A parameterization process: from a functorial point of view
type: Item
instance of: scholarly article
zbMATH Open document ID: 1269.68064
DOI: 10.1142/S0129054112500050
author: César Domínguez
author: Dominique Duval
published in: International Journal of Foundations of Computer Science
publication date: 2012-08-30T00:00:00Z
Mathematics Subject Classification ID: 68Q70
zbMATH DE Number: 6073941
zbMATH Keywords: parameterization process
zbMATH Keywords: symbolic computation system
zbMATH Keywords: categorical formalization
describes a project that uses: EAT
describes a project that uses: Kenzo
MaRDI profile type: Publication
cites work: Q3997112
cites work: Diagrammatic logic applied to a parameterisation process
cites work: Object oriented institutions to specify symbolic computation systems
cites work: Effective homology of bicomplexes, formalized in Coq
cites work: A hidden agenda
cites work: An object-oriented interpretation of the EAT system
cites work: Specification of abstract data types
cites work: Universal coalgebra: A theory of systems
full work available at URL: s0129054112500050
OpenAlex ID: W2109909359
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title: A parameterization process: from a functorial point of view
review text: From the Introduction: ``Kenzo and its predecessor EAT are software systems devoted to symbolic computation in algebraic topology. They carry out calculations of homology groups of complex topological spaces, namely iterated loop spaces.NEWLINENEWLINEThis paper deals with generalization by parameterization in the sense of Kenzo and EAT, so that our parameters are symbolic constants of a given type, that will be replaced by arguments which are elements in a given set. The notion of parameterization in programming and specification languages bears several meanings, where the parameter may be a type or a specification. For instance, in object oriented programming, parametric polymorphism is called generic programming, in C++ it is characterized by the use of template parameters to represent abstract data types. On the other hand, in algebraic specifications, a parameterized specification is defined as a morphism of specifications where the parameter is the source and the parameter passing is defined as a pushout [\textit{H. Ehrig} et al., Lect. Notes Comput. Sci. 85, 157--168 (1980; Zbl 0456.68101)].NEWLINENEWLINEA theory \(\Theta\) can be presented by a specification \(\Sigma\), this means that \(\Sigma\) generates \(\Theta\).NEWLINENEWLINEThe parameterization process and its associated parameter passing process have been described for each given theory \(\Theta\), but in fact they have the property of preserving the theory structure, which can be stated precisely in a categorical framework: this is the aim of this paper.''NEWLINENEWLINEThe authors also prove the following: ``Given a model of the parameterized specification, each interpretation of the parameter, called an argument, provides a model of the given specification. Moreover, under some relevant terminality assumption, this correspondence between the arguments and the models of the given specification is a bijection.''
reviewed by: Nelson Martins-Ferreira
description: scientific article; zbMATH DE number 6073941