2023-06-21: John Power (University of Bath)

Sat, 21 Oct 2023 21:24:08 +0100

John Power (University of Bath)

Computational Effects in Mathematical Perspective

Abstract

In the late 1980's, Eugenio Moggi introduced the idea of "monads as notions of computation", the latter more recently called computational effects, supported by several impressive examples. He used the definition of monad but did not make substantial use of mathematics that gives rise to monads. In category theory, monads systematically arise from universal algebra. But universal algebra can also be understood, from a category theoretic perspective, in terms of Lawvere theories, this fact shedding considerable light on computational effects, in particular the operations that give rise to effects. That observation has been fundamental to a deep, further development, giving rise to the notion of algebraic effect. I shall try to explain the conceptual line of thought that gives rise to algebraic effects, modelled by Lawvere theories and thence my monads. It was joint work primarily with Gordon Plotkin but also with others, notably Martin Hyland.

2023-06-21 14:00:00 UTC
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