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sav08:abstract_interpretation_recipe [2008/05/08 12:40] vkuncak |
sav08:abstract_interpretation_recipe [2008/05/20 12:14] vkuncak |
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| * $E \subseteq V \times V$ are control-flow graph edges | * $E \subseteq V \times V$ are control-flow graph edges | ||
| * $r : E \to 2^{PS \times PS}$, so each $r(p_1,p_2) \subseteq PS \times PS$ is relation describing the meaning of command between $p_1$ and $p_2$ | * $r : E \to 2^{PS \times PS}$, so each $r(p_1,p_2) \subseteq PS \times PS$ is relation describing the meaning of command between $p_1$ and $p_2$ | ||
| + | We can define meaning of program in this form using [[Collecting Semantics]]. | ||
| ===== Summary of key steps ==== | ===== Summary of key steps ==== | ||
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| * extend $sp^{\#}$ to work on control-flow graphs, by defining $F^\# : (V \to A) \to (V \to A)$ as follows (below, $g^{\#} : V \to A$) | * extend $sp^{\#}$ to work on control-flow graphs, by defining $F^\# : (V \to A) \to (V \to A)$ as follows (below, $g^{\#} : V \to A$) | ||
| \[ | \[ | ||
| - | F^{\#}(g^{\#})(p_2) = g^{\#}(p_2) \sqcup \bigsqcup_{(p_1,p_2) \in E} sp^{\#}(g^{\#}(p_1),r(p_1,p_2)) | + | F^{\#}(g^{\#})(p') = g^{\#}(p') \sqcup \bigsqcup_{(p,p') \in E} sp^{\#}(g^{\#}(p),r(p,p')) |
| \] | \] | ||
| which is analogous to [[Collecting Semantics]] | which is analogous to [[Collecting Semantics]] | ||