Capture-Avoiding and Hygienic Program Transformations (incl. Proofs)

Program transformations in terms of abstract syntax trees compromise referential integrity by introducing variable capture. Variable capture occurs when in the generated program a variable declaration accidentally shadows the intended target of a variable reference. Existing transformation systems either do not guarantee the avoidance of variable capture or impair the implementation of transformations.
We present an algorithm called name-fix that automatically eliminates variable capture from a generated program by systematically renaming variables. name-fix is guided by a graph representation of the binding structure of a program, and requires name-resolution algorithms for the source language and the target language of a transformation. name-fix is generic and works for arbitrary transformations in any transformation system that supports origin tracking for names. We verify the correctness of name-fix and identify an interesting class of transformations for which name-fix provides hygiene. We demonstrate the applicability of name-fix for implementing capture-avoiding substitution, inlining, lambda lifting, and compilers for two domain-specific languages.