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sav07_homework_3 [2007/03/31 19:44] vkuncak |
sav07_homework_3 [2007/03/31 19:48] vkuncak |
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| \end{equation*} | \end{equation*} | ||
| 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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| \end{equation*} | \end{equation*} | ||
| for all $c$ and $a$. | for all $c$ and $a$. | ||
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| **2.** Show that the condition $(*)$ is equivalent to the conjunction of these two conditions: | **2.** Show that the condition $(*)$ is equivalent to the conjunction of these two conditions: | ||
| \begin{eqnarray*} | \begin{eqnarray*} | ||
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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. | ||
| ==== Weakest preconditions and relations ==== | ==== Weakest preconditions and relations ==== | ||