{"id":362,"date":"2017-09-23T00:13:18","date_gmt":"2017-09-22T16:13:18","guid":{"rendered":"https:\/\/colliot.me\/?p=362"},"modified":"2017-11-20T10:24:29","modified_gmt":"2017-11-20T02:24:29","slug":"%e3%80%90c-%e6%a8%a1%e6%9d%bf%e5%85%83%e7%bc%96%e7%a8%8b%e5%85%a5%e9%97%a8%e3%80%91%e5%9c%a8%e7%bc%96%e8%af%91%e6%9c%9f%e5%ae%9e%e7%8e%b0-peano-%e6%95%b0","status":"publish","type":"post","link":"https:\/\/colliot.org\/zh\/2017\/09\/%e3%80%90c-%e6%a8%a1%e6%9d%bf%e5%85%83%e7%bc%96%e7%a8%8b%e5%85%a5%e9%97%a8%e3%80%91%e5%9c%a8%e7%bc%96%e8%af%91%e6%9c%9f%e5%ae%9e%e7%8e%b0-peano-%e6%95%b0\/","title":{"rendered":"\u3010C++ \u6a21\u677f\u5143\u7f16\u7a0b\u5165\u95e8\u3011\u5728\u7f16\u8bd1\u671f\u5b9e\u73b0 Peano \u6570"},"content":{"rendered":"

<\/p>\n

\u57fa\u672c\u77e5\u8bc6<\/h3>\n

\u7c7b\u578b\u7684\u51fd\u6570<\/h4>\n

\u6211\u4eec\u90fd\u77e5\u9053\u6a21\u677f\u53ef\u4ee5\u63a5\u53d7\u7c7b\u578b\u4f5c\u4e3a\u300c\u53c2\u6570\u300d\u3002\u540c\u6837\u5730\u6211\u4eec\u4e5f\u53ef\u4ee5\u6709\u300c\u8fd4\u56de\u503c\u300d\uff0c\u4ece\u800c\u6784\u9020\u7c7b\u578b\u7684\u51fd\u6570\u3002\u57fa\u672c\u7684\u8303\u5f0f\u662f\uff1a<\/p>\n

template<class T>\r\nstruct Computed {\r\n  using type = T;\r\n}<\/pre>\n
\u8fd9\u5c31\u6784\u9020\u4e86\u4e00\u4e2a\u540d\u4e3a Computed<\/code> \u7684\uff0c\u63a5\u6536\u4e00\u4e2a\u7c7b\u578b\u53c2\u6570\uff0c\u8fd4\u56de\u8fd9\u4e2a\u7c7b\u578b\u672c\u8eab\u7684\u51fd\u6570\uff0c\u7528\u6cd5\u5982 Computed<float>::type<\/code>\uff0c\u8fd9\u4e2a\u7c7b\u578b\u5e94\u5f53\u8fd8\u662f `float`\u3002
\n\u4e3a\u4ec0\u4e48\u8981\u5305\u4e00\u5c42 struct<\/code>\uff1f\u8fd9\u662f\u56e0\u4e3a C++ \u4e0d\u652f\u6301\u5bf9 using<\/code> \u7684\u7279\u5316\u3002\u8fd9\u6837\u7684\u4ee3\u7801\u662f\u4e0d\u884c\u7684\uff1a<\/p>\n
template <class T>\r\nusing computed<T> = T;\r\n\r\ntemplate<>\r\nusing computed<int> = double;<\/pre>\n
\u81f3\u4e8e\u4e3a\u4ec0\u4e48\u4e0d\u652f\u6301\uff0c\u6211\u6ca1\u6709\u4e86\u89e3\u3002<\/p>\n
\u7279\u5316<\/h4>\n
\u4ec0\u4e48\u662f\u7279\u5316\uff1f\u4f60\u53ef\u4ee5\u7406\u89e3\u4e3a\u6a21\u5f0f\u5339\u914d\uff0c\u5c31\u50cf Haskell \u4e2d\u7684\u5199\u6cd5\u4e00\u6837\u3002<\/p>\n
