On Upper Bounds on the Church-Rosser Theorem
arXiv:1701.00637 · doi:10.4204/EPTCS.235.2
Abstract
The Church-Rosser theorem in the type-free lambda-calculus is well investigated both for beta-equality and beta-reduction. We provide a new proof of the theorem for beta-equality with no use of parallel reductions, but simply with Takahashi's translation (Gross-Knuth strategy). Based on this, upper bounds for reduction sequences on the theorem are obtained as the fourth level of the Grzegorczyk hierarchy.
In Proceedings WPTE 2016, arXiv:1701.00233