Abstract
A methodology is introduced based on first-order logic, for the design and decomposition of abstract domains for abstract interpretation. First, an assertion language is chosen that describes the properties of interest. Next, abstract domains are defined to be suitably chosen sets of assertions. Finally, computer representations of abstract domains are defined in the expected way, as isomorphic copies of their specification in the assertion language. In order to decompose abstract domains, the notion of prime (conjunctive) factorization of sets of assertions is introduced. We illustrate this approach by considering typical abstract domains for ground-dependency and aliasing analysis in logic programming.
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