{"id":1955,"date":"2016-01-07T06:00:28","date_gmt":"2016-01-07T04:00:28","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1955"},"modified":"2016-01-15T07:40:48","modified_gmt":"2016-01-15T05:40:48","slug":"formula-dual","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/formula-dual\/","title":{"rendered":"F\u00f3rmula dual"},"content":{"rendered":"<p>Las f\u00f3rmulas proposicionales construidas con las constantes verdadero (\u22a4), falso (\u22a5), las variables proposicionales y las conectivas de negaci\u00f3n (\u00ac), conjunci\u00f3n (\u2227) y disyunci\u00f3n (\u2228) se pueden definir usando el siguiente tipo de datos<\/p>\n<pre lang=\"text\"> \n   data Prop = Const Bool\n             | Var Char\n             | Neg Prop\n             | Conj Prop Prop\n             | Disj Prop Prop\n             deriving (Eq, Show)\n<\/pre>\n<p>Por ejemplo, la f\u00f3rmula (A \u2227 \u22a5) \u2228 (\u22a4 \u2227 B) se representa por<\/p>\n<pre lang=\"text\"> \n   Disj (Conj (Var 'A') (Const False)) (Conj (Const True) (Var 'B'))\n<\/pre>\n<p>La f\u00f3rmula dual de una f\u00f3rmula p es la f\u00f3rmula obtenida intercambiando en p las \u2227 por \u2228 y tambi\u00e9n las \u22a4 por \u22a5. Por ejemplo, la dual de (A \u2227 \u22a5) \u2228 (\u22a4 \u2227 B) es (A \u2228 \u22a4) \u2227 (\u22a5 \u2228 B)<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\"> \n   dual :: Prop -> Prop\n<\/pre>\n<p>tal que (dual p) es la dual de p. Por ejemplo,<\/p>\n<pre lang=\"text\"> \n   \u03bb> dual (Disj (Conj (Var 'A') (Const False)) (Conj (Const True) (Var 'B')))\n   Conj (Disj (Var 'A') (Const True)) (Disj (Const False) (Var 'B'))\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\ndata Prop = Const Bool\n          | Var Char\n          | Neg Prop\n          | Conj Prop Prop\n          | Disj Prop Prop\n          deriving (Eq, Show)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\ndual1 :: Prop -> Prop\ndual1 (Const True)  = Const False\ndual1 (Const False) = Const True\ndual1 (Var x)       = Var x\ndual1 (Neg p)       = Neg  (dual1 p)\ndual1 (Conj p q)    = Disj (dual1 p) (dual1 q) \ndual1 (Disj p q)    = Conj (dual1 p) (dual1 q) \n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\ndual2 :: Prop -> Prop\ndual2 (Const b)  = Const (not b)\ndual2 (Conj p q) = Disj (dual2 p) (dual2 q)\ndual2 (Disj p q) = Conj (dual2 p) (dual2 q)\ndual2 p          = p\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Las f\u00f3rmulas proposicionales construidas con las constantes verdadero (\u22a4), falso (\u22a5), las variables proposicionales y las conectivas de negaci\u00f3n (\u00ac), conjunci\u00f3n (\u2227) y disyunci\u00f3n (\u2228) se pueden definir usando el siguiente tipo de datos data Prop = Const Bool | Var Char | Neg Prop | Conj Prop Prop | Disj Prop Prop deriving (Eq,&#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":[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\/1955"}],"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=1955"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1955\/revisions"}],"predecessor-version":[{"id":1994,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1955\/revisions\/1994"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}