an:06305279
Zbl 1338.03017
Komori, Yuichi; Matsuda, Naosuke; Yamakawa, Fumika
A simplified proof of the Church-Rosser theorem
EN
Stud. Log. 102, No. 1, 175-183 (2014).
00329691
2014
j
03B40
\(\lambda\)-calculus; Church-Rosser theorem; confluence theorem; parallel reduction; Takahashi translation
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)], \textit{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.
Zbl 0661.03008; Zbl 0827.68060