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      The Universal Algebra of Computational Effects: Lawvere Theories and Monads

      Workshop on Mathematically Structured Functional Programming (MSFP 2006) (MSFP)

      Mathematically Structured Functional Programming

      2 July 2006

      Lawvere Theories, Monads, Computational Effects

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          Lawvere theories were defined in 1963 as a category theoretic axiomatisation of the notion of a clone of an equational theory. A connection was soon established with the notion of monad, which had been extant in algebraic topology for the previous decade. Monads, although mathematically the less direct and less malleable formulation, rapidly gained precedence. In 1987, they were proposed as a unified model of computational effects, but without reference to universal algebra. But universal algebra is central to the idea of computational effect, as it provides a theoretical foundation for the computational operations that give rise to the effect. Recognition of that fact has led to renewed prominence of the notion of Lawvere theory. We study the history of the development, in particular asking why Lawvere theories were eclipsed by monads, and how the renewed interest in them in the setting of computational effects might develop.

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          Author and article information

          July 2006
          July 2006
          : 1
          Laboratory for Foundations of Computer Science, School of Informatics, University of Edinburgh

          King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK
          © John Power. Published by BCS Learning and Development Ltd. Workshop on Mathematically Structured Functional Programming (MSFP 2006), Kuressaare, Estonia

          This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

          Workshop on Mathematically Structured Functional Programming (MSFP 2006)
          Kuressaare, Estonia
          2 July 2006
          Electronic Workshops in Computing (eWiC)
          Mathematically Structured Functional Programming
          Product Information: 1477-9358BCS Learning & Development
          Self URI (journal page): https://ewic.bcs.org/
          Electronic Workshops in Computing


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