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We report on yet another formalization of the Church-Rosser property in lambda-calculi, carried out with the proof environment BELUGA.After the well-known proofs of confluence for β -reduction in the untyped settings, with and without Takahashi's complete developments method, we concentrate on η-reduction and obtain the result for β η modularly.We further extend the analysis to typedcalculi, in particular System F. Finally, we investigate the idea of pursuing the encoding directly in BELUGA's meta-logic, as well as the use of BELUGA's logic programming engine to search for counterexamples.
Momigliano et al. (Sun,) studied this question.