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sav07_lecture_3 [2007/03/29 21:05] kremena.diatchka |
sav07_lecture_3 [2007/03/30 21:55] vkuncak |
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| Note: when proving our verification condition, instead of proving that semantics of relation implies error=false, it's same as proving that the formula for set sp(U,r) implies error=false, where U is the universal relation, or, in terms of formulas, computing the strongest postcondition of formula 'true'. | Note: when proving our verification condition, instead of proving that semantics of relation implies error=false, it's same as proving that the formula for set sp(U,r) implies error=false, where U is the universal relation, or, in terms of formulas, computing the strongest postcondition of formula 'true'. | ||
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| ==== Weakest preconditions ==== | ==== Weakest preconditions ==== | ||
| While symbolic execution computes formula by going forward along the program syntax tree, [[sav07_lecture_2#weakest_preconditions|weakest precondition]] computes formula by going backward. | While symbolic execution computes formula by going forward along the program syntax tree, [[sav07_lecture_2#weakest_preconditions|weakest precondition]] computes formula by going backward. | ||
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| + | \begin{equation*} | ||
| + | wp(r,P) = \{ s_1 \mid \forall s_2. (s_1,s_2) \in r \rightarrow s_2 \in P \} | ||
| + | \end{equation*} | ||
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| We know that the weakest precondition holds following conditions for each relation r and sets Q1, Q2: | We know that the weakest precondition holds following conditions for each relation r and sets Q1, Q2: | ||
| wp(r, Q1 ∧ Q2) = wp(r,Q1) ∧ wp(r,Q2) | wp(r, Q1 ∧ Q2) = wp(r,Q1) ∧ wp(r,Q2) | ||