Determinisation of relational substitutions in ordered categories with domain

Authors:
Wolfram Kahl
Affiliations:
McMaster University, Hamilton, Ontario, Canada
Venue:
RelMiCS'08/AKA'08 Proceedings of the 10th international conference on Relational and kleene algebra methods in computer science, and 5th international conference on Applications of kleene algebra
Year:
2008

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Abstract

We present two different relational generalisations of substitutions, show that they both produce locally ordered categories with domain, and then develop the single-morphism "determiniser" concept that relies only on this framework, while still corresponding to conventional two-morphism unification in both examples. Central to this development is the determinacy concept of "characterisation by domain" introduced by Desharnais and Möller for Kleene algebras with domain; this is here applied in the weakest possible setting.