{"id":297724,"date":"2024-05-20T16:35:11","date_gmt":"2024-05-20T08:35:11","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/297724.html"},"modified":"2024-05-20T16:35:38","modified_gmt":"2024-05-20T08:35:38","slug":"%e5%a6%82%e4%bd%95%e7%90%86%e8%a7%a3-induction-recursion","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/297724.html","title":{"rendered":"\u5982\u4f55\u7406\u89e3 induction-recursion"},"content":{"rendered":"

\"\u5982\u4f55\u7406\u89e3<\/p>\n

\u5f52\u7eb3-\u9012\u5f52\uff08Induction-Recursion\uff09\u662f\u4e00\u79cd\u5f3a\u5927\u7684\u6570\u5b66\u8bc1\u660e\u65b9\u6cd5\u548c\u7a0b\u5e8f\u8bbe\u8ba1\u8303\u5f0f\uff0c\u7528\u6765\u540c\u65f6\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\u548c\u51fd\u6570\u3001\u5b9e\u73b0\u540c\u65f6\u5f52\u7eb3\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\u548c\u5bf9\u5176\u8fdb\u884c\u9012\u5f52\u64cd\u4f5c\u3002\u5728\u7a0b\u5e8f\u8bed\u8a00\u7406\u8bba\u4e2d\uff0c\u8fd9\u4e00\u6982\u5ff5\u5c24\u5176\u5173\u952e\uff0c\u56e0\u4e3a\u5b83\u5141\u8bb8\u6784\u5efa\u76f8\u4e92\u4f9d\u8d56\u7684\u6570\u636e\u548c\u64cd\u4f5c\u3002\u5f52\u7eb3\u5b9a\u4e49<\/strong>\u5141\u8bb8\u6211\u4eec\u6784\u5efa\u8d77\u6570\u636e\u7ed3\u6784\u7684\u5f62\u5f0f\uff0c\u800c<\/strong>\u9012\u5f52<\/strong>\u5219\u63d0\u4f9b\u4e86\u5bf9\u8fd9\u4e9b\u6570\u636e\u7ed3\u6784\u8fdb\u884c\u64cd\u4f5c\u7684\u65b9\u6cd5\u3002<\/p>\n<\/p>\n

\u5f52\u7eb3-\u9012\u5f52\u6700\u5178\u578b\u7684\u7279\u70b9\u5728\u4e8e\u5176\u4e92\u76f8\u5b9a\u4e49\u7684\u7279\u6027\u3002\u4e3e\u4f8b\u6765\u8bf4\uff0c\u8003\u8651\u5b9a\u4e49\u4e00\u79cd\u65e0\u9650\u7684\u6811\u72b6\u6570\u636e\u7ed3\u6784\uff0c\u6811\u7684\u6bcf\u4e00\u4e2a\u8282\u70b9\u53ef\u80fd\u5305\u542b\u5bf9\u8be5\u7ed3\u6784\u4e0d\u540c\u90e8\u5206\u7684\u5f15\u7528\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u6570\u636e\u7684\u7ed3\u6784\uff08\u5f52\u7eb3\u90e8\u5206\uff09\u548c\u5bf9\u6570\u636e\u7684\u8bbf\u95ee\uff08\u9012\u5f52\u90e8\u5206\uff09\u662f\u4ea4\u7ec7\u5728\u4e00\u8d77\u7684\u3002\u8fdb\u884c\u5f52\u7eb3-\u9012\u5f52\u5b9a\u4e49\u65f6\uff0c\u6211\u4eec\u65e2\u9700\u8981\u6e05\u695a\u5730\u63cf\u8ff0\u7ed3\u6784\u7684\u6bcf\u4e00\u5c42\u6784\u9020\u5982\u4f55\u5f52\u7eb3\uff0c\u4e5f\u9700\u8981\u5b9a\u4e49\u5728\u8fd9\u79cd\u6570\u636e\u7ed3\u6784\u4e0a\u7684\u9012\u5f52\u64cd\u4f5c\uff0c\u8fd9\u8981\u6c42\u6211\u4eec\u6709\u975e\u5e38\u7cbe\u51c6\u7684\u63cf\u8ff0\uff0c\u4ee5\u786e\u4fdd\u6574\u4e2a\u5b9a\u4e49\u65e2\u4e0d\u81ea\u76f8\u77db\u76fe\u4e5f\u662f\u5b8c\u5907\u7684\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u5f52\u7eb3\u5b9a\u4e49\u548c\u9012\u5f52\u64cd\u4f5c\u7684\u57fa\u7840\u7406\u89e3<\/h3>\n<\/p>\n

