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.

翻译：本文引入幺半流的概念。幺半流是因果流函数（可在笛卡尔幺半范畴中定义）向任意对称幺半范畴的推广。正如流为纯函数的数据流编程提供语义，幺半流为以对称幺半范畴表示过程理论的数据流编程提供语义。幺半流同样构成反馈幺半范畴。正如我们可以使用余归纳流演算来推理信号流图，我们可以使用余归纳弦图来推理反馈幺半范畴。作为示例，我们研究了一种随机数据流语言的句法，其语义由随机幺半流实现。