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Date	IP Address
2024-01-26	115.227.28.77 (ClassC)
2025-03-12	47.100.82.212 (ClassC)

HTTP/1.1 200 OKServer: nginx/1.18.0 (Ubuntu)Date: Wed, 12 Mar 2025 09:43:32 GMTContent-Type: text/htmlContent-Length: 68036Last-Modified: Sun, 29 Dec 2024 13:04:15 GMTConnection: keep-aliveETag: 677148cf-109c4Accept-Ranges: bytes

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contentwebsite>meta propertyog:title content数学小站>meta propertyog:url contenthttps://lookeng.cn/index.html>meta propertyog:site_name content数学小站>meta propertyog:description content符号计算 & 形式化>meta propertyog:locale contentzh_CN>meta propertyarticle:author contentRex Wang>meta nametwitter:card contentsummary>link relcanonical hrefhttps://lookeng.cn/>script classnext-config data-namepage typeapplication/json>{sidebar:,isHome:true,isPost:false,lang:zh-CN,comments:,permalink:,path:index.html,title:}/script>script classnext-config data-namecalendar typeapplication/json>/script>title>数学小站/title>    noscript>    link relstylesheet href/css/noscript.css>  /noscript>!-- hexo injector head_end start -->link relstylesheet hrefhttps://cdn.jsdelivr.net/npm/katex@0.12.0/dist/katex.min.css>link relstylesheet hrefhttps://cdn.jsdelivr.net/npm/hexo-math@4.0.0/dist/style.css>!-- hexo injector head_end end -->/head>body itemscope itemtypehttp://schema.org/WebPage classuse-motion>  div classheadband>/div>  main classmain>    div classcolumn>      header classheader itemscope itemtypehttp://schema.org/WPHeader>div classsite-brand-container>  div classsite-nav-toggle>    div classtoggle aria-label切换导航栏 rolebutton>        span classtoggle-line>/span>        span classtoggle-line>/span>        span classtoggle-line>/span>    /div>  /div>  div classsite-meta>    a href/ classbrand relstart>      i classlogo-line>/i>      h1 classsite-title>数学小站/h1>      i classlogo-line>/i>    /a>  /div>  div classsite-nav-right>    div classtoggle popup-trigger aria-label搜索 rolebutton>        i classfa fa-search fa-fw fa-lg>/i>    /div>  /div>/div>nav classsite-nav>  ul classmain-menu menu>li classmenu-item menu-item-home>a href/ relsection>i classfa fa-home fa-fw>/i>首页/a>/li>li classmenu-item menu-item-about>a href/about/ relsection>i classfa fa-user fa-fw>/i>关于/a>/li>li classmenu-item menu-item-tags>a href/tags/ relsection>i classfa fa-tags fa-fw>/i>标签/a>/li>li classmenu-item menu-item-categories>a href/categories/ relsection>i classfa fa-th fa-fw>/i>分类/a>/li>li classmenu-item menu-item-archives>a href/archives/ relsection>i classfa fa-archive fa-fw>/i>归档/a>/li>      li classmenu-item menu-item-search>        a rolebutton classpopup-trigger>i classfa fa-search fa-fw>/i>搜索        /a>      /li>  /ul>/nav>  div classsearch-pop-overlay>    div classpopup search-popup>div classsearch-header>  span classsearch-icon>    i classfa fa-search>/i>  /span>  div classsearch-input-container>    input autocompleteoff autocapitalizeoff maxlength80           placeholder搜索... spellcheckfalse           typesearch classsearch-input>  /div>  span classpopup-btn-close rolebutton>    i classfa fa-times-circle>/i>  /span>/div>div classsearch-result-container no-result>  div classsearch-result-icon>    i classfa fa-spinner fa-pulse fa-5x>/i>  /div>/div>    /div>  /div>/header>            aside classsidebar>    div classsidebar-inner sidebar-overview-active>      ul classsidebar-nav>        li classsidebar-nav-toc>          文章目录        /li>        li classsidebar-nav-overview>          站点概览        /li>      /ul>      div classsidebar-panel-container>        !--noindex-->        div classpost-toc-wrap sidebar-panel>        /div>        !--/noindex-->        div classsite-overview-wrap sidebar-panel>          div classsite-author animated itempropauthor itemscope itemtypehttp://schema.org/Person>    img classsite-author-image itempropimage altRex Wang      src/images/avatar.jpg>  p classsite-author-name itempropname>Rex Wang/p>  div classsite-description itempropdescription>符号计算 & 形式化/div>/div>div classsite-state-wrap animated>  nav classsite-state>      div classsite-state-item site-state-posts>        a href/archives/>          span classsite-state-item-count>27/span>          span classsite-state-item-name>日志/span>        /a>      /div>      div classsite-state-item site-state-categories>          a href/categories/>        span classsite-state-item-count>2/span>        span classsite-state-item-name>分类/span>/a>      /div>      div classsite-state-item site-state-tags>          a href/tags/>        span classsite-state-item-count>4/span>        span classsite-state-item-name>标签/span>/a>      /div>  /nav>/div>  div classlinks-of-author animated>      span classlinks-of-author-item>        a hrefhttps://github.com/RexWzh titleGitHub → https://github.com/RexWzh relnoopener me target_blank>i classfab fa-github fa-fw>/i>GitHub/a>      /span>      span classlinks-of-author-item>        a href/zhihong@stu.ecnu.edu.cn titleE-Mail → zhihong@stu.ecnu.edu.cn relnoopener me>i classfa fa-envelope fa-fw>/i>E-Mail/a>      /span>  /div>        /div>      /div>    /div>      /aside>    /div>    div classmain-inner index posts-expand>          div classpost-block>      article itemscope itemtypehttp://schema.org/Article classpost-content lang>    link itempropmainEntityOfPage hrefhttps://lookeng.cn/2023/10/28/hello-world/>    span hidden itempropauthor itemscope itemtypehttp://schema.org/Person>      meta itempropimage content/images/avatar.jpg>      meta itempropname contentRex Wang>    /span>    span hidden itemproppublisher itemscope itemtypehttp://schema.org/Organization>      meta itempropname content数学小站>      meta itempropdescription content符号计算 & 形式化>    /span>    span hidden itemproppost itemscope itemtypehttp://schema.org/CreativeWork>      meta itempropname contentundefined | 数学小站>      meta itempropdescription content>    /span>      header classpost-header>        h2 classpost-title itempropname headline>          a href/2023/10/28/hello-world/ classpost-title-link itempropurl>Hello World!