an:04079377
Zbl 0661.03008
Takahashi, Masako
Parallel reductions in \(\lambda\)-calculus
EN
J. Symb. Comput. 7, No. 2, 113-123 (1989).
00169496
1989
j
03B40
parallel reduction; \(\lambda\)-calculus
The notion of parallel reduction is extracted from the Tait-Martin-L??f proof of the Church-Rosser theorem (for \(\beta\)-reduction). We define parallel \(\beta\)-, \(\eta\)- and \(\beta\) \(\eta\)-reduction by induction, and use them to give simple proofs of some fundamental theorems in \(\lambda\)- calculus; the normal reduction theorem for \(\beta\)-reduction, that for \(\beta\) \(\eta\)-reduction, the postponement theorem of \(\eta\)-reduction (in \(\beta\) \(\eta\)-reduction), and some others.