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arXiv:1807.05923cs.LO

What is algebraic about algebraic effects and handlers?

Andrej Bauer

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.

arXiv comments
Journal reference
DOI
Subjects
cs.LOLogic in Computer Science cs.PLProgramming Languages

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Linked by 3 identifiable commenters in 4 comments across 3 threads, from Feb 2022 to May 2026. Found in 1 HN submission from Apr 2025 to Apr 2025. Open submission discussions.

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Discussed in comments3 threads

  1. Algebraic Effects for the Rest of Us 1 comment

    • Here is an article by Andrej Bauer answering the exact question, "What is algebraic about algebraic effects and handlers?": https://arxiv.org/abs/1807.05923v2 Contrary to the claim from the comment you are replying to, according to Andrej Bauer, "algebraic" does not refer to the…

      hutaoView on HNParent context

  2. What is algebraic about algebraic effects? 2 comments

    • I would encourage anyone interested in this question to check out the paper "What is algebraic about algebraic effects and handlers?" (https://arxiv.org/abs/1807.05923) which is a write-up of the lecture series linked in the post above. I don't think the paper is too difficult…

      oisdkView on HNParent context

    • > For one, if algebraic isn't aiming at the ideas in an algebra, then they absolutely should be using a different name. Algebraic effects are certainly algebraic, they're just not directly related to algebraic data types. Both ideas are using "algebraic" at different levels, and…

      oisdkView on HNParent context

  3. Structurally-Typed Condition Handling 1 comment

    • Obligatory link to “ What is algebraic about algebraic effects and handlers?” https://arxiv.org/abs/1807.05923

      klysmView on HNParent context

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