/a>        /h2>        div classpost-meta-container>          div classpost-meta>      i classfa fa-thumb-tack styletransform: rotate(330deg);>/i> font colorBLACK>置顶/font>      span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar>/i>      /span>      span classpost-meta-item-text>发表于/span>      time title创建时间：2023-10-28 20:59:29 itempropdateCreated datePublished datetime2023-10-28T20:59:29+08:00>2023-10-28/time>    /span>    span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar-check>/i>      /span>      span classpost-meta-item-text>更新于/span>      time title修改时间：2024-12-28 21:25:10 itempropdateModified datetime2024-12-28T21:25:10+08:00>2024-12-28/time>    /span>      span id/2023/10/28/hello-world/ classpost-meta-item twikoo_visitors data-flag-titleHello World! title阅读次数>      span classpost-meta-item-icon>        i classfar fa-eye>/i>      /span>      span classpost-meta-item-text>阅读次数：/span>      span idtwikoo_visitors>/span>    /span>      span classpost-meta-break>/span>    span classpost-meta-item title字数>      span classpost-meta-item-icon>        i classfar fa-file-word>/i>      /span>      span classpost-meta-item-text>字数：/span>      span>492/span>    /span>    span classpost-meta-item title时间>      span classpost-meta-item-icon>        i classfar fa-clock>/i>      /span>      span classpost-meta-item-text>时间 ≈/span>      span>2 分钟/span>    /span>/div>        /div>      /header>                div classpost-body itemproparticleBody>          p>欢迎来到 lookeng.cn，博客定位是与数学关联的一切一切，这里是置顶博客，整理已写博文和计划展开的话题，欢迎交流~/p>          !--noindex-->            div classpost-button>              a classbtn href/2023/10/28/hello-world/>                阅读全文 »              /a>            /div>          !--/noindex-->                  /div>                footer classpost-footer>        div classpost-eof>/div>          /footer>  /article>/div>              div classpost-block>      article itemscope itemtypehttp://schema.org/Article classpost-content lang>    link itempropmainEntityOfPage hrefhttps://lookeng.cn/2024/12/29/lean/tutorial/repl-tutorial/>    span hidden itempropauthor itemscope itemtypehttp://schema.org/Person>      meta itempropimage content/images/avatar.jpg>      meta itempropname contentRex Wang>    /span>    span hidden itemproppublisher itemscope itemtypehttp://schema.org/Organization>      meta itempropname content数学小站>      meta itempropdescription content符号计算 & 形式化>    /span>    span hidden itemproppost itemscope itemtypehttp://schema.org/CreativeWork>      meta itempropname contentundefined | 数学小站>      meta itempropdescription content>    /span>      header classpost-header>        h2 classpost-title itempropname headline>          a href/2024/12/29/lean/tutorial/repl-tutorial/ classpost-title-link itempropurl>Lean4 REPL 使用教程/a>        /h2>        div classpost-meta-container>          div classpost-meta>      span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar>/i>      /span>      span classpost-meta-item-text>发表于/span>            time title创建时间：2024-12-29 21:02:34 / 修改时间：21:03:45 itempropdateCreated datePublished datetime2024-12-29T21:02:34+08:00>2024-12-29/time>    /span>    span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-folder>/i>      /span>      span classpost-meta-item-text>分类于/span>        span itempropabout itemscope itemtypehttp://schema.org/Thing>          a href/categories/%E5%BD%A2%E5%BC%8F%E5%8C%96/ itempropurl relindex>span itempropname>形式化/span>/a>        /span>    /span>      span id/2024/12/29/lean/tutorial/repl-tutorial/ classpost-meta-item twikoo_visitors data-flag-titleLean4 REPL 使用教程 title阅读次数>      span classpost-meta-item-icon>        i classfar fa-eye>/i>      /span>      span classpost-meta-item-text>阅读次数：/span>      span idtwikoo_visitors>/span>    /span>      span classpost-meta-break>/span>    span classpost-meta-item title字数>      span classpost-meta-item-icon>        i classfar fa-file-word>/i>      /span>      span classpost-meta-item-text>字数：/span>      span>6.6k/span>    /span>    span classpost-meta-item title时间>      span classpost-meta-item-icon>        i classfar fa-clock>/i>      /span>      span classpost-meta-item-text>时间 ≈/span>      span>24 分钟/span>    /span>/div>        /div>      /header>                div classpost-body itemproparticleBody>          p>REPL (Read-Eval-Print Loop) 是一个交互式编程环境，它允许用户输入命令，执行并看到结果。Lean 4 REPL 基于 JSON 通信的交互式环境，它支持三种工作模式。/p>          !--noindex-->            div classpost-button>              a classbtn href/2024/12/29/lean/tutorial/repl-tutorial/>                阅读全文 »              /a>            /div>          !--/noindex-->                  /div>                footer classpost-footer>        div classpost-eof>/div>          /footer>  /article>/div>              div classpost-block>      article itemscope itemtypehttp://schema.org/Article classpost-content lang>    link itempropmainEntityOfPage hrefhttps://lookeng.cn/2024/12/15/lean/tutorial/lake-project/>    span hidden itempropauthor itemscope itemtypehttp://schema.org/Person>      meta itempropimage content/images/avatar.jpg>      meta itempropname contentRex Wang>    /span>    span hidden itemproppublisher itemscope itemtypehttp://schema.org/Organization>      meta itempropname content数学小站>      meta itempropdescription content符号计算 & 形式化>    /span>    span hidden itemproppost itemscope itemtypehttp://schema.org/CreativeWork>      meta itempropname contentundefined | 数学小站>      meta itempropdescription content>    /span>      header classpost-header>        h2 classpost-title itempropname headline>          a href/2024/12/15/lean/tutorial/lake-project/ classpost-title-link itempropurl>elan 和 lake 基本用法/a>        /h2>        div classpost-meta-container>          div classpost-meta>      span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar>/i>      /span>      span classpost-meta-item-text>发表于/span>      time title创建时间：2024-12-15 12:19:44 itempropdateCreated datePublished datetime2024-12-15T12:19:44+08:00>2024-12-15/time>    /span>    span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar-check>/i>      /span>      span classpost-meta-item-text>更新于/span>      time title修改时间：2024-12-28 21:25:10 itempropdateModified datetime2024-12-28T21:25:10+08:00>2024-12-28/time>    /span>      span id/2024/12/15/lean/tutorial/lake-project/ classpost-meta-item twikoo_visitors data-flag-titleelan 和 lake 基本用法 title阅读次数>      span classpost-meta-item-icon>        i classfar fa-eye>/i>      /span>      span classpost-meta-item-text>阅读次数：/span>      span idtwikoo_visitors>/span>    /span>      span classpost-meta-break>/span>    span classpost-meta-item title字数>      span classpost-meta-item-icon>        i classfar fa-file-word>/i>      /span>      span classpost-meta-item-text>字数：/span>      span>1.3k/span>    /span>    span classpost-meta-item title时间>      span classpost-meta-item-icon>        i classfar fa-clock>/i>      /span>      span classpost-meta-item-text>时间 ≈/span>      span>5 分钟/span>    /span>/div>        /div>      /header>                div classpost-body itemproparticleBody>          p>Lake 基本用法。/p>          !--noindex-->            div classpost-button>              a classbtn href/2024/12/15/lean/tutorial/lake-project/>                阅读全文 »              /a>            /div>          !--/noindex-->                  /div>                footer classpost-footer>        div classpost-eof>/div>          /footer>  /article>/div>              div classpost-block>      article itemscope itemtypehttp://schema.org/Article classpost-content lang>    link itempropmainEntityOfPage hrefhttps://lookeng.cn/2024/12/15/lean/tutorial/lean-fp-intro/>    span hidden itempropauthor itemscope itemtypehttp://schema.org/Person>      meta itempropimage content/images/avatar.jpg>      meta itempropname contentRex Wang>    /span>    span hidden itemproppublisher itemscope itemtypehttp://schema.org/Organization>      meta itempropname content数学小站>      meta itempropdescription content符号计算 & 形式化>    /span>    span hidden itemproppost itemscope itemtypehttp://schema.org/CreativeWork>      meta itempropname contentundefined | 数学小站>      meta itempropdescription content>    /span>      header classpost-header>        h2 classpost-title itempropname headline>          a href/2024/12/15/lean/tutorial/lean-fp-intro/ classpost-title-link itempropurl>Lean 教程(二) ｜ 函数式编程/a>        /h2>        div classpost-meta-container>          div classpost-meta>      span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar>/i>      /span>      span classpost-meta-item-text>发表于/span>      time title创建时间：2024-12-15 10:43:52 itempropdateCreated datePublished datetime2024-12-15T10:43:52+08:00>2024-12-15/time>    /span>    span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar-check>/i>      /span>      span classpost-meta-item-text>更新于/span>      time title修改时间：2024-12-28 21:25:10 itempropdateModified datetime2024-12-28T21:25:10+08:00>2024-12-28/time>    /span>      span id/2024/12/15/lean/tutorial/lean-fp-intro/ classpost-meta-item twikoo_visitors data-flag-titleLean 教程(二) ｜ 函数式编程 title阅读次数>      span classpost-meta-item-icon>        i classfar fa-eye>/i>      /span>      span classpost-meta-item-text>阅读次数：/span>      span idtwikoo_visitors>/span>    /span>      span classpost-meta-break>/span>    span classpost-meta-item title字数>      span classpost-meta-item-icon>        i classfar fa-file-word>/i>      /span>      span classpost-meta-item-text>字数：/span>      span>6.4k/span>    /span>    span classpost-meta-item title时间>      span classpost-meta-item-icon>        i classfar fa-clock>/i>      /span>      span classpost-meta-item-text>时间 ≈/span>      span>23 分钟/span>    /span>/div>        /div>      /header>                div classpost-body itemproparticleBody>          p>学习 Lean 的途径很多，具体取决于你的背景和偏好，这些教程有偏重数学的也有偏重编程的。/p>          !--noindex-->            div classpost-button>              a classbtn href/2024/12/15/lean/tutorial/lean-fp-intro/>                阅读全文 »              /a>            /div>          !--/noindex-->                  /div>                footer classpost-footer>        div classpost-eof>/div>          /footer>  /article>/div>              div classpost-block>      article itemscope itemtypehttp://schema.org/Article classpost-content lang>    link itempropmainEntityOfPage hrefhttps://lookeng.cn/2024/12/02/lean/pantograph/>    span hidden itempropauthor itemscope itemtypehttp://schema.org/Person>      meta itempropimage content/images/avatar.jpg>      meta itempropname contentRex Wang>    /span>    span hidden itemproppublisher itemscope itemtypehttp://schema.org/Organization>      meta itempropname content数学小站>      meta itempropdescription content符号计算 & 形式化>    /span>    span hidden itemproppost itemscope itemtypehttp://schema.org/CreativeWork>      meta itempropname contentundefined | 数学小站>      meta itempropdescription content>    /span>      header classpost-header>        h2 classpost-title itempropname headline>          a href/2024/12/02/lean/pantograph/ classpost-title-link itempropurl>pantograph/a>        /h2>        div classpost-meta-container>          div classpost-meta>      span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar>/i>      /span>      span classpost-meta-item-text>发表于/span>      time title创建时间：2024-12-02 09:32:08 itempropdateCreated datePublished datetime2024-12-02T09:32:08+08:00>2024-12-02/time>    /span>    span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar-check>/i>      /span>      span classpost-meta-item-text>更新于/span>      time title修改时间：2024-12-28 21:25:10 itempropdateModified datetime2024-12-28T21:25:10+08:00>2024-12-28/time>    /span>      span id/2024/12/02/lean/pantograph/ classpost-meta-item twikoo_visitors data-flag-titlepantograph title阅读次数>      span classpost-meta-item-icon>        i classfar fa-eye>/i>      /span>      span classpost-meta-item-text>阅读次数：/span>      span idtwikoo_visitors>/span>    /span>      span classpost-meta-break>/span>    span classpost-meta-item title字数>      span classpost-meta-item-icon>        i classfar fa-file-word>/i>      /span>      span classpost-meta-item-text>字数：/span>      span>1.4k/span>    /span>    span classpost-meta-item title时间>      span classpost-meta-item-icon>        i classfar fa-clock>/i>      /span>      span classpost-meta-item-text>时间 ≈/span>      span>5 分钟/span>    /span>/div>        /div>      /header>                div classpost-body itemproparticleBody>          p>TODO/p>          !