Abstraction of Syntax

Vijay Victor D'Silva, Daniel Kroening

Abstract: The theory of abstract interpretation is a conceptual framework for reasoning about approximation of semantics. We ask if the creative process of designing an approximation can be studied mathematically. Semantic approximations, whether studied in a purely mathematical setting, or implemented in a static analyser, must have a representation. We apply abstract interpretation to syntactic representations and study abstraction of syntax. We show that semantic abstractions and syntactic abstractions are different, and identify criteria for deriving semantic abstractions by purely syntactic means. As a case study, we show that descriptions of numeric abstract domains can be derived by abstraction of syntax.