We introduce the notion of functional dependencies of abstract interpretations relatively to a binary operator of composition. Functional dependencies are obtained by a functional composition of abstract domains, and provide a systematic approach to construct new abstract domains. In particular, we study the case of autodependencies, namely monotone operators on a given abstract domain. Under s...

A critical component of an abstract interpretation algorithm is the abstract domain, and traditionally, it is manually defined. Recently, automatic abstract interpretation techniques have emerged. A prominent technique, called Counter Example Guided Abstraction Refinement (CEGAR), and is based on an iterative process given a target property. Beginning with an abstract domain with a low level of...

In 1997, Cousot introduced a hierarchy where semantics are related with each other by abstract interpretation. In this field we consider the standard abstract domain transformers, devoted to refine abstract domains in order to include attribute independent and relational information, respectively the reduced product and power of abstract domains, as domain operations to systematically design an...

In abstract interpretation, the choice of an abstract domain fixes a limit on the precision of the inductive invariants that one can express; however, for a given abstract domain A, there is a most-precise (“strongest”, “best”) inductiveA-invariant for each program. Many techniques have been developed in abstract interpretation for finding overapproximate solutions, but only a few algorithms ha...

The specific problem that motivates this paper is how to obtain abstract descriptions of the meanings of imported predicates (such as built-ins) that can be used when analysing a module of a logic program with respect to some abstract domain. We assume that abstract descriptions of the imported predicates are available in terms of some “standard” assertions. The first task is to define an abstr...

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Static global analyses based on abstract interpretation have been used to derive properties of programs. The analyses differ in the expressiveness of the abstract domains and the precision and efficiency of domain operations. We extend an abstract domain defined by Jacobs and Langen and present new abstract domain operations to derive freeness, groundness, and sharing of variables in logic prog...