--noindex-->            div classpost-button>              a classbtn href/2024/12/02/lean/pantograph/>                阅读全文 »              /a>            /div>          !--/noindex-->                  /div>                footer classpost-footer>        div classpost-eof>/div>          /footer>  /article>/div>              div classpost-block>      article itemscope itemtypehttp://schema.org/Article classpost-content lang>    link itempropmainEntityOfPage hrefhttps://lookeng.cn/2024/11/28/lean/lean-tools/>    span hidden itempropauthor itemscope itemtypehttp://schema.org/Person>      meta itempropimage content/images/avatar.jpg>      meta itempropname contentRex Wang>    /span>    span hidden itemproppublisher itemscope itemtypehttp://schema.org/Organization>      meta itempropname content数学小站>      meta itempropdescription content符号计算 & 形式化>    /span>    span hidden itemproppost itemscope itemtypehttp://schema.org/CreativeWork>      meta itempropname contentundefined | 数学小站>      meta itempropdescription content>    /span>      header classpost-header>        h2 classpost-title itempropname headline>          a href/2024/11/28/lean/lean-tools/ classpost-title-link itempropurl>Lean 代码交互方案/a>        /h2>        div classpost-meta-container>          div classpost-meta>      span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar>/i>      /span>      span classpost-meta-item-text>发表于/span>      time title创建时间：2024-11-28 21:13:09 itempropdateCreated datePublished datetime2024-11-28T21:13:09+08:00>2024-11-28/time>    /span>    span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar-check>/i>      /span>      span classpost-meta-item-text>更新于/span>      time title修改时间：2024-12-28 21:25:10 itempropdateModified datetime2024-12-28T21:25:10+08:00>2024-12-28/time>    /span>      span id/2024/11/28/lean/lean-tools/ classpost-meta-item twikoo_visitors data-flag-titleLean 代码交互方案 title阅读次数>      span classpost-meta-item-icon>        i classfar fa-eye>/i>      /span>      span classpost-meta-item-text>阅读次数：/span>      span idtwikoo_visitors>/span>    /span>      span classpost-meta-break>/span>    span classpost-meta-item title字数>      span classpost-meta-item-icon>        i classfar fa-file-word>/i>      /span>      span classpost-meta-item-text>字数：/span>      span>417/span>    /span>    span classpost-meta-item title时间>      span classpost-meta-item-icon>        i classfar fa-clock>/i>      /span>      span classpost-meta-item-text>时间 ≈/span>      span>2 分钟/span>    /span>/div>        /div>      /header>                div classpost-body itemproparticleBody>          p>TODO/p>          !--noindex-->            div classpost-button>              a classbtn href/2024/11/28/lean/lean-tools/>                阅读全文 »              /a>            /div>          !--/noindex-->                  /div>                footer classpost-footer>        div classpost-eof>/div>          /footer>  /article>/div>              div classpost-block>      article itemscope itemtypehttp://schema.org/Article classpost-content lang>    link itempropmainEntityOfPage hrefhttps://lookeng.cn/2024/11/26/imo/alphaproof-analyse/>    span hidden itempropauthor itemscope itemtypehttp://schema.org/Person>      meta itempropimage content/images/avatar.jpg>      meta itempropname contentRex Wang>    /span>    span hidden itemproppublisher itemscope itemtypehttp://schema.org/Organization>      meta itempropname content数学小站>      meta itempropdescription content符号计算 & 形式化>    /span>    span hidden itemproppost itemscope itemtypehttp://schema.org/CreativeWork>      meta itempropname contentundefined | 数学小站>      meta itempropdescription content>    /span>      header classpost-header>        h2 classpost-title itempropname headline>          a href/2024/11/26/imo/alphaproof-analyse/ classpost-title-link itempropurl>Alphaproof 技术解析，策略及研究/a>        /h2>        div classpost-meta-container>          div classpost-meta>      span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar>/i>      /span>      span classpost-meta-item-text>发表于/span>      time title创建时间：2024-11-26 12:52:53 itempropdateCreated datePublished datetime2024-11-26T12:52:53+08:00>2024-11-26/time>    /span>    span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar-check>/i>      /span>      span classpost-meta-item-text>更新于/span>      time title修改时间：2024-12-28 21:25:10 itempropdateModified datetime2024-12-28T21:25:10+08:00>2024-12-28/time>    /span>      span id/2024/11/26/imo/alphaproof-analyse/ classpost-meta-item twikoo_visitors data-flag-titleAlphaproof 技术解析，策略及研究 title阅读次数>      span classpost-meta-item-icon>        i classfar fa-eye>/i>      /span>      span classpost-meta-item-text>阅读次数：/span>      span idtwikoo_visitors>/span>    /span>      span classpost-meta-break>/span>    span classpost-meta-item title字数>      span classpost-meta-item-icon>        i classfar fa-file-word>/i>      /span>      span classpost-meta-item-text>字数：/span>      span>1.6k/span>    /span>    span classpost-meta-item title时间>      span classpost-meta-item-icon>        i classfar fa-clock>/i>      /span>      span classpost-meta-item-text>时间 ≈/span>      span>6 分钟/span>    /span>/div>        /div>      /header>                div classpost-body itemproparticleBody>          p>Alphaproof 技术解析，当前问题及相关研究/p>          !--noindex-->            div classpost-button>              a classbtn href/2024/11/26/imo/alphaproof-analyse/>                阅读全文 »              /a>            /div>          !