A parameterization process: From a functorial point of view

  1. DomÍnguez, C. 1
  2. Duval, D. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

  2. 2 Laboratoire Jean Kuntzmann
    info

    Laboratoire Jean Kuntzmann

    Grenoble, Francia

    GRID grid.464181.e

Journal:
International Journal of Foundations of Computer Science

ISSN: 0129-0541

Year of publication: 2012

Volume: 23

Issue: 1

Pages: 225-242

Type: Article

Export: RIS
DOI: 10.1142/S0129054112500050 SCOPUS: 2-s2.0-84857598270 WoS: 000300443600015 arXiv: 0908.4491 lock_openOpen access editor
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Summary

The parameterization process used in the symbolic computation systems Kenzo and EAT is studied here as a general construction in a categorical framework. This parameterization process starts from a given specification and builds a parameterized specification by adding a parameter as a new variable to some operations. Given a model of the parameterized specification, each interpretation of the parameter, called an argument, provides a model of the given specification. Moreover, under some relevant terminality assumption, this correspondence between the arguments and the models of the given specification is a bijection. It is proved in this paper that the parameterization process is provided by a functor and the subsequent parameter passing process by a natural transformation. Various categorical notions are used, mainly adjoint functors, pushouts and lax colimits. © 2012 World Scientific Publishing Company.