Formalising and Verifying Reference Attribute Grammars in Coq

Abstract

Reference attribute grammars are a powerful formalism for concisely specifying and implementing static analyses. While they have proven their merit in practical applications, no attempt has so far been made to rigorously verify correctness properties of the resulting systems. We present a general method for formalising reference attribute grammars in the theorem prover Coq. The formalisation is supported by tools for generating standard definitions from an abstract description and custom proof tactics to help automate verification. As a small but typical application, we show how closure analysis for the untyped lambda calculus can easily be implemented and proved correct with respect to an operational semantics. To evaluate the feasibility of our approach on larger systems, we implement name lookup for a naming core calculus of Java and give a formal correctness proof of the centrepiece of a rename refactoring for this language.KeywordsClosure AnalysisAbstract SyntaxMember ClassSyntax TreeAttribute GrammarThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.