# 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

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topDomínguez, 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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