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sav07_lecture_4_skeleton [2007/03/22 20:43] vkuncak |
sav07_lecture_4_skeleton [2007/03/22 23:12] olivier.gobet |
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| We use weakest preconditions, although you could also use strongest postconditions or any other variants of the conversion from programs to formulas. | We use weakest preconditions, although you could also use strongest postconditions or any other variants of the conversion from programs to formulas. | ||
| - | |||
| ===== More on wp ===== | ===== More on wp ===== | ||
| Line 18: | Line 17: | ||
| === wp of havoc === | === wp of havoc === | ||
| - | Can we derive wp(Q,havoc(x)? | + | Can we derive wp(Q,havoc(x))? |
| * By consider havoc(x) as (... [] x=-1 [] x = 0 [] x = 1 [] ...) ? | * By consider havoc(x) as (... [] x=-1 [] x = 0 [] x = 1 [] ...) ? | ||
| * From relational definition? | * From relational definition? | ||
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| Benefit: if there is x_{n+1} that is not changed, we do not need to write its properties in the loop invariant. This can make loop invariant shorter. | Benefit: if there is x_{n+1} that is not changed, we do not need to write its properties in the loop invariant. This can make loop invariant shorter. | ||
| - | ==== References about weakest precondition (in construction) ==== | + | |
| + | |||
| + | ==== References about weakest precondition (under construction) ==== | ||
| + | * (some online references will come here) | ||
| * Back, Wright: Refinement Calculus | * Back, Wright: Refinement Calculus | ||
| - | * Dijkstra | + | * Edsger W. Dijkstra: A Discipline of Programming |
| - | * Hoare, He | + | * C. A. R. Hoare, He Jifeng: Unifying Theories of Programming |
| ===== Modeling data structures ===== | ===== Modeling data structures ===== | ||
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| * [[Gallier Logic Book]], Chapter 10.6 | * [[Gallier Logic Book]], Chapter 10.6 | ||
| * {{nelsonoppen80decisionprocedurescongruenceclosure.pdf|the original paper by Nelson and Oppen}} | * {{nelsonoppen80decisionprocedurescongruenceclosure.pdf|the original paper by Nelson and Oppen}} | ||
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