Dependent Vector Types for Multirate Faust

Abstract : Faust is a functional programming language dedicated to the specification of executable monorate synchronous mu- sical applications. To extend Faust capabilities to domains such as spectral processing, we introduce here a multi- rate extension of the core Faust language. The key idea is to link rate changes to data structure manipulation op- erations: creating a vector-valued output signal divides the rate of input signals by the vector size, while serializing vectors multiplies rates accordingly. This interplay be- tween vectors and rates is made possible in the language static semantics by the introduction of dependent types. We present a typing semantics, a denotational semantics and a correctness theorem that show that this extension preserves the language synchonous characteristics. This new design is under implementation in the Faust compiler.