--/noindex-->                  /div>                footer classpost-footer>        div classpost-eof>/div>          /footer>  /article>/div>              div classpost-block>      article itemscope itemtypehttp://schema.org/Article classpost-content lang>    link itempropmainEntityOfPage hrefhttps://lookeng.cn/2024/11/17/imo/kaggle-solution/>    span hidden itempropauthor itemscope itemtypehttp://schema.org/Person>      meta itempropimage content/images/avatar.jpg>      meta itempropname contentRex Wang>    /span>    span hidden itemproppublisher itemscope itemtypehttp://schema.org/Organization>      meta itempropname content数学小站>      meta itempropdescription content符号计算 & 形式化>    /span>    span hidden itemproppost itemscope itemtypehttp://schema.org/CreativeWork>      meta itempropname contentundefined | 数学小站>      meta itempropdescription content>    /span>      header classpost-header>        h2 classpost-title itempropname headline>          a href/2024/11/17/imo/kaggle-solution/ classpost-title-link itempropurl>AIMO | Kaggle 本地环境搭建/a>        /h2>        div classpost-meta-container>          div classpost-meta>      span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar>/i>      /span>      span classpost-meta-item-text>发表于/span>      time title创建时间：2024-11-17 11:49:18 itempropdateCreated datePublished datetime2024-11-17T11:49:18+08:00>2024-11-17/time>    /span>    span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar-check>/i>      /span>      span classpost-meta-item-text>更新于/span>      time title修改时间：2024-12-28 21:25:01 itempropdateModified datetime2024-12-28T21:25:01+08:00>2024-12-28/time>    /span>      span id/2024/11/17/imo/kaggle-solution/ classpost-meta-item twikoo_visitors data-flag-titleAIMO | Kaggle 本地环境搭建 title阅读次数>      span classpost-meta-item-icon>        i classfar fa-eye>/i>      /span>      span classpost-meta-item-text>阅读次数：/span>      span idtwikoo_visitors>/span>    /span>      span classpost-meta-break>/span>    span classpost-meta-item title字数>      span classpost-meta-item-icon>        i classfar fa-file-word>/i>      /span>      span classpost-meta-item-text>字数：/span>      span>1k/span>    /span>    span classpost-meta-item title时间>      span classpost-meta-item-icon>        i classfar fa-clock>/i>      /span>      span classpost-meta-item-text>时间 ≈/span>      span>4 分钟/span>    /span>/div>        /div>      /header>                div classpost-body itemproparticleBody>          h2 id唠唠闲话>a classmarkdownIt-Anchor href#唠唠闲话>/a> 唠唠闲话/h2>h2 id配置-kaggle>a classmarkdownIt-Anchor href#配置-kaggle>/a> 配置 Kaggle/h2>p>安装 Kaggle 的 Python 包，用于下载竞赛代码和公开的笔记本：/p>figure classhighlight bash>table>tr>td classgutter>pre>span classline>1/span>br>/pre>/td>td classcode>pre>span classline>pip install kaggle/span>br>/pre>/td>/tr>/table>/figure>p>下载需要鉴权，在 Kaggle a target_blank relnoopener hrefhttps://kaggle.com/settings>个人设置页/a>，下载密钥：/p>p>img srchttps://qiniu.wzhecnu.cn/FileBed/source/20241124202102.png alt20241124202102 />/p>p>将密钥文件 code>kaggle.json/code> 放到 code>~/.kaggle/code> 目录下。/p>p>Kaggle 运行代码的工作区为 code>/kaggle/code> 目录，输入通常放在 code>input/code> 目录，当前 notebook 所处的目录为 code>working/code>，模型输出文件，提交结果通常放在 code>output/code> 。/p>p>特别地，code>sys.path/code> 会根据具体竞赛添加相关代码所在的目录，以便直接在当前工作区 code>import/code>。/p>p>比如 AIMO2 的情况：/p>figure classhighlight py>table>tr>td classgutter>pre>span classline>1/span>br>span classline>2/span>br>/pre>/td>td classcode>pre>span classline>span classkeyword>import/span> sys/span>br>span classline>sys.path/span>br>/pre>/td>/tr>/table>/figure>p>输出：/p>figure classhighlight python>table>tr>td classgutter>pre>span classline>1/span>br>span classline>2/span>br>span classline>3/span>br>span classline>4/span>br>span classline>5/span>br>span classline>6/span>br>span classline>7/span>br>span classline>8/span>br>span classline>9/span>br>span classline>10/span>br>span classline>11/span>br>span classline>12/span>br>span classline>13/span>br>span classline>14/span>br>/pre>/td>td classcode>pre>span classline>span classstring>'/kaggle/lib/kagglegym'/span>,/span>br>span classline> span classstring>'/kaggle/lib'/span>,/span>br>span classline> span classstring>'/kaggle/input/ai-mathematical-olympiad-progress-prize-2'/span>,/span>br>span classline> span classstring>'/opt/conda/lib/python310.zip'/span>,/span>br>span classline> span classstring>'/opt/conda/lib/python3.10'/span>,/span>br>span classline> span classstring>'/opt/conda/lib/python3.10/lib-dynload'/span>,/span>br>span classline> span classstring>''/span>,/span>br>span classline> span classstring>'/root/.local/lib/python3.10/site-packages'/span>,/span>br>span classline> span classstring>'/opt/conda/lib/python3.10/site-packages'/span>,/span>br>span classline> span classstring>'/root/src/BigQuery_Helper'/span>,/span>br>span classline> span classstring>'/kaggle/input/ai-mathematical-olympiad-progress-prize-2/kaggle_evaluation'/span>,/span>br>span classline> span classstring>'/kaggle/input/ai-mathematical-olympiad-progress-prize-2/kaggle_evaluation/core/generated'/span>,/span>br>span classline> span classstring>'/kaggle/input/ai-mathematical-olympiad-progress-prize-2/kaggle_evaluation/core'/span>,/span>br>span classline> span classstring>'/kaggle/input/ai-mathematical-olympiad-progress-prize-2/kaggle_evaluation/core/generated'/span>/span>br>/pre>/td>/tr>/table>/figure>h2 id提交指南>a classmarkdownIt-Anchor href#提交指南>/a> 提交指南/h2>h3 id模板代码>a classmarkdownIt-Anchor href#模板代码>/a> 模板代码/h3>p>下载竞赛的模板代码：/p>figure classhighlight bash>table>tr>td classgutter>pre>span classline>1/span>br>/pre>/td>td classcode>pre>span classline>kaggle kernels pull ryanholbrook/aimo-2-submission-demo/span>br>/pre>/td>/tr>/table>/figure>p>这个 Jupyter Notebook 介绍了竞赛规范：要求设置一个评估 API 的服务，用以响应推理请求。在对隐藏测试集进行评估时，由 code>aimo_2_gateway/code> 定义的客户端将在一个不同的容器中运行，能够直接访问隐藏测试集，并依次以随机顺序处理每一个问题。/p>p>相关逻辑在模板中定义好了，只需编写预测函数：/p>ul>li>将下边函数替换为推理代码/li>li>该函数应返回一个在 0 到 999 之间的整数/li>li>除首次预测外，每个预测必须在问题提供后的 30 分钟内返回。