Abstract
The proofs of the Church–Rosser theorems for β, η, and β ∪ η reduction in untyped λ-calculus are formalized in Isabelle/HOL, an implementation of Higher Order Logic in the generic theorem prover Isabelle. For β-reduction, both the standard proof and Takahashi's are given and compared. All proofs are based on a general theory of commutating relations that supports an almost geometric style of reasoning about confluence diagrams.
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Nipkow, T. More Church–Rosser Proofs. Journal of Automated Reasoning 26, 51–66 (2001). https://doi.org/10.1023/A:1006496715975
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DOI: https://doi.org/10.1023/A:1006496715975