template<class T>\r\nstruct Computed {\r\n  using type = T;\r\n}\r\n\r\ntemplate<>\r\nstruct Computed<int> {\r\n  using type = double;\r\n}<\/pre>\n
\u8fd9\u6837\u5f53\u4f60\u8c03\u7528 Computed<bool>::type<\/code> \u65f6\uff0c\u5f97\u5230\u7684\u7ed3\u679c\u662f bool<\/code>\uff0c\u800c\u8c03\u7528Computed<int>::type<\/code>\u5f97\u5230\u7684\u7ed3\u679c\u5374\u662fdouble<\/code>\u3002\u5f53\u7136\u8fd9\u79cd\u5339\u914d\u662f\u9075\u5faa\u4e00\u5b9a\u89c4\u5219\u7684\uff0c\u6bd4\u5982\u66f4\u300c\u5177\u4f53\u300d\u7684\u7279\u5316\u4f18\u5148\u5339\u914d\uff0c\u8fd9\u8ddf Haskell \u8c01\u5728\u524d\u8c01\u5148\u8bd5\u7740\u5339\u914d\u4e0d\u592a\u4e00\u6837\u3002\u5728 Haskell \u4e2d\u5c31\u597d\u6bd4\uff1a<\/p>\n
data Type = Bool | Double | Int\r\n\r\ncomputed :: Type -> Type\r\ncomputed Int = Double\r\ncomputed t = t<\/pre>\n
\u5b9e\u9645\u4e0a\u6709\u4e86\u8fd9\u5c42\u5bf9\u5e94\uff0c\u5982\u679c\u4f60\u77e5\u9053\u600e\u4e48\u5728 Haskell \u4e2d\u5b9e\u73b0 Peano \u6570\uff0c\u90a3\u4e48 C++ \u4e2d\u7684\u5b9e\u73b0\u57fa\u672c\u5c31\u662f\u65e0\u8111\u7ffb\u8bd1\u4e86\u3002\u5982\u679c\u4f60\u4e0d\u77e5\u9053\u600e\u4e48\u5728 Haskell \u4e2d\u5b9e\u73b0 Peano \u6570\uff0c\u90a3\u4f60\u77e5\u9053 Peano \u6570\u662f\u4ec0\u4e48\uff0c\u4e5f\u80fd\u5927\u5dee\u4e0d\u5dee\u77e5\u9053\u7b54\u6848\u4e86\u3002<\/p>\n
Peano \u6570<\/h3>\n
Peano \u6570\u662f\u4ec0\u4e48\uff1fPeano \u6570\u662f\u5f52\u7eb3\u5b9a\u4e49\u7684\u81ea\u7136\u6570\uff0c\u51c6\u786e\u5730\u8bf4\u5e94\u8be5\u662f\u4e00\u4e2a\u8868\u73b0\u5f62\u5982\u76f4\u89c9\u4e2d\u300c\u81ea\u7136\u6570\u300d\u7684\u516c\u7406\u7cfb\u7edf\uff0c\u4e5f\u5c31\u662f\u300c\u81ea\u7136\u6570\u300d\u7684\u5f62\u5f0f\u5316\u3002\u8fd9\u4e2a\u7cfb\u7edf\u91cc\u53ea\u6709\u4e24\u4e2a\u7b26\u53f7\uff0cZero<\/code>\u2014\u2014\u8868\u793a 0<\/code>\uff0c\u4ee5\u53ca Succ<\/code>\u2014\u2014\u8868\u793a\u540e\u7ee7\u3002\u90a3\u4e48 1<\/code> \u5c31\u662f Succ<Zero><\/code>\uff0c2<\/code> \u5c31\u662f Succ<Succ<Zero>><\/code>\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff08\u5f52\u7eb3\uff0c\u5176\u5b9e\u5c31\u662f\u300c\u4ee5\u6b64\u7c7b\u63a8\u300d\u7684\u5f62\u5f0f\u5316\uff09\u3002
\n\u6211\u4eec\u53ef\u4ee5\u5728 C++ \u4e2d\u5982\u6b64\u8868\u8ff0\uff1a<\/p>\n
struct Peano {};\r\nstruct Zero: Peano {};\r\ntemplate<class T>\r\nstruct Succ: Peano {};<\/pre>\n
