibles"},"content":{"rendered":"<p>Las expresiones aritm\u00e9ticas con variables pueden representarse usando el siguiente tipo de datos<\/p>\n<pre lang=\"text\">\n   data Expr = C Int\n             | V Char\n             | S Expr Expr\n             | P Expr Expr\n<\/pre>\n<p>Por ejemplo, la expresi\u00f3n <code>2\u00b7(a+5)<\/code> se representa por<\/p>\n<pre lang=\"text\">\n   P (C 2) (S (V 'a') (C 5))\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   reducible :: Expr -> Bool\n<\/pre>\n<p>tal que <code>reducible a<\/code> se verifica si <code>a<\/code> es una expresi\u00f3n reducible; es decir, contiene una operaci\u00f3n en la que los dos operandos son n\u00fameros. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   reducible (S (C 3) (C 4))             == True\n   reducible (S (C 3) (V 'x'))           == False\n   reducible (S (C 3) (P (C 4) (C 5)))   == True\n   reducible (S (V 'x') (P (C 4) (C 5))) == True\n   reducible (S (C 3) (P (V 'x') (C 5))) == False\n   reducible (C 3)                       == False\n   reducible (V 'x')                     == 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\">\ndata Expr = C Int\n          | V Char\n          | S Expr Expr\n          | P Expr Expr\n\nreducible :: Expr -> Bool\nreducible (C _)           = False\nreducible (V _)           = False\nreducible (S (C _) (C _)) = True\nreducible (S a b)         = reducible a || reducible b\nreducible (P (C _) (C _)) = True\nreducible (P a b)         = reducible a || reducible b\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom dataclasses import dataclass\n\n\n@dataclass\nclass Expr:\n    pass\n\n@dataclass\nclass C(Expr):\n    x: int\n\n@dataclass\nclass V(Expr):\n    x: str\n\n@dataclass\nclass S(Expr):\n    x: Expr\n    y: Expr\n\n@dataclass\nclass P(Expr):\n    x: Expr\n    y: Expr\n\ndef reducible(e: Expr) -> bool:\n    match e:\n        case C(_):\n            return False\n        case V(_):\n            return False\n        case S(C(_), C(_)):\n            return True\n        case S(a, b):\n            return reducible(a) or reducible(b)\n        case P(C(_), C(_)):\n            return True\n        case P(a, b):\n            return reducible(a) or reducible(b)\n    assert False\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Las expresiones aritm\u00e9ticas con variables pueden representarse usando el siguiente tipo de datos data Expr = C Int | V Char | S Expr Expr | P Expr Expr Por ejemplo, la expresi\u00f3n 2\u00b7(a+5) se representa por P (C 2) (S (V &#8216;a&#8217;) (C 5)) Definir la funci\u00f3n reducible :: Expr -> Bool tal que&#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":[582],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7783"}],"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=7783"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7783\/revisions"}],"predecessor-version":[{"id":7785,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7783\/revisions\/7785"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7783"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7783"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7783"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}