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penglei committed May 22, 2021
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29 changes: 29 additions & 0 deletions content/post/isabelle-note1/index.adoc
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////
title: Isabelle笔记(一)
date: 2021-04-30T09:00:00+08:00

draft: true
categories: [Formal]
tags: [Isabelle, Proof Assistant]
////

= Isabelle笔记(一)
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Isabelle是一个实现形式逻辑的通用系统,其中Isabelle/HOL是Isabelle处理高阶逻辑的特化系统。
HOL 是 `Higher-Order Logic` 的简写。 具体地,在Isabelle中,HOL是通过组合 Function Programming和Logic来提供的。

//<!--more-->

== 基础

Isabelle底层使用ML语言实现,其语法也受到ML的影响。Isabelle/Isar是Isabelle的一个扩展,几乎隐藏了所有底层实现语言的细节。
因此,Isabelle/HOL的完整简写应该是 Isabelle/Isar/HOL。

使用Isabelle是以理论(`theory`)为中心, `theory` 由具名的 `type` 、 `function` 、 `theorem` 列表构成。

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<pre class="nowrap">..............................macOS..............................
. .
. +----------+ .
. | APP | .
. +----------+ .
. | eg: 1.2.3.4 pf rdr-to +------------------+ . +---------------+
. | +-----------&gt;| transprant proxy +---&gt;| socks5 server +---&gt;outside world
. v | +------------------+ . +---------------+ (eg: 1.2.3.4)
. +----+--+ +--+--+ 127.0.0.1:12345 .
. | en0 +--------------&gt;| lo0 | .
. +-------+ pf route-to +-----+ .
. .
.................................................................</pre>
<pre class="nowrap">.........................macOS............................
. (userspace) .
. 127.0.0.1:12345 .
. +----------+ +------------------+ . +---------------+
. | APP | | transprant proxy +-------&gt;| socks5 server +---&gt;outside world
. +----------+ +------------------+ . +---------------+ (eg: 1.2.3.4)
. | eg: 1.2.3.4 ^ .
+======|==================================|===============
. | (kernel space) | .
. | pf rdr | .
. | +-----------+ .
. v | .
. +----+--+ +--+--+ .
. | en0 +--------------&gt;| lo0 | .
. +-------+ pf route-to +-----+ .
. .
..........................................................</pre>
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<p>第二条规则 <strong>route-to</strong> 表示将本地任何地址访问1.2.3.4的TCP流量路由到另一个地址</p>
<p>第一条规则 <strong>rdr</strong> 表示将进入lo0、协议为TCP、任何来源、目的地址是1.2.3.4的流量转发到 <code>127.0.0.01:12456</code> </p>
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<p>第一条规则 <strong>rdr-to</strong> 表示将进入lo0接口上的流量转发到另一个地址</p>
<p>第二条规则 <strong>route-to</strong> 表示将从本地任何地址(一台设备可能有多个IP地址)访问1.2.3.4的TCP流量路由到另一个地址(这里是lo0 127.0.0.1)</p>
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