A unifying model of variables and names

  • Authors:
  • Marino Miculan;Kidane Yemane

  • Affiliations:
  • Dept. of Mathematics and Computing Science, University of Udine, Udine, Italy;Dept. of Information Technology, Uppsala University, Uppsala, Sweden

  • Venue:
  • FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
  • Year:
  • 2005

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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 admits a definition of distinction-aware simultaneous substitutions. As a substantial application example, we give the first semantic interpretation of Miller-Tiu's $FO\lambda^{\nabla}$ logic.