Transforming Abstract Interpretations by Abstract Interpretation - New Challenges in Language-based Security

In this paper we exploit abstract interpretation for transforming abstract domains and semantics. The driving force in both transformations is making domains and semantics, ie abstract interpretations themselves, complete, namely precise, for some given observation. We prove that a common geometric pattern is shared by all these transformations, both at the domain and semantic level. This pattern is based on the notion residuated closures, which in our case can be viewed as an instance of abstract interpretation. We consider these operations in the context of language-based security, and show how domain and semantic transformations model security policies and attackers, opening new perspectives in the model of information flow in programming languages.