Proof Repair across Type Equivalences

Abstract

We describe a new approach to automatically repairing broken proofs in response to changes in type definitions in the Coq proof assistant. Our approach combines a configurable proof term transformation with a proof term to tactic script decompiler. The proof term transformation implements transport across certain equivalences in a way that is suitable for repair and does not rely on axioms beyond those Coq assumes.We have implemented this approach in Pumpkin Pi, an extension to the Pumpkin Patch Coq plugin suite for proof repair. We have used Pumpkin Pi to support a benchmark from a user study, ease development with dependent types, port functions and proofs between unary and binary natural numbers, and support an industrial proof engineer to more easily interoperate between Coq and other verification tools.