Induction-recursion\u7406\u89e3\u7684\u6838\u5fc3\u5728\u4e8e\u628a\u63e1\u5f52\u7eb3\u5b9a\u4e49<\/strong>\uff08inductive definitions\uff09\u548c\u9012\u5f52\u64cd\u4f5c<\/strong>\uff08recursive operations\uff09\u4e4b\u95f4\u7684\u76f8\u4e92\u5173\u8054\u3002<\/p>\n<\/p>\n

\u5f52\u7eb3\u5b9a\u4e49\u7684\u6982\u5ff5<\/h4>\n<\/p>\n

\u5f52\u7eb3\u5b9a\u4e49<\/strong>\u662f\u4ece\u7b80\u5355\u7684\u57fa\u7840\u60c5\u5f62\u5f00\u59cb\uff0c\u901a\u8fc7\u9010\u6b65\u6dfb\u52a0\u89c4\u5219\u6765\u6784\u5efa\u66f4\u590d\u6742\u7684\u7ed3\u6784\u6216\u8bc1\u660e\u3002\u901a\u8fc7\u786e\u4fdd\u5b9a\u4e49\u6db5\u76d6\u6240\u6709\u53ef\u80fd\u7684\u60c5\u51b5\uff0c\u5f52\u7eb3\u5b9a\u4e49\u4fdd\u969c\u4e86\u7ed3\u6784\u7684\u5b8c\u6574\u6027\u548c\u6b63\u5f0f\u6027\u3002<\/p>\n<\/p>\n

\u5f52\u7eb3\u5b9a\u4e49\u7684\u4e00\u4e2a\u5178\u578b\u4f8b\u5b50\u662f\u5bf9\u81ea\u7136\u6570\u7684\u5b9a\u4e49\u3002\u81ea\u7136\u6570\u53ef\u4ee5\u5b9a\u4e49\u4e3a\u4ece0\u5f00\u59cb\uff0c\u6bcf\u6b21\u901a\u8fc7\u52a01\u6765\u6784\u5efa\u540e\u7eed\u7684\u6570\u3002\u5728\u8fd9\u91cc\uff0c\u57fa\u7840\u60c5\u5f62\u662f\u65700\uff0c\u800c\u6784\u5efa\u89c4\u5219\u662f\u201c\u5bf9\u4efb\u4f55\u81ea\u7136\u6570n\uff0cn+1\u4e5f\u662f\u81ea\u7136\u6570\u201d\u3002\u8fd9\u6837\u7684\u6784\u5efa\u89c4\u5219\u53ef\u4ee5\u5e94\u7528\u591a\u6b21\u4ee5\u5efa\u7acb\u6574\u4e2a\u81ea\u7136\u6570\u96c6\u3002<\/p>\n<\/p>\n

