A formal treatment of the barendregt variable convention in rule inductions

Authors:
Christian Urban;Michael Norrish
Affiliations:
Ludwig-Maximilians-University Munich;Canberra Research Lab., National ICT Australia (NICTA)
Venue:
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Year:
2005

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Abstract

Barendregt's variable convention simplifies many informal proofs in the λ-calculus by allowing the consideration of only those bound variables that have been suitably chosen. Barendregt does not give a formal justification for the variable convention, which makes it hard to formalise such informal proofs. In this paper we show how a form of the variable convention can be built into the reasoning principles for rule inductions. We give two examples explaining our technique.