El siguiente tipo de dato algebraico representa las expresiones booleanas construidas con una variable (X), las constantes verdadera (V) y falsa (F), la negaci\u00f3n (Neg) y la disyunci\u00f3n (Dis):<\/p>\n
\n data Expr = X\n | V\n | F\n | Neg Expr\n | Dis Expr Expr\n deriving (Eq, Ord, Show)\n<\/pre>\nPor ejemplo, la expresi\u00f3n (\u00acX v V) se representa por (Dis (Neg X) V).<\/p>\n
Definir las funciones<\/p>\n
\n valor :: Expr -> Bool -> Bool \n simplifica :: Expr -> Expr\n<\/pre>\ntales que (valor p i) es el valor de la expresi\u00f3n p cuando se le asigna a X el valor i. Por ejemplo,<\/p>\n
\n valor (Neg X) True == False\n valor (Neg F) True == True\n valor (Dis X (Neg X)) True == True\n valor (Dis X (Neg X)) False == True\n<\/pre>\ny (simplifica p) es la expresi\u00f3n obtenida aplic\u00e1ndole a p las siguientes reglas de simplificaci\u00f3n:<\/p>\n
\n Neg V = F\n Neg F = V\n Neg (Neg q) = q\n Dis V q = V\n Dis F q = q\n Dis q V = V\n Dis q F = F\n Dis q q = q\n<\/pre>\nPor ejemplo,<\/p>\n
\n simplifica (Dis X (Neg (Neg X))) == X\n simplifica (Neg (Dis (Neg (Neg X)) F)) == Neg X\n simplifica (Dis (Neg F) F) == V\n simplifica (Dis (Neg V) (Neg (Dis (Neg X) F))) == X\n simplifica (Dis (Neg V) (Neg (Dis (Neg (Neg X)) F))) == Neg X\n<\/pre>\nComprobar con QuickCheck que para cualquier expresi\u00f3n p y cualquier booleano i se verifica que (valor (simplifica p) i) es igual a (valor p i).<\/p>\n
Nota<\/strong>: Escribir las soluciones usando la siguiente plantilla que contiene un generador de expresiones booleanas<\/p>\n\nimport Test.QuickCheck\nimport Control.Monad \n\ndata Expr = X\n | V\n | F\n | Neg Expr\n | Dis Expr Expr\n deriving (Eq, Ord, Show)\n\nvalor :: Expr -> Bool -> Bool \nvalor = undefined\n\nsimplifica :: Expr -> Expr\nsimplifica = undefined\n\n-- La propiedad es\nprop_simplifica :: Expr -> Bool -> Bool\nprop_simplifica p i = undefined\n\n-- La comprobaci\u00f3n es\n\n-- Generador de expresi\u00f3ns\ninstance Arbitrary Expr where\n arbitrary = sized expr\n where expr n | n <= 0 = atom\n | otherwise = oneof [ atom\n , liftM Neg subexpr\n , liftM2 Dis subexpr subexpr ]\n where atom = oneof [elements [X,V,F]]\n subexpr = expr (n `div` 2)\n<\/pre>\nSoluciones<\/h4>\n\nimport Test.QuickCheck\nimport Control.Monad \n\ndata Expr = X\n | V\n | F\n | Neg Expr\n | Dis Expr Expr\n deriving (Eq, Ord, Show)\n\nvalor :: Expr -> Bool -> Bool \nvalor X i = i\nvalor V _ = True\nvalor F _ = False\nvalor (Neg p) i = not (valor p i)\nvalor (Dis p q) i = valor p i || valor q i\n\nsimplifica :: Expr -> Expr\nsimplifica X = X\nsimplifica V = V\nsimplifica F = F\nsimplifica (Neg p) = negacion (simplifica p)\n where negacion V = F\n negacion F = V\n negacion (Neg p) = p\n negacion p = Neg p\nsimplifica (Dis p q) = disyuncion (simplifica p) (simplifica q)\n where disyuncion V q = V\n disyuncion F q = q\n disyuncion q V = V\n disyuncion q F = q\n disyuncion p q | p == q = p\n | otherwise = Dis p q\n\n-- La propiedad es\nprop_simplifica :: Expr -> Bool -> Bool\nprop_simplifica p i =\n valor (simplifica p) i == valor p i\n\n-- La comprobaci\u00f3n es\n-- ghci> quickCheck prop_simplifica\n-- +++ OK, passed 100 tests.\n\n-- Generador de expresiones\ninstance Arbitrary Expr where\n arbitrary = sized expr\n where expr n | n <= 0 = atom\n | otherwise = oneof [ atom\n , liftM Neg subexpr\n , liftM2 Dis subexpr subexpr ]\n where atom = oneof [elements [X,V,F]]\n subexpr = expr (n `div` 2)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"El siguiente tipo de dato algebraico representa las expresiones booleanas construidas con una variable (X), las constantes verdadera (V) y falsa (F), la negaci\u00f3n (Neg) y la disyunci\u00f3n (Dis): data Expr = X | V | F | Neg Expr | Dis Expr Expr deriving (Eq, Ord, Show) Por ejemplo, la expresi\u00f3n (\u00acX v V)…<\/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":[7],"tags":[6,146,133],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/899"}],"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=899"}],"version-history":[{"count":7,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/899\/revisions"}],"predecessor-version":[{"id":1379,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/899\/revisions\/1379"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=899"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=899"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}