Coinductive Streams in Monoidal Categories
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916906419617792 |
|---|---|
| author | Di Lavore, Elena de Felice, Giovanni Román, Mario |
| author_facet | Di Lavore, Elena de Felice, Giovanni Román, Mario |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_14494 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Coinductive Streams in Monoidal Categories Di Lavore, Elena de Felice, Giovanni Román, Mario Logic in Computer Science Category Theory 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. |
| title | Coinductive Streams in Monoidal Categories |
| topic | Logic in Computer Science Category Theory |
| url | https://arxiv.org/abs/2212.14494 |