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sav07_lecture_3_skeleton [2007/03/21 10:53] vkuncak |
sav07_lecture_3_skeleton [2007/03/21 10:58] vkuncak |
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| This idea is important in static analysis. | This idea is important in static analysis. | ||
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| Symbolic execution converts programs into formulas by going forward. It is therefore somewhat analogous to the way an [[interpreter]] for the language would work. | Symbolic execution converts programs into formulas by going forward. It is therefore somewhat analogous to the way an [[interpreter]] for the language would work. | ||
| + | Avoid renaming all the time. | ||
| + | |||
| + | SE(F,k, c1; c2) = SE(F & R(c1), k+1, c2) (update formula) | ||
| + | |||
| + | SE(F,k,(c1 [] c2); c2) = SE(F, k, c1) | SE(F,k,c2) (explore both branches) | ||
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| + | Note: how many branches do we get? | ||
| Strongest postcondition: | Strongest postcondition: | ||
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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. | 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. | ||
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| ==== Weakest preconditions ==== | ==== Weakest preconditions ==== | ||
| While symbolic execution computes formula by going forward along the program syntax tree, weakest precondition computes formula by going backward. | While symbolic execution computes formula by going forward along the program syntax tree, weakest precondition computes formula by going backward. | ||
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| + | wp(Q, x=t) = | ||
| + | wp(Q, assume F) = | ||
| + | wp(Q, assert F) = | ||
| + | wp(Q, c1 [] c2) = | ||
| + | wp(Q, c1 ; c2) = | ||
| ==== Inferring Loop Invariants ==== | ==== Inferring Loop Invariants ==== | ||