2009/08/25 by Dominique Duval, Duval, Dominique, César Domínguez +1
Computer Science · Mathematics · #Category Theory (math.CT) #FOS: Computer and information sciences #FOS: Mathematics #Formal Methods in Verification #Homotopy and Cohomology in Algebraic Topology #Logic in Computer Science (cs.LO) #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.0908.3634
openalex publication_date 2009/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.