/li>/ul>figure classhighlight python>table>tr>td classgutter>pre>span classline>1/span>br>span classline>2/span>br>span classline>3/span>br>span classline>4/span>br>span classline>5/span>br>span classline>6/span>br>span classline>7/span>br>span classline>8/span>br>span classline>9/span>br>span classline>10/span>br>span classline>11/span>br>span classline>12/span>br>span classline>13/span>br>span classline>14/span>br>span classline>15/span>br>span classline>16/span>br>span classline>17/span>br>span classline>18/span>br>span classline>19/span>br>span classline>20/span>br>span classline>21/span>br>span classline>22/span>br>span classline>23/span>br>/pre>/td>td classcode>pre>span classline>span classkeyword>import/span> os/span>br>span classline>span classkeyword>import/span> pandas span classkeyword>as/span> pd/span>br>span classline>span classkeyword>import/span> polars span classkeyword>as/span> pl/span>br>span classline>span classkeyword>import/span> kaggle_evaluation.aimo_2_inference_server/span>br>span classline>/span>br>span classline>span classkeyword>def/span> span classtitle function_>predict/span>(span classparams>id_: pl.DataFrame, question: pl.DataFrame/span>) -> pl.DataFrame | pd.DataFrame:/span>br>span classline>    span classstring>"""Make a prediction."""/span>/span>br>span classline>    span classcomment># Unpack values/span>/span>br>span classline>    id_  id_.item(span classnumber>0/span>)/span>br>span classline>    question  question.item(span classnumber>0/span>)/span>br>span classline>    span classcomment># Make a prediction/span>/span>br>span classline>    prediction  span classnumber>0/span>  span classcomment># model.predict(question)/span>/span>br>span classline>    span classkeyword>return/span> pl.DataFrame({span classstring>'id'/span>: id_, span classstring>'answer'/span>: span classnumber>0/span>})/span>br>span classline>/span>br>span classline>inference_server  kaggle_evaluation.aimo_2_inference_server.AIMO2InferenceServer(predict)/span>br>span classline>span classkeyword>if/span> os.getenv(span classstring>'KAGGLE_IS_COMPETITION_RERUN'/span>):/span>br>span classline>    inference_server.serve()/span>br>span classline>span classkeyword>else/span>:/span>br>span classline>    inference_server.run_local_gateway(/span>br>span classline>        (/span>br>span classline>            span classstring>'/kaggle/input/ai-mathematical-olympiad-progress-prize-2/test.csv'/span>,/span>br>span classline>        )/span>br>span classline>    )/span>br>/pre>/td>/tr>/table>/figure>p>注意事项：提交后在隐藏测试集上运行时，需在启动后 15 分钟内调用 code>inference_server.serve()/code>，否则网关将会抛出错误。如果加载模型需要超过 15 分钟，可以在首次预测调用中加载，因为首次调用不受 30 分钟响应期限的限制。/p>h3 id搭建本地环境>a classmarkdownIt-Anchor href#搭建本地环境>/a> 搭建本地环境/h3>p>查看竞赛模板的工作目录，容易发现 code>input/code> 下存在一个评估代码 code>ai-mathematical-olympiad-progress-prize-2/code>。/p>figure classhighlight bash>table>tr>td classgutter>pre>span classline>1/span>br>span classline>2/span>br>span classline>3/span>br>span classline>4/span>br>span classline>5/span>br>span classline>6/span>br>span classline>7/span>br>span classline>8/span>br>span classline>9/span>br>span classline>10/span>br>span classline>11/span>br>span classline>12/span>br>span classline>13/span>br>span classline>14/span>br>span classline>15/span>br>span classline>16/span>br>span classline>17/span>br>span classline>18/span>br>span classline>19/span>br>span classline>20/span>br>span classline>21/span>br>span classline>22/span>br>span classline>23/span>br>span classline>24/span>br>span classline>25/span>br>span classline>26/span>br>/pre>/td>td classcode>pre>span classline>span classcomment># tree /kaggle//span>/span>br>span classline>/kaggle/span>br>span classline>|-- input/span>br>span classline>|   `-- ai-mathematical-olympiad-progress-prize-2/span>br>span classline>|       |-- AIMO_Progress_Prize_2_Reference_Problems_Solutions.pdf/span>br>span classline>|       |-- kaggle_evaluation/span>br>span classline>|       |   |-- __init__.py/span>br>span classline>|       |   |-- aimo_2_gateway.py/span>br>span classline>|       |   |-- aimo_2_inference_server.py/span>br>span classline>|       |   `-- core/span>br>span classline>|       |       |-- __init__.py/span>br>span classline>|       |       |-- base_gateway.py/span>br>span classline>|       |       |-- generated/span>br>span classline>|       |       |   |-- __init__.py/span>br>span classline>|       |       |   |-- kaggle_evaluation_pb2.py/span>br>span classline>|       |       |   `-- kaggle_evaluation_pb2_grpc.py/span>br>span classline>|       |       |-- kaggle_evaluation.proto/span>br>span classline>|       |       |-- relay.py/span>br>span classline>|       |       `-- templates.py/span>br>span classline>|       |-- reference.csv/span>br>span classline>|       |-- sample_submission.csv/span>br>span classline>|       `-- test.csv/span>br>span classline>|-- lib/span>br>span classline>|   `-- kaggle/span>br>span classline>|       `-- gcp.py/span>br>span classline>`-- working/span>br>/pre>/td>/tr>/table>/figure>p>这是竞赛官方的代码接口，可以通过命令下载查看：/p>figure classhighlight bash>table>tr>td classgutter>pre>span classline>1/span>br>/pre>/td>td classcode>pre>span classline>kaggle competitions download -c ai-mathematical-olympiad-progress-prize-2/span>br>/pre>/td>/tr>/table>/figure>p>将私有数据集替换提交的 code>test.csv/code> 文件，之后就可以在本地调试了。/p>figure classhighlight bash>table>tr>td classgutter>pre>span classline>1/span>br>span classline>2/span>br>span classline>3/span>br>span classline>4/span>br>span classline>5/span>br>span classline>6/span>br>span classline>7/span>br>span classline>8/span>br>span classline>9/span>br>/pre>/td>td classcode>pre>span classline>inference_server  kaggle_evaluation.aimo_2_inference_server.AIMO2InferenceServer(predict)/span>br>span classline>span classkeyword>if/span> os.getenv(span classstring>'KAGGLE_IS_COMPETITION_RERUN'/span>):/span>br>span classline>    inference_server.serve()/span>br>span classline>span classkeyword>else/span>:/span>br>span classline>    inference_server.run_local_gateway(/span>br>span classline>        (/span>br>span classline>            span classstring>'/kaggle/input/ai-mathematical-olympiad-progress-prize-2/test.csv'/span>,/span>br>span classline>        )/span>br>span classline>    )/span>br>/pre>/td>/tr>/table>/figure>h3 id简单示例>a classmarkdownIt-Anchor href#简单示例>/a> 简单示例/h3>p>下边举一个提交例子，用 vLLM 运行原始的 DeepSeek-7b 模型，实测能答对两题。