{"id":7781,"date":"2023-01-13T07:00:57","date_gmt":"2023-01-13T05:00:57","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7781"},"modified":"2022-12-30T18:20:11","modified_gmt":"2022-12-30T16:20:11","slug":"13-ene-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/13-ene-23\/","title":{"rendered":"Sustituci\u00f3n en una expresi\u00f3n aritm\u00e9tica"},"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     deriving (Eq, Show)\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   sustitucion :: Expr -> [(Char, Int)] -> Expr\n<\/pre>\n<p>tal que <code>sustitucion e s<\/code> es la expresi\u00f3n obtenida sustituyendo las variables de la expresi\u00f3n <code>e<\/code> seg\u00fan se indica en la sustituci\u00f3n <code>s<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> sustitucion (P (V 'z') (S (C 3) (V 'x'))) [('x',7),('z',9)]\n   P (C 9) (S (C 3) (C 7))\n   \u03bb> sustitucion (P (V 'z') (S (C 3) (V 'y'))) [('x',7),('z',9)]\n   P (C 9) (S (C 3) (V 'y'))\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  deriving (Eq, Show)\n\nsustitucion :: Expr -> [(Char, Int)] -> Expr\nsustitucion e []          = e\nsustitucion (V c) ((d,n):ps)\n  | c == d                = C n\n  | otherwise             = sustitucion (V c) ps\nsustitucion (C n) _      = C n\nsustitucion (S e1 e2) ps = S (sustitucion e1 ps) (sustitucion e2 ps)\nsustitucion (P e1 e2) ps = P (sustitucion e1 ps) (sustitucion e2 ps)\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 sustitucion(e: Expr, ps: list[tuple[str, int]]) -> Expr:\n    match (e, ps):\n        case(e, []):\n            return e\n        case (V(c), ps):\n            if c == ps[0][0]:\n                return C(ps[0][1])\n            return sustitucion(V(c), ps[1:])\n        case (C(n), _):\n            return C(n)\n        case (S(e1, e2), ps):\n            return S(sustitucion(e1, ps), sustitucion(e2, ps))\n        case (P(e1, e2), ps):\n            return P(sustitucion(e1, ps), sustitucion(e2, ps))\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 deriving (Eq, Show) 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 sustitucion :: Expr ->&#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\/7781"}],"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=7781"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7781\/revisions"}],"predecessor-version":[{"id":7782,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7781\/revisions\/7782"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7781"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7781"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7781"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}