Purely functional formalization of Unit Generator for sound programming.

• Simple Notation of connection between UGens with referencial transparancy.
• Different from Faust and Kronos, it aims to be more strictly pure-functional formalization neither with block algebra nor meta-construction of audio graph, but with a lambda calculus
• Its final goal is to be able to describe Upsampling/Downsampling/Multirate Processing/Delay/Table Lookup without using any special primitives in addition to describing stateful function.
• Considered to be used as an intermediate representation for sound programming language.

• Implement Prototype with haskell
• express recursion
• describe sequencial connection
• UGen runner which takes input data stream as list
• split/merge data flow
• compose many UGens with high order function
• delay/ringbuffer/table lookup
• multirate
  • down/upsample
  • vector processing like FFT
  • combination with functional reactive programming
• Make translater to lower-level expression like LLVM IR
  • optimization
  • make interpreter
  • realtime processing

• E. Brandt, “Temporal type constructors for computer music programming,” School of Computer Science, Carnegie Mellon University, 2002.
• B. R. Gaster, N. Renney, and T. Mitchell, “OUTSIDE THE BLOCK SYNDICATE: TRANSLATING FAUST’S ALGEBRA OF BLOCKS TO THE ARROWS FRAMEWORK,”,Proceedings of the 1st International Faust Conference, 2018.
• R. B. Dannenberg, “UGG: A Unit Generator Generator”, Proceedings of the 2018 International Computer Music Conference, International Computer Music Association, 2018.
• V. Norilo, “Kronos: A Declarative Metaprogramming Language for Digital Signal Processing,” Computer Music Journal, vol. 39, no. 4, pp. 30–48, 2015, doi: 10.1162/10.11.
• B. T. y Widemann and M. Lepper, “Foundations of Total Functional Data-Flow Programming,” Jun. 2014, doi: 10.4204/eptcs.153.10.
• C. Reach, “INCREMENTAL FUNCTIONAL REACTIVE PROGRAMMING FOR INTERACTIVE MUSIC SIGNAL PROCESSING”, Proc. of the 16th Int. Conference on Digital Audio Effects (DAFx-13), 2013.

Copyright Tomoya Matsuura 2021 https://matsuuratomoya.com

MIT License.