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sav08:definition_of_set_constraints [2008/05/22 11:41] vkuncak |
sav08:definition_of_set_constraints [2008/05/22 11:51] vkuncak |
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| Is every set expression in set constraints monotonic? ++|Set difference is not monotonic in second argument.++ | Is every set expression in set constraints monotonic? ++|Set difference is not monotonic in second argument.++ | ||
| + | |||
| ===== Conditional Constraints ===== | ===== Conditional Constraints ===== | ||
| + | |||
| + | Let us simplify this expression: | ||
| + | \[ | ||
| + | f^{-2}(f(S,T)) = | ||
| + | \] | ||
| + | ++| | ||
| + | \[ | ||
| + | = f^{-2}(\{ f(s,t) \mid s \in S, t \in T \}) | ||
| + | \] | ||
| + | ++ | ||
| + | ++| | ||
| + | \[ | ||
| + | = \{ s_1 \in S \mid \exists t_1 \in T \} | ||
| + | \] | ||
| + | ++ | ||
| + | ++| | ||
| + | \[ | ||
| + | = \left\{ \begin{array}{rl} | ||
| + | S, \mbox{ if } T \neq \emptyset \\ | ||
| + | \emptyset, \mbox{ if } T = \emptyset | ||
| + | \end{array} | ||
| + | \right. | ||
| + | \] | ||
| + | ++ | ||
| An important property we would like to have in this semantic is a very intuitive one : \[ [[f^{-1}(f(S_1, S_2))]] = [[S_1]] \] | An important property we would like to have in this semantic is a very intuitive one : \[ [[f^{-1}(f(S_1, S_2))]] = [[S_1]] \] | ||