Static Analysis in Finitely Supported Mathematics

Abstract

Finitely Supported Mathematics represents the Zermelo-Fraenkel mathematics reformulated in the frameworkof invariant sets. We develop a theory of abstract interpretationswhich is consistent to the principles of constructingthe Finitely Supported Mathematics. We first translate thenotions of lattices and Galois connections into the frameworkof invariant sets, and then present their properties in termsof finitely supported objects. Later, we introduce the notionsof invariant correctness relation and invariant representationfunction, we emphasize an equivalence between them, and weestablish the relationship between these notions and invariantGalois connections. Finally, we provide some widening andnarrowing techniques in order to approximate the least fixedpoints of finitely supported transition functions.