Abstract
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.
Supported under EU TMR grant # ERBFMRXCT-980170: LINEAR. Work done in part while visiting LFCS, University of Edinburgh from Heriot-Watt University.
Supported by a grant from LFCS, University of Edinburgh.
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Vestergaard, R., Brotherston, J. (2001). A Formalised First-Order Con uence Proof for the λ-Calculus Using One-Sorted Variable Names (Barendregt Was Right after all ... almost). In: Middeldorp, A. (eds) Rewriting Techniques and Applications. RTA 2001. Lecture Notes in Computer Science, vol 2051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45127-7_23
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DOI: https://doi.org/10.1007/3-540-45127-7_23
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