{"id":8000,"date":"2023-03-30T06:00:47","date_gmt":"2023-03-30T04:00:47","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8000"},"modified":"2023-03-09T13:31:27","modified_gmt":"2023-03-09T11:31:27","slug":"30-mar-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/30-mar-23\/","title":{"rendered":"Relaciones reflexivas"},"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   reflexiva :: Eq a => Rel a -> Bool\n<\/pre>\n<p>tal que <code>reflexiva r<\/code> se verifica si la relaci\u00f3n <code>r<\/code> es reflexiva. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   reflexiva (R ([1,3],[(1,1),(1,3),(3,3)]))    ==  True\n   reflexiva (R ([1,2,3],[(1,1),(1,3),(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\">\nmodule Relaciones_reflexivas where\n\nimport Relaciones_binarias (Rel(R))\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nreflexiva :: Eq a => Rel a -> Bool\nreflexiva (R ([], _))   = True\nreflexiva (R (x:xs, ps)) = (x, x) `elem` ps && reflexiva  (R (xs, ps))\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nreflexiva2 :: Eq a => Rel a -> Bool\nreflexiva2 (R (us,ps)) = and [(x,x) `elem` ps | x <- us]\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nreflexiva3 :: Eq a => Rel a -> Bool\nreflexiva3 (R (us,ps)) = all (`elem` ps) [(x,x) | x <- us]\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nreflexiva4 :: Eq a => Rel a -> Bool\nreflexiva4 (R (us,ps)) = all (\\x -> (x,x) `elem` ps) us\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_reflexiva :: Rel Int -> Bool\nprop_reflexiva r =\n  all (== reflexiva r)\n      [reflexiva2 r,\n       reflexiva3 r,\n       reflexiva4 r]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_reflexiva\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 random import choice, randint, sample\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 reflexiva(r: Rel[A]) -> bool:\n    (us, ps) = r\n    if not us:\n        return True\n    return (us[0], us[0]) in ps and reflexiva((us[1:], ps))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef reflexiva2(r: Rel[A]) -> bool:\n    (us, ps) = r\n    return all(((x,x) in ps for x in us))\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef reflexiva3(r: Rel[A]) -> bool:\n    (us, ps) = r\n    for x in us:\n        if (x, x) not in ps:\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_reflexiva(n: int) -> None:\n    r = relacionArbitraria(n)\n    res = reflexiva(r)\n    assert reflexiva2(r) == res\n    assert reflexiva3(r) == res\n\n# La comprobaci\u00f3n es\n#    > poetry run pytest -q Relaciones_reflexivas.py\n#    1 passed in 0.41s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo de las relaciones binarias, definir la funci\u00f3n reflexiva :: Eq a => Rel a -> Bool tal que reflexiva r se verifica si la relaci\u00f3n r es reflexiva. Por ejemplo, reflexiva (R ([1,3],[(1,1),(1,3),(3,3)])) == True reflexiva (R ([1,2,3],[(1,1),(1,3),(3,3)])) == False Soluciones A continuaci\u00f3n se muestran las soluciones en Haskell y las soluciones&#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\/8000"}],"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=8000"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8000\/revisions"}],"predecessor-version":[{"id":8002,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8000\/revisions\/8002"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8000"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8000"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8000"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}