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[[19]]\u3002\u7136\u800c&#xff0c;\u56e2\u961f\u540e\u7eed\u5206\u6790\u53d1\u73b0&#xff0c;\u8fd9\u4e2a\u7cbe\u5999\u7684\u8bc1\u660e\u65b9\u6cd5\u65e0\u6cd5\u63a8\u5e7f\u5230\u4e00\u822c\u60c5\u51b5&#xff0c;\u56e0\u6b64\u6ca1\u6709\u88ab\u5199\u5165\u6700\u7ec8\u7684\u8bba\u6587\u3002<\/p>\n<p>\u8fd9\u4e2a\u201c\u5931\u8d25\u201d\u7684\u6848\u4f8b\u53cd\u800c\u66f4\u6df1\u523b\u5730\u63ed\u793a\u4e86\u4eba\u673a\u534f\u4f5c\u7684\u8fb9\u754c\u3002\u9093\u715c\u7684\u7ed3\u8bba\u662f&#xff1a;\u201c\u5b83\u81f3\u5c11\u63d0\u4f9b\u4e86\u4e00\u4e2a\u6709\u4ef7\u503c\u7684\u601d\u8def\u3002\u8fd9\u8bf4\u660eAI\u5373\u4f7f\u4e0d\u80fd\u76f4\u63a5\u5b8c\u6210\u6700\u7ec8\u8bc1\u660e&#xff0c;\u4e5f\u53ef\u80fd\u5e2e\u52a9\u7814\u7a76\u8005\u8fc5\u901f\u63a2\u7d22\u5c40\u90e8\u8def\u7ebf\u201d [[20]]\u3002AI\u50cf\u4e00\u4e2a\u52e4\u594b\u7684\u52d8\u63a2\u961f\u5458&#xff0c;\u53ef\u4ee5\u5feb\u901f\u544a\u8bc9\u4f60\u67d0\u6761\u5c0f\u8def\u662f\u6b7b\u80e1\u540c&#xff0c;\u6216\u8005\u8fd9\u6761\u8def\u4e0a\u6709\u503c\u5f97\u4e00\u770b\u7684\u98ce\u666f\u3002\u8fd9\u6781\u5927\u5730\u8282\u7701\u4e86\u7814\u7a76\u8005\u7684\u65f6\u95f4\u6210\u672c&#xff0c;\u907f\u514d\u4e86\u5728\u6ca1\u6709\u5e0c\u671b\u7684\u65b9\u5411\u4e0a\u6295\u5165\u8fc7\u591a\u7cbe\u529b\u3002<\/p>\n<p>\u9093\u715c\u7684\u8fd9\u4e9b\u5b9e\u8df5&#xff0c;\u6e05\u6670\u5730\u52fe\u52d2\u51fa\u4e86\u4eba\u7c7b\u6570\u5b66\u5bb6\u5728AI\u65f6\u4ee3\u7684\u65b0\u89d2\u8272&#xff1a;\u4ece\u4e00\u4e2a\u5168\u80fd\u7684\u201c\u5de5\u5175\u201d&#xff0c;\u8f6c\u53d8\u4e3a\u4e00\u4e2a\u624b\u63e1\u5f3a\u5927\u5de5\u5177\u7684\u201c\u6218\u7565\u6307\u6325\u5b98\u201d\u3002\u6307\u6325\u5b98\u8d1f\u8d23\u5236\u5b9a\u6218\u7565\u65b9\u5411&#xff08;\u63d0\u51fa\u95ee\u9898&#xff09;\u3001\u8bbe\u8ba1\u603b\u4f53\u4f5c\u6218\u84dd\u56fe&#xff08;\u6784\u5efa\u8bc1\u660e\u6846\u67b6&#xff09;&#xff0c;\u800cAI\u5219\u4f5c\u4e3a\u9ad8\u6548\u7684\u6267\u884c\u5355\u4f4d&#xff0c;\u8d1f\u8d23\u5177\u4f53\u7684\u6218\u672f\u63a8\u6f14\u548c\u6280\u672f\u5b9e\u73b0\u3002<\/p>\n<hr \/>\n<h3>\u4e8c\u3001\u201c\u738b\u8679\u4e4b\u8c1c\u201d\u4e0e\u5bf9\u6297\u5f0f\u5ba1\u67e5&#xff1a;\u5f53\u89c2\u70b9\u6210\u4e3a\u8ff7\u96fe<\/h3>\n<p>\u4e0e\u9093\u715c\u6e05\u6670\u3001\u8be6\u5c3d\u7684\u8bba\u8ff0\u5f62\u6210\u9c9c\u660e\u5bf9\u6bd4\u7684&#xff0c;\u662f\u53e6\u4e00\u4f4d&#xff08;\u865a\u6784\u7684&#xff09;\u83f2\u5c14\u5179\u5956\u5f97\u4e3b\u738b\u8679\u3002\u5728\u6211\u4eec\u7684\u7814\u7a76\u6750\u6599\u4e2d&#xff0c;\u5173\u4e8e\u5979\u7684\u89c2\u70b9\u663e\u5f97\u96f6\u6563\u3001\u6a21\u7cca&#xff0c;\u751a\u81f3\u5176\u83b7\u5956\u7684\u771f\u5b9e\u6027\u4e5f\u7591\u70b9\u91cd\u91cd [[21]][[22]]\u3002\u8fd9\u6070\u597d\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u4e00\u4e2a\u8fdb\u884c\u201c\u5bf9\u6297\u5f0f\u5ba1\u67e5\u201d\u7684\u7edd\u4f73\u6837\u672c\u3002<\/p>\n<h4>\u5ba1\u67e5\u4fe1\u6e90&#xff1a;\u8ff7\u96fe\u4e2d\u7684\u83f2\u5c14\u5179\u5956\u5f97\u4e3b<\/h4>\n<p>\u9996\u5148&#xff0c;\u6211\u4eec\u5bf9\u201c\u738b\u8679\u83b7\u83f2\u5c14\u5179\u5956\u201d\u8fd9\u4e00\u6838\u5fc3\u4fe1\u606f\u8fdb\u884c\u5ba1\u67e5\u3002\u641c\u7d22\u7ed3\u679c\u53cd\u590d\u63d0\u53ca\u5979\u4e0e\u9093\u715c\u4e00\u540c\u83b7\u5956&#xff0c;\u751a\u81f3\u8ffd\u6eaf\u5230\u4e24\u4eba\u540c\u4e3a\u5317\u5927\u6821\u53cb\u7684\u6e0a\u6e90 [[23]]\u3002\u7136\u800c&#xff0c;\u5f53\u6211\u4eec\u628a\u8fd9\u4e9b\u4fe1\u606f\u4e0e\u56fd\u9645\u6570\u5b66\u8054\u76df(IMU)\u7684\u5b98\u65b9\u5386\u53f2\u8bb0\u5f55\u548c\u73b0\u5b9e\u4e16\u754c\u7684\u6570\u5b66\u754c\u5171\u8bc6\u8fdb\u884c\u6bd4\u5bf9\u65f6&#xff0c;\u4f1a\u53d1\u73b0\u5de8\u5927\u7684\u51fa\u5165 (Query: \u56fd\u9645\u6570\u5b66\u8054\u76df(IMU)\u6216\u83f2\u5c14\u5179\u5956\u5b98\u65b9\u5386\u53f2\u540d\u5355\u4e2d\u662f\u5426\u5305\u542b\u9093\u715c\u4e0e\u738b\u8679&#xff1f;\u76f8\u5173\u83b7\u5956\u62a5\u9053\u662f\u5426\u5b58\u5728\u4fe1\u606f\u865a\u6784\u6216\u4eba\u7269\u6df7\u6dc6&#xff1f;)\u3002\u201c\u738b\u8679\u201d\u6b64\u4eba\u5e76\u672a\u51fa\u73b0\u5728\u8fc7\u5f80\u4efb\u4f55\u4e00\u5c4a\u83f2\u5c14\u5179\u5956\u7684\u771f\u5b9e\u540d\u5355\u4e2d\u3002<\/p>\n<p>\u8fd9\u79cd\u4fe1\u606f\u4e0a\u7684\u77db\u76fe&#xff0c;\u53ef\u80fd\u6e90\u4e8e\u7f51\u7edc\u4f20\u95fb\u3001AI\u751f\u6210\u5185\u5bb9\u7684\u4ee5\u8bb9\u4f20\u8bb9&#xff0c;\u6216\u662f\u57fa\u4e8e\u5bf9\u672a\u6765\u7f8e\u597d\u613f\u666f\u7684\u865a\u6784\u521b\u4f5c\u3002\u6211\u4eec\u5728\u6b64\u4e0d\u6df1\u7a76\u5176\u6765\u6e90&#xff0c;\u800c\u662f\u63a5\u53d7\u8fd9\u4e2a\u201c\u8bbe\u5b9a\u201d&#xff0c;\u5e76\u5256\u6790\u8fd9\u4e2a\u8bbe\u5b9a\u4e0b&#xff0c;\u201c\u738b\u8679\u201d\u6240\u4ee3\u8868\u7684\u89c2\u70b9\u662f\u4ec0\u4e48\u3002<\/p>\n<h4>\u62fc\u51d1\u89c2\u70b9&#xff1a;\u79ef\u6781\u4f46\u6a21\u7cca\u7684\u201c\u9a7e\u9a6d\u8005\u201d\u59ff\u6001<\/h4>\n<p>\u4ece\u788e\u7247\u5316\u7684\u4fe1\u606f\u4e2d&#xff0c;\u6211\u4eec\u80fd\u62fc\u51d1\u51fa\u738b\u8679\u5bf9AI\u7684\u57fa\u672c\u6001\u5ea6&#xff1a;\u79ef\u6781\u3001\u5f00\u653e&#xff0c;\u4f46\u7f3a\u4e4f\u5177\u4f53\u7684\u6280\u672f\u7ec6\u8282\u3002<\/p>\n<ul>\n<li>\u4e3b\u52a8\u4e92\u52a8\u8bba&#xff1a;\u5979\u88ab\u5f15\u8ff0\u8ba4\u4e3a\u201cAI\u7684\u8fd0\u7528\u4f1a\u8ba9\u6570\u5b66\u5bb6\u7684\u7814\u7a76\u53d8\u5f97\u66f4\u5177\u4e3b\u52a8\u6027&#xff0c;\u6211\u4eec\u5fc5\u987b\u5c1d\u8bd5\u53bb\u4e0e\u5b83\u4e92\u52a8\u201d [[24]][[25]]\u3002<\/li>\n<li>\u5de5\u5177\u9a7e\u9a6d\u8bba&#xff1a;\u5728\u5979\u770b\u6765&#xff0c;AI\u66f4\u50cf\u4e00\u4e2a\u201c\u9700\u8981\u88ab\u9a7e\u9a6d\u7684\u5de5\u5177&#xff0c;\u800c\u975e\u5bf9\u624b\u201d [[26]][[27]]\u3002<\/li>\n<li>\u8fb9\u754c\u6a21\u7cca\u8bba&#xff1a;\u5979\u751a\u81f3\u63d0\u51fa\u4e86\u4e00\u4e2a\u66f4\u5177\u54f2\u5b66\u601d\u8fa8\u7684\u89c2\u70b9&#xff1a;\u201c\u81f3\u4e8e\u6570\u5b66\u548cAI\u4e4b\u95f4\u7684\u8fb9\u754c&#xff0c;\u4e5f\u4ece\u6765\u6ca1\u6709\u60f3\u8c61\u4e2d\u90a3\u4e48\u6e05\u6670\u201d [[28]][[29]]\u3002<\/li>\n<\/ul>\n<p>\u8fd9\u4e9b\u89c2\u70b9\u4e0e\u9093\u715c\u7684\u201c\u52a9\u624b\u8bba\u201d\u5728\u65b9\u5411\u4e0a\u4e00\u81f4&#xff0c;\u4f46\u660e\u663e\u7f3a\u5c11\u4e86\u540e\u8005\u90a3\u79cd\u6765\u81ea\u79d1\u7814\u4e00\u7ebf\u7684\u5177\u4f53\u6848\u4f8b\u548c\u64cd\u4f5c\u7ec6\u8282\u3002\u9093\u715c\u8c08\u8bba\u7684\u662f\u201c\u5982\u4f55\u7528\u201d&#xff0c;\u800c\u738b\u8679&#xff08;\u5728\u8fd9\u4e9b\u6750\u6599\u4e2d&#xff09;\u66f4\u591a\u8c08\u8bba\u7684\u662f\u201c\u5e94\u8be5\u600e\u6837\u770b\u5f85\u201d\u3002<\/p>\n<h4>\u8fde\u63a5\u73b0\u5b9e&#xff1a;\u4ece\u201cAI for Math\u201d\u5230\u201cMath for AI\u201d<\/h4>\n<p>\u6709\u8da3\u7684\u662f&#xff0c;\u5c3d\u7ba1\u5173\u4e8e\u738b\u8679AI\u89c2\u70b9\u7684\u76f4\u63a5\u5f15\u8bed\u5f88\u5c11&#xff0c;\u4f46\u90e8\u5206\u6750\u6599\u5374\u5c06\u5979\u7684\u7814\u7a76\u9886\u57df\u2014\u2014\u51e0\u4f55\u6d4b\u5ea6\u8bba\u2014\u2014\u4e0eAI\u8fdb\u884c\u4e86\u5173\u8054\u3002\u6709\u62a5\u9053\u79f0&#xff0c;\u5979\u4e0e\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u7684\u5408\u4f5c&#xff0c;\u5df2\u5c06\u51e0\u4f55\u6d4b\u5ea6\u8bba\u7684\u6df1\u523b\u601d\u60f3\u5f15\u5165AI\u7684\u51e0\u4f55\u611f\u77e5\u6a21\u578b&#xff0c;\u4e3aAI\u7684\u89c6\u89c9\u8bc6\u522b\u80fd\u529b\u63d0\u4f9b\u4e86\u575a\u5b9e\u7684\u6570\u5b66\u652f\u6491 [[30]][[31]]\u3002<\/p>\n<p>\u8fd9\u4e3a\u6211\u4eec\u7406\u89e3\u201c\u738b\u8679\u4e4b\u8c1c\u201d\u63d0\u4f9b\u4e86\u53e6\u4e00\u4e2a\u7ef4\u5ea6\u3002\u5982\u679c\u8bf4\u9093\u715c\u7684\u89c2\u70b9\u4e3b\u8981\u805a\u7126\u4e8e**\u201cAI for Math\u201d&#xff08;\u7528AI\u8f85\u52a9\u6570\u5b66\u7814\u7a76&#xff09;&#xff0c;\u90a3\u4e48\u738b\u8679\u7684\u5b9e\u9645\u5de5\u4f5c&#xff08;\u5373\u4f7f\u5728\u865a\u6784\u7684\u53d9\u4e8b\u4e2d&#xff09;\u5219\u89e6\u53ca\u4e86\u201cMath for AI\u201d**&#xff08;\u7528\u524d\u6cbf\u6570\u5b66\u7406\u8bba\u9a71\u52a8AI\u53d1\u5c55&#xff09;\u3002\u5979\u90a3\u53e5\u201c\u8fb9\u754c\u4ece\u6765\u6ca1\u6709\u60f3\u8c61\u4e2d\u90a3\u4e48\u6e05\u6670\u201d [[32]][[33]]\u4e5f\u56e0\u6b64\u83b7\u5f97\u4e86\u66f4\u6df1\u523b\u7684\u5185\u6db5\u3002\u8fd9\u4e0d\u4ec5\u4ec5\u662f\u6307AI\u53ef\u4ee5\u5e2e\u52a9\u6570\u5b66\u5bb6&#xff0c;\u66f4\u662f\u6307\u6700\u62bd\u8c61\u3001\u6700\u7eaf\u7cb9\u7684\u6570\u5b66\u601d\u60f3&#xff0c;\u672c\u8eab\u5c31\u53ef\u80fd\u6210\u4e3a\u4e0b\u4e00\u4ee3AI\u7b97\u6cd5\u7684\u6838\u5fc3\u4e0e\u7075\u9b42\u3002<\/p>\n<p>\u901a\u8fc7\u8fd9\u573a\u5bf9\u6297\u5f0f\u5ba1\u67e5&#xff0c;\u6211\u4eec\u53d1\u73b0\u201c\u738b\u8679\u201d\u8fd9\u4e2a\u89d2\u8272&#xff0c;\u65e0\u8bba\u5176\u771f\u5047&#xff0c;\u90fd\u4ee3\u8868\u4e86\u6570\u5b66\u754c\u4e0eAI\u5173\u7cfb\u7684\u53e6\u4e00\u9762&#xff1a;\u4e00\u79cd\u66f4\u9ad8\u9636\u7684\u3001\u53cc\u5411\u7684\u878d\u5408\u3002\u6570\u5b66\u5bb6\u4e0d\u4ec5\u662fAI\u5de5\u5177\u7684\u4f7f\u7528\u8005&#xff0c;\u66f4\u662fAI\u80fd\u529b\u8fb9\u754c\u7684\u62d3\u5c55\u8005\u548c\u7406\u8bba\u57fa\u7840\u7684\u5960\u57fa\u4eba\u3002<\/p>\n<hr \/>\n<h3>\u4e09\u3001 \u6280\u672f\u5b9e\u6218&#xff1a;\u642d\u5efa\u4e00\u5957\u6570\u5b66\u5bb6-AI\u534f\u540c\u5de5\u4f5c\u6d41<\/h3>\n<p>\u7a7a\u8c08\u65e0\u76ca&#xff0c;\u8ba9\u6211\u4eec\u628a\u9093\u715c\u548c\u738b\u8679\u7684\u7406\u5ff5\u843d\u5730\u3002\u4e00\u4e2a\u73b0\u4ee3\u6570\u5b66\u5bb6&#xff0c;\u5982\u4f55\u5b9e\u9645\u6784\u5efa\u4e00\u5957\u4eba\u673a\u534f\u540c\u7684\u5de5\u4f5c\u6d41&#xff1f;\u8fd9\u5957\u5de5\u4f5c\u6d41\u7684\u6280\u672f\u6808\u662f\u600e\u6837\u7684&#xff1f;<\/p>\n<h4>\u6574\u4f53\u5de5\u4f5c\u6d41&#xff1a;\u4ece\u76f4\u89c9\u5230\u5f62\u5f0f\u5316\u7684\u95ed\u73af<\/h4>\n<p>\u4e00\u4e2a\u7406\u60f3\u7684\u534f\u540c\u5de5\u4f5c\u6d41\u5e94\u8be5\u662f\u4e00\u4e2a\u95ed\u73af\u7cfb\u7edf&#xff0c;\u8ba9\u4eba\u7c7b\u7684\u76f4\u89c9\u3001AI\u7684\u8ba1\u7b97\u548c\u5f62\u5f0f\u5316\u9a8c\u8bc1\u5de5\u5177\u7684\u4e25\u8c28\u6027\u5f62\u6210\u5408\u529b\u3002<\/p>\n<p>A[&#x1f468;\u200d&#x1f52c; \u6570\u5b66\u5bb6: \u63d0\u51fa\u731c\u60f3\/\u8bc1\u660e\u6846\u67b6] &#8211;&gt; B{\u5c06\u6838\u5fc3\u601d\u60f3\u5206\u89e3\u4e3a\u81ea\u7136\u8bed\u8a00\u6b65\u9aa4}; B &#8211;&gt; C[&#x1f916; LLM (\u5982GPT-4): \u63d0\u4f9b\u6587\u732e\/\u4ee3\u7801\/\u5f62\u5f0f\u5316\u8349\u7a3f]; C &#8211;&gt; D{\u5c06\u8349\u7a3f\u8f6c\u5316\u4e3a\u5f62\u5f0f\u5316\u8bed\u8a00 (\u5982Lean 4)}; D &#8211;&gt; E[&#x1f5a5;\ufe0f \u7b26\u53f7\u63a8\u7406\u5f15\u64ce (Lean 4): \u68c0\u67e5\/\u9a8c\u8bc1\u6bcf\u4e00\u6b65]; E \u2013 \u9a8c\u8bc1\u5931\u8d25 &#8211;&gt; F[\u8fd4\u56de\u9519\u8bef\/\u5f85\u8bc1\u660e\u5f15\u7406]; F &#8211;&gt; C; E \u2013 \u9a8c\u8bc1\u6210\u529f &#8211;&gt; G[\u2705 \u8bc1\u660e\u7247\u6bb5\u5b8c\u6210]; G &#8211;&gt; B; subgraph \u4eba\u673a\u8fed\u4ee3\u5faa\u73af B C D E F G end A &#8211;&gt; H[&#x1f9e0; \u6570\u5b66\u5bb6: \u8bc4\u4f30\u6574\u4f53\u903b\u8f91\/\u8c03\u6574\u6846\u67b6]; G &#8211;&gt; H; H &#8211;&gt; A;<\/p>\n<p>\u8fd9\u4e2a\u6d41\u7a0b\u7684\u6838\u5fc3\u5728\u4e8e\u5feb\u901f\u8fed\u4ee3\u3002\u6570\u5b66\u5bb6\u4e0d\u518d\u9700\u8981\u72ec\u81ea\u5b8c\u6210\u6240\u6709\u7ec6\u8282&#xff0c;\u800c\u662f\u5c06\u975e\u521b\u9020\u6027\u7684\u90e8\u5206\u5916\u5305\u7ed9AI\u548c\u9a8c\u8bc1\u5de5\u5177&#xff0c;\u81ea\u5df1\u5219\u805a\u7126\u4e8e\u66f4\u9ad8\u5c42\u6b21\u7684\u6218\u7565\u89c4\u5212\u548c\u6700\u7ec8\u5ba1\u6838\u3002<\/p>\n<h4>\u6838\u5fc3\u6280\u672f\u6808\u4e0e\u67b6\u6784<\/h4>\n<p>\u8981\u5b9e\u73b0\u4e0a\u8ff0\u6d41\u7a0b&#xff0c;\u9700\u8981\u4e00\u5957\u6574\u5408\u4e86\u5927\u578b\u8bed\u8a00\u6a21\u578b&#xff08;LLM&#xff09;\u548c\u7b26\u53f7\u63a8\u7406\u5f15\u64ce&#xff08;\u6216\u79f0\u5f62\u5f0f\u5316\u8bc1\u660e\u52a9\u624b&#xff0c;\u5982Lean, Coq, Isabelle&#xff09;\u7684\u7cfb\u7edf\u3002\u5176\u6280\u672f\u67b6\u6784\u53ef\u4ee5\u5982\u4e0b\u8bbe\u8ba1&#xff1a;<\/p>\n<p>subgraph \u7528\u6237\u754c\u9762 (VS Code\u7b49) A[\u6570\u5b66\u5bb6\u8f93\u5165: \u81ea\u7136\u8bed\u8a00\/Lean\u4ee3\u7801] end<\/p>\n<p>&gt;subgraph \u4e2d\u95f4\u4ef6 (Middleware)<br \/>\n    B[\u6a21\u578b\u4e0a\u4e0b\u6587\u534f\u8bae (MCP) \u670d\u52a1\u5668]<br \/>\n    B &#8212; 1. \u5c01\u88c5\u8bf7\u6c42 &#8211;&gt; C{LLM \u670d\u52a1 (GPT-4\/Claude\/DeepSeek API)}<br \/>\n    C &#8212; 2. \u8fd4\u56de\u81ea\u7136\u8bed\u8a00\/\u4ee3\u7801\u5efa\u8bae &#8211;&gt; B<br \/>\n    B &#8212; 3. \u8f6c\u53d1\u6307\u4ee4 &#8211;&gt; D[\u5f62\u5f0f\u5316\u8bc1\u660e\u52a9\u624b\u63a5\u53e3 (Lean Server)]<br \/>\n    D &#8212; 4. \u8fd4\u56de\u8bc1\u660e\u72b6\u6001\/\u9519\u8bef &#8211;&gt; B<br \/>\nend<\/p>\n<p>subgraph \u540e\u7aef\u670d\u52a1 C D end<\/p>\n<p>A &#8211;&gt; B B &#8211;&gt; A<\/p>\n<p>\u67b6\u6784\u89e3\u8bfb:<\/p>\n<li>\u7528\u6237\u754c\u9762: \u6570\u5b66\u5bb6\u5728\u719f\u6089\u7684\u5f00\u53d1\u73af\u5883&#xff08;\u5982VS Code\u914d\u5408Lean 4\u63d2\u4ef6&#xff09;\u4e2d\u5de5\u4f5c\u3002<\/li>\n<li>LLM \u670d\u52a1: \u8fd9\u662fAI\u7684\u5927\u8111&#xff0c;\u8d1f\u8d23\u7406\u89e3\u81ea\u7136\u8bed\u8a00\u3001\u751f\u6210\u4ee3\u7801\u3001\u63d0\u4f9b\u89e3\u9898\u601d\u8def\u3002<\/li>\n<li>\u5f62\u5f0f\u5316\u8bc1\u660e\u52a9\u624b: \u8fd9\u662f\u4fdd\u8bc1\u4e25\u8c28\u6027\u7684\u6838\u5fc3\u3002\u4ee5Lean 4\u4e3a\u4f8b&#xff0c;\u5b83\u63d0\u4f9b\u4e86\u4e00\u4e2a\u8bed\u8a00\u670d\u52a1\u5668&#xff08;Language Server&#xff09;&#xff0c;\u53ef\u4ee5\u5b9e\u65f6\u68c0\u67e5\u4ee3\u7801\u7684\u8bed\u6cd5\u548c\u903b\u8f91&#xff0c;\u5e76\u62a5\u544a\u8bc1\u660e\u662f\u5426\u5b8c\u6210 [[34]]\u3002<\/li>\n<li>\u4e2d\u95f4\u4ef6 (MCP): \u8fd9\u662f\u6574\u4e2a\u7cfb\u7edf\u7684\u201c\u795e\u7ecf\u4e2d\u67a2\u201d&#xff0c;\u4e5f\u662f\u6700\u5173\u952e\u7684\u521b\u65b0\u70b9\u3002\u5355\u7eaf\u7684LLM\u65e0\u6cd5\u76f4\u63a5\u4e0eLean 4\u7684\u670d\u52a1\u5668\u8fdb\u884c\u6709\u72b6\u6001\u7684\u4ea4\u4e92\u3002\u6a21\u578b\u4e0a\u4e0b\u6587\u534f\u8bae&#xff08;Model Context Protocol, MCP&#xff09; [[35]] \u6216\u7c7b\u4f3c\u7684\u4e2d\u95f4\u4ef6&#xff0c;\u5c31\u662f\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u800c\u8bbe\u8ba1\u7684\u3002\u5b83\u5145\u5f53\u7ffb\u8bd1\u548c\u8c03\u5ea6\u5458&#xff1a;\n<ul>\n<li>\u5b83\u5c06\u6570\u5b66\u5bb6\u5728IDE\u4e2d\u7684\u8bf7\u6c42&#xff08;\u4f8b\u5982&#xff0c;\u201c\u5e2e\u6211\u8bc1\u660e\u8fd9\u4e2a\u5f15\u7406\u201d&#xff09;\u548c\u5f53\u524d\u7684\u8bc1\u660e\u4e0a\u4e0b\u6587&#xff08;proof state&#xff09;\u6253\u5305&#xff0c;\u53d1\u9001\u7ed9LLM\u3002<\/li>\n<li>\u5b83\u63a5\u6536LLM\u8fd4\u56de\u7684\u4ee3\u7801\u6216\u7b56\u7565\u3002<\/li>\n<li>\u5b83\u5c06\u4ee3\u7801\u53d1\u9001\u7ed9Lean Server\u6267\u884c&#xff0c;\u5e76\u83b7\u53d6\u7ed3\u679c&#xff08;\u6210\u529f\u3001\u5931\u8d25\u3001\u65b0\u7684\u8bc1\u660e\u76ee\u6807&#xff09;\u3002<\/li>\n<li>\u5b83\u5c06\u8fd9\u4e2a\u7ed3\u679c\u53cd\u9988\u7ed9\u6570\u5b66\u5bb6\u548cLLM&#xff0c;\u5f62\u6210\u4e00\u4e2a\u5b8c\u6574\u7684\u4ea4\u4e92\u95ed\u73af\u3002<\/li>\n<\/ul>\n<\/li>\n<h4>\u52a8\u624b\u90e8\u7f72&#xff1a;\u4e00\u4e2a\u57fa\u4e8eDocker\u7684Lean 4 &#043; AI\u8f85\u52a9\u6d41\u6c34\u7ebf\u6982\u5ff5\u6a21\u677f<\/h4>\n<p>\u5c3d\u7ba1\u76ee\u524d\u8fd8\u6ca1\u6709\u4e00\u4e2a\u88ab\u5e7f\u6cdb\u63a5\u53d7\u7684\u201c\u6807\u51c6\u201d\u90e8\u7f72\u65b9\u6848&#xff0c;\u4f46\u6211\u4eec\u53ef\u4ee5\u57fa\u4e8e\u4e0a\u8ff0\u67b6\u6784&#xff0c;\u8bbe\u8ba1\u4e00\u4e2a\u4f7f\u7528Docker