{"id":511,"date":"2025-09-13T23:48:06","date_gmt":"2025-09-13T15:48:06","guid":{"rendered":"https:\/\/www.bertzzz-horizon.xyz\/?p=511"},"modified":"2025-09-18T13:14:13","modified_gmt":"2025-09-18T05:14:13","slug":"%e7%ae%80%e5%8d%95%e7%9a%84-lambda-calculus%ef%bc%88%e6%8b%89%e5%a7%86%e8%be%be%e6%bc%94%e7%ae%97%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.bertzzz-horizon.xyz\/?p=511","title":{"rendered":"\u7b80\u5355\u7684 Lambda Calculus\uff08\u62c9\u59c6\u8fbe\u6f14\u7b97\uff09"},"content":{"rendered":"\n

<\/p>\n\n\n\n

\u672c\u6587\u4e3b\u8981\u662f\u5bf9 Learn X in Y minutes \u7684 Lambda Calculus<\/a> \u7684\u90e8\u5206\u7ffb\u8bd1\u3002\u540c\u65f6\u53c2\u8003\u4e86 The Lambda Calculus –
Stanford Encyclopedia of Philosophy<\/a>\u3002<\/p>\n\n\n\n

P.S. \u5efa\u8bae\u5148\u8bfb\u540e\u8005\uff0c\u901a\u8bfb\u540e\u6709\u4e00\u5b9a\u7684\u8ba4\u8bc6\u5373\u53ef\uff0c\u4e4b\u540e\u518d\u4ece\u524d\u8005\u5904\u9a8c\u8bc1\u4e00\u4e0b\u3002<\/p>\n\n\n\n

\n\n\n\n

Lambda \u6f14\u7b97\uff08\"\lambda-calculus<strong>\"<\/strong>\uff09<\/strong>\u662f\u7531 Alonzo Church \u539f\u521b\u7684\u4e00\u79cd\u4e16\u754c\u4e0a\u6700\u5c0f\u7684\u7f16\u7a0b\u8bed\u8a00\u3002\u5373\u4fbf\u6ca1\u6709\u6570\u5b57\u3001\u5b57\u7b26\u4e32\u3001\u5e03\u5c14\u503c\u7b49\u4efb\u4f55\u975e\u51fd\u6570\u6570\u636e\u7c7b\u578b\uff0c\u5176\u4ecd\u7136\u53ef\u4ee5\u7528\u4e8e\u8868\u793a\u4efb\u4f55\u56fe\u7075\u673a\u3002<\/p>\n\n\n\n

\u62c9\u59c6\u8fbe\u6f14\u7b97\u7531\u4e09\u4e2a\u90e8\u5206\u7ec4\u6210\uff1a\u53d8\u91cf\u3001\u51fd\u6570\u4ee5\u53ca\u5e94\u7528\u3002<\/p>\n\n\n\n

\u540d\u79f0<\/td>\u8bed\u6cd5<\/td>\u5b9e\u4f8b<\/td>\u89e3\u91ca<\/td><\/tr>
\u53d8\u91cf<\/td>\"<name>\"<\/td>\"x\"<\/td>\u540d\u4e3a\"x\"\u7684\u53d8\u91cf<\/td><\/tr>
\u51fd\u6570<\/td>\"\lambda<parameters>.<body>\"<\/td>\"\lambda x.x\"<\/td>\u5f62\u53c2\u4e3a\"x\"\u4e14\u4e3b\u4f53\u4e3a\"x\"\u7684\u51fd\u6570<\/td><\/tr>
\u5e94\u7528<\/td>\"<function><variable or function>\"<\/td>\"(\lambda x.x)a\"<\/td>\u4ee5\u5b9e\u53c2\"a\"\u8c03\u7528\u51fd\u6570\"\lambda x.x\"<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u6700\u57fa\u672c\u7684\u51fd\u6570\u662fidentity function: \"\lambda x.x\"\uff0c\u4ee3\u8868\u7740\"f(x)=x\"\uff0c\u7b2c\u4e00\u4e2a\"x\"\u662f\u51fd\u6570\u7684\u53c2\u6570\uff0c\u7b2c\u4e8c\u4e2a\u662f\u51fd\u6570\u4f53\u3002<\/p>\n\n\n\n

