Visible Type Application

The Hindley-Milner (HM) type system automatically infers the types at which polymorphic functions are used. In HM, the inferred types are unambiguous, and every expression has a principal type. However, type inference is sometimes unwieldy or impossible, especially in the presence of type system extensions such as type classes and typelevel functions. Even here, programmers cannot provide type arguments explicitly, as HM requires types to be invisible. We describe an extension to HM that allows for visible type application. Our extension requires a novel type inference algorithm, yet its declarative presentation is a simple extension to HM. We prove that our extended system is a conservative extension of HM and admits principal types. We then extend our approach to a higher-rank type system with bidirectional type-checking. We have implemented this system in the Glasgow Haskell Compiler and show how our approach scales in the presence of complex type system features.