The Different Aspects of Monads and Mixins

Around twenty years ago two important developments happened in the areas of modularity and reuse in programming languages. On the one hand, Moggi showed how computational effects found in impure languages could be simulated using the notion of monads from category theory. Inspired by Moggi’s work, Wadler showed how monads could be used to structure (purely functional) programs. On the other hand, work by Cook showed how variations of mixins could model different notions of inheritance (normally found in object-oriented languages) in simple, elegant and compositional ways, by using traditional techniques of fixed-point theory. Monads and mixins are helpful to handle different aspects of modularity and reuse in programming languages, yet they have been largely explored independently. In this paper we show that the combination of monads and mixins leads to a simple aspectoriented programming (AOP) style that can be used effectively in purely functional programming languages to write elegant, reusable and modular programs.