/p>p>下载示例代码：/p>figure classhighlight bash>table>tr>td classgutter>pre>span classline>1/span>br>/pre>/td>td classcode>pre>span classline>kaggle kernels pull tianjiajun177/aimo2-vllm-deepseek-math-7b-instruct-infer-l4-4/span>br>/pre>/td>/tr>/table>/figure>p>选择计算配置为 GPU L4 * 4：/p>p>img srchttps://qiniu.wzhecnu.cn/FileBed/source/20241124095433.png alt20241124095433 />/p>p>显存大小为 23G * 4，这个大小能运行量化的 72B 模型，但每周只有 30 h 运行时间。/p>p>展开 input 选项卡，添加对应模型参数：/p>p>img srchttps://qiniu.wzhecnu.cn/FileBed/source/20241124094800.png alt20241124094800 />/p>p>此时 code>input/code> 目录多了 deepseek 模型：/p>figure classhighlight bash>table>tr>td classgutter>pre>span classline>1/span>br>span classline>2/span>br>span classline>3/span>br>span classline>4/span>br>span classline>5/span>br>span classline>6/span>br>span classline>7/span>br>span classline>8/span>br>span classline>9/span>br>span classline>10/span>br>span classline>11/span>br>span classline>12/span>br>span classline>13/span>br>span classline>14/span>br>span classline>15/span>br>span classline>16/span>br>/pre>/td>td classcode>pre>span classline>span classcomment># tree /kaggle//span>/span>br>span classline>/kaggle//span>br>span classline>|-- input/span>br>span classline>|   |-- deepseek-math-7b-instruct/span>br>span classline>|   |   `-- transformers/span>br>span classline>|   |       `-- main/span>br>span classline>|   |           `-- 1/span>br>span classline>|   |               |-- LICENSE/span>br>span classline>|   |               |-- README.md/span>br>span classline>|   |               |-- config.json/span>br>span classline>|   |               |-- generation_config.json/span>br>span classline>|   |               |-- model-00001-of-00002.safetensors/span>br>span classline>|   |               |-- model-00002-of-00002.safetensors/span>br>span classline>|   |               |-- model.safetensors.index.json/span>br>span classline>|   |               |-- tokenizer.json/span>br>span classline>|   |               `-- tokenizer_config.json/span>br>/pre>/td>/tr>/table>/figure>p>先配置 vLLM 推理服务：/p>figure classhighlight py>table>tr>td classgutter>pre>span classline>1/span>br>span classline>2/span>br>span classline>3/span>br>span classline>4/span>br>span classline>5/span>br>span classline>6/span>br>span classline>7/span>br>span classline>8/span>br>span classline>9/span>br>span classline>10/span>br>span classline>11/span>br>span classline>12/span>br>span classline>13/span>br>span classline>14/span>br>span classline>15/span>br>span classline>16/span>br>span classline>17/span>br>span classline>18/span>br>span classline>19/span>br>span classline>20/span>br>span classline>21/span>br>span classline>22/span>br>span classline>23/span>br>span classline>24/span>br>span classline>25/span>br>/pre>/td>td classcode>pre>span classline>span classcomment># 初始化/span>/span>br>span classline>llm  vllm.LLM(/span>br>span classline>    span classstring>"/kaggle/input/deepseek-math-7b-instruct/transformers/main/1"/span>,/span>br>span classline>    tensor_parallel_sizespan classnumber>4/span>,/span>br>span classline>    gpu_memory_utilizationspan classnumber>0.95/span>, /span>br>span classline>    trust_remote_codespan classliteral>True/span>,/span>br>span classline>    dtypespan classstring>"half"/span>, /span>br>span classline>    enforce_eagerspan classliteral>True/span>,/span>br>span classline>    swap_spacespan classnumber>2/span>, span classcomment># L4×4/span>/span>br>span classline>)/span>br>span classline>tokenizer  llm.get_tokenizer()/span>br>span classline>/span>br>span classline>span classcomment># 模型推理/span>/span>br>span classline>span classkeyword>def/span> span classtitle function_>generate_text_vllm/span>(span classparams>requests, tokenizer, model/span>):/span>br>span classline>    sampling_params  vllm.SamplingParams(/span>br>span classline>        temperaturespan classnumber>0.00/span>,/span>br>span classline>        seedspan classnumber>42/span>, /span>br>span classline>        max_tokensspan classnumber>1024/span>/span>br>span classline>    )/span>br>span classline>    responses  model.generate(requests, sampling_paramssampling_params, use_tqdmspan classliteral>False/span>)/span>br>span classline>    response_text_list  /span>br>span classline>    span classkeyword>for/span> response span classkeyword>in/span> responses:/span>br>span classline>        span classcomment># total_tokens + len(response.outputs0.token_ids)/span>/span>br>span classline>        response_text_list.append(response.outputsspan classnumber>0/span>.text)/span>br>span classline>    span classkeyword>return/span> response_text_list/span>br>/pre>/td>/tr>/table>/figure>p>然后来编写 code>predict/code> 函数：/p>figure classhighlight py>table>tr>td classgutter>pre>span classline>1/span>br>span classline>2/span>br>span classline>3/span>br>span classline>4/span>br>span classline>5/span>br>span classline>6/span>br>span classline>7/span>br>span classline>8/span>br>span classline>9/span>br>span classline>10/span>br>span classline>11/span>br>span classline>12/span>br>span classline>13/span>br>span classline>14/span>br>span classline>15/span>br>span classline>16/span>br>span classline>17/span>br>span classline>18/span>br>span classline>19/span>br>/pre>/td>td classcode>pre>span classline>span classcomment># instruction prompt/span>/span>br>span classline>tool_instruction  span classstring>'\nPlease solve the problem above, and put your final answer within \\boxed{}.'/span>/span>br>span classline>/span>br>span classline>span classkeyword>def/span> span classtitle function_>predict/span>(span classparams>id_: pl.Series, question: pl.Series/span>) -> pl.DataFrame | pd.DataFrame:/span>br>span classline>    span classstring>"""Make a prediction."""