Verifying Well-Typedness Preservation of Refactorings using Scope Graphs

The goal of automated refactoring is to reduce maintenance effort. To realize this, programmers need to be able to trust or manually check that refactorings actually preserve behavior. To allow programmers to focus on such checks, automated refactorings should preserve program well-typedness. However, historically automated refactorings in popular IDEs could break well-typedness. The reason is that modern languages have complex name binding semantics which makes it hard to guarantee well-typedness in general. In recent work, scope graphs have been proposed as a uniform model for name binding. The model supports complex name binding patterns, and its uniformity makes it attractive to consider for verifying that refactorings preserve well-typedness. This paper explores how to prove that refactorings preserve well-typedness, using scope graphs. We consider a simple refactoring for merging modules in a toy module language, and prove that this refactoring preserves well-typedness. We give a generic template for proving well-typedness preservation using scope graphs, and discuss how this template relates to refactorings more generally.