Automatically generating the dynamic semantics of gradually typed languages

Many language designers have adopted gradual typing. However, there remains open questions regarding how to gradualize languages. Cimini and Siek (2016) created a methodology and algorithm to automatically generate the type system of a gradually typed language from a fully static version of the language. In this paper, we address the next challenge of how to automatically generate the dynamic semantics of gradually typed languages. Such languages typically use an intermediate language with explicit casts. Our first result is a methodology for generating the syntax, type system, and dynamic semantics of the intermediate language with casts. Next, we present an algorithm that formalizes and automates the methodology, given a language definition as input. We show that our approach is general enough to automatically gradualize several languages, including features such as polymorphism, recursive types and exceptions. We prove that our algorithm produces languages that satisfy the key correctness criteria of gradual typing. Finally, we implement the algorithm, generating complete specifications of gradually typed languages in lambda-Prolog, including executable interpreters.