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A simplified proof of the Church-Rosser theorem. (English) Zbl 1338.03017
Summary: Takahashi translation \(\ast\) is a translation which means reducing all of the redexes in a \(\lambda\)-term simultaneously. In [J. Symb. Comput. 7, No. 2, 113–123 (1989; Zbl 0661.03008); Inf. Comput. 118, No. 1, 120–127 (1995; Zbl 0827.68060)], M. Takahashi gave a simple proof of the Church-Rosser confluence theorem by using the notion of parallel reduction and Takahashi translation. Our aim of this paper is to give a simpler proof of Church-Rosser theorem using only the notion of Takahashi translation.

MSC:
03B40 Combinatory logic and lambda calculus
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References:
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