{"id":8015,"date":"2023-04-07T06:00:29","date_gmt":"2023-04-07T04:00:29","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8015"},"modified":"2023-03-18T20:03:23","modified_gmt":"2023-03-18T18:03:23","slug":"07-abr-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/07-abr-23\/","title":{"rendered":"Relaciones irreflexivas"},"content":{"rendered":"<p>Usando el <a href=\"https:\/\/bit.ly\/3IVVqOT\">tipo de las relaciones binarias<\/a>, definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   irreflexiva :: Eq a => Rel a -> Bool\n<\/pre>\n<p>tal que <code>irreflexiva r<\/code> se verifica si la relaci\u00f3n <code>r<\/code> es irreflexiva; es decir, si ning\u00fan elemento de su universo est\u00e1 relacionado con \u00e9l mismo. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   irreflexiva (R ([1,2,3],[(1,2),(2,1),(2,3)]))  ==  True\n   irreflexiva (R ([1,2,3],[(1,2),(2,1),(3,3)]))  ==  False\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\">\nimport Relaciones_binarias (Rel(R))\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nirreflexiva :: Eq a => Rel a -> Bool\nirreflexiva (R (u,g)) = and [(x,x) `notElem` g | x <- u]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nirreflexiva2 :: Eq a => Rel a -> Bool\nirreflexiva2 (R(u,g)) = all (\\x -> (x,x) `notElem` g) u\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nirreflexiva3 :: Eq a => Rel a -> Bool\nirreflexiva3 (R(u,g)) = aux u\n  where aux []     = True\n        aux (x:xs) = (x,x) `notElem` g && aux xs\n\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_irreflexiva :: Rel Int -> Bool\nprop_irreflexiva r =\n  all (== irreflexiva r)\n      [irreflexiva2 r,\n       irreflexiva3 r]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_irreflexiva\n--    +++ OK, passed 100 tests.\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom typing import TypeVar\n\nfrom hypothesis import given\nfrom hypothesis import strategies as st\n\nfrom src.Relaciones_binarias import Rel, relacionArbitraria\n\nA = TypeVar('A')\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef irreflexiva(r: Rel[A]) -> bool:\n    (u, g) = r\n    return all(((x, x) not in g for x in u))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef irreflexiva2(r: Rel[A]) -> bool:\n    (u, g) = r\n    def aux(xs: list[A]) -> bool:\n        if not xs:\n            return True\n        return (xs[0], xs[0]) not in g and aux(xs[1:])\n\n    return aux(u)\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef irreflexiva3(r: Rel[A]) -> bool:\n    (u, g) = r\n    for x in u:\n        if (x, x) in g:\n            return False\n    return True\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(st.integers(min_value=0, max_value=10))\ndef test_irreflexiva(n: int) -> None:\n    r = relacionArbitraria(n)\n    res = irreflexiva(r)\n    assert irreflexiva2(r) == res\n    assert irreflexiva3(r) == res\n\n# La comprobaci\u00f3n es\n#    > poetry run pytest -q Relaciones_irreflexivas.py\n#    1 passed in 0.12s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo de las relaciones binarias, definir la funci\u00f3n irreflexiva :: Eq a => Rel a -> Bool tal que irreflexiva r se verifica si la relaci\u00f3n r es irreflexiva; es decir, si ning\u00fan elemento de su universo est\u00e1 relacionado con \u00e9l mismo. Por ejemplo, irreflexiva (R ([1,2,3],[(1,2),(2,1),(2,3)])) == True irreflexiva (R ([1,2,3],[(1,2),(2,1),(3,3)])) ==&#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":[576],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8015"}],"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=8015"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8015\/revisions"}],"predecessor-version":[{"id":8016,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8015\/revisions\/8016"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8015"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8015"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8015"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}