Close Encounters of the Higher Kind Emulating Constructor Classes in Standard ML

In our recent work [5] on automating Isabelle proofs, we discovered that several proof search problems can be elegantly expressed as a monadic program. Unfortunately, Standard ML does not natively support the kinds of polymorphism required to easily express a Monad abstraction, nor similar abstractions such as Applicative and Functor . In this paper, we present a technique for encoding constructor classes such as Monad, which relies only on the Standard ML module system. Several others have attempted to enable constructor classes in Standard ML by changing the language. While it is tempting to customise the language by adding new features, new features tend to cause duplication [2] and inconsistency [3]. Furthermore, avoiding language extensions makes our approach transferable to all other ML dialects with a module system. Our contributions are twofold: we develop a usable library for monads, monad transformers, applicatives, and more in Standard ML, and demonstrate an elegant technique using ML functors to elaborate minimal definitions of each abstraction to avoid code duplication. For example, given a minimal definition of the list monad, e.g. return and bind, our library derives other basic functions, such as >=>, join, and liftM automatically. Moreover, using the hierarchical relationship among constructor classes, our library automatically instantiates list as a member of the parent classes, e.g. applicative and functor. Thus, for each monad, users can derive more than twenty functions from two manually written functions, i.e. return and bind.