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Communication Dans Un Congrès Année : 2023

Weakening and Iterating Laws using String Diagrams

Affaiblir et itérer des lois en utilisant les diagrammes de cordes

Résumé

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.
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Dates et versions

hal-04085131 , version 1 (28-04-2023)

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Paternité

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Alexandre Goy. Weakening and Iterating Laws using String Diagrams. MFPS XXXVIII, Jul 2022, Ithaca, NY, United States. ⟨10.46298/entics.10482⟩. ⟨hal-04085131⟩
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