Gradual Typing for Annotated Type Systems

Annotated type systems include additional information in types to make them more expressive and to gather intensional information about programs. Gradual types enable a seamless transition between statically and dynamically checked properties of values. Gradual annotation typing applies the ideas of gradual typing to the annotation part of a type system. We present a generic approach to transform a type system with annotated base types into a system which gradualizes the information contained in the annotations. We prove generic type safety for the gradualized extensions and similar generic versions of the blame theorem for a calculus with run-time annotations. We relate this calculus to a more efficient calculus which elides run-time annotations in the statically annotated parts. We further introduce and prove correct a syntactic transformation that eliminates run-time annotation tests by enlarging the statically annotated parts.