Object oriented institutions to specify symbolic computation systems

César Domínguez; Laureano Lambán; Julio Rubio

RAIRO - Theoretical Informatics and Applications (2007)

  • Volume: 41, Issue: 2, page 191-214
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Domínguez, César, Lambán, Laureano, and Rubio, Julio. "Object oriented institutions to specify symbolic computation systems." RAIRO - Theoretical Informatics and Applications 41.2 (2007): 191-214. <http://eudml.org/doc/250045>.

@article{Domínguez2007,
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. },
author = {Domínguez, César, Lambán, Laureano, Rubio, Julio},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Institution; symbolic computation; specification; object orientation},
language = {eng},
month = {7},
number = {2},
pages = {191-214},
publisher = {EDP Sciences},
title = {Object oriented institutions to specify symbolic computation systems},
url = {http://eudml.org/doc/250045},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Domínguez, César
AU - Lambán, Laureano
AU - Rubio, Julio
TI - Object oriented institutions to specify symbolic computation systems
JO - RAIRO - Theoretical Informatics and Applications
DA - 2007/7//
PB - EDP Sciences
VL - 41
IS - 2
SP - 191
EP - 214
AB - 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.
LA - eng
KW - Institution; symbolic computation; specification; object orientation
UR - http://eudml.org/doc/250045
ER -

References

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