Nominal Techniques in Isabelle/HOL

  • Christian Urban
  • Christine Tasson
Conference paper

DOI: 10.1007/11532231_4

Volume 3632 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Urban C., Tasson C. (2005) Nominal Techniques in Isabelle/HOL. In: Nieuwenhuis R. (eds) Automated Deduction – CADE-20. CADE 2005. Lecture Notes in Computer Science, vol 3632. Springer, Berlin, Heidelberg

Abstract

In this paper we define an inductive set that is bijective with the α-equated lambda-terms. Unlike de-Bruijn indices, however, our inductive definition includes names and reasoning about this definition is very similar to informal reasoning on paper. For this we provide a structural induction principle that requires to prove the lambda-case for fresh binders only. The main technical novelty of this work is that it is compatible with the axiom-of-choice (unlike earlier nominal logic work by Pitts et al); thus we were able to implement all results in Isabelle/HOL and use them to formalise the standard proofs for Church-Rosser and strong-normalisation.

Keywords

Lambda-calculus nominal logic structural induction theorem-assistants 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Christian Urban
    • 1
  • Christine Tasson
    • 2
  1. 1.Ludwig-Maximilians-University Munich 
  2. 2.ENS Cachan Paris