Coinductive Monoidal Streams (Di Lavore, de Felive, Roman, 2023)

Abstract

We introduce monoidal streams. Monoidal streams are a generalization of causal stream functions, which can be defined in cartesian monoidal categories, to arbitrary symmetric monoidal categories. In the same way that streams provide semantics to dataflow programming with pure functions, monoidal streams provide semantics to dataflow programming with theories of processes represented by a symmetric monoidal category. Monoidal streams also form a feedback monoidal category. In the same way that we can use a coinductive stream calculus to reason about signal flow graphs, we can use coinductive string diagrams to reason about feedback monoidal categories. As an example, we study syntax for a stochastic dataflow language, with semantics in stochastic monoidal streams.

— (https://arxiv.org/abs/2212.14494)

@article{coinductive25,
   title={Coinductive Streams in Monoidal Categories},
   volume={Volume 21, Issue 3},
   ISSN={1860-5974},
   url={http://dx.doi.org/10.46298/lmcs-21(3:18)2025},
   DOI={10.46298/lmcs-21(3:18)2025},
   journal={Logical Methods in Computer Science},
   publisher={Centre pour la Communication Scientifique Directe (CCSD)},
   author={Di Lavore, Elena and de Felice, Giovanni and Román, Mario},
   year={2025},
   month=aug 
}

Extended version of Monoidal Streams for Dataflow Programming (Di Lavore, de Felice, Roman, 2022).

Tags: monoidal stream.