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sav08:hoare_logic [2008/03/03 10:31] pedagand |
sav08:hoare_logic [2009/02/25 14:34] vkuncak |
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| * $sp(P,r) \subseteq Q$ | * $sp(P,r) \subseteq Q$ | ||
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| ===== Hoare Triples, Preconditions, Postconditions on Formulas and Commands ===== | ===== Hoare Triples, Preconditions, Postconditions on Formulas and Commands ===== | ||
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| We then similarly extend the notion of $sp(P,r)$ and $wp(r,Q)$ to work on formulas and commands. We use the same notation and infer from the context whether we are dealing with sets and relations or formulas and commands. | We then similarly extend the notion of $sp(P,r)$ and $wp(r,Q)$ to work on formulas and commands. We use the same notation and infer from the context whether we are dealing with sets and relations or formulas and commands. | ||
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| + | ===== Composing Hoare Triples ===== | ||
| + | |||
| + | \[ | ||
| + | \frac{ \{P\} c_1 \{Q\}, \ \ \{Q\} c_2 \{R\} } | ||
| + | { \{P\} c_1 ; c_2 \{ R \} } | ||
| + | \] | ||
| ===== Further reading ===== | ===== Further reading ===== | ||
| * {{sav08:backwright98refinementcalculus.pdf|Refinement Calculus Book by Back, Wright}} | * {{sav08:backwright98refinementcalculus.pdf|Refinement Calculus Book by Back, Wright}} | ||