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On Upper Bounds on the Church-Rosser Theorem

Research paper by Ken-etsu Fujita

Indexed on: 03 Jan '17Published on: 03 Jan '17Published in: arXiv - Computer Science - Logic in Computer Science



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.