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sav08:conjunctions_of_predicates [2008/05/08 12:46] vkuncak |
sav08:conjunctions_of_predicates [2009/04/01 03:21] (current) vkuncak |
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====== Abstract Interpretation with Conjunctions of Predicates ====== | ====== Abstract Interpretation with Conjunctions of Predicates ====== | ||
- | Parameters: a finite set of formulas ${\cal P} = P_1,\ldots,P_n$ in program variables. | + | Parameters: a finite set of formulas ${\cal P} = \{ P_0, P_1,\ldots,P_n\}$ in program variables. Suppose $P_0$ is the predicate 'false'. |
- | for $a \in A$ we have $a \subseteq {\cal P}$ | + | Let $A = 2^{\cal P}$, so for $a \in A$ we have $a \subseteq {\cal P}$. |
- | Using [[Abstract Interpretation Recipe]] we construct: | + | We design analysis using [[Abstract Interpretation Recipe]]. |
- | * abstract domain: truth values of predicates | + | |
- | * concretization function: states given by truth values | + | |
- | * abstraction function | + | |
- | * best abstract post for simple programming language | + | |
- | Finite lattice. | + | Define a syntactic order on $(A,\le)$ |
+ | |||
+ | Finite lattice. | ||
+ | |||
+ | Defining $\gamma$. | ||
+ | |||
+ | Defining $\alpha$. | ||
+ | |||
+ | Is it the case that $\alpha(\gamma(a))=a$? | ||
+ | |||
+ | Using a theorem prover to compute $sp^\#$. | ||
- | Two different orders. |