on collecting semantics for program analysis

n/

Transforming semantics by abstract interpretation

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 and compare semantics of programming languages by abstract interpretation. We first prove that natural semantics can be decomposed in terms of complementary attribute independent observables, leading to an algebraic characterization of the symmetric structure of the hierarchy. Moreover, we characterize some structural property of semantics, such as their compositionality, in terms of simple abstract domain equations. This provides an equational presentation of most well known semantics, which is parametric on the observable and structural property of the semantics, making it possible to systematically derive abstract semantics, e.g. for program analysis, as solutions of abstract domain equations

"Optimal" Collecting Semantics for Analysis in a Hierarchy of Logic Program Semantics

In this paper we apply abstract interpretation to systematically derive, compose and compare semantics according to their expressive power. The main results are: (1) a definition of a hierarchy of collecting semantics, including well known semantics for logic programs, where semantics can be related to each other by abstract interpretation; (2) a characterization of collecting and abstract semantics in terms of collecting and abstract models for a program; (3) a correspondence between collecting and abstract models providing a ``logical'' interpretation of the typical loss of precision of abstract interpretation-based analysis; (4) a systematic approach to derive and compose collecting semantics in a lattice-theoretic environment; (5) a constructive characterization for the ``best'' collecting semantics for analysis