\u90a3\u4e48\u52a0\u6cd5\u53c8\u662f\u4ec0\u4e48\u5462\uff1f\u4ece\u4f8b\u5b50\u51fa\u53d1\uff0c\u6211\u4eec\u9700\u8981\u5b9a\u4e49\u4e00\u4e2a\u4e24\u4e2a\u7c7b\u578b\u53c2\u6570\u7684\u6a21\u677f\uff1a<\/p>\n
template<class T1, class T2>\r\nstruct Add {\r\n  using type = ???;\r\n}<\/pre>\n
\u6ee1\u8db3\u76f4\u89c9\u4e2d\u7684\u8fd0\u7b97\u89c4\u5f8b\uff0c\u6bd4\u5982 2+1=3<\/code>\uff0c\u7ffb\u8bd1\u6210 C++ \u5c31\u662f Add<Succ<Succ<Zero>>, Succ<Zero>>::type = Succ<Succ<Succ<Zero>>><\/code>\u3002\u5f53\u7136\u7c7b\u578b\u4e4b\u95f4\u6ca1\u6709\u7b49\u4e8e\u53f7\uff0c\u51c6\u786e\u5730\u8bf4\u5e94\u8be5\u7528 std::is_same<T1, T2><\/code>\uff0c\u8fd9\u5176\u5b9e\u4e5f\u662f\u901a\u8fc7\u7279\u5316\u5b9e\u73b0\u7684\uff0c\u6bd4\u5982\uff08\u793a\u610f\uff0c\u975e\u5b98\u65b9\u5b9e\u73b0\uff09\uff1a<\/p>\n
template<class T, class U>\r\nstruct is_same {\r\n  static constexpr bool value = false;\r\n};\r\n \r\ntemplate<class T>\r\nstruct is_same<T, T> {\r\n  static constexpr bool value = true;\r\n};<\/pre>\n
\u90a3\u4e48\u5982\u4f55\u5b9a\u4e49\u52a0\u6cd5\u5462\uff1f\u5bf9\u4e8e\u6709\u9650\u7684\u5143\u7d20\uff0c\u6211\u4eec\u5f53\u7136\u53ef\u4ee5\u4e3a\u6bcf\u4e00\u4e2a\u5b9e\u4f8b\u505a\u7279\u5316\uff0c\u6bd4\u5982\uff1a<\/p>\n
template<>\r\nstruct Add<Succ<Succ<Zero>>, Succ<Zero>> {\r\n  using type = Succ<Succ<Succ<Zero>>>;\r\n}<\/pre>\n
\u4e5f\u5c31\u662f\u6253\u8868\u3002C++ \u7f16\u8bd1\u5668\u7684\u6a21\u677f\u6df1\u5ea6\u4e00\u822c\u90fd\u662f\u6709\u9650\u7684\uff0c\u6240\u4ee5\u8fd9\u7406\u8bba\u4e0a\u662f\u53ef\u4ee5\u5728\u5b9e\u9645\u64cd\u4f5c\u4e2d\u8986\u76d6\u6240\u6709\u7528\u4f8b\u7684\u3002\u4f46\u662f\u8fd9\u660e\u663e\u592a\u50bb\u4e86\u3002\u5176\u5b9e\u52a0\u6cd5\u7684\u5b9a\u4e49\u53ea\u9700\u8981\u4e24\u6761\u89c4\u5219\u5c31\u53ef\u4ee5\u8986\u76d6\uff1a0 + b = b, (Succ a) + b = Succ (a + b)<\/code>\u3002\u7ffb\u8bd1\u6210 C++ \u5c31\u662f\uff1a<\/p>\n
template<class T1, class T2>\r\nstruct Add;\r\n\r\ntemplate<class T>\r\nstruct Add<Zero, T> {\r\n  using type = T;\r\n};\r\n\r\ntemplate<class T1, class T2>\r\nstruct Add<Succ<T1>, T2> {\r\n  using type = Succ<typename Add<T1, T2>::type>\r\n};<\/pre>\n
