{"id":7537,"date":"2022-11-25T09:07:41","date_gmt":"2022-11-25T07:07:41","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7537"},"modified":"2022-12-14T11:32:51","modified_gmt":"2022-12-14T09:32:51","slug":"25-nov-22","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/25-nov-22\/","title":{"rendered":"El tipo de los n\u00fameros naturales"},"content":{"rendered":"<p>El tipo de los n\u00fameros raturales se puede definir por<\/p>\n<pre lang=\"text\">\n   data Nat = Cero | Suc Nat\n     deriving (Show, Eq)\n<\/pre>\n<p>de forma que <code>Suc (Suc (Suc Cero))<\/code> representa el n\u00famero 3.<\/p>\n<p>Definir las siguientes funciones<\/p>\n<pre lang=\"text\">\n   nat2int :: Nat -> Int\n   int2nat :: Int -> Nat\n   suma    :: Nat -> Nat -> Nat\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li><code>nat2int n<\/code> es el n\u00famero entero correspondiente al n\u00famero natural <code>n<\/code>. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     nat2int (Suc (Suc (Suc Cero)))  ==  3\n<\/pre>\n<ul>\n<li><code>int2nat n<\/code> es el n\u00famero natural correspondiente al n\u00famero entero <code>n<\/code>. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     int2nat 3  ==  Suc (Suc (Suc Cero))\n<\/pre>\n<ul>\n<li><code>suma m n<\/code> es la suma de los n\u00famero naturales <code>m<\/code> y <code>n<\/code>. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     \u03bb> suma (Suc (Suc Cero)) (Suc Cero)\n     Suc (Suc (Suc Cero))\n     \u03bb> nat2int (suma (Suc (Suc Cero)) (Suc Cero))\n     3\n     \u03bb> nat2int (suma (int2nat 2) (int2nat 1))\n     3\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 Nat = Cero | Suc Nat\n  deriving (Show, Eq)\n\nnat2int :: Nat -> Int\nnat2int Cero    = 0\nnat2int (Suc n) = 1 + nat2int n\n\nint2nat :: Int -> Nat\nint2nat 0 = Cero\nint2nat n = Suc (int2nat (n-1))\n\nsuma :: Nat -> Nat -> Nat\nsuma Cero    n = n\nsuma (Suc m) n = Suc (suma m n)\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@dataclass\nclass Nat:\n    pass\n\n@dataclass\nclass Cero(Nat):\n    pass\n\n@dataclass\nclass Suc(Nat):\n    n: Nat\n\ndef nat2int(n: Nat) -> int:\n    match n:\n        case Cero():\n            return 0\n        case Suc(n):\n            return 1 + nat2int(n)\n    assert False\n\ndef int2nat(n: int) -> Nat:\n    if n == 0:\n        return Cero()\n    return Suc(int2nat(n - 1))\n\ndef suma(m: Nat, n: Nat) -> Nat:\n    match m:\n        case Cero():\n            return n\n        case Suc(m):\n            return Suc(suma(m, n))\n    assert False\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El tipo de los n\u00fameros raturales se puede definir por data Nat = Cero | Suc Nat deriving (Show, Eq) de forma que Suc (Suc (Suc Cero)) representa el n\u00famero 3. Definir las siguientes funciones nat2int :: Nat -> Int int2nat :: Int -> Nat suma :: Nat -> Nat -> Nat tales que nat2int&#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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7537"}],"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=7537"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7537\/revisions"}],"predecessor-version":[{"id":7640,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7537\/revisions\/7640"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7537"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7537"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7537"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}