A Unifying Model of Variables and Names

Abstract. We investigate a category theoretic model where both “variables” and “names”, usually viewed as separate notions, are particular cases of the more general notion of distinction. The key aspect of this model is to consider functors over the category of irreflexive, symmetric finite relations. The models previously proposed for the notions of “variables” and “names” embed faithfully in the new one, and initial algebra/final coalgebra constructions can be transferred from the formers to the latter. Moreover, the new model allows for defining distinction-aware simultaneous substitutions as clone-like structures. Finally, we apply this model to develop the first semantic interpretation of the FOλ logic.

• Type: Conference
• Year: 2005
• Where: FOSSACS
• Authors: Marino Miculan, Kidane Yemane
• Keywords: Applied Computing, Category Theoretic Model, FOSSACS 2005, Separate Notions, Symmetric finite Relations