\n\n\n\n

\u81ea\u7531\u53d8\u91cf\u4e0e\u7ea6\u675f\u53d8\u91cf<\/strong><\/p>\n\n\n\n

\u5728\u51fd\u6570\"\lambda x.x\"\u4e2d\uff0c”\"x\"“\u88ab\u79f0\u4f5c\u7ea6\u675f\u53d8\u91cf\uff0c\u56e0\u4e3a\u5176\u65e2\u5728\u53c2\u6570\u4e2d\uff0c\u53c8\u5728\u51fd\u6570\u4f53\u4e2d\u3002<\/p>\n\n\n\n

\u5728\"\lambda x.y\"\u4e2d\uff0c\"y\"\u88ab\u79f0\u4f5c\u81ea\u7531\u53d8\u91cf\uff0c\u56e0\u4e3a\u5176\u672a\u88ab\u9884\u5148\u58f0\u660e\u3002<\/p>\n\n\n\n

\n\n\n\n

\u6c42\u503c<\/strong><\/p>\n\n\n\n

\u6c42\u503c\u64cd\u4f5c\u901a\u8fc7\"\beta\"\u5316\u7b80(\"\beta - reduction\")\u5b8c\u6210\uff0c\u5176\u672c\u8d28\u4e0a\u662f\u8bcd\u6cd5\u4f5c\u7528\u57df\u7684\u66ff\u6362\u3002<\/p>\n\n\n\n

\u5f53\u5bf9\"(\lambda x.x)a\"\u6c42\u503c\u65f6\uff0c\u6211\u4eec\u5c06\u51fd\u6570\u4e3b\u4f53\u4e2d\u51fa\u73b0\u7684\u6240\u6709\"x\"\u66ff\u6362\u4e3a\"a\"\u3002<\/p>\n\n\n\n

\"(\lambda x.x)a\"\u7684\u6c42\u503c\u7ed3\u679c\u662f:\"a\";
\"(\lambda x.y)a\"\u7684\u6c42\u503c\u7ed3\u679c\u662f:\"y\"\u3002<\/p>\n\n\n\n

P.S. \u8fd9\u6216\u8bb8\u4e0d\u592a\u76f4\u89c2\uff0c\u56e0\u6b64\u6211\u591a\u52a0\u4e86\u4e00\u4e2a\u4f8b\u5b50\uff1a\u5f53\u6211\u4eec\u8981\u6c42\u4e00\u4e2a\u591a\u9879\u5f0f\u7684\u503c\uff0c\u4f8b\u5982\"x^2-2 \cdot x+5\"\u5728\"x=2\"\u65f6\u7684\u503c\uff0c\u4f7f\u7528\"\lambda\"\u6f14\u7b97\u6765\u8868\u793a\u8fd9\u4e2a\u60c5\u51b5:
\"(\lambda x[x^2 - 2 \cdot x + 5])2 \Rightarrow 2^2 - 2 \cdot 2 + 5 \Rightarrow 5\"<\/em><\/p>\n\n\n\n

\u4f60\u4e5f\u53ef\u4ee5\u521b\u9020\u66f4\u9ad8\u9636\u7684\u51fd\u6570:<\/p>\n\n\n\n

\"(\lambda x.(\lambda y.x))a\"\u6c42\u503c\u4e3a\"\lambda y.a\"<\/p>\n\n\n\n

\u5373\u4f7f\"\lambda\"\u6f14\u7b97\u901a\u5e38\u6765\u8bf4\u53ea\u652f\u6301\u5355\u53c2\u6570\u51fd\u6570\uff0c\u6211\u4eec\u4ecd\u7136\u53ef\u4ee5\u901a\u8fc7\u4e00\u79cd\u540d\u4e3a\u67ef\u91cc\u5316(Currying)\u7684\u6280\u5de7\u6765\u521b\u5efa\u591a\u53c2\u6570\u51fd\u6570\u3002<\/p>\n\n\n\n

\"(\lambda x.\lambda y.\lambda z.xyz)\"\u76f8\u5f53\u4e8e\"f(x, y, z) = ( (x y) z)\"<\/p>\n\n\n\n

P.S. \"(\lambda x.\lambda y.\lambda z.xyz)\"\u5b9e\u9645\u4e0a\u662f”\u4f9d\u6b21\u8fdb\u884c\u51fd\u6570\u5e94\u7528”\uff0c\u5373\"\lambda x.\"\u63a5\u53d7\u7b2c\u4e00\u4e2a\u53c2\u6570x\uff0c\u4f20\u9012\u7ed9\"\lambda y.\lambda z.xyz\"\uff0c\u4ee5\u6b64\u7c7b\u63a8\uff0c\u8fd9\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u4e09\u5c42\u5d4c\u5957\uff0c\u4f9d\u6b21\u7b49\u5f85\u53c2\u6570\u4f20\u7ed9\"x,y,z\"\u3002<\/p>\n\n\n\n

