Formalization of Insertion/Deletion Codes and the Levenshtein Metric in Lean

Formalization deals with expressing definitions or theorems and proofs at the level of fundamental logic, which allows for automatic verification by computer programs. We report on work done formalizing definitions and theorems in coding theory using the Lean theorem prover, released by Microsoft Research and Carnegie Mellon University in 2015. We formalize fundamental concepts regarding error-correcting codes capable of correcting insertions, deletions, or combinations of insertions and deletions. In particular, we formalize definitions and theorems about subsequences and supersequences, the Levenshtein distance, insertion/deletion spheres, and insertion/deletion codes.