{"id":762,"date":"2014-12-02T08:09:28","date_gmt":"2014-12-02T06:09:28","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=762"},"modified":"2021-04-25T17:07:26","modified_gmt":"2021-04-25T15:07:26","slug":"expresiones-aritmetica-normalizadas-1-2","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/expresiones-aritmetica-normalizadas-1-2\/","title":{"rendered":"Expresiones aritm\u00e9tica normalizadas"},"content":{"rendered":"<h4>Enunciado<\/h4>\n<pre lang=\"text\">\n-- El siguiente tipo de dato representa expresiones construidas con\n-- variables, sumas y productos\n--    data Expr = V String\n--              | S Expr Expr\n--              | P Expr Expr\n-- Por ejemplo, x*(y+z) se representa por (P (V \"x\") (S (V \"y\") (V \"z\"))) \n-- \n-- Una expresi\u00f3n es un t\u00e9rmino si es un producto de variables. Por\n-- ejemplo, x*(y*z) es un t\u00e9rmino pero x+(y*z) ni x*(y+z) lo son.\n--\n-- Una expresi\u00f3n est\u00e1 en forma normal si es una suma de t\u00e9rminos. Por\n-- ejemplo, x*(y*z) y x+(y*z) est\u00e1 en forma normal; pero x*(y+z) y\n-- (x+y)*(x+z) no lo est\u00e1n. \n-- \n-- Definir las funciones \n--    esTermino, esNormal :: Expr -> Bool\n-- tales que\n-- + (esTermino a) se verifica si a es un t\u00e9rmino. Por ejemplo,\n--      esTermino (V \"x\")                                    == True\n--      esTermino (P (V \"x\") (P (V \"y\") (V \"z\")))            == True\n--      esTermino (P (V \"x\") (S (V \"y\") (V \"z\")))            == False\n--      esTermino (S (V \"x\") (P (V \"y\") (V \"z\")))            == False\n-- + (esNormal a) se verifica si a est\u00e1 en forma normal. Por ejemplo,\n--      esNormal (V \"x\")                                     == True\n--      esNormal (P (V \"x\") (P (V \"y\") (V \"z\")))             == True\n--      esNormal (S (V \"x\") (P (V \"y\") (V \"z\")))             == True\n--      esNormal (P (V \"x\") (S (V \"y\") (V \"z\")))             == False\n--      esNormal (P (S (V \"x\") (V \"y\")) (S (V \"y\") (V \"z\"))) == False\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\ndata Expr = V String\n          | S Expr Expr\n          | P Expr Expr\n\nesTermino :: Expr -> Bool\nesTermino (V _)   = True\nesTermino (S _ _) = False\nesTermino (P a b) = esTermino a && esTermino b\n\nesNormal :: Expr -> Bool\nesNormal (S a b) = esNormal a && esNormal b\nesNormal a       = esTermino a\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Enunciado &#8212; El siguiente tipo de dato representa expresiones construidas con &#8212; variables, sumas y productos &#8212; data Expr = V String &#8212; | S Expr Expr &#8212; | P Expr Expr &#8212; Por ejemplo, x*(y+z) se representa por (P (V \u00abx\u00bb) (S (V \u00aby\u00bb) (V \u00abz\u00bb))) &#8212; &#8212; Una expresi\u00f3n es un t\u00e9rmino si&#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":[6,133],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/762"}],"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=762"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/762\/revisions"}],"predecessor-version":[{"id":870,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/762\/revisions\/870"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=762"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=762"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}