/span>/span>br>span classline>    span classcomment># Unpack values/span>/span>br>span classline>    id_  id_.item(span classnumber>0/span>)/span>br>span classline>    question  question.item(span classnumber>0/span>)/span>br>span classline>    span classcomment># Make a prediction/span>/span>br>span classline>    prompt  question + tool_instruction/span>br>span classline>    generate_text  generate_text_vllm(prompt, tokenizer, llm)span classnumber>0/span>/span>br>span classline>    answer  span classnumber>0/span>/span>br>span classline>    span classkeyword>try/span>:/span>br>span classline>        result_output  re.findall(span classstring>r'\\boxed\{(\d+)\}'/span>, generate_text)/span>br>span classline>        answer  span classbuilt_in>int/span>(result_output-span classnumber>1/span>.strip()) % span classnumber>1000/span>/span>br>span classline>    span classkeyword>except/span>:/span>br>span classline>        span classbuilt_in>print/span>(span classstring>'error'/span>)/span>br>span classline>        answer  random.randint(span classnumber>0/span>, span classnumber>999/span>)/span>br>span classline>    span classkeyword>return/span> pl.DataFrame({span classstring>'id'/span>: id_, span classstring>'answer'/span>: answer})/span>br>/pre>/td>/tr>/table>/figure>          /div>                footer classpost-footer>        div classpost-eof>/div>          /footer>  /article>/div>              div classpost-block>      article itemscope itemtypehttp://schema.org/Article classpost-content lang>    link itempropmainEntityOfPage hrefhttps://lookeng.cn/2024/10/15/imo/imo-p1-algebra-alphaproof-o1/>    span hidden itempropauthor itemscope itemtypehttp://schema.org/Person>      meta itempropimage content/images/avatar.jpg>      meta itempropname contentRex Wang>    /span>    span hidden itemproppublisher itemscope itemtypehttp://schema.org/Organization>      meta itempropname content数学小站>      meta itempropdescription content符号计算 & 形式化>    /span>    span hidden itemproppost itemscope itemtypehttp://schema.org/CreativeWork>      meta itempropname contentundefined | 数学小站>      meta itempropdescription content>    /span>      header classpost-header>        h2 classpost-title itempropname headline>          a href/2024/10/15/imo/imo-p1-algebra-alphaproof-o1/ classpost-title-link itempropurl>AlphaProof 解题分析与启发 | IMO 系列/a>        /h2>        div classpost-meta-container>          div classpost-meta>      span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar>/i>      /span>      span classpost-meta-item-text>发表于/span>      time title创建时间：2024-10-15 10:18:41 itempropdateCreated datePublished datetime2024-10-15T10:18:41+08:00>2024-10-15/time>    /span>    span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar-check>/i>      /span>      span classpost-meta-item-text>更新于/span>      time title修改时间：2024-12-28 21:25:01 itempropdateModified datetime2024-12-28T21:25:01+08:00>2024-12-28/time>    /span>      span id/2024/10/15/imo/imo-p1-algebra-alphaproof-o1/ classpost-meta-item twikoo_visitors data-flag-titleAlphaProof 解题分析与启发 | IMO 系列 title阅读次数>      span classpost-meta-item-icon>        i classfar fa-eye>/i>      /span>      span classpost-meta-item-text>阅读次数：/span>      span idtwikoo_visitors>/span>    /span>      span classpost-meta-break>/span>    span classpost-meta-item title字数>      span classpost-meta-item-icon>        i classfar fa-file-word>/i>      /span>      span classpost-meta-item-text>字数：/span>      span>4.4k/span>    /span>    span classpost-meta-item title时间>      span classpost-meta-item-icon>        i classfar fa-clock>/i>      /span>      span classpost-meta-item-text>时间 ≈/span>      span>16 分钟/span>    /span>/div>        /div>      /header>                div classpost-body itemproparticleBody>          p>我们从数学角度和形式化角度分析了 AlphaProof 的工作。模型技术角度也有许多值得深入研究的内容，如数据合成方式、策略空间的定义、以及采用的搜索算法等，这些我们在 IMO 后续系列中整理介绍。/p>          !--noindex-->            div classpost-button>              a classbtn href/2024/10/15/imo/imo-p1-algebra-alphaproof-o1/>                阅读全文 »              /a>            /div>          !--/noindex-->                  /div>                footer classpost-footer>        div classpost-eof>/div>          /footer>  /article>/div>              div classpost-block>      article itemscope 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span classpost-meta-item-icon>        i classfar fa-calendar>/i>      /span>      span classpost-meta-item-text>发表于/span>      time title创建时间：2024-10-15 10:12:26 itempropdateCreated datePublished datetime2024-10-15T10:12:26+08:00>2024-10-15/time>    /span>    span classpost-meta-item>      span classpost-meta-item-icon>        i classfar fa-calendar-check>/i>      /span>      span classpost-meta-item-text>更新于/span>      time title修改时间：2024-12-28 21:25:10 itempropdateModified datetime2024-12-28T21:25:10+08:00>2024-12-28/time>    /span>      span id/2024/10/15/lean/iclr2024-formal-proof-lean/ classpost-meta-item twikoo_visitors data-flag-titleICLR 2025 | 数学形式化工作速览 title阅读次数>      span classpost-meta-item-icon>        i classfar fa-eye>/i>      /span>      span classpost-meta-item-text>阅读次数：/span>      span idtwikoo_visitors>/span>    /span>      span classpost-meta-break>/span>    span classpost-meta-item title字数>      span classpost-meta-item-icon>        i classfar fa-file-word>/i>      /span>      span classpost-meta-item-text>字数：/span>      span>38k/span>    /span>    span classpost-meta-item title时间>      span classpost-meta-item-icon>        i classfar fa-clock>/i>      /span>      span classpost-meta-item-text>时间 ≈/span>      span>2:17/span>    /span>/div>        /div>      /header>                div classpost-body itemproparticleBody>          p>数学形式化的目的是提供一个完全客观和可验证的证明过程，使得任何了解该形式体系的人都能够检查证明的正确性，而不需要对证明本身进行主观判断。由于数学形式化能用于消除模型幻觉，在当下格外受到关注。/p>          !--noindex-->            div classpost-button>              a classbtn href/2024/10/15/lean/iclr2024-formal-proof-lean/>                阅读全文 »              /a>            /div>          !--/noindex-->                  /div>                footer classpost-footer>        div classpost-eof>/div>          /footer>  /article>/div>      nav classpagination>    span classpage-number current>1/span>a classpage-number href/page/2/>2/a>a classpage-number href/page/3/>3/a>a classextend next relnext title下一页 aria-label下一页 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