TY - GEN

T1 - FAUST AND REACTIVE FUNCTIONS

T2 - 19th Sound and Music Computing Conference, SMC 2022

AU - Connell, Nicholas

N1 - Funding Information:
I owe a great debt of gratitude to my dissertation supervisor Guy McCusker whose help and advice was instrumental!

PY - 2022/7/12

Y1 - 2022/7/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85137669918&partnerID=8YFLogxK

M3 - Chapter in a published conference proceeding

AN - SCOPUS:85137669918

T3 - Proceedings of the Sound and Music Computing Conferences

SP - 740

EP - 749

BT - SMC/JIM/IFC 2022 - Proceedings of the 19th Sound and Music Computing Conference

A2 - Michon, Romain

A2 - Pottier, Laurent

A2 - Orlarey, Yann

PB - Sound and Music Computing Network

Y2 - 5 June 2022 through 12 June 2022

ER -