{"id":7963,"date":"2023-03-23T06:00:34","date_gmt":"2023-03-23T04:00:34","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7963"},"modified":"2023-02-22T20:48:28","modified_gmt":"2023-02-22T18:48:28","slug":"23-mar-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/23-mar-23\/","title":{"rendered":"TAD de los conjuntos: Todos los elementos verifican una propiedad"},"content":{"rendered":"<p>Utilizando el <a href=\"https:\/\/bit.ly\/3HbB7fo\">tipo abstracto de datos de los conjuntos<\/a> definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   todos :: Ord a => (a -> Bool) -> Conj a -> Bool\n<\/pre>\n<p>tal que <code>todos p c<\/code> se verifica si todos los elemsntos de <code>c<\/code> verifican el predicado <code>p<\/code>.  Por ejemplo,<\/p>\n<pre lang=\"text\">\n   todos even (inserta 4 (inserta 6 vacio))  ==  True\n   todos even (inserta 4 (inserta 7 vacio))  ==  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 TAD.Conjunto (Conj, vacio, inserta, esVacio, menor, elimina)\nimport TAD_Transformaciones_conjuntos_listas (conjuntoAlista, listaAconjunto)\nimport Test.QuickCheck.HigherOrder\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\ntodos :: Ord a => (a -> Bool) -> Conj a -> Bool\ntodos p c\n  | esVacio c = True\n  | otherwise = p mc && todos p rc\n  where mc = menor c\n        rc = elimina mc c\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\ntodos2 :: Ord a => (a -> Bool) -> Conj a -> Bool\ntodos2 p c = all p (conjuntoAlista c)\n\n-- La funci\u00f3n conjuntoAlista est\u00e1 definida en el ejercicio\n-- \"Transformaciones entre conjuntos y listas\" que se encuentra\n-- en https:\/\/bit.ly\/3RexzxH\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_todos :: (Int -> Bool) -> [Int] -> Bool\nprop_todos p xs =\n  todos p c == todos2 p c\n  where c = listaAconjunto xs\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck' prop_todos\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 __future__ import annotations\n\nfrom abc import abstractmethod\nfrom copy import deepcopy\nfrom typing import Callable, Protocol, TypeVar\n\nfrom hypothesis import given\n\nfrom src.TAD.conjunto import (Conj, conjuntoAleatorio, elimina, esVacio,\n                              inserta, menor, vacio)\nfrom src.TAD_Transformaciones_conjuntos_listas import conjuntoAlista\n\nclass Comparable(Protocol):\n    @abstractmethod\n    def __lt__(self: A, otro: A) -> bool:\n        pass\n\nA = TypeVar('A', bound=Comparable)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef todos(p: Callable[[A], bool], c: Conj[A]) -> bool:\n    if esVacio(c):\n        return True\n    mc = menor(c)\n    rc = elimina(mc, c)\n    return p(mc) and todos(p, rc)\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef todos2(p: Callable[[A], bool], c: Conj[A]) -> bool:\n    return all(p(x) for x in conjuntoAlista(c))\n\n# La funci\u00f3n conjuntoAlista est\u00e1 definida en el ejercicio\n# \"Transformaciones entre conjuntos y listas\" que se encuentra\n# en https:\/\/bit.ly\/3RexzxH\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef todos3Aux(p: Callable[[A], bool], c: Conj[A]) -> bool:\n    while not esVacio(c):\n        mc = menor(c)\n        c = elimina(mc, c)\n        if not p(mc):\n            return False\n    return True\n\ndef todos3(p: Callable[[A], bool], c: Conj[A]) -> bool:\n    _c = deepcopy(c)\n    return todos3Aux(p, _c)\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef todos4Aux(p: Callable[[A], bool], c: Conj[A]) -> bool:\n    while not c.esVacio():\n        mc = c.menor()\n        c.elimina(mc)\n        if not p(mc):\n            return False\n    return True\n\ndef todos4(p: Callable[[A], bool], c: Conj[A]) -> bool:\n    _c = deepcopy(c)\n    return todos4Aux(p, _c)\n\n# Comprobaci\u00f3n de equivalencia de las definiciones\n# ================================================\n\n# La propiedad es\n@given(c=conjuntoAleatorio())\ndef test_todos(c: Conj[int]) -> None:\n    r = todos(lambda x: x % 2 == 0, c)\n    assert todos2(lambda x: x % 2 == 0, c) == r\n    assert todos3(lambda x: x % 2 == 0, c) == r\n    assert todos4(lambda x: x % 2 == 0, c) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q TAD_TodosVerificanConj.py\n#    1 passed in 0.28s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Utilizando el tipo abstracto de datos de los conjuntos definir la funci\u00f3n todos :: Ord a => (a -> Bool) -> Conj a -> Bool tal que todos p c se verifica si todos los elemsntos de c verifican el predicado p. Por ejemplo, todos even (inserta 4 (inserta 6 vacio)) == True todos even&#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":[331,585],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7963"}],"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=7963"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7963\/revisions"}],"predecessor-version":[{"id":7987,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7963\/revisions\/7987"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7963"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7963"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}