Proving renaming for Haskell via dependent types : a case-study in refactoring soundness

Abstract

We present a formally verified renaming refactoring for a subset of Haskell 98 giving a case-study in proving soundness properties of Haskell refactorings. Our renaming is implemented in the dependently- typed language Idris, which allows us to encode soundness proofs as an integral part of the implementation. We give the formal definition of our static semantics for our Haskell 98 subset, which we encode as part of the AST, ensuring that only well-formed programs may be represented and transformed. This forms a foundation upon which refactorings can be formally specified. We then define soundness of refactoring implementations as conformity to their specification. We demonstrate our approach via renaming, a canonical and well-understood refactoring, giving its implementation alongside its formal specification and soundness proof.