What is algebraic about algebraic effects and handlers?

Andrej Bauer
7/16/2018
cs.LOcs.PL

Official code: yallop/effects-bibliography (1,154 stars, last commit 2026-10-18).

Abstract

This note recapitulates and expands the contents of a tutorial on the mathematical theory of algebraic effects and handlers which I gave at the Dagstuhl seminar 18172 "Algebraic effect handlers go mainstream". It is targeted roughly at the level of a doctoral student with some amount of mathematical training, or at anyone already familiar with algebraic effects and handlers as programming concepts who would like to know what they have to do with algebra. We draw an uninterrupted line of thought between algebra and computational effects. We begin on the mathematical side of things, by reviewing the classic notions of universal algebra: signatures, algebraic theories, and their models. We then generalize and adapt the theory so that it applies to computational effects. In the last step we replace traditional mathematical notation with one that is closer to programming languages.

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Code Implementations(1)

yallop/effects-bibliographyOfficial100%

A collaborative bibliography of work related to the theory and practice of computational effects

1,15493Mar 17, 20163 days ago
algebraic-effectsbibliographyeffect-handlers

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Cite this paper

@article{bauer2018what,
  title  = {What is algebraic about algebraic effects and handlers?},
  author = {Andrej Bauer},
  year   = {2018},
  eprint = {1807.05923},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1807.05923}
}

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