Transforming Semantics by Abstract Interpretation

By: Roberto Giacobazzi and Isabella Mastroeni

Roberto Giacobazzi
Dip. di Informatica
Univ. di Verona
Strada Le Grazie a Ca' Vignal 2
I-37134 Verona, Italy
giaco@sci.univr.it

Isabella Mastroeni
Dip. di Informatica
Univ. di Verona
Strada Le Grazie a Ca' Vignal 2
I-37134 Verona, Italy
mastroeni@sci.univr.it

Abstract:

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 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.