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sav07_lecture_3_skeleton [2007/03/20 14:54] vkuncak |
sav07_lecture_3_skeleton [2007/03/20 18:06] vkuncak |
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===== Converting programs (with simple values) to formulas ===== | ===== Converting programs (with simple values) to formulas ===== | ||
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<latex> | <latex> | ||
\{((x_0,y_0),(x,y)) \mid F \} | \{((x_0,y_0),(x,y)) \mid F \} | ||
- | </latex> | + | </latex> |
where F is some formula that has x,y,x_0,y_0 as free variables. | where F is some formula that has x,y,x_0,y_0 as free variables. | ||
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* correct | * correct | ||
* efficient | * efficient | ||
- | * create formulas that we can prove later | + | * create formulas that we can effectively prove later |
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+ | What exactly do we prove about the formula R( c ) ? | ||
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+ | We prove that this formula is **valid** | ||
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+ | R( c ) -> error=false | ||
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when c is a basic command. | when c is a basic command. | ||
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We can apply these rules to reduce the size of formulas. | We can apply these rules to reduce the size of formulas. | ||
- | ==== Papers ==== | + | ==== Abstraction ==== |
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+ | * for proving properties | ||
+ | * for finding errors | ||
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+ | ==== Symbolic execution ==== | ||
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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. It is based on the notion of strongest postcondition. | ||
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+ | ==== Weakest preconditions ==== | ||
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+ | While symbolic execution computes formula by going forward along the program syntax tree, weakest precondition computes formula by going backward. | ||
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+ | ===== Proving quantifier-free linear arithmetic formulas ===== | ||
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+ | ===== Papers ===== | ||
* Verification condition generation in Spec#: http://research.microsoft.com/~leino/papers/krml157.pdf | * Verification condition generation in Spec#: http://research.microsoft.com/~leino/papers/krml157.pdf |