\u9012\u5f52\u64cd\u4f5c\u7684\u6982\u5ff5<\/h4>\n<\/p>\n

\u9012\u5f52\u64cd\u4f5c<\/strong>\u662f\u6307\u5728\u5b9a\u4e49\u51fd\u6570\u6216\u7b97\u6cd5\u65f6\u5f15\u7528\u81ea\u8eab\u7684\u65b9\u6cd5\u3002\u5b83\u901a\u5e38\u6d89\u53ca\u4e24\u4e2a\u90e8\u5206\uff1a\u57fa\u7840\u60c5\u5f62\u548c\u9012\u5f52\u6b65\u9aa4\u3002\u57fa\u7840\u60c5\u5f62\u4e3a\u9012\u5f52\u8c03\u7528\u63d0\u4f9b\u76f4\u63a5\u7684\u8ba1\u7b97\u7ed3\u679c\uff0c\u907f\u514d\u4e86\u65e0\u9650\u5faa\u73af\uff1b\u800c\u9012\u5f52\u6b65\u9aa4\u5219\u5c06\u95ee\u9898\u5206\u89e3\u4e3a\u66f4\u5c0f\u7684\u5b50\u95ee\u9898\uff0c\u5e76\u5bf9\u5176\u8fdb\u884c\u76f8\u540c\u5904\u7406\u3002<\/p>\n<\/p>\n

\u9012\u5f52\u64cd\u4f5c\u7684\u4e00\u4e2a\u7ecf\u5178\u4f8b\u5b50\u662f\u8ba1\u7b97\u9636\u4e58\u51fd\u6570\u3002\u9636\u4e58\u51fd\u6570n!\u5b9a\u4e49\u4e3a1\u5230n\u4e4b\u95f4\u6240\u6709\u81ea\u7136\u6570\u7684\u4e58\u79ef\uff0c\u5176\u9012\u5f52\u5b9a\u4e49\u53ef\u4ee5\u9010\u6b65\u63a8\u5e7f\u5230\u6240\u6709\u6b63\u6574\u6570\u3002<\/p>\n<\/p>\n

\u4e8c\u3001\u5f52\u7eb3-\u9012\u5f52\u5728\u6570\u636e\u7c7b\u578b\u5b9a\u4e49\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n

\u5f52\u7eb3-\u9012\u5f52\u4e0d\u4ec5\u4ec5\u662f\u4e00\u4e2a\u6982\u5ff5\uff0c\u5b83\u5728\u7f16\u7a0b\u8bed\u8a00\u7684\u7c7b\u578b\u7cfb\u7edf\u8bbe\u8ba1\u548c\u5b9e\u73b0\u4e2d\u626e\u6f14\u7740\u91cd\u8981\u89d2\u8272\u3002<\/p>\n<\/p>\n

\u6570\u636e\u7c7b\u578b\u7684\u5f52\u7eb3-\u9012\u5f52\u5b9a\u4e49<\/h4>\n<\/p>\n

\u5728\u7f16\u7a0b\u8bed\u8a00\u4e2d\uff0c\u6570\u636e\u7c7b\u578b\u7684\u5b9a\u4e49<\/strong>\u5f80\u5f80\u662f\u901a\u8fc7\u5f52\u7eb3-\u9012\u5f52\u7684\u65b9\u5f0f\u6765\u8fdb\u884c\u7684\u3002\u8fd9\u6837\u7684\u6570\u636e\u7c7b\u578b\u5305\u542b\u6570\u636e\u7ed3\u6784\u548c\u64cd\u4f5c\u8fd9\u4e24\u4e2a\u76f8\u4e92\u4f9d\u8d56\u7684\u90e8\u5206\u3002<\/p>\n<\/p>\n

\u4f8b\u5982\uff0c\u4e00\u4e2a\u4ee3\u6570\u6570\u636e\u7c7b\u578b\uff08\u5982Haskell\u4e2d\u7684\u7c7b\u578b\uff09\u53ef\u4ee5\u901a\u8fc7\u5217\u51fa\u5b83\u7684\u4e00\u7cfb\u5217\u6784\u9020\u5668\u6765\u5f52\u7eb3\u5b9a\u4e49\u3002\u540c\u65f6\u5b9a\u4e49\u5728\u8fd9\u79cd\u7c7b\u578b\u4e4b\u4e0a\u7684\u51fd\u6570\u901a\u5e38\u9700\u8981\u9012\u5f52\u5730\u5904\u7406\u8fd9\u79cd\u7c7b\u578b\u7684\u503c\uff0c\u6bd4\u5982\u5728\u5217\u8868\u3001\u6811\u7b49\u6570\u636e\u7ed3\u6784\u4e0a\u7684\u64cd\u4f5c\u3002<\/p>\n<\/p>\n

