{"id":8007,"date":"2023-04-03T06:00:53","date_gmt":"2023-04-03T04:00:53","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8007"},"modified":"2023-03-11T14:51:55","modified_gmt":"2023-03-11T12:51:55","slug":"03-abr-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/03-abr-23\/","title":{"rendered":"Composici\u00f3n de relaciones binarias"},"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   composicion :: Eq a => Rel a -> Rel a -> Rel a\n<\/pre>\n<p>tal que <code>composicion r s<\/code> es la composici\u00f3n de las relaciones <code>r<\/code> y <code>s<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> composicion (R ([1,2],[(1,2),(2,2)])) (R ([1,2],[(2,1)]))\n   R ([1,2],[(1,1),(2,1)])\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\ncomposicion :: Eq a => Rel a -> Rel a -> Rel a\ncomposicion (R (u1,g1)) (R (_,g2)) =\n  R (u1,[(x,z) | (x,y) <- g1, (y',z) <- g2, y == y'])\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\ncomposicion2 :: Eq a => Rel a -> Rel a -> Rel a\ncomposicion2 (R (u1,g1)) (R (_,g2)) =\n  R (u1, aux g1)\n  where aux [] = []\n        aux ((x,y):g1') = [(x,z) | (y',z) <- g2, y == y'] ++ aux g1'\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_composicion :: Rel Int -> Rel Int -> Bool\nprop_composicion r1 r2 =\n  composicion r1 r2 == composicion2 r1 r2\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_composicion\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 composicion(r1: Rel[A], r2: Rel[A]) -> Rel[A]:\n    (u1, g1) = r1\n    (_,  g2) = r2\n    return (u1, [(x, z) for (x, y) in g1 for (u, z) in g2 if y == u])\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef composicion2(r1: Rel[A], r2: Rel[A]) -> Rel[A]:\n    (u1, g1) = r1\n    (_,  g2) = r2\n    def aux(g: list[tuple[A, A]]) -> list[tuple[A, A]]:\n        if not g:\n            return []\n        (x, y) = g[0]\n        return [(x, z) for (u, z) in g2 if y == u] + aux(g[1:])\n\n    return (u1, aux(g1))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef composicion3(r1: Rel[A], r2: Rel[A]) -> Rel[A]:\n    (u1, g1) = r1\n    (_,  g2) = r2\n    r: list[tuple[A, A]] = []\n    for (x, y) in g1:\n        r = r + [(x, z) for (u, z) in g2 if y == u]\n    return (u1, r)\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(st.integers(min_value=0, max_value=10),\n       st.integers(min_value=0, max_value=10))\ndef test_simetrica(n: int, m: int) -> None:\n    r1 = relacionArbitraria(n)\n    r2 = relacionArbitraria(m)\n    res = composicion(r1, r2)\n    assert composicion2(r1, r2) == res\n    assert composicion2(r1, r2) == res\n\n# La comprobaci\u00f3n es\n#    > poetry run pytest -q Composicion_de_relaciones_binarias_v2.py\n#    1 passed in 0.19s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo de las relaciones binarias, definir la funci\u00f3n composicion :: Eq a => Rel a -> Rel a -> Rel a tal que composicion r s es la composici\u00f3n de las relaciones r y s. Por ejemplo, \u03bb> composicion (R ([1,2],[(1,2),(2,2)])) (R ([1,2],[(2,1)])) R ([1,2],[(1,1),(2,1)]) Soluciones A continuaci\u00f3n se muestran las soluciones en&#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\/8007"}],"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=8007"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8007\/revisions"}],"predecessor-version":[{"id":8008,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8007\/revisions\/8008"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8007"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8007"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8007"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}