Hidden Specification of a Functional System

Domínguez, César; Lambán, Laureano; Pascual, Vico; Rubio, Julio

doi:10.1007/3-540-45654-6_43

Cited by 2 publications

(3 citation statements)

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“…In [10] we tried to introduce a similar diagram with the usual notion of institution morphism (non forward, i.e. where sentences are translated contravariantly with respect to models).…”

Section: A Diagram Of Institution Encodingsmentioning

confidence: 99%

“…If this technique is intended to be used in the relationship between the coalgebraic institution and the hidden institution, we find that it is only possible if the hidden institution is restricted to equations in one hidden variable. This detail, that was overlooked in [10], expresses the relationship between hidden algebras and coalgebras included in [6].…”

Section: A Diagram Of Institution Encodingsmentioning

confidence: 99%

“…On the one hand, the institutional description could be extended to other parts of the EAT system or introduced into the specification of structures in the Kenzo system [11], an objectoriented Sergeraert's program (successor of EAT). For example, in [10] the specification of the functorial relationship between data structures of EAT is studied and in [9] the inheritance relationship between Kenzo structures is tackled, although both works lack an institutional description (if such a thing is possible). Besides, it should be established whether the theoretical results obtained here can be applied to other symbolic computation systems apart from EAT or Kenzo.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

See 2 more Smart Citations

Object oriented institutions to specify symbolic computation systems

Domínguez¹,

Lambán²,

Rubio³

2007

RAIRO-Theor. Inf. Appl.

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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.Mathematics Subject Classification. 68Q65, 68Q60.

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“…In [10] we tried to introduce a similar diagram with the usual notion of institution morphism (non forward, i.e. where sentences are translated contravariantly with respect to models).…”

Section: A Diagram Of Institution Encodingsmentioning

confidence: 99%

Section: A Diagram Of Institution Encodingsmentioning

confidence: 99%