\u5f52\u7eb3-\u9012\u5f52\u6570\u636e\u7c7b\u578b\u7684\u64cd\u4f5c<\/h4>\n<\/p>\n

\u5b9a\u4e49\u597d\u7684\u6570\u636e\u7c7b\u578b\u9700\u8981\u5bf9\u5176\u8fdb\u884c\u64cd\u4f5c\u3002\u9012\u5f52\u51fd\u6570<\/strong>\u5728\u8fd9\u91cc\u53d8\u5f97\u975e\u5e38\u6709\u7528\uff0c\u56e0\u4e3a\u5b83\u4eec\u53ef\u4ee5\u81ea\u7136\u5730\u5904\u7406\u9012\u5f52\u5b9a\u4e49\u7684\u6570\u636e\u7ed3\u6784\u3002\u5728\u5904\u7406\u6811\u5f62\u7ed3\u6784\u65f6\uff0c\u9012\u5f52\u7684\u601d\u60f3\u80fd\u591f\u975e\u5e38\u5339\u914d\u6811\u5f62\u7684\u81ea\u7136\u7ed3\u6784\u3002\u6211\u4eec\u53ef\u4ee5\u9488\u5bf9\u6811\u7684\u6bcf\u4e00\u4e2a\u5b50\u6811\u9012\u5f52\u5730\u8c03\u7528\u76f8\u540c\u7684\u5904\u7406\u51fd\u6570\u3002<\/p>\n<\/p>\n

\u4e09\u3001\u5f52\u7eb3-\u9012\u5f52\u8bc1\u660e\u65b9\u6cd5\u5728\u6570\u5b66\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n

\u5f52\u7eb3-\u9012\u5f52<\/strong>\u4e5f\u662f\u6570\u5b66\u8bc1\u660e\u4e2d\u7684\u4e00\u4e2a\u91cd\u8981\u5de5\u5177\uff0c\u5c24\u5176\u5728\u5904\u7406\u65e0\u7a77\u7ed3\u6784\u6216\u6027\u8d28\u7684\u8bc1\u660e\u65f6\u3002<\/p>\n<\/p>\n

\u5f52\u7eb3\u8bc1\u660e<\/h4>\n<\/p>\n

\u7528\u4e8e\u8bc1\u660e\u67d0\u6027\u8d28\u5bf9\u6240\u6709\u81ea\u7136\u6570\u6210\u7acb\u65f6\uff0c\u6211\u4eec\u901a\u5e38\u4f1a\u501f\u52a9\u5f52\u7eb3\u6cd5\u3002\u901a\u8fc7\u8bc1\u660e\u8fd9\u4e00\u6027\u8d28\u5bf9\u65700\u6210\u7acb\uff08\u57fa\u7840\u60c5\u5f62\uff09\uff0c\u5e76\u8fdb\u4e00\u6b65\u8bc1\u660e\u5982\u679c\u5b83\u5bf9\u4efb\u610f\u6570n\u6210\u7acb\uff0c\u5219\u5bf9n+1\u4e5f\u6210\u7acb\uff08\u5f52\u7eb3\u6b65\u9aa4\uff09\uff0c\u6211\u4eec\u53ef\u4ee5\u786e\u4fe1\u8be5\u6027\u8d28\u5bf9\u6240\u6709\u81ea\u7136\u6570\u6210\u7acb\u3002<\/p>\n<\/p>\n

