Gradual typing has become a standard mechanism for both progressively adding types to dynamically typed languages and liberalising existing type systems, and recent developments have produced the Gradualizer and Abstracting Gradual Typing (AGT) for systematically lifting a typed language to a corresponding gradual language. AGT applies the principles of abstract interpretation to a language’s underlying predicates and functions: we have used this technique to build a library in the dependently typed language Agda for automatically generating different type systems over the same language of terms. Our mechanisation takes an abstract description of a type system indexed by a functor and then generates a variety of different type systems, including gradual typing.

Programming languages PhD student at VUW working on Grace.