\u6709\u65f6\uff0c\"\lambda xy.<body>\"\u4e5f\u53ef\u4ee5\u8868\u793a\u4e3a\"\lambda x.\lambda y.<body>\"<\/p>\n\n\n\n

\u91cd\u8981\u7684\u662f\u8981\u8ba4\u8bc6\u5230\u4f20\u7edf\u7684 lambda \u6f14\u7b97\u6ca1\u6709\u6570\u5b57\u3001\u5b57\u7b26\u6216\u4efb\u4f55\u975e\u51fd\u6570\u6570\u636e\u7c7b\u578b\uff01<\/strong><\/p>\n\n\n\n

\u91cd\u8981\u7684\u662f\u8981\u8ba4\u8bc6\u5230\u4f20\u7edf\u7684 lambda \u6f14\u7b97\u6ca1\u6709\u6570\u5b57\u3001\u5b57\u7b26\u6216\u4efb\u4f55\u975e\u51fd\u6570\u6570\u636e\u7c7b\u578b\uff01<\/strong><\/p>\n\n\n\n

\u91cd\u8981\u7684\u662f\u8981\u8ba4\u8bc6\u5230\u4f20\u7edf\u7684 lambda \u6f14\u7b97\u6ca1\u6709\u6570\u5b57\u3001\u5b57\u7b26\u6216\u4efb\u4f55\u975e\u51fd\u6570\u6570\u636e\u7c7b\u578b\uff01<\/strong><\/p>\n\n\n\n

\n\n\n\n

\u5e03\u5c14\u903b\u8f91<\/strong><\/p>\n\n\n\n

\u5728 lambda \u6f14\u7b97\u4e2d\u6ca1\u6709 “True” \u6216 “False”\uff0c\u751a\u81f3\u6ca1\u6709 1 \u6216 0\u3002<\/p>\n\n\n\n

\u5728 lambda \u6f14\u7b97\u4e2d\uff1a<\/p>\n\n\n\n

T \u7531 \"\lambda x. \lambda y.x\"\u8868\u793a\uff1b<\/p>\n\n\n\n

F \u7531 \"\lambda x. \lambda y.y\"\u8868\u793a\u3002<\/p>\n\n\n\n

\u9996\u5148\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u4e00\u4e2a if \u51fd\u6570 \"\lambda btf\"\uff0c\u5176\u5728 \"b\" \u4e3a True \u7684\u65f6\u5019\u8fd4\u56de \"t\"\uff0c\u5728 \"b\" \u4e3a False \u7684\u65f6\u5019\u8fd4\u56de \"f\"\u3002<\/p>\n\n\n\n

\"IF\" \u76f8\u5f53\u4e8e\uff1a \"\lambda b.\lambda t.\lambda f.\text{b t f}\"<\/p>\n\n\n\n

\u4f7f\u7528 \"IF\" \u6211\u4eec\u5c31\u53ef\u4ee5\u5b9a\u4e49\u57fa\u672c\u7684\u5e03\u5c14\u903b\u8f91\u64cd\u4f5c\uff1a<\/p>\n\n\n\n

\"\text{a AND b}\" \u76f8\u5f53\u4e8e\uff1a \"\lambda ab.\text{IF a b F}\"\uff1b<\/p>\n\n\n\n

\"\text{a OR b}\" \u76f8\u5f53\u4e8e\uff1a\"\lambda ab.\text{IF a T b}\"\uff1b<\/p>\n\n\n\n

\"\text{NOT a}\" \u76f8\u5f53\u4e8e\uff1a\"\lambda a.\text{IF a F T}\"\u3002<\/p>\n\n\n\n

\u6ce8\u610f\uff1a\"\text{IF a b c}\"\u672c\u8d28\u4e0a\u662f\u5728\u8bf4\uff1a\"\text{IF( ( a b ) c )}\"<\/p>\n\n\n\n

\n\n\n\n

\u6570\u5b57<\/strong><\/p>\n\n\n\n

\u5c3d\u7ba1 lambda \u6f14\u7b97\u4e2d\u6ca1\u6709\u6570\u5b57\uff0c\u6211\u4eec\u4ecd\u7136\u53ef\u4ee5\u4f7f\u7528\u4e18\u5947\u6570\u5b57\u5bf9\u6570\u5b57\u8fdb\u884c\u7f16\u7801\u3002<\/p>\n\n\n\n

