Alexandre Goy - Weakening and Iterating Laws using String Diagrams

entics:10482 - Electronic Notes in Theoretical Informatics and Computer Science, February 22, 2023, Volume 1 - Proceedings of MFPS XXXVIII - https://doi.org/10.46298/entics.10482
Weakening and Iterating Laws using String DiagramsArticle

Authors: Alexandre Goy

    Distributive laws are a standard way of combining two monads, providing a compositional approach for reasoning about computational effects in semantics. Situations where no such law exists can sometimes be handled by weakening the notion of distributive law, still recovering a composite monad. A celebrated result from Eugenia Cheng shows that combining $n$ monads is possible by iterating more distributive laws, provided they satisfy a coherence condition called the Yang-Baxter equation. Moreover, the order of composition does not matter, leading to a form of associativity. The main contribution of this paper is to generalise the associativity of iterated composition to weak distributive laws in the case of $n = 3$ monads. To this end, we use string-diagrammatic notation, which significantly helps make increasingly complex proofs more readable. We also provide examples of new weak distributive laws arising from iteration.


    Volume: Volume 1 - Proceedings of MFPS XXXVIII
    Published on: February 22, 2023
    Accepted on: December 15, 2022
    Submitted on: December 14, 2022
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Category Theory
    Funding:
      Source : OpenAIRE Graph
    • Quantitative Reasoning Methods for Probabilistic Logics; Funder: French National Research Agency (ANR); Code: ANR-20-CE48-0005

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