Central submonads and notions of computation: Soundness, completeness and internal languages

T Carette, L Lemonnier… - 2023 38th Annual ACM …, 2023 - ieeexplore.ieee.org
Monads in category theory are algebraic structures that can be used to model computational
effects in programming languages. We show how the notion of" centre", and more generally" …

The Semantics of Effects: Centrality, Quantum Control and Reversible Recursion

L Lemonnier - arXiv preprint arXiv:2406.07216, 2024 - arxiv.org
This thesis revolves around an area of computer science called" semantics". We work with
operational semantics, equational theories, and denotational semantics. The first …

[PDF][PDF] Central Submonads and Notions of Computation

T Carette, L Lemonnier, V Zamdzhiev - CoRR, 2022 - algrewr.pages.math.cnrs.fr
• In a Lawvere theory T, we say that f: An→ An′ and g: Am→ Am′ commute if and only if
fm′◦ gn (also written f⋆ g) and gn′◦ fm (also written g⋆ f) are equal, up to isomorphism.• If …