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Applied Categorical Structures

, Volume 11, Issue 1, pp 69–94 | Cite as

Algebraic Operations and Generic Effects

  • Gordon Plotkin
  • John Power
Article

Abstract

Given a complete and cocomplete symmetric monoidal closed category V and a symmetric monoidal V-category C with cotensors and a strong V-monad T on C, we investigate axioms under which an ObC-indexed family of operations of the form α x :(Tx) v →(Tx) w provides semantics for algebraic operations on the computational λ-calculus. We recall a definition for which we have elsewhere given adequacy results, and we show that an enrichment of it is equivalent to a range of other possible natural definitions of algebraic operation. In particular, we define the notion of generic effect and show that to give a generic effect is equivalent to giving an algebraic operation. We further show how the usual monadic semantics of the computational λ-calculus extends uniformly to incorporate generic effects. We outline examples and non-examples and we show that our definition also enriches one for call-by-name languages with effects.

algebraic operation computational effect Lawvere theory monad 

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Gordon Plotkin
    • 1
  • John Power
    • 1
  1. 1.School of InformaticsUniversity of EdinburghEdinburghU.K

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