A formalised first-order confluence proof for the λ-calculus using one-sorted variable names

  • Authors:

  • René Vestergaard;James Brotherston

  • Affiliations:

  • Japan Advanced Institute of Science and Technology, Tatsunokuchi, Ishikawa 923-1292, Japan;Mathematical Reasoning Group, Division of Informatics, University of Edinburgh, 80 South Bridge, Edinburgh EH1 1HN, Scotland, UK

  • Venue:
  • Information and Computation - RTA 2001
  • Year:
  • 2003

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Abstract

We present the titular proof development that has been verified in Isabelle/HOL. As a first, the proof is conducted exclusively by the primitive proof principles of the standard syntax and of 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 of the λ-calculus coincides with Curry's and Hindley's when terms are considered equal up to α-equivalence and (ii) that the confluence properties of all considered systems are equivalent.