Takahashi, Masako Parallel reductions in \(\lambda\)-calculus. (English) Zbl 0661.03008 J. Symb. Comput. 7, No. 2, 113-123 (1989). The notion of parallel reduction is extracted from the Tait-Martin-Löf 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. Cited in 1 ReviewCited in 12 Documents MSC: 03B40 Combinatory logic and lambda calculus Keywords:parallel reduction; \(\lambda\)-calculus PDF BibTeX XML Cite \textit{M. Takahashi}, J. Symb. Comput. 7, No. 2, 113--123 (1989; Zbl 0661.03008) Full Text: DOI OpenURL References: [1] Barendregt, H.P., () [2] Klop, J.W., () [3] Levy, J.J., An algebraic interpretation of the λ-β-K calculus and a labelled λ-calculus, Springer lec. notes comp., 37, 147-165, (1975) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.