an:06987965
Zbl 1436.03104
Fujita, Ken-etsu
The Church-Rosser theorem and quantitative analysis of witnesses
EN
Inf. Comput. 263, 52-56 (2018).
00423601
2018
j
03B40
lambda-calculus; Church-Rosser theorem; upper bounds on reduction length; parallel reduction; reduction strategies; Takahashi's translation; Gross-Knuth reduction strategy; Grzegorczyk hