From 63481a9b61edfccd64629226b47c628ca89704ac Mon Sep 17 00:00:00 2001 From: Ranger Date: Wed, 23 Dec 2020 20:36:50 +0800 Subject: [PATCH] Update Lec 14 on pointer analysis via datalog. --- SUMMARY.md | 7 +- .../image-20201223184349163.png | Bin 0 -> 513169 bytes .../image-20201223184415502.png | Bin 0 -> 326782 bytes .../image-20201223185015690.png | Bin 0 -> 131538 bytes .../image-20201223185231533.png | Bin 0 -> 95052 bytes .../image-20201223185504296.png | Bin 0 -> 150038 bytes .../image-20201223185750701.png | Bin 0 -> 186107 bytes .../image-20201223185957740.png | Bin 0 -> 144544 bytes .../image-20201223190539380.png | Bin 0 -> 265009 bytes .../image-20201223190710495.png | Bin 0 -> 100147 bytes .../image-20201223190916420.png | Bin 0 -> 23202 bytes .../image-20201223191303096.png | Bin 0 -> 192701 bytes .../image-20201223191451507.png | Bin 0 -> 223114 bytes .../image-20201223191716873.png | Bin 0 -> 227061 bytes .../image-20201223192111827.png | Bin 0 -> 61968 bytes 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[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) diff --git a/ch5/05-01-Datalog-Based-PA.assets/image-20201223184349163.png b/ch5/05-01-Datalog-Based-PA.assets/image-20201223184349163.png new file mode 100644 index 0000000000000000000000000000000000000000..1afb6e87ab12f383b61651ca765c60ce38eb0ef9 GIT binary patch literal 513169 zcmZ6zcRZKx`#-ELQdDN7D20-h(V&cm$VhfsWoGZP5|UX&h(wv$BSJ(XlAS#>v-ckN z^Ll?Dzx(&S?|(jz_b0qw*L7a!c^uDmTrcEqU#B2rAR{3mp}2WNLV<*24+ROy&UMn= z_!kR#W;qg)V=)D2&~ zb>>BRSy^G)ix(Md*LI%q@}?fwAr(kI&B3AaGUmoq`rO+0XFL{@=>^r*lcjUQ&#kPZ zx}HR-hO~t_Om=?i74qM4+?`U4^nd-&$9CR2+wK3qe{`puh>1D=zkch#pZ{T`rr7)c z`^Utg1cMv@`}6RdH_l&|6#xHx3H~ujnAPOemH&QoAXbqh!+GOz#N{V6VPRo%rw=En zX0dr5VBW8(sc8~_{r`Sk_LUL~#`uX7|NV=XqwQqp3yc2pnR3(a!o7lmf?<3t|M$Y% zuQdi8B)(OV4O*_(LG}OrvHJ)a2g83q|6lj7@LRtACFR-Er%!*wugj^ZBupq0 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z1h{z*8FSamVgDX1rr9;}_Z+HLN=F$4sZaYw`~Nl`!V-wdUZnq>*uPf>PEkz!&nWPF zQ}dDF-@EyB{m>sPb$^DdKVPkO{*%M|{Xe+R9shrJ*Yt{;Vrp`d6iGO3L<$`00L>8E zvy?}Ukf7F3iDLG8q8$&>J#>UZX@(?vpF^Wo5&iueHa0pMFVp_v!~Md-JEHCAhp-Z2 z{Jf=QWuW+`*z}eIEr0r?QiwM2`Dq_1!9~gJ<3O+QdEnj$>hK3XdUSaAD0=;)r$WK4 z1?C~7d1-(p^ld~jp + +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** \ No newline at end of file diff --git a/ch5/ch5.md b/ch5/ch5.md new file mode 100644 index 0000000..34db46d --- /dev/null +++ b/ch5/ch5.md @@ -0,0 +1,3 @@ +# 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。

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