\u6ce8\u610f\u90a3\u4e2a typename<\/code>\uff0cgcc \u5e76\u4e0d\u77e5\u9053\u540e\u9762\u90a3\u4e2a ::type<\/code> \u6210\u5458\u662f\u7c7b\u578b\u8fd8\u662f\u53d8\u91cf\uff0c\u6240\u4ee5\u9700\u8981 typename<\/code>\u5173\u952e\u5b57\u7684\u63d0\u793a\u3002
\n\u8fd9\u5c31\u7b97\u5199\u5b8c\u4e86\uff0c\u4f60\u53ef\u4ee5\u6d4b\u8bd5\u770b\u770b\uff0c\u662f\u4e0d\u662f\u6ee1\u8db3 std::is_same<Add<Succ<Succ<Zero>>, Succ<Zero>>::type, Succ<Succ<Succ<Zero>>>>::value == true<\/code>\uff08\u9700\u8981 <type_traits><\/code> \u5934\u6587\u4ef6\uff0c\u6216\u8005\u4e0a\u9762\u81ea\u5df1\u5199\u7684\u90a3\u4e2a\u6a21\u677f\uff08\u90a3\u5c31\u4e0d\u7528\u52a0 std::\uff09\u3002\u8fd9\u4e48\u5d4c\u5957\u7740\u5199 Succ<\/code> \u592a\u7e41\u7410\u4e86\uff0c\u4e5f\u4e0d\u65b9\u4fbf\u770b\uff0c\u4f60\u53ef\u4ee5\u7b80\u5355\u5730\u5199\u4e00\u4e2a\u6a21\u677f\u6765\u4ece\u6574\u6570\u751f\u6210\u7c7b\u578b\uff1a<\/p>\n
template<int v>\r\nstruct peano {\r\n  using type = Succ<typename peano<v - 1>::type>;\r\n};\r\n\r\ntemplate<>\r\nstruct peano<0> {\r\n  using type = Zero;\r\n};<\/pre>\n
\u7136\u540e\u5c31\u53ef\u4ee5\u53bb\u9a8c\u8bc1 Add<<peano<2>::type, peano<1>::type>::type<\/code> \u662f\u4e0d\u662f\u7b49\u4e8e peano<3>::type<\/code> \u4e86\u3002
\n\u81f3\u4e8e\u52a0\u51cf\u4e58\u9664\u7684\u5176\u4ed6\u8fd0\u7b97\uff0c\u6bd4\u8f83\u554a\u5947\u5076\u6027\u554a\u5176\u4ed6\u7684\u51fd\u6570\uff0c\u53ea\u8981\u4f60\u61c2\u5f97\u4e86\u52a0\u6cd5\uff0c\u6050\u6015\u5c31\u4e0d\u96be\u4e86\u3002<\/p>\n
\u7ec3\u4e60\uff1a<\/h3>\n
\u5728 Peano numbers | Codewars<\/a> \u5b8c\u6210\u52a0\u51cf\u4e58\u9664\u3001\u5947\u5076\u6027\u548c\u6bd4\u8f83\u5927\u5c0f\u7684\u64b0\u5199\uff0c\u5e76\u901a\u8fc7\u6d4b\u8bd5\u3002<\/p>\n
\n
\u5e7f\u544a\u65f6\u95f4\uff1a<\/span><\/h3>\n<\/div>\n
<\/figure>\n
\n
Codewars.com<\/span><\/a> \u662f\u4e00\u4e2a\u5f88\u597d\u7684\u7efc\u5408\u6027\u3001\u6e38\u620f\u5316 OJ\uff0c\u9664\u4e86\u7b97\u6cd5\uff08\u591a\u662f\u5165\u95e8\u7ea7\u7684\uff09\u4e4b\u5916\uff0c\u8003\u5bdf\u8bed\u8a00\u7279\u6027\uff08\u8f83\u4e3a\u6df1\u5165\uff09\u662f\u5176\u4e00\u5927\u4eae\u70b9\uff0c\u540c\u65f6\u6709\u5f88\u591a Haskell \u65b9\u9762\u7684\u5185\u5bb9\uff0c\u5305\u62ec\u6211\u4eec\u559c\u95fb\u4e50\u89c1\u7684<\/span>\u8bfb\u8bba\u6587\u7136\u540e\u5b8c\u5f62\u586b\u7a7a<\/span>\u3002\u9898\u56fe\u662f Codewars \u4e0a\u4e0a\u8ff0\u7ec3\u4e60\u7684\u754c\u9762\u622a\u56fe\u3002<\/span><\/div>\n<\/div>\n
