{"id":8029,"date":"2023-04-13T06:00:00","date_gmt":"2023-04-13T04:00:00","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8029"},"modified":"2023-03-30T10:47:12","modified_gmt":"2023-03-30T08:47:12","slug":"13-abr-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/13-abr-23\/","title":{"rendered":"Clausura sim\u00e9trica"},"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   clausuraSimetrica :: Eq a => Rel a -> Rel a\n<\/pre>\n<p>tal que <code>clausuraSimetrica r<\/code> es la clausura sim\u00e9trica de <code>r<\/code>; es decir, la menor relaci\u00f3n sim\u00e9trica que contiene a r. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> clausuraSimetrica (R ([1,3,5],[(1,1),(3,1),(1,5)]))\n   R ([1,3,5],[(1,1),(3,1),(1,5),(1,3),(5,1)])\n<\/pre>\n<p>Comprobar con QuickCheck que clausuraSimetrica es sim\u00e9trica.<\/p>\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 Data.List (union)\nimport Relaciones_simetricas (simetrica)\nimport Test.QuickCheck\n\nclausuraSimetrica :: Eq a => Rel a -> Rel a\nclausuraSimetrica (R (u,g)) =\n  R (u, g `union` [(y,x) | (x,y) <- g])\n\n-- La propiedad es\nprop_ClausuraSimetrica :: Rel Int -> Bool\nprop_ClausuraSimetrica r =\n  simetrica (clausuraSimetrica r)\n\n-- La funci\u00f3n simetrica est\u00e1 definida en el ejercicio\n-- \"Relaciones sim\u00e9tricas\" que se encuentra en\n-- https:\/\/bit.ly\/3zlO2rH\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_ClausuraSimetrica\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\nfrom src.Relaciones_simetricas import simetrica\n\nA = TypeVar('A')\n\ndef clausuraSimetrica(r: Rel[A]) -> Rel[A]:\n    (u, g) = r\n    return (u, list(set(g) | {(y, x) for (x,y) in g}))\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    assert simetrica(clausuraSimetrica(r))\n\n# La funci\u00f3n simetrica est\u00e1 definida en el ejercicio\n# \"Relaciones sim\u00e9tricas\" que se encuentra en\n# https:\/\/bit.ly\/3zlO2rH\n\n# La comprobaci\u00f3n es\n#    > poetry run pytest -q Clausura_simetrica.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 clausuraSimetrica :: Eq a => Rel a -> Rel a tal que clausuraSimetrica r es la clausura sim\u00e9trica de r; es decir, la menor relaci\u00f3n sim\u00e9trica que contiene a r. Por ejemplo, \u03bb> clausuraSimetrica (R ([1,3,5],[(1,1),(3,1),(1,5)])) R ([1,3,5],[(1,1),(3,1),(1,5),(1,3),(5,1)]) Comprobar con QuickCheck que clausuraSimetrica es sim\u00e9trica&#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\/8029"}],"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=8029"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8029\/revisions"}],"predecessor-version":[{"id":8030,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8029\/revisions\/8030"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8029"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8029"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8029"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}