Towards Proof Repair in Cubical Agda

Recent work introduced an algorithm and tool in Coq to automatically repair broken proofs in response to changes that correspond to type equivalences. We report on case studies for manual proof repair across type equivalences using an adaptation of this algorithm in Cubical Agda. Crucially, these case studies capture proof repair use cases that were challenging to impossible in prior work in Coq due to type theoretic limitations, highlighting three benefits to working in Cubical Agda: (1) quotient types enrich the space of repairs we can express as type equivalences, (2) dependent path equality makes it possible to internally state and prove correctness of repaired proofs relative to the original proofs, and (3) functional extensionality and transport make it simple to move between slow and fast computations after repair. They also highlight two challenges of working in Cubical Agda, namely those introduced by: (1) lack of tools for automation, and (2) proof relevance, especially as it interacts with definitional equality. We detail these benefits and challenges in hopes to set the stage for later work in proof repair bridging the benefits of both languages.