\u540e\u8bb0<\/h3>\n
\u5f53\u7136\u6211\u4eec\u8fd8\u53ef\u4ee5\u8fdb\u4e00\u6b65\u300c\u8bc1\u660e\u300d\u6211\u4eec\u5370\u8c61\u4e2d\u7684\u7ed3\u8bba\uff0c\u6bd4\u5982\u52a0\u6cd5\u662f\u6ee1\u8db3\u4ea4\u6362\u5f8b\u7684\uff0c\u52a0\u6cd5\u548c\u4e58\u6cd5\u662f\u6ee1\u8db3\u5206\u914d\u7387\u7684\uff0c\u7b49\u7b49\u3002\u8fd9\u5c31\u662f\u540e\u8bdd\u4e86\u3002<\/p>","protected":false},"excerpt":{"rendered":"
\u57fa\u672c\u77e5\u8bc6 \u7c7b\u578b\u7684\u51fd\u6570 \u6211\u4eec\u90fd\u77e5\u9053\u6a21\u677f\u53ef\u4ee5\u63a5\u53d7\u7c7b\u578b\u4f5c\u4e3a\u300c\u53c2\u6570\u300d\u3002\u540c\u6837\u5730\u6211\u4eec\u4e5f\u53ef\u4ee5\u6709\u300c\u8fd4\u56de\u503c\u300d\uff0c\u4ece\u800c\u6784\u9020\u7c7b\u578b\u7684\u51fd\u6570 … Continue reading “\u3010C++ \u6a21\u677f\u5143\u7f16\u7a0b\u5165\u95e8\u3011\u5728\u7f16\u8bd1\u671f\u5b9e\u73b0 Peano \u6570”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":370,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[16],"tags":[26,28,27,29],"_links":{"self":[{"href":"https:\/\/colliot.org\/zh\/wp-json\/wp\/v2\/posts\/362"}],"collection":[{"href":"https:\/\/colliot.org\/zh\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/colliot.org\/zh\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/colliot.org\/zh\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/colliot.org\/zh\/wp-json\/wp\/v2\/comments?post=362"}],"version-history":[{"count":9,"href":"https:\/\/colliot.org\/zh\/wp-json\/wp\/v2\/posts\/362\/revisions"}],"predecessor-version":[{"id":426,"href":"https:\/\/colliot.org\/zh\/wp-json\/wp\/v2\/posts\/362\/revisions\/426"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/colliot.org\/zh\/wp-json\/wp\/v2\/media\/370"}],"wp:attachment":[{"href":"https:\/\/colliot.org\/zh\/wp-json\/wp\/v2\/media?parent=362"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/colliot.org\/zh\/wp-json\/wp\/v2\/categories?post=362"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/colliot.org\/zh\/wp-json\/wp\/v2\/tags?post=362"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}