Abstraction of Syntax

Abstract

The theory of abstract interpretation is a conceptual frame- work for reasoning about approximation of semantics. We ask if the creative process of designing an approximation can be studied mathe- matically. Semantic approximations, whether studied in a purely mathe- matical setting, or implemented in a static analyser, must have a repre- sentation. 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.