This work presents an object-oriented calculus based on higher-order mixin construction via mixin composition, where some software engineering requirements are modeled in a formal setting allowing to prove the absence of message-not-understood run-time errors. Mixin composition is shown to be a valuable language feature enabling a cleaner object-oriented design and development. In what we believe being quite a general framework, we give directions for designing a programming language equipped with higher-order mixins, although our study is not based on any already existing object-oriented language.