\u5f52\u7eb3\u6cd5\u7684\u8981\u70b9\u5728\u4e8e\u4e0d\u65ad\u91cd\u590d\u5e94\u7528\u5f52\u7eb3\u5047\u8bbe\u6765\u5efa\u7acb\u66f4\u4e00\u822c\u7684\u7ed3\u679c\u3002\u8fd9\u79cd\u65b9\u6cd5\u7684\u6210\u529f\u5728\u4e8e\u8bc1\u660e\u9002\u7528\u4e8e\u6bcf\u4e00\u6b65\u6784\u9020\u7684\u6027\u8d28\uff0c\u4ece\u800c\u786e\u4fdd\u4e86\u6574\u4f53\u7ed3\u6784\u7684\u666e\u9002\u6027\u3002<\/p>\n<\/p>\n

\u9012\u5f52\u8bc1\u660e<\/h4>\n<\/p>\n

\u5728\u6570\u5b66\u4e0a\uff0c\u9012\u5f52\u8bc1\u660e\u901a\u5e38\u6d89\u53ca\u6784\u5efa\u4e00\u4e2a\u6216\u591a\u4e2a\u9012\u5f52\u5e8f\u5217\u6765\u8bc1\u660e\u7279\u5b9a\u6027\u8d28\u3002\u9012\u5f52\u5e8f\u5217\u4f9d\u6258\u4e8e\u66f4\u7b80\u5355\u7684\u9879\u6216\u60c5\u5f62\uff0c\u901a\u8fc7\u9012\u5f52\u7684\u65b9\u5f0f\u53bb\u6784\u5efa\u66f4\u590d\u6742\u7684\u9879\u3002<\/p>\n<\/p>\n

\u901a\u8fc7\u8ffd\u8e2a\u9012\u5f52\u5e8f\u5217\u7684\u884c\u4e3a\uff0c\u6211\u4eec\u53ef\u4ee5\u8bc1\u660e\u590d\u6742\u7ed3\u6784\u7684\u5c5e\u6027\u6216\u884c\u4e3a\u3002\u7279\u522b\u662f\u5728\u5904\u7406\u7ec4\u5408\u6570\u5b66\u95ee\u9898\u6216\u65e0\u9650\u5e8f\u5217\u65f6\uff0c\u9012\u5f52\u8bc1\u660e\u65b9\u6cd5\u7ecf\u5e38\u88ab\u4f7f\u7528\u3002<\/p>\n<\/p>\n

\u56db\u3001\u5f52\u7eb3-\u9012\u5f52\u5728\u7a0b\u5e8f\u8bbe\u8ba1\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n

\u5728\u7a0b\u5e8f\u8bbe\u8ba1\u4e2d\uff0c\u5f52\u7eb3-\u9012\u5f52<\/strong>\u4e0d\u4ec5\u7528\u4e8e\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\u548c\u51fd\u6570\uff0c\u540c\u65f6\u4e5f\u7528\u4e8e\u6784\u5efa\u7b97\u6cd5\u548c\u8fdb\u884c\u7a0b\u5e8f\u9a8c\u8bc1\u3002<\/p>\n<\/p>\n

\u5f52\u7eb3-\u9012\u5f52\u7b97\u6cd5\u7684\u8bbe\u8ba1<\/h4>\n<\/p>\n

\u4f7f\u7528\u5f52\u7eb3-\u9012\u5f52\u8bbe\u8ba1\u7b97\u6cd5\u53ef\u4ee5\u8ba9\u7b97\u6cd5\u7684\u63cf\u8ff0\u66f4\u52a0\u81ea\u7136\u548c\u6e05\u6670\u3002\u5728\u590d\u6742\u7684\u7b97\u6cd5\u8bbe\u8ba1\u4e2d\uff0c\u5c06\u95ee\u9898\u5206\u89e3\u4e3a\u53ef\u901a\u8fc7\u9012\u5f52\u89e3\u51b3\u7684\u66f4\u5c0f\u95ee\u9898\u5f80\u5f80\u662f\u4e00\u79cd\u6709\u6548\u7684\u7b56\u7565\u3002<\/p>\n<\/p>\n