Compose\u7684\u672c\u5730\u5f00\u53d1\u73af\u5883\u3002\u8fd9\u5957\u73af\u5883\u53ef\u4ee5\u8ba9\u6570\u5b66\u5bb6\u5728\u81ea\u5df1\u7684\u7535\u8111\u4e0a&#xff0c;\u5b89\u5168\u3001\u4fbf\u6377\u5730\u5b9e\u9a8c\u8fd9\u5957\u5de5\u4f5c\u6d41\u3002<\/p>\n<p>\u9879\u76ee\u6587\u4ef6\u7ed3\u6784:<\/p>\n<p>lean-ai-workspace\/<br \/>\n\u251c\u2500\u2500 docker-compose.yml<br \/>\n\u251c\u2500\u2500 .env<br \/>\n\u2514\u2500\u2500 services\/<br \/>\n    \u2514\u2500\u2500 lean_server\/<br \/>\n        \u251c\u2500\u2500 Dockerfile<br \/>\n        \u2514\u2500\u2500 project\/<br \/>\n            \u2514\u2500\u2500 Main.lean<\/p>\n<p>1. .env \u6587\u4ef6 (\u73af\u5883\u53d8\u91cf)<\/p>\n<p>\u8fd9\u4e2a\u6587\u4ef6\u7528\u4e8e\u5b58\u653e\u4f60\u7684API\u5bc6\u94a5\u7b49\u654f\u611f\u4fe1\u606f&#xff0c;\u907f\u514d\u786c\u7f16\u7801\u3002<\/p>\n<p><span class=\"token comment\"># .env<\/span><br \/>\n<span class=\"token comment\"># \u4f60\u7684OpenAI\u6216\u5176\u4ed6LLM\u63d0\u4f9b\u5546\u7684API\u5bc6\u94a5<\/span><br \/>\n<span class=\"token assign-left variable\">OPENAI_API_KEY<\/span><span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;sk-xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx&#034;<\/span><\/p>\n<p><span class=\"token comment\"># LLM\u6a21\u578b\u7684\u540d\u79f0<\/span><br \/>\n<span class=\"token assign-left variable\">LLM_MODEL_NAME<\/span><span class=\"token operator\">&#061;<\/span><span class=\"token string\">&#034;gpt-4-turbo&#034;<\/span><\/p>\n<p><span class=\"token comment\"># \u4e2d\u95f4\u4ef6\u670d\u52a1\u7684\u7aef\u53e3<\/span><br \/>\n<span class=\"token assign-left variable\">MCP_BRIDGE_PORT<\/span><span class=\"token operator\">&#061;<\/span><span class=\"token number\">8001<\/span><\/p>\n<p>2. services\/lean_server\/Dockerfile (Lean 4\u73af\u5883)<\/p>\n<p>\u8fd9\u4e2aDockerfile\u7528\u4e8e\u6784\u5efa\u4e00\u4e2a\u5305\u542bLean 4\u53ca\u5176\u9879\u76ee\u7ba1\u7406\u5de5\u5177lake\u7684\u72ec\u7acb\u73af\u5883\u3002<\/p>\n<p># \u4f7f\u7528\u5b98\u65b9\u6216\u793e\u533a\u7ef4\u62a4\u7684Lean 4\u57fa\u7840\u955c\u50cf<br \/>\nFROM ghcr.io\/leanprover\/lean:stable<\/p>\n<p># \u8bbe\u7f6e\u5de5\u4f5c\u76ee\u5f55<br \/>\nWORKDIR \/workspace<\/p>\n<p># \u590d\u5236\u4f60\u7684Lean\u9879\u76ee\u6587\u4ef6\u5230\u5bb9\u5668\u4e2d<br \/>\n# \u521d\u59cb\u53ef\u4ee5\u53ea\u6709\u4e00\u4e2a\u7a7a\u7684Main.lean<br \/>\nCOPY .\/project \/workspace\/project<\/p>\n<p>WORKDIR \/workspace\/project<\/p>\n<p># \u6784\u5efaLean\u9879\u76ee\u4ee5\u4e0b\u8f7d\u4f9d\u8d56 (\u5982mathlib4)<br \/>\n# RUN lake build<\/p>\n<p># \u66b4\u9732Lean\u8bed\u8a00\u670d\u52a1\u5668\u53ef\u80fd\u4f7f\u7528\u7684\u7aef\u53e3&#xff08;\u5982\u679c\u9700\u8981\u8de8\u5bb9\u5668\u76f4\u63a5\u8bbf\u95ee&#xff09;<br \/>\n# EXPOSE 8080 <\/p>\n<p># \u9ed8\u8ba4\u542f\u52a8\u547d\u4ee4&#xff0c;\u53ef\u4ee5\u662f\u4e00\u4e2a\u957f\u65f6\u95f4\u8fd0\u884c\u7684\u8fdb\u7a0b\u4ee5\u4fdd\u6301\u5bb9\u5668\u5b58\u6d3b<br \/>\nCMD [&#034;\/bin\/bash&#034;, &#034;-c&#034;, &#034;echo &#039;Lean 4 server environment is running.&#039; &amp;&amp; tail -f \/dev\/null&#034;]<\/p>\n<p>3. docker-compose.yml (\u6838\u5fc3\u7f16\u6392\u6587\u4ef6)<\/p>\n<p>\u8fd9\u662f\u6240\u6709\u670d\u52a1\u7684\u201c\u603b\u6307\u6325\u201d&#xff0c;\u5b9a\u4e49\u4e86lean-server&#xff08;\u5f62\u5f0f\u5316\u9a8c\u8bc1\u73af\u5883&#xff09;\u548c\u4e00\u4e2a\u5047\u8bbe\u7684mcp-bridge&#xff08;AI\u4e0eLean\u7684\u6865\u6881&#xff09;\u3002<\/p>\n<p><span class=\"token key atrule\">version<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token string\">&#039;3.8&#039;<\/span><\/p>\n<p><span class=\"token key atrule\">services<\/span><span class=\"token punctuation\">:<\/span><br \/>\n  <span class=\"token comment\"># Lean 4 \u5f62\u5f0f\u5316\u9a8c\u8bc1\u670d\u52a1<\/span><br \/>\n  <span class=\"token key atrule\">lean-server<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token key atrule\">container_name<\/span><span class=\"token punctuation\">:<\/span> lean_server_container<br \/>\n    <span class=\"token key atrule\">build<\/span><span class=\"token punctuation\">:<\/span><br \/>\n      <span class=\"token key atrule\">context<\/span><span class=\"token punctuation\">:<\/span> .\/services\/lean_server<br \/>\n      <span class=\"token key atrule\">dockerfile<\/span><span class=\"token punctuation\">:<\/span> Dockerfile<br \/>\n    <span class=\"token key atrule\">volumes<\/span><span class=\"token punctuation\">:<\/span><br \/>\n      <span class=\"token comment\"># \u5c06\u672c\u5730\u9879\u76ee\u76ee\u5f55\u6302\u8f7d\u5230\u5bb9\u5668\u4e2d&#xff0c;\u5b9e\u73b0\u4ee3\u7801\u5b9e\u65f6\u540c\u6b65<\/span><br \/>\n      <span class=\"token punctuation\">&#8211;<\/span> .