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sav07_homework_3 [2007/03/31 19:45] vkuncak |
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| where $r^{-1}$ denotes the inverse of relation $r$. In other words, computing weakest preconditions corresponds to propagating possible errors backwards. | where $r^{-1}$ denotes the inverse of relation $r$. In other words, computing weakest preconditions corresponds to propagating possible errors backwards. | ||
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| **3.** Let $\alpha$ and $\gamma$ satisfy the condition of Galois connection. Show that the following three conditions are equivalent: | **3.** Let $\alpha$ and $\gamma$ satisfy the condition of Galois connection. Show that the following three conditions are equivalent: | ||
| - | * $c = \gamma(\alpha(c))$ for all $c$ | + | * $\alpha(\gamma(a)) = a$ for all $a$ |
| - | * $\gamma$ is a [[wk>surjective function]] | + | * $\alpha$ is a [[wk>surjective function]] |
| - | * $\alpha$ is an [[wk>injective function]] | + | * $\gamma$ is an [[wk>injective function]] |
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| + | **4.** State the condition for $c=\gamma(\alpha(c))$ to hold for all $c$. When $C$ is the set of concrete states and $A$ is a domain of static analysis, is it more reasonable to expect that $c=\gamma(\alpha(c))$ or $\alpha(\gamma(a)) = a$ to be satisfied, and why? | ||
| ==== Weakest preconditions and relations ==== | ==== Weakest preconditions and relations ==== | ||