\u4f8b\u5982\uff0c\u5206\u6cbb\u7b97\u6cd5<\/strong>\u5c31\u662f\u901a\u8fc7\u5c06\u4e00\u4e2a\u5927\u95ee\u9898\u5206\u5272\u6210\u82e5\u5e72\u5c0f\u95ee\u9898\uff0c\u9012\u5f52\u5730\u89e3\u51b3\u8fd9\u4e9b\u5c0f\u95ee\u9898\u540e\u518d\u5408\u5e76\u7ed3\u679c\u6765\u89e3\u51b3\u6574\u4e2a\u95ee\u9898\u3002\u5f52\u7eb3-\u9012\u5f52\u7b97\u6cd5\u975e\u5e38\u9002\u7528\u4e8e\u89e3\u51b3\u7c7b\u4f3c\u4e8e\u6392\u5e8f\u3001\u641c\u7d22\u7b49\u95ee\u9898\u3002<\/p>\n<\/p>\n

\u5f52\u7eb3-\u9012\u5f52\u7684\u7a0b\u5e8f\u9a8c\u8bc1<\/h4>\n<\/p>\n

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\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n

FAQs: Understanding induction-recursion<\/strong><\/p>\n

    \n
  1. \n

    What is induction-recursion and how does it relate to mathematical reasoning?<\/strong>
    \nInduction-recursion is a powerful technique used in mathematical and computational logic. It combines two important principles: induction and recursion. Induction is a proof technique that allows us to prove statements for an infinite number of cases by showing that if a statement is true in one case, it must also be true in the next case. Recursion, on the other hand, is a way to define mathematical objects or functions in terms of simpler versions of themselves. Induction-recursion combines these principles to define complex mathematical objects or structures in a stepwise manner, allowing for precise reasoning and the construction of intricate structures in mathematics.<\/p>\n<\/li>\n

  2. \n

    How is induction-recursion used in computer science and programming languages?<\/strong>
    \nInduction-recursion finds applications in computer science and programming language theory. It is particularly useful in the study of type theory, where it can be used to define and reason about complex data types. By using induction-recursion, we can define a type by simultaneously defining its values and its properties. This approach is especially beneficial for defining recursively dependent types, where the definition of a type depends on values or properties of the same type. Induction-recursion allows for elegant and concise definitions in programming languages, making it easier to reason about and prove properties of programs.<\/p>\n<\/li>\n

  3. \n

    Can you provide an example of induction-recursion in action?<\/strong>
    \nCertAI<\/a>nly! An example of induction-recursion is the definition of the type of natural numbers in type theory. We can define the type "nat" by simultaneously providing constructors for its values and the properties that they satisfy. The constructors include a base case "zero" for the value 0, and a recursive case "succ" that takes a natural number and returns the next natural number. The properties include the reflexivity of equality, which states that every natural number is equal to itself. By using an induction-recursion principle, we can define the type of natural numbers and reason about its properties in a concise and rigorous manner.<\/p>\n<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"\u5f52\u7eb3-\u9012\u5f52\uff08Induction-Recursion\uff09\u662f\u4e00\u79cd\u5f3a\u5927\u7684\u6570\u5b66\u8bc1\u660e\u65b9\u6cd5\u548c\u7a0b\u5e8f\u8bbe\u8ba1\u8303\u5f0f\uff0c\u7528\u6765\u540c\u65f6\u5b9a\u4e49\u6570\u636e\u7c7b […]","protected":false},"author":3,"featured_media":297753,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/297724"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=297724"}],"version-history":[{"count":0,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/297724\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/297753"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=297724"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=297724"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=297724"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}