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

Vestergaard, R; Brotherston, J; (2003) A formalised first-order confluence proof for the λ-calculus using one-sorted variable names. Information and Computation , 183 (2) 212 - 244. 10.1016/S0890-5401(03)00023-3.

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Abstract

We present the titular proof of 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.

Type:Article
Title:A formalised first-order confluence proof for the λ-calculus using one-sorted variable names
DOI:10.1016/S0890-5401(03)00023-3
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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