Dependent Types for Multi-Rate Flows in Synchronous Programming

Abstract: Synchronous programming languages emerged in the 1980s as tools for implementing reactive systems, which interact with events from physical environments and often must do so under strict timing constraints. In this report, we encode inside ATS various real-time primitives in an experimental synchronous language called Prelude, where ATS is a statically typed language with an ML-like functional core that supports both dependent types (of DML-style) and linear types. We show that the verification requirements imposed on these primitives can be formally expressed in terms of dependent types in ATS. Moreover, we modify the Prelude compiler to automatically generate ATS code from Prelude source. This modified compiler allows us to solely rely on typechecking in ATS to discharge proof obligations originating from the need to typecheck Prelude code. Whereas ATS is typically used as a general purpose programming language, we hereby demonstrate that it can also be conveniently used to support some forms of advanced static checking in languages equipped with less expressive types.