A Formalised First-Order Con uence Proof for the λ-Calculus Using One-Sorted Variable Names (Barendregt Was Right after all ... almost)

  • René Vestergaard
  • James Brotherston
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2051)


We present the titular proof development which has been implemented in Isabelle/HOL. As a first, the proof is conducted exclusively by the primitive induction principles of the standard syntax and the considered reduction relations: the naive way, so to speak. Curiously, the Barendregt Variable Convention takes on a central technical role in the proof. We also show (i) that our presentation coincides with Curry’s and Hindley’s when terms are considered equal up-to α and (ii) that the con uence properties of all considered calculi are equivalent.


Free Variable Abstract Syntax Rule Induction Complete Development Structural Induction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • René Vestergaard
    • 1
  • James Brotherston
    • 2
  1. 1.CNRS-IMLMarseilleFrance
  2. 2.University of EdinburghScotlandUK

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