Algebraic operations and generic effects
type: Item
instance of: scholarly article
title: Algebraic operations and generic effects
zbMATH Open document ID: 1023.18006
DOI: 10.1023/A:1023064908962
author: Gordon D. Plotkin
author: John Power
published in: Applied Categorical Structures
publication date: 2003-06-09T00:00:00Z
review text: \textit{E. Moggi} [in: Proc. LICS '89, IEEE Press, 14-23 and Inf. Comput. 93, 55-92 (1991; Zbl 0723.68073)] introduced the idea of giving a unified category-theoretic semantics for computational effects, modeling each of them in the Kleisli category of an appropriate strong monad on a base category with finite products. However, the calculus of Moggi's semantics models does not contain operations, the constructs that actually create the effects. In order to model constructive operations that arise in describing computational effects, the authors consider, given a complete and cocomplete symmetric monoidal closed category \({\mathcal V}\) and a symmetric monoidal \({\mathcal V}\)-category \({\mathcal C}\) with cotensors and a strong \({\mathcal V}\)-monad \(\mathbb{T}\) on \({\mathcal C}\), axioms under which an Ob \({\mathcal C}\)-indexed family of operations of the form \(\alpha_x: (\mathbb{T} x)^v\to(\mathbb{T} x)^w\) provides semantics for algebraic operations on the computational \(\lambda\)-calculus.
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 18C50
Mathematics Subject Classification ID: 68Q55
Mathematics Subject Classification ID: 03B40
zbMATH DE Number: 1925062
zbMATH Keywords: algebraic operation
zbMATH Keywords: computational effect
zbMATH Keywords: Lawvere theory
zbMATH Keywords: monad
zbMATH Keywords: category-theoretic semantics
zbMATH Keywords: Kleisli category
zbMATH Keywords: strong monad
zbMATH Keywords: Moggi's semantics models
zbMATH Keywords: computational \(\lambda\)-calculus
MaRDI profile type: Publication
full work available at URL: a:1023064908962
OpenAlex ID: W1606211906
description: scientific article; zbMATH DE number 1925062