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Object oriented institutions to specify symbolic computationsystems

Published online by Cambridge University Press:  18 July 2007

César Domínguez ,
Laureano Lambán  and
Julio Rubio
César Domínguez
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio Vives, Luis de Ulloa s/n, E-26004 Logroño, La Rioja, Spain cesar.dominguez@dmc.unirioja.es; laureano.lamban@dmc.unirioja.es; julio.rubio@dmc.unirioja.es
Laureano Lambán
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio Vives, Luis de Ulloa s/n, E-26004 Logroño, La Rioja, Spain cesar.dominguez@dmc.unirioja.es; laureano.lamban@dmc.unirioja.es; julio.rubio@dmc.unirioja.es
Julio Rubio
Affiliation:
Departamento de Matemáticas y Computación, Universidad de La Rioja, Edificio Vives, Luis de Ulloa s/n, E-26004 Logroño, La Rioja, Spain cesar.dominguez@dmc.unirioja.es; laureano.lamban@dmc.unirioja.es; julio.rubio@dmc.unirioja.es
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Abstract

The specification of the data structures used in EAT, a softwaresystem for symbolic computation in algebraic topology, is based onan operation that defines a link among different specificationframeworks like hidden algebras and coalgebras. In this paper,this operation is extended using the notion of institution, givingrise to three institution encodings. These morphisms define acommutative diagram which shows three possible views of the sameconstruction, placing it in an equational algebraic institution,in a hidden institution or in a coalgebraic institution. Moreover,these morphisms can be used to obtain a new description of thefinal objects of the categories of algebras in these frameworks,which are suitable abstract models for the EAT data structures.Thus, our main contribution is a formalization allowing us toencode a family of data structures by means of a single algebra(which can be described as a coproduct on the image of theinstitution morphisms). With this aim, new particular definitionsof hidden and coalgebraic institutions are presented.

Keywords

Institutionsymboliccomputationspecificationobject orientation

Information

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 41 , Issue 2 , April 2007 , pp. 191 - 214
Copyright
© EDP Sciences, 2007

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