Dynamic typing as staged type inference

Dynamic typing extends statically typed languages with a universal datatype, simplifying programs which must manipulate other programs as data, such as distributed, persistent, interpretive and generic programs. Current approaches, however, limit the use of polymorphism in dynamic values, and can be syntactically awkward.We introduce a new approach to dynamic typing, based on staged computation, which allows a single type-reconstruction algorithm to execute partly at compile time and partly at run-time. This approach seamlessly extends a single type system to accommodate types that are only known at run-time, while still supporting both type inference and polymorphism. The system is significantly more expressive than other approaches. Furthermore it can be implemented efficiently; most of the type inference is done at compile-time, leaving only some residual unification for run-time.We demonstrate our approach by examples in a small polymorphic functional language, and present its type system, type reconstruction algorithm, and operational semantics. Our proposal could also be readily adapted to many other programming languages.