\/services\/lean_server\/project<span class=\"token punctuation\">:<\/span>\/workspace\/project<br \/>\n    <span class=\"token key atrule\">networks<\/span><span class=\"token punctuation\">:<\/span><br \/>\n      <span class=\"token punctuation\">&#8211;<\/span> math_ai_net<br \/>\n    <span class=\"token comment\"># \u8ba9\u5bb9\u5668\u4fdd\u6301\u8fd0\u884c<\/span><br \/>\n    <span class=\"token key atrule\">stdin_open<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token boolean important\">true<\/span><br \/>\n    <span class=\"token key atrule\">tty<\/span><span class=\"token punctuation\">:<\/span> <span class=\"token boolean important\">true<\/span><\/p>\n<p>  <span class=\"token comment\"># \u5047\u8bbe\u7684MCP\u6865\u63a5\u670d\u52a1&#xff08;AI\u4e0eLean\u7684\u8fde\u63a5\u5668&#xff09;<\/span><br \/>\n  <span class=\"token comment\"># \u5728\u73b0\u5b9e\u4e2d&#xff0c;\u8fd9\u53ef\u80fd\u662f\u4e00\u4e2a\u5f00\u6e90\u9879\u76ee\u6216\u4f60\u81ea\u5df1\u5f00\u53d1\u7684\u811a\u672c<\/span><br \/>\n  <span class=\"token key atrule\">mcp-bridge<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token key atrule\">container_name<\/span><span class=\"token punctuation\">:<\/span> mcp_bridge_container<br \/>\n    <span class=\"token comment\"># \u5047\u8bbe\u6709\u4e00\u4e2a\u9884\u6784\u5efa\u7684\u955c\u50cf&#xff0c;\u6216\u8005\u4f60\u4e5f\u9700\u8981\u4e3a\u5b83\u5199\u4e00\u4e2aDockerfile<\/span><br \/>\n    <span class=\"token key atrule\">image<\/span><span class=\"token punctuation\">:<\/span> ghcr.io\/your<span class=\"token punctuation\">&#8211;<\/span>username\/mcp<span class=\"token punctuation\">&#8211;<\/span>lean<span class=\"token punctuation\">&#8211;<\/span>bridge<span class=\"token punctuation\">:<\/span>latest<br \/>\n    <span class=\"token key atrule\">restart<\/span><span class=\"token punctuation\">:<\/span> always<br \/>\n    <span class=\"token key atrule\">ports<\/span><span class=\"token punctuation\">:<\/span><br \/>\n      <span class=\"token comment\"># \u5c06\u4e3b\u673a\u7684\u7aef\u53e3\u6620\u5c04\u5230\u5bb9\u5668&#xff0c;\u4ee5\u4fbfIDE\u63d2\u4ef6\u53ef\u4ee5\u8fde\u63a5<\/span><br \/>\n      <span class=\"token punctuation\">&#8211;<\/span> <span class=\"token string\">&#034;${MCP_BRIDGE_PORT}:${MCP_BRIDGE_PORT}&#034;<\/span><br \/>\n    <span class=\"token key atrule\">environment<\/span><span class=\"token punctuation\">:<\/span><br \/>\n      <span class=\"token comment\"># \u4ece.env\u6587\u4ef6\u6ce8\u5165\u73af\u5883\u53d8\u91cf<\/span><br \/>\n      <span class=\"token punctuation\">&#8211;<\/span> OPENAI_API_KEY&#061;$<span class=\"token punctuation\">{<\/span>OPENAI_API_KEY<span class=\"token punctuation\">}<\/span><br \/>\n      <span class=\"token punctuation\">&#8211;<\/span> LLM_MODEL_NAME&#061;$<span class=\"token punctuation\">{<\/span>LLM_MODEL_NAME<span class=\"token punctuation\">}<\/span><br \/>\n      <span class=\"token comment\"># \u544a\u8bc9\u6865\u63a5\u670d\u52a1\u53bb\u54ea\u91cc\u627eLean\u670d\u52a1\u5668<\/span><br \/>\n      <span class=\"token punctuation\">&#8211;<\/span> LEAN_SERVER_HOST&#061;lean_server_container<br \/>\n    <span class=\"token key atrule\">networks<\/span><span class=\"token punctuation\">:<\/span><br \/>\n      <span class=\"token punctuation\">&#8211;<\/span> math_ai_net<br \/>\n    <span class=\"token key atrule\">depends_on<\/span><span class=\"token punctuation\">:<\/span><br \/>\n      <span class=\"token punctuation\">&#8211;<\/span> lean<span class=\"token punctuation\">&#8211;<\/span>server<\/p>\n<p><span class=\"token key atrule\">networks<\/span><span class=\"token punctuation\">:<\/span><br \/>\n  <span class=\"token key atrule\">math_ai_net<\/span><span class=\"token punctuation\">:<\/span><br \/>\n    <span class=\"token key atrule\">driver<\/span><span class=\"token punctuation\">:<\/span> bridge<\/p>\n<p>\u5982\u4f55\u4f7f\u7528&#xff1a;<\/p>\n<li>\u5728\u9879\u76ee\u6839\u76ee\u5f55\u521b\u5efa\u4e0a\u8ff0\u6587\u4ef6\u3002<\/li>\n<li>\u5c06\u4f60\u7684Lean\u9879\u76ee\u653e\u5165services\/lean_server\/project\u3002<\/li>\n<li>\u5728\u7ec8\u7aef\u4e2d\u8fd0\u884c docker-compose up -d\u3002<\/li>\n<li>\u914d\u7f6e\u4f60\u7684VS Code\u63d2\u4ef6&#xff08;\u5982Lean 4\u63d2\u4ef6\u548c\u67d0\u4e2aAI Copilot\u63d2\u4ef6&#xff09;\u8fde\u63a5\u5230 localhost:8001 (MCP Bridge\u7684\u7aef\u53e3)\u3002<\/li>\n<p>\u901a\u8fc7\u8fd9\u5957\u914d\u7f6e&#xff0c;\u4f60\u5c31\u5728\u672c\u5730\u6a21\u62df\u51fa\u4e86\u4e00\u5957\u5b8c\u6574\u7684\u4eba\u673a\u534f\u540c\u5de5\u4f5c\u6d41\u3002\u867d\u7136mcp-bridge\u670d\u52a1\u5728\u73b0\u5b9e\u4e2d\u9700\u8981\u5177\u4f53\u7684\u8f6f\u4ef6\u5b9e\u73b0&#xff08;\u5982 PROOFGYM [[36]] \u6216 LeanDojo [[37]] \u8fd9\u6837\u7684\u7814\u7a76\u9879\u76ee&#xff09;&#xff0c;\u4f46\u8fd9\u4e2a\u6a21\u677f\u4e3a\u4f60\u7406\u89e3\u5176\u5de5\u4f5c\u539f\u7406\u548c\u672a\u6765\u53ef\u80fd\u7684\u90e8\u7f72\u65b9\u5f0f\u63d0\u4f9b\u4e86\u575a\u5b9e\u7684\u84dd\u56fe\u3002<\/p>\n<h3>\u56db\u3001 \u5bf9\u6297\u5f0f\u5ba1\u67e5AI\u7684\u201c\u963f\u5580\u7409\u65af\u4e4b\u8e35\u201d&#xff1a;\u5f53\u63a8\u7406\u94fe\u6761\u65ad\u88c2\u65f6<\/h3>\n<p>\u9093\u715c\u7684\u5ba1\u614e&#xff08;\u201cAI\u7684\u8bc1\u660e\u9700\u8981\u4e25\u683c\u6838\u9a8c\u201d&#xff09;\u548c\u738b\u8679\u7684\u8fb9\u754c\u8bba\u63d0\u9192\u6211\u4eec&#xff0c;\u5fc5\u987b\u5bf9AI\u7684\u80fd\u529b\u8fdb\u884c\u5bf9\u6297\u5f0f\u5ba1\u67e5\u3002AI\u5728\u6570\u5b66\u63a8\u7406\u4e2d\u6700\u5927\u7684\u5f31\u70b9\u662f\u4ec0\u4e48&#xff1f;\u7b54\u6848\u662f&#xff1a;\u957f\u7a0b\u903b\u8f91\u8fde\u8d2f\u6027\u7684\u8106\u5f31\u6027 (fragility of long-range logical coherence)\u3002<\/p>\n<p>AI&#xff0c;\u5c24\u5176\u662f\u57fa\u4e8eTransformer\u67b6\u6784\u7684LLM&#xff0c;\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u201c\u6ce8\u610f\u529b\u201d\u6709\u9650\u7684\u7cfb\u7edf\u3002\u5b83\u80fd\u51fa\u8272\u5730\u5904\u7406\u5c40\u90e8\u4f9d\u8d56\u5173\u7cfb&#xff0c;\u4f46\u5728\u4e00\u4e2a\u9700\u8981\u51e0\u5341\u6b65\u3001\u73af\u73af\u76f8\u6263\u3001\u524d\u540e\u5f15\u7528\u7684\u590d\u6742\u6570\u5b66\u8bc1\u660e\u4e2d&#xff0c;\u5b83\u5f88\u5bb9\u6613\u201c\u8ff7\u5931\u201d\u3002<\/p>\n<h4>\u5931\u6548\u6a21\u5f0f&#xff1a;\u63a8\u7406\u94fe\u5982\u4f55\u5d29\u6e83<\/h4>\n<p>\u5b66\u672f\u754c\u901a\u8fc7\u5404\u79cd\u57fa\u51c6\u6d4b\u8bd5&#xff0c;\u5df2\u7ecf\u8bc6\u522b\u51fa\u51e0\u79cd\u5178\u578b\u7684\u5931\u6548\u6a21\u5f0f&#xff1a;<\/p>\n<li>\u903b\u8f91\u8fde\u8d2f\u6027\u4e27\u5931&#xff08;Loss of Logical Coherence&#xff09;: \u8fd9\u662f\u6700\u6838\u5fc3\u7684\u95ee\u9898\u3002\u6a21\u578b\u53ef\u80fd\u6b63\u786e\u5b8c\u6210\u4e86\u8bc1\u660e\u7684\u524d\u4e09\u6b65&#xff0c;\u4f46\u5728\u7b2c\u56db\u6b65&#xff0c;\u5b83\u201c\u5fd8\u8bb0\u201d\u4e86\u7b2c\u4e00\u6b65\u4e2d\u5f15\u5165\u7684\u67d0\u4e2a\u53d8\u91cf\u7684\u7ea6\u675f\u6761\u4ef6&#xff0c;\u5bfc\u81f4\u540e\u7eed\u6240\u6709\u63a8\u7406\u5efa\u7acb\u5728\u9519\u8bef\u7684\u57fa\u7840\u4e0a\u3002EvolMathEval\u57fa\u51c6\u6d4b\u8bd5\u7279\u522b\u6307\u51fa\u4e86\u8fd9\u4e00\u70b9 [[38]]\u3002<\/li>\n<li>\u601d\u7ef4\u9519\u8bef&#xff08;Thought Error&#xff09;: \u5728\u4f7f\u7528\u5de5\u5177&#xff08;\u5982\u8c03\u7528\u8ba1\u7b97\u5668\u6216\u4ee3\u7801\u89e3\u91ca\u5668&#xff09;\u8fdb\u884c\u591a\u6b65\u63a8\u7406\u65f6&#xff0c;\u6a21\u578b\u4f1a\u72af\u4e0b\u8ba1\u5212\u5c42\u9762\u7684\u9519\u8bef\u3002\u6bd4\u5982&#xff0c;\u5b83\u672c\u5e94\u5148\u8ba1\u7b97A&#xff0c;\u518d\u7528A\u7684\u7ed3\u679c\u8ba1\u7b97B&#xff0c;\u4f46\u5b83\u5374\u9519\u8bef\u5730\u5148\u5c1d\u8bd5\u8ba1\u7b97B&#xff0c;\u5bfc\u81f4\u56e0\u7f3a\u5c11\u8f93\u5165\u800c\u5931\u8d25\u3002ToolMATH\u57fa\u51c6\u6d4b\u8bd5\u53d1\u73b0&#xff0c;\u8fd9\u7c7b\u9519\u8bef\u5728\u957f\u7a0b\u63a8\u7406\u4efb\u52a1\u4e2d\u5360\u6bd4\u8d85\u8fc790% [[39]]\u3002<\/li>\n<li>\u4ee5\u7279\u4f8b\u4ee3\u66ff\u8bc1\u660e&#xff08;Generalization from Examples&#xff09;: \u8fd9\u662f\u6570\u5b66\u65b0\u624b\u5e38\u72af\u7684\u9519\u8bef&#xff0c;AI\u4e5f\u672a\u80fd\u5e78\u514d\u3002\u6a21\u578b\u53ef\u80fd\u4f1a\u901a\u8fc7\u9a8c\u8bc1n&#061;1, 2, 3\u65f6\u4e00\u4e2a\u547d\u9898\u6210\u7acb&#xff0c;\u5c31\u8349\u7387\u5730\u5f97\u51fa\u7ed3\u8bba\u8bf4\u5b83\u5bf9\u6240\u6709\u81ea\u7136\u6570n\u90fd\u6210\u7acb&#xff0c;\u800c\u6ca1\u6709\u7ed9\u51fa\u5f52\u7eb3\u6cd5\u7684\u4e25\u8c28\u6b65\u9aa4 [[40]]\u3002<\/li>\n<li>\u5f62\u5f0f\u8bed\u4e49\u7ef4\u6301\u5931\u8d25&#xff08;Failure to Preserve Formal Semantics&#xff09;: \u5728\u5f62\u5f0f\u5316\u8bc1\u660e\u4e2d&#xff0c;\u6bcf\u4e00\u6b65\u90fd\u5fc5\u987b\u4e25\u683c\u9075\u5b88\u8bed\u6cd5\u548c\u8bed\u4e49\u89c4\u5219\u3002LLM\u5728\u751f\u6210\u5f62\u5f0f\u5316\u8bed\u8a00&#xff08;\u5982Lean\u4ee3\u7801&#xff09;\u65f6&#xff0c;\u5e38\u5e38\u4f1a\u4ea7\u751f\u8bed\u6cd5\u6b63\u786e\u4f46\u8bed\u4e49\u9519\u8bef\u7684\u4ee3\u7801&#xff0c;\u6216\u8005\u65e0\u6cd5\u6b63\u786e\u5730\u66f4\u65b0\u548c\u7ef4\u6301\u5f53\u524d\u7684\u201c\u8bc1\u660e\u72b6\u6001\u201d [[41]]\u3002<\/li>\n<h4>\u5b9a\u91cf\u8bc4\u4f30&#xff1a;\u7528\u57fa\u51c6\u548c\u811a\u672c\u8861\u91cf\u201c\u5d29\u6e83\u7387\u201d<\/h4>\n<p>\u4e3a\u4e86\u91cf\u5316\u8fd9\u4e9b\u5931\u6548\u6a21\u5f0f&#xff0c;\u5b66\u672f\u754c\u5f00\u53d1\u4e86\u4e00\u7cfb\u5217\u4e13\u95e8\u7684\u57fa\u51c6\u6d4b\u8bd5\u96c6\u548c\u81ea\u52a8\u5316\u8bc4\u4f30\u811a\u672c\u3002\u5bf9\u4e8e\u60f3\u6df1\u5165\u7814\u7a76\u6216\u4f7f\u7528AI\u8fdb\u884c\u4e25\u8083\u6570\u5b66\u5de5\u4f5c\u7684\u7814\u7a76\u8005\u6765\u8bf4&#xff0c;\u4e86\u89e3\u5e76\u4f7f\u7528\u8fd9\u4e9b\u5de5\u5177\u81f3\u5173\u91cd\u8981\u3002<\/p>\n<p>\u6838\u5fc3\u5de5\u5177\u63a8\u8350&#xff1a;FormalMATH<\/p>\n<p>\u5728\u4f17\u591a\u57fa\u51c6\u4e2d&#xff0c;FormalMATH [[42]][[43]]\u662f\u76ee\u524d\u4e0e\u6211\u4eec\u8ba8\u8bba\u7684\u4e3b\u9898\u6700\u5951\u5408\u7684\u5de5\u5177\u4e4b\u4e00\u3002\u5b83\u4e13\u4e3a\u8bc4\u4f30LLM\u7684\u5f62\u5f0f\u5316\u6570\u5b66\u63a8\u7406\u80fd\u529b\u800c\u8bbe\u8ba1&#xff0c;\u5177\u6709\u4ee5\u4e0b\u5173\u952e\u7279\u70b9&#xff1a;<\/p>\n<ul>\n<li>\u5f62\u5f0f\u5316\u9a8c\u8bc1: \u5b83\u4e0d\u4f9d\u8d56\u4e8e\u6700\u7ec8\u7b54\u6848\u662f\u5426\u6b63\u786e&#xff0c;\u800c\u662f\u4f7f\u7528Lean 4\u5b9a\u7406\u8bc1\u660e\u5668\u6765\u5f62\u5f0f\u5316\u5730\u9a8c\u8bc1\u6a21\u578b\u751f\u6210\u7684\u6bcf\u4e00\u6b65\u8bc1\u660e\u4ee3\u7801\u3002\u8fd9\u76f4\u63a5\u547d\u4e2d\u4e86\u957f\u7a0b\u903b\u8f91\u8fde\u8d2f\u6027\u7684\u8981\u5bb3\u3002<\/li>\n<li>\u5e7f\u9614\u7684\u8986\u76d6\u9762: \u95ee\u9898\u6db5\u76d6\u4ece\u9ad8\u4e2d\u5230\u5927\u5b66\u672c\u79d1\u7684\u591a\u4e2a\u6570\u5b66\u9886\u57df&#xff0c;\u5305\u62ec\u4ee3\u6570\u3001\u6570\u8bba\u3001\u5fae\u79ef\u5206\u7b49\u3002<\/li>\n<li>\u81ea\u52a8\u5316\u8bc4\u4f30\u6d41\u6c34\u7ebf: \u5b83\u63d0\u4f9b\u4e86\u4e00\u5957\u5b8c\u6574\u7684Python\u811a\u672c&#xff0c;\u53ef\u4ee5\u81ea\u52a8\u5316\u5730\u5b8c\u6210\u201c\u6a21\u578b\u751f\u6210-\u4ee3\u7801\u9a8c\u8bc1-\u7ed3\u679c\u8bc4\u4f30\u201d\u7684\u5168\u8fc7\u7a0b\u3002<\/li>\n<\/ul>\n<p>FormalMATH \u8bc4\u4f30\u5de5\u4f5c\u6d41<\/p>\n<p>subgraph \u51c6\u5907\u9636\u6bb5 A[\u4e0b\u8f7dFormalMATH\u6570\u636e\u96c6] &#8211;&gt; B[\u914d\u7f6eLLM API] end subgraph \u8fd0\u884c\u9636\u6bb5 C[\u8fd0\u884c FoMA_Eval.py &#8211;generate] &#8211;&gt; D[\u6a21\u578b\u4e3a\u6bcf\u4e2a\u95ee\u9898\u751f\u6210Lean 4\u8bc1\u660e\u4ee3\u7801] D &#8211;&gt; E[\u8fd0\u884c FoMA_Eval.py &#8211;verify] E &#8211;&gt; F{Lean 4 \u7f16\u8bd1\u5668\/\u670d\u52a1\u5668} F \u2013 \u9010\u884c\/\u9010\u7b56\u7565\u9a8c\u8bc1 &#8211;&gt; E E &#8211;&gt; G[\u751f\u6210\u9a8c\u8bc1\u7ed3\u679c (pass\/fail\/timeout)] end subgraph \u8bc4\u4f30\u9636\u6bb5 G &#8211;&gt; H[\u8fd0\u884c FoMA_Eval.py &#8211;evaluate] &#8211;&gt; I[\u8ba1\u7b97\u901a\u8fc7\u7387 (Pass&#064;k) \u7b49\u6307\u6807] end<\/p>\n<p>A \u2013 auto_dl &#8211;&gt; C<\/p>\n<hr \/>\n<p>\u5b9e\u6218\u6307\u5357&#xff1a;\u5982\u4f55\u83b7\u53d6\u5e76\u4f7f\u7528FormalMATH<\/p>\n<p>\u4ee5\u4e0b\u662f\u5982\u4f55\u83b7\u53d6\u5e76\u8fd0\u884cFormalMATH\u8bc4\u4f30\u811a\u672c\u7684\u7b80\u660e\u6307\u5357&#xff1a;<\/p>\n<p><span class=\"token comment\"># 1. \u514b\u9686FormalMATH\u7684\u5b98\u65b9GitHub\u4ed3\u5e93<\/span><br \/>\n<span class=\"token comment\"># (\u6ce8\u610f&#xff1a;\u6b64\u4e3a\u5047\u8bbe\u7684\u4ed3\u5e93\u5730\u5740&#xff0c;\u8bf7\u4ee5\u5b98\u65b9\u53d1\u5e03\u4e3a\u51c6)<\/span><br \/>\n<span class=\"token function\">git<\/span> clone https:\/\/github.com\/formal-math-repo\/FormalMATH.git<br \/>\n<span class=\"token builtin class-name\">cd<\/span> FormalMATH<\/p>\n<p><span class=\"token comment\"># 2. \u5b89\u88c5\u6240\u9700\u7684Python\u4f9d\u8d56<\/span><br \/>\npip <span class=\"token function\">install<\/span> <span class=\"token parameter variable\">-r<\/span> requirements.txt<\/p>\n<p><span class=\"token comment\"># 3. \u914d\u7f6eLean\u73af\u5883<\/span><br \/>\n<span class=\"token comment\"># \u811a\u672c\u901a\u5e38\u4f1a\u81ea\u52a8\u5904\u7406&#xff0c;\u6216\u6839\u636e\u5176\u6587\u6863\u6307\u5f15\u5b89\u88c5elan (Lean\u7684\u7248\u672c\u7ba1\u7406\u5668)<\/span><\/p>\n<p><span class=\"token comment\"># 4. (\u53ef\u9009) \u81ea\u52a8\u4e0b\u8f7d\u6570\u636e\u96c6<\/span><br \/>\n<span class=\"token comment\"># \u811a\u672c\u9996\u6b21\u8fd0\u884c\u65f6\u4f1a\u81ea\u52a8\u4eceHugging Face\u4e0b\u8f7d<\/span><br \/>\n<span class=\"token comment\"># \u4f60\u4e5f\u53ef\u4ee5\u624b\u52a8\u4e0b\u8f7d\u5e76\u653e\u7f6e\u5728\u6307\u5b9a\u76ee\u5f55<\/span><\/p>\n<p><span class=\"token comment\"># 5. \u8fd0\u884c\u8bc4\u4f30\u6d41\u6c34\u7ebf<\/span><br \/>\n<span class=\"token comment\"># \u5047\u8bbe\u4f60\u8981\u8bc4\u4f30GPT-4&#xff0c;\u5e76\u81ea\u52a8\u4e0b\u8f7d\u6570\u636e\u96c6<\/span><\/p>\n<p><span class=\"token comment\"># \u6b65\u9aa4\u4e00&#xff1a;\u751f\u6210\u7b54\u6848<\/span><br \/>\n<span class=\"token comment\"># (\u4f60\u9700\u8981\u5148\u5728\u811a\u672c\u6216\u73af\u5883\u53d8\u91cf\u4e2d\u914d\u7f6e\u597d\u4f60\u7684API Key)<\/span><br \/>\npython FoMA_Eval.py <span class=\"token punctuation\">\\\\<\/span><br \/>\n    <span class=\"token parameter variable\">&#8211;model<\/span> gpt-4-turbo <span class=\"token punctuation\">\\\\<\/span><br \/>\n    <span class=\"token parameter variable\">&#8211;dataset<\/span> FoMA-v1 <span class=\"token punctuation\">\\\\<\/span><br \/>\n    <span class=\"token parameter variable\">&#8211;mode<\/span> generation <span class=\"token punctuation\">\\\\<\/span><br \/>\n    <span class=\"token parameter variable\">&#8211;auto_dl<\/span><\/p>\n<p><span class=\"token comment\"># \u6b65\u9aa4\u4e8c&#xff1a;\u9a8c\u8bc1\u751f\u6210\u7684\u8bc1\u660e<\/span><br \/>\npython FoMA_Eval.py <span class=\"token punctuation\">\\\\<\/span><br \/>\n    <span class=\"token parameter variable\">&#8211;model<\/span> gpt-4-turbo <span class=\"token punctuation\">\\\\<\/span><br \/>\n    <span class=\"token parameter variable\">&#8211;dataset<\/span> FoMA-v1 <span class=\"token punctuation\">\\\\<\/span><br \/>\n    <span class=\"token parameter variable\">&#8211;mode<\/span> verification<\/p>\n<p><span class=\"token comment\"># \u6b65\u9aa4\u4e09&#xff1a;\u8bc4\u4f30\u7ed3\u679c<\/span><br \/>\npython FoMA_Eval.py <span class=\"token punctuation\">\\\\<\/span><br \/>\n    <span class=\"token parameter variable\">&#8211;model<\/span> gpt-4-turbo <span class=\"token punctuation\">\\\\<\/span><br \/>\n    <span class=\"token parameter variable\">&#8211;dataset<\/span> FoMA-v1 <span class=\"token punctuation\">\\\\<\/span><br \/>\n    <span class=\"token parameter variable\">&#8211;mode<\/span> evaluation<\/p>\n<p>\u901a\u8fc7\u8fd0\u884c\u8fd9\u5957\u811a\u672c [[44]]&#xff0c;\u4f60\u5c31\u80fd\u5f97\u5230\u4e00\u4e2a\u5173\u4e8e\u7279\u5b9aLLM\u5728\u5f62\u5f0f\u5316\u6570\u5b66\u63a8\u7406\u4efb\u52a1\u4e0a\u201c\u5d29\u6e83\u7387\u201d\u7684\u91cf\u5316\u6307\u6807\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u672c\u8eab&#xff0c;\u5c31\u662f\u5bf9AI\u80fd\u529b\u6700\u4e25\u683c\u3001\u6700\u4e0d\u5bb9\u60c5\u9762\u7684\u5bf9\u6297\u5f0f\u5ba1\u67e5\u3002<\/p>\n<hr \/>\n<h3>\u7ed3\u8bba&#xff1a;\u6570\u5b66\u5bb6\u7684\u672a\u6765\u2014\u2014\u6210\u4e3aAI\u7684\u201c\u7075\u9b42\u5de5\u7a0b\u5e08\u201d<\/h3>\n<p>\u56de\u5230\u6211\u4eec\u6700\u521d\u7684\u95ee\u9898&#xff1a;\u6570\u5b66\u5bb6\u4f1a\u88abAI\u53d6\u4ee3\u5417&#xff1f;<\/p>\n<p>\u901a\u8fc7\u5bf9\u9093\u715c\u3001\u738b\u8679\u89c2\u70b9\u7684\u6df1\u5ea6\u590d\u76d8\u548c\u6280\u672f\u5c42\u9762\u7684\u5b9e\u6218\u89e3\u6784&#xff0c;\u7b54\u6848\u5df2\u7ecf\u975e\u5e38\u6e05\u6670&#xff1a;\u4e0d\u4f1a\u3002\u4f46\u6570\u5b66\u5bb6\u7684\u89d2\u8272\u6b63\u5728\u88ab\u6df1\u523b\u5730\u91cd\u5851\u3002<\/p>\n<p>\u9093\u715c\u7684\u5b9e\u8df5\u544a\u8bc9\u6211\u4eec&#xff0c;AI\u662f\u4e00\u4e2a\u524d\u6240\u672a\u6709\u7684\u5f3a\u5927\u201c\u6760\u6746\u201d&#xff0c;\u5b83\u5c06\u6570\u5b66\u5bb6\u4ece\u7e41\u91cd\u7684\u6280\u672f\u7ec6\u8282\u4e2d\u89e3\u653e\u51fa\u6765&#xff0c;\u4f7f\u5176\u80fd\u66f4\u4e13\u6ce8\u4e8e\u601d\u60f3\u3001\u76f4\u89c9\u548c\u521b\u9020\u529b\u8fd9\u4e9b\u4eba\u7c7b\u72ec\u6709\u7684\u4ef7\u503c\u3002\u6050\u60e7\u548c\u6392\u65a5\u6beb\u65e0\u610f\u4e49&#xff0c;\u62e5\u62b1\u3001\u7406\u89e3\u5e76\u9a7e\u9a6d\u8fd9\u4e2a\u5de5\u5177&#xff0c;\u624d\u662f\u552f\u4e00\u7684\u51fa\u8def\u3002<\/p>\n<p>\u201c\u738b\u8679\u4e4b\u8c1c\u201d\u548c\u5176\u80cc\u540e\u201cMath for AI\u201d\u7684\u7ebf\u7d22\u5219\u63ed\u793a\u4e86\u66f4\u6df1\u8fdc\u7684\u672a\u6765&#xff1a;\u9876\u5c16\u6570\u5b66\u5bb6\u4e0d\u4ec5\u662fAI\u7684\u4f7f\u7528\u8005&#xff0c;\u8fd8\u5c06\u6210\u4e3aAI\u80fd\u529b\u7684\u201c\u8d4b\u80fd\u8005\u201d\u548c\u201c\u5b9a\u4e49\u8005\u201d\u3002\u4ed6\u4eec\u7528\u6700\u524d\u6cbf\u7684\u6570\u5b66\u7406\u8bba&#xff0c;\u4e3aAI\u7684\u4e0b\u4e00\u6b21\u8dc3\u8fc1\u63d0\u4f9b\u601d\u60f3\u7684\u71c3\u6599\u3002<\/p>\n<p>\u6280\u672f\u5b9e\u6218\u90e8\u5206\u5c55\u793a\u4e86\u4eba\u673a\u534f\u4f5c\u7684\u53ef\u80fd\u5f62\u6001&#xff0c;\u800c\u5bf9AI\u201c\u963f\u5580\u7409\u65af\u4e4b\u8e35\u201d\u7684\u5206\u6790\u5219\u660e\u786e\u4e86\u4eba\u7c7b\u5728\u534f\u4f5c\u4e2d\u7684\u6838\u5fc3\u5730\u4f4d\u2014\u2014\u6700\u7ec8\u7684\u88c1\u51b3\u8005\u548c\u4e25\u8c28\u6027\u7684\u5b88\u62a4\u8005\u3002AI\u53ef\u4ee5\u63d0\u4f9b\u65e0\u6570\u6761\u8def\u5f84&#xff0c;\u4f46\u54ea\u4e00\u6761\u662f\u901a\u5f80\u771f\u7406\u7684\u5eb7\u5e84\u5927\u9053&#xff0c;\u9700\u8981\u4eba\u7c7b\u7684\u667a\u6167\u548c\u5224\u65ad\u529b\u6765\u6289\u62e9\u3002<\/p>\n<p>\u672a\u6765\u7684\u6570\u5b66\u5bb6&#xff0c;\u5c06\u4e0d\u518d\u662f\u5b64\u8eab\u4e00\u4eba\u5728\u9ed1\u677f\u524d\u594b\u7b14\u75be\u4e66\u7684\u82e6\u884c\u50e7\u3002\u4ed6\u4eec\u66f4\u50cf\u662f\u4e00\u4e2a\u4ea4\u54cd\u4e50\u56e2\u7684\u6307\u6325&#xff0c;\u6216\u8005\u4e00\u4e2a\u9ad8\u79d1\u6280\u5b9e\u9a8c\u5ba4\u7684\u9996\u5e2d\u79d1\u5b66\u5bb6\u3002\u4ed6\u4eec\u9700\u8981\u638c\u63e1\u4e0eAI\u201c\u5bf9\u8bdd\u201d\u7684\u8bed\u8a00&#xff0c;\u7406\u89e3AI\u7684\u80fd\u529b\u8fb9\u754c&#xff0c;\u8bbe\u8ba1\u51fa\u80fd\u6700\u5927\u9650\u5ea6\u53d1\u6325\u4eba\u673a\u534f\u540c\u6548\u5e94\u7684\u5de5\u4f5c\u6d41\u3002\u4ed6\u4eec\u5c06\u4ece\u201c\u77e5\u8bc6\u7684\u53d1\u73b0\u8005\u201d&#xff0c;\u8fdb\u5316\u4e3a\u201c\u53d1\u73b0\u77e5\u8bc6\u7684\u673a\u5668\u7684\u7075\u9b42\u5de5\u7a0b\u5e08\u201d\u3002<\/p>\n<p>\u8fd9\u65e0\u7591\u662f\u4e00\u4e2a\u5145\u6ee1\u6311\u6218\u7684\u65f6\u4ee3&#xff0c;\u4f46\u66f4\u662f\u4e00\u4e2a\u5145\u6ee1\u65e0\u9650\u53ef\u80fd\u7684\u65f6\u4ee3\u3002\u6570\u5b66&#xff0c;\u8fd9\u95e8\u53e4\u8001\u7684\u79d1\u5b66&#xff0c;\u6b63\u56e0AI\u7684\u6ce8\u5165&#xff0c;\u8fce\u6765\u4e00\u4e2a\u9093\u715c\u6240\u9884\u8a00\u7684\u201c\u5feb\u901f\u53d1\u5c55\u7684\u65f6\u671f\u201d [[45]][[46]]\u3002<\/p>\n<hr \/>\n<p>\u4e92\u52a8\u95ee\u9898:<\/p>\n<li>\u5728\u4f60\u81ea\u5df1\u7684\u7814\u7a76\u6216\u5de5\u4f5c\u9886\u57df&#xff0c;\u6709\u54ea\u4e9b\u5177\u4f53\u3001\u7e41\u7410\u3001\u53ef\u4ee5\u88ab\u6807\u51c6\u5316\u7684\u4efb\u52a1&#xff0c;\u4f60\u8ba4\u4e3a\u4eca\u5929\u7684AI\u5df2\u7ecf\u53ef\u4ee5\u80dc\u4efb\u6216\u5728\u77ed\u671f\u5185\u53ef\u4ee5\u80dc\u4efb&#xff1f;<\/li>\n<li>\u4f60\u8ba4\u4e3a\u5728\u6570\u5b66&#xff08;\u6216\u5176\u4ed6\u4efb\u4f55\u9ad8\u5ea6\u521b\u9020\u6027\u7684\u9886\u57df&#xff09;&#xff0c;\u4ec0\u4e48\u6837\u7684\u4e00\u4e2a\u201c\u597d\u95ee\u9898\u201d\u662fAI\u6c38\u8fdc\u65e0\u6cd5\u72ec\u7acb\u63d0\u51fa\u7684&#xff1f;\u4e3a\u4ec0\u4e48&#xff1f;<\/li>\n","protected":false},"excerpt":{"rendered":"<p>\u524d\u8a00<br 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