A rule-based approach for designing and composing abstract domains

Abstract interpretation allows constructing sound static analysis tools by safely approximating program semantics. Frameworks for abstract interpretation typically provide an implementation of a specialized iteration strategy to compute an abstract fixpoint, as well as a number of abstract domains in order to approximate different program properties. However, the design and implementation of additional domains, as well as their combinations, is eventually necessary to successfully prove arbitrary program properties. We propose a rule-based methodology for rapid design and prototyping of new domains and combining existing ones, with a focus on the analysis of logic programs. We provide several examples for domains combining numerical properties and data types and apply them to proving complex program properties.