# Formal proof of correctness of Levenshtein distance

Has anyone formalized, in a proof assistant (constructively!) the correctness of the computation of Levenshtein distance ? The related Q&A on here is about paper proofs. Searching around did not come up with any leads.

Note that I'm equally interested in correctness as that of a proof of optimality, i.e. knowing that an algorithm returns a correct sequence of edits, from which the distance is trivially computed, is quite interesting too. That the sequence is optimal can be a second step.