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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 software system for symbolic computation in algebraic topology, is based on an operation that defines a link among different specification frameworks like hidden algebras and coalgebras. In this paper, this operation is extended using the notion of institution, giving rise to three institution encodings. These morphisms define a commutative diagram which shows three possible views of the same construction, 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 the final 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 to encode a family of data structures by means of a single algebra (which can be described as a coproduct on the image of the institution morphisms). With this aim, new particular definitions of hidden and coalgebraic institutions are presented.

Keywords

Institutionsymbolic computationspecificationobject orientation
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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