FAUST AND REACTIVE FUNCTIONS: A TRACED PROP OF SIGNALS AND SIGNAL RELATIONS

I propose a categorical interpretation of the algebra presented by Orlarey et al in their paper An Algebra For Block Diagrams [1]. The category in question is the Traced Prop of Relations on Signals. Where Sequential and Parallel composition are relational composition and monoidal product respectively, and Recursive composition is a combination of these, the Trace and more. In this interpretation reactive functions correspond to signal processors. I prove the theorem that the trace of any delayed reactive function is a reactive function. This makes explicit the need for an implicit delay in the definition of Recursion. Furthermore, I show, by way of preserving reactivity and functionality, that each of the five main FAUST operators returns a valid signal processor when fed two of them.