Parametric polymorphism is one of the lynchpins of modern typed programming. A function that can work seamlessly over a variety of types simplifies code, helps to avoid errors introduced through duplication, and and is easy to maintain. However, polymorphism comes at a very real cost, one that each language with support for polymorphism has paid in different ways. This paper describes this cost, proposes a theoretically simple way to reason about the cost—that kinds, not types, are calling conventions—and details one approach to dealing with polymorphism that works in the context of a language, Haskell, that prizes both efficiency and a principled type system.

This approach, levity polymorphism, allows the user to abstract over calling conventions; we detail and verify restrictions that are necessary in order to compile levity-polymorphic functions. Levity polymorphism has opened up surprising new opportunities for library design in Haskell.