Abstract Interpretation from a Topological Perspective

Abstract

We develop abstract interpretation from topological principles by relaxing the definitions of open set and continuity; key results still hold. We study families of closed and open sets and show they generate post- and pre-condition analyses, respectively. Giacobazzi's forwards- and backwards-complete functions are characterized by the topologically closed and continuous maps, respectively. Finally, we show that Smyth's upper and lower topologies for powersets induce the overapproximating and underapproximating transition functions used for abstract-model checking.