Enforcing QVT-R with mu-calculus and games

QVT-R is the standard Object Management Group bidirectional transformation language. In previous work, we gave a precise game-theoretic semantics for the checkonly semantics of QVT-R transformations, including the recursive invocation of relations which is allowed and used, but not defined, by the QVT standard. In this paper, we take up the problem of enforce semantics, where the standard attempts formality, but at crucial points lapses into English. We show that our previous semantics can be extended to enforce mode, giving a precise semantics taking the standard into account.