A Type System for Julia

Abstract: The Julia programming language was designed to fill the needs of scientific computing by combining the benefits of productivity and performance languages. Julia allows users to write untyped scripts easily without needing to worry about many implementation details, as do other productivity languages. If one just wants to get the work done-regardless of how efficient or general the program might be, such a paradigm is ideal. Simultaneously, Julia also allows library developers to write efficient generic code that can run as fast as implementations in performance languages such as C or Fortran. This combination of user-facing ease and library developer-facing performance has proven quite attractive, and the language has increasing adoption. With adoption comes combinatorial challenges to correctness. Multiple dispatch -- Julia's key mechanism for abstraction -- allows many libraries to compose "out of the box." However, it creates bugs where one library's requirements do not match what another provides. Typing could address this at the cost of Julia's flexibility for scripting. I developed a "best of both worlds" solution: gradual typing for Julia. My system forms the core of a gradual type system for Julia, laying the foundation for improving the correctness of Julia programs while not getting in the way of script writers. My framework allows methods to be individually typed or untyped, allowing users to write untyped code that interacts with typed library code and vice versa. Typed methods then get a soundness guarantee that is robust in the presence of both dynamically typed code and dynamically generated definitions. I additionally describe protocols, a mechanism for typing abstraction over concrete implementation that accommodates one common pattern in Julia libraries, and describe its implementation into my typed Julia framework.