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sav08:semantics_of_sign_analysis_domain [2008/05/07 23:29] giuliano |
sav08:semantics_of_sign_analysis_domain [2009/03/26 13:22] vkuncak |
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| ====== Semantics of Sign Analysis Domain ====== | ====== Semantics of Sign Analysis Domain ====== | ||
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| + | Recall [[Sign Analysis for Expressions and Programs]] | ||
| Concrete domain $C$: sets of states: $2^{\mathbb{Z}^3}$ (three variables) | Concrete domain $C$: sets of states: $2^{\mathbb{Z}^3}$ (three variables) | ||
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| \] | \] | ||
| ++++ | ++++ | ||
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| ===== Constructing an Abstract Lattice ===== | ===== Constructing an Abstract Lattice ===== | ||
| - | Definibe: | + | Define: |
| \[ | \[ | ||
| a_1 \preceq a_2 \iff \gamma(a_1) \subseteq \gamma(a_2) | a_1 \preceq a_2 \iff \gamma(a_1) \subseteq \gamma(a_2) | ||
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| Yes, because of the properties of $\subseteq$. | Yes, because of the properties of $\subseteq$. | ||
| + | Is it a lattice? | ||
| ===== Abstract Postcondition ===== | ===== Abstract Postcondition ===== | ||
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| The computed set of program states will contain the most precise set of program states. | The computed set of program states will contain the most precise set of program states. | ||
| - | ===== Fixpoints in Sign Lattice ===== | ||