Compositional Optimization of Disjunctive Abstract Interpretations

Interpretations Roberto Giacobazzi ? Francesco Ranzato ?? ? Dipartimento di Informatica, Universit`a di Pisa Corso Italia 40, 56125 Pisa, Italy giaco@di.unipi.it ?? Dipartimento di Matematica Pura ed Applicata, Universit`a di Padova Via Belzoni 7, 35131 Padova, Italy franz@hilbert.math.unipd.it Abstract. We define the inverse operation for disjunctive completion, introducing the notion of least disjunctive basis for an abstract domain D: this is the most abstract domain inducing the same disjunctive completion as D. We show that the least disjunctive basis exists in most cases, and study its properties in relation with reduced product of abstract interpretations. The resulting framework is powerful enough to be applied to arbitrary abstract domains for analysis, providing advanced algebraic methods for domain manipulation and optimization. These notions are applied to abstract domains for analysis of functional and logic programming languages. 1 Introduction It is widely ackn..