\u5bf9\u4e8e\u4efb\u4f55\u4e00\u4e2a\u6570\u5b57 n\uff1a\"n=\lambda f.f^{n}\"\uff0c\u6240\u4ee5\uff1a<\/p>\n\n\n\n

\"0=\lambda f.\lambda x.x\"<\/p>\n\n\n\n

\"1=\lambda f.\lambda x.\text{f x}\"<\/p>\n\n\n\n

\"2=\lambda f.\lambda x.\text{f ( f x )}\"<\/p>\n\n\n\n

\"3=\lambda f.\lambda x.\text{f ( f ( f x ) )}\"<\/p>\n\n\n\n

P.S. \u53ef\u4ee5\u6ce8\u610f\u5230\uff0c\u5b9e\u9645\u4e0a\u6211\u4eec\u4f7f\u7528\u201c\u6b21\u6570\u201d\u6765\u5b9a\u4e49\u81ea\u7136\u6570\u3002<\/p>\n\n\n\n

\u4e3a\u4e86\u589e\u52a0\u4e18\u5947\u6570\uff0c\u6211\u4eec\u4f7f\u7528 \u540e\u7ee7\u51fd\u6570(successor function) \"\text{S(n) = n + 1}\"\uff1a<\/p>\n\n\n\n

\"S = \lambda n.\lambda f.\lambda x.\text{f ( ( n f ) x )}\"<\/p>\n\n\n\n

\u4f7f\u7528\u540e\u7ee7\u51fd\u6570\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u52a0\u6cd5\uff1a<\/p>\n\n\n\n

\"\text{ADD} = \lambda ab.\text{(a S)b}\"<\/p>\n\n\n\n

P.S. \u6211\u4eec\u5b9a\u4e49\u7684ADD\u4e2d\u7684\"a\"\u7684\u610f\u601d\u662f\u91cd\u590d\"a\"\u6b21S\uff0c\u5373\"\text{ADD 2 3 = S(S(3))}\"\uff0c\"S(3)=4\"\uff0c\u518d\"S(4)=5\"\u3002\u540c\u65f6\u8981\u6ce8\u610f\uff0c\u6b64\u5904\u5e76\u4e0d\u662f\u201c\u5b9a\u4e49\u201d\"\text{(a S)b}\"\u4e2d\u7684a\u4ee3\u8868\u6b21\u6570\uff0c\u8fd9\u662f\u4e25\u683c\u7684\"\beta\"\u5316\u7b80\u7684\u7ed3\u679c\u3002\u5982\u679c\u4f60\u53ea\u9700\u8981\u7b80\u5355\u7684\"\lambda\"\u6f14\u7b97\u77e5\u8bc6\u6765\u5feb\u901f\u5165\u95e8\uff0c\u90a3\u4e48\u5230\u8fd9\u91cc\u5df2\u7ecf\u8db3\u591f\u4e86\u3002\u540e\u6587\u7684Get even smaller\u90e8\u5206\u5c06\u4f1a\u63d0\u5230\u66f4\u591a\u7684\u70ab\u9177\u7684\u6f14\u7b97\u65b9\u5f0f\uff0c\u6211\u5e94\u8be5\u4f1a\u540e\u7eed\u5355\u72ec\u7ffb\u8bd1\u4e00\u7bc7\u66f4\u8be6\u7ec6\u7684\u5173\u4e8e\u5b83\u4eec\u7684\u6587\u7ae0\uff0c\u800c\u4e0d\u662f\u5728\u8fd9\u91cc\u63d0\u5230\u3002<\/p>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

\u672c\u6587\u4e3b\u8981\u662f\u5bf9 Learn X in Y minutes \u7684 Lambda Calculus \u7684\u90e8\u5206\u7ffb\u8bd1\u3002\u540c\u65f6\u53c2 […]<\/p>\n","protected":false},"author":1,"featured_media":550,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[7],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/www.bertzzz-horizon.xyz\/wordpress\/wp-content\/uploads\/2025\/09\/nmdb.png","_links":{"self":[{"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/posts\/511"}],"collection":[{"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=511"}],"version-history":[{"count":29,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/posts\/511\/revisions"}],"predecessor-version":[{"id":551,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/posts\/511\/revisions\/551"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=\/wp\/v2\/media\/550"}],"wp:attachment":[{"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=511"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=511"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.bertzzz-horizon.xyz\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}