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A New Foundation for Nominal Isabelle

  • Brian Huffman
  • Christian Urban
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6172)

Abstract

Pitts et al introduced a beautiful theory about names and binding based on the notions of permutation and support. The engineering challenge is to smoothly adapt this theory to a theorem prover environment, in our case Isabelle/HOL. We present a formalisation of this work that differs from our earlier approach in two important respects: First, instead of representing permutations as lists of pairs of atoms, we now use a more abstract representation based on functions. Second, whereas the earlier work modeled different sorts of atoms using different types, we now introduce a unified atom type that includes all sorts of atoms. Interestingly, we allow swappings, that is permutations build from two atoms, to be ill-sorted. As a result of these design changes, we can iron out inconveniences for the user, considerably simplify proofs and also drastically reduce the amount of custom ML-code. Furthermore we can extend the capabilities of Nominal Isabelle to deal with variables that carry additional information. We end up with a pleasing and formalised theory of permutations and support, on which we can build an improved and more powerful version of Nominal Isabelle.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Brian Huffman
    • 1
  • Christian Urban
    • 2
  1. 1.Portland State University 
  2. 2.Technical University of Munich 

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