{"id":7789,"date":"2023-01-18T06:00:58","date_gmt":"2023-01-18T04:00:58","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7789"},"modified":"2022-12-31T12:55:22","modified_gmt":"2022-12-31T10:55:22","slug":"18-ene-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/18-ene-23\/","title":{"rendered":"Valor de expresiones aritm\u00e9ticas generales"},"content":{"rendered":"<p>Las operaciones de suma, resta y  multiplicaci\u00f3n se pueden representar mediante el siguiente tipo de datos<\/p>\n<pre lang=\"text\">\n   data Op = S | R | M\n<\/pre>\n<p>La expresiones aritm\u00e9ticas con dichas operaciones se pueden representar mediante el siguiente tipo de dato algebraico<\/p>\n<pre lang=\"text\">\n   data Expr = C Int\n             | A Op Expr Expr\n<\/pre>\n<p>Por ejemplo, la expresi\u00f3n<\/p>\n<pre lang=\"text\">\n   (7-3)+(2*5)\n<\/pre>\n<p>se representa por<\/p>\n<pre lang=\"text\">\n   A S (A R (C 7) (C 3)) (A M (C 2) (C 5))\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   valor :: Expr -> Int\n<\/pre>\n<p>tal que <code>valor e<\/code> es el valor de la expresi\u00f3n <code>e<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   valor (A S (A R (C 7) (C 3)) (A M (C 2) (C 5)))  ==  14\n   valor (A M (A R (C 7) (C 3)) (A S (C 2) (C 5)))  ==  28\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 Op = S | R | M\n\ndata Expr = C Int\n          | A Op Expr Expr\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nvalor :: Expr -> Int\nvalor (C x)      = x\nvalor (A o e1 e2) = aplica o (valor e1) (valor e2)\n  where aplica :: Op -> Int -> Int -> Int\n        aplica S x y = x+y\n        aplica R x y = x-y\n        aplica M x y = x*y\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nvalor2 :: Expr -> Int\nvalor2 (C n)    = n\nvalor2 (A o x y) = sig o (valor2 x) (valor2 y)\n  where sig :: Op -> Int -> Int -> Int\n        sig S = (+)\n        sig M = (*)\n        sig R = (-)\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom dataclasses import dataclass\nfrom enum import Enum\n\nOp = Enum('Op', ['S', 'R', 'M'])\n\n@dataclass\nclass Expr:\n    pass\n\n@dataclass\nclass C(Expr):\n    x: int\n\n@dataclass\nclass A(Expr):\n    o: Op\n    x: Expr\n    y: Expr\n\ndef aplica(o: Op, x: int, y: int) -> int:\n    match o:\n        case Op.S:\n            return x + y\n        case Op.R:\n            return x - y\n        case Op.M:\n            return x * y\n    assert False\n\ndef valor(e: Expr) -> int:\n    match e:\n        case C(x):\n            return x\n        case A(o, e1, e2):\n            return aplica(o, valor(e1), valor(e2))\n    assert False\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Las operaciones de suma, resta y multiplicaci\u00f3n se pueden representar mediante el siguiente tipo de datos data Op = S | R | M La expresiones aritm\u00e9ticas con dichas operaciones se pueden representar mediante el siguiente tipo de dato algebraico data Expr = C Int | A Op Expr Expr Por ejemplo, la expresi\u00f3n (7-3)+(2*5)&#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\/7789"}],"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=7789"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7789\/revisions"}],"predecessor-version":[{"id":7791,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7789\/revisions\/7791"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}