A parameterization process as a categorical construction

Dominique Duval (1) , César Dominguez (2)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques
2 Department of Mathematics and Computer Science - Departamento de Matematicas y Computacion

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 transforming some operations into parameterized operations, which depend on one additional variable called the parameter. 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 free functor and the subsequent parameter passing process by a natural transformation. Various categorical notions are used, mainly adjoint functors, pushouts and lax colimits.

Domaines: Logique en informatique [cs.LO]; Catégories et ensembles [math.CT]

Dominique Duval, César Dominguez. A parameterization process as a categorical construction. 2009. ⟨hal-00411061⟩