Weakening and Iterating Laws using String Diagrams


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 more 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. 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.

To appear in Mathematical Foundations of Programming Semantics
Alexandre Goy
Alexandre Goy

I am interested in theoretical computer science, especially logic, category theory, coalgebra, and probabilistic aspects of these topics.