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+++ b/SUMMARY.md
@@ -27,4 +27,9 @@
* [上下文敏感分析（下）](ch3/context-sensitivity/03-05-cs2.md)
## 指针分析应用
-* [安全应用——污点分析](ch4/04-01-security.md)
\ No newline at end of file
+
+* [安全应用——污点分析](ch4/04-01-security.md)
+
+## 指针分析的另一种样子
+
+* [声明式指针分析算法](ch5/05-01-Datalog-Based-PA.md)
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+# Datalog-Based Program Analysis
+
+Datalog是一种命令式（Declarative）的编程语言。
+
+主要内容如下：
+
+1. Motivation
+2. Introduction to Datalog
+3. Pointer Analysis via Datalog
+4. Taint Analysis via Datalog
+
+# Motivation
+
+如果用Imperative的编程方式做指针分析，很麻烦。
+
+
+
+而如果用Declarative的方式做编程分析，能够极大地简化实现。
+
+
+
+# Introduction to Datalog
+
+接下来学习一个船新的语言——Datalog，它实际上是大名鼎鼎的Prolog的一个子集。
+
+`Datalog=Data+Logic(and,or,not)`
+
+- 没有副作用
+- 没有控制流
+- 没有函数
+- 不是图灵完备的
+
+## Data
+
+### Predicates
+
+谓词(Predicates)是datalog中的一个主要组成部分，可以看作是数据所组成的一个表(table of data)，每一行都代表一个事实(fact)。例如：
+
+
+
+### Atoms
+
+原子(Atoms)是Datalog中的基本元素，组成和例子如下：
+
+
+
+Atoms可以分成两类
+
+- Relational Atoms
+ - 
+- Arithmetic Atoms
+ - 如`age >= 18`
+
+## Logic
+
+### Datalog Rules & Logic And
+
+Datalog使用规则来进行推导(inference)，其定义如下：
+
+
+
+当Body中的所有表达式都为True时，Head才为True，如：
+
+
+
+求解过程(Interpretation of Datalog Rules)——枚举Body中所有关系表达式的可能取值组合，进而得到新的predicate/table。例如：
+
+
+
+
+
+谓词分为两类：EDB & IDB。
+
+- EDB (extensional database)
+ - 在程序运行前，这些数据已经给定
+- IDB (intensional database)
+ - 这一类数据仅由规则推导得来
+
+例如：
+
+
+
+### Logic Or
+
+以上例子实际上是逻辑与，而逻辑或则有两种实现方式：
+
+
+
+此外还需要考虑运算优先级的问题，建议在书写程序时用括号明确地标识期望的运算优先级：`H<-A,(B;C)`。
+
+### Logic Not/Negation
+
+
+
+### Recursion
+
+
+
+## Rule Satety
+
+讲到这里，停下来思考一下，这两条Rules看起来有什么问题吗？
+
+- `A(x) <- B(y), x > y.`
+- `A(x) <- B(y), !C(x,y).`
+
+
+
+~~第一次学看不出问题也没问题的~~
+
+由于x有无限的取值能满足规则，所以**生成的A是一个无限大的关系**。因此上述两条规则是不安全的。在Datalog中，只接受安全的规则。
+
+这里我们需要记住一个判定的准则：**如果规则中的每个变量至少在一个non-nageted relational atom中出现一次，那么这个规则是安全的**。
+
+*这实际上是借助已有的predicates（它们必定是有限的）来限制变量的取值范围。*
+
+---
+
+类似地，还有这样的规则：
+
+`A(x) <- B(x), !A(x)`
+
+
+
+对应地有第二个准则：**不要把recursion和negation写在同一条规则里**，*即避免写出非A推导出A这样的规则*。
+
+## Execution of Datalog Program
+
+
+
+Datalog的两大重要特性：
+
+- 单调性。因为事实（facts）不会被删除的。
+- 必然终止。
+ - 事实的数量是**单调**的。
+ - 由Rule Safety，所能得到的IDB的大小也是**有限**的。
+
+# Pointer Analysis via Datalog
+
+了解了Datalog的基本语法和性质，我们就可以用它来实现声明式的指针分析算法。其中三个重要的部分对应如下：
+
+- EDB：从程序的语义分析中能得到的与指针相关的信息
+- IDB：指针分析的结果
+- Rules：指针分析的规则
+
+
+
+和之前一样，我们把Call放到最后处理。
+
+## Datalog Model-EDB&IDB
+
+我们首先需要对前四条语句建模。输入的EDB代表了4个存储相应类型语句的table，输出为Variable和Field的指向关系。
+
+
+
+一个关于EDB的例子如下：
+
+
+
+## Datalog Rules
+
+Body按照红线所示代表前提，Head按照蓝线所示代表结论。
+
+
+
+## Example
+
+利用刚刚讲解的算法和Datalog的执行规则，分析这一段代码，给出推导结束后的IDB。
+
+```java
+b = new C();
+a = b;
+c = new C();
+c.f = a;
+d = c;
+c.f = d;
+e = d.f;
+```
+
+结果如下：
+
+
+
+## PA with Calls
+
+回顾指针分析中Call的规则：
+
+
+
+### This
+
+首先，我们需要引入新的EDB和IDB：
+
+（VCall即Virtual Call，ThisVar即This Variable）
+
+
+
+我们能够同时知道三个信息：
+
+1. this指向对象o
+2. 方法m是可达的
+3. 方法m可达是因为在l行处存在对方法m的调用
+
+
+
+### Parameters
+
+接下来要处理参数的传递，与之前类似，引入EDB标识Argument(调用语句行号，参数标号和参数本身)和Parameter(被调用方法，参数标号和参数本身)：
+
+
+
+而对应用Datalog书写的规则如果用自然语言描述，就是处理行号l处对m的调用时，根据形参和实参的信息，将实参已经有的指向关系传递给形参数。
+
+
+
+### Return Value
+
+引入EDB：
+
+
+
+对应的Datalog Rule，处理返回值的指向关系：
+
+
+
+### Sum up
+
+以上三个部分总结起来，就能得到以下的Datalog Rules。
+
+
+
+进而能得到全程序的分析算法如下。值得一提的是，在VarPointsTo规则中，添加Reachable(m)跳过不可达方法中的对象。而其他规则不需要加这一条件，则是因为它们都有VarPointsTo规则作为Body的一部分。
+
+
+
+# Taint Analysis via Datalog
+
+## Datalog Model
+
+同样需要用户提供Source和Sink。输出被标记的数据可能流到的Sink方法。
+
+## Datalog Rules
+
+说明：这里参数列表中用`—`表示通配符，即不关心枚举时这个位置取什么值。
+
+
+
+# Key Points
+
+- Pros
+ - **Succinct** and **readable**
+ - **Easy** to implement
+ - **Benefit from off-the-shelf optimized Datalog engines**
+- Cons
+ - **Restricted expressiveness**, i.e., it is impossible or inconvenient to express some logics
+ - Cannot fully control **performance**
+- Overall Review
+ - **Datalog** language
+ - How to implement **pointer analysis via Datalog**
+ - How to implement **taint analysis via Datalog**
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+# 声明式指针分析
+
+指针分析除了像之前一样用命令式语言来实现，也可以用声明式的算法实现。