Abstract

Nominal techniques are based on the idea of sets with a finitely-supported atoms-permutation action.

We consider the idea of nominal renaming sets, which are sets with a finitely-supported atoms-renaming action; renamings can identify atoms, permutations cannot. We show that nominal renaming sets exhibit many of the useful qualities found in (permutative) nominal sets; an elementary sets-based presentation, inductive datatypes of syntax up to binding, cartesian closure, and being a topos. Unlike is the case for nominal sets, the notion of names-abstraction coincides with functional abstraction. Thus we obtain a concrete presentation of sheaves on the category of finite sets in the form of a category of sets with structure.

Keywords

Nominal renaming sets nominal sets abstract syntax with binding 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Murdoch J. Gabbay
    • 1
  • Martin Hofmann
    • 2
  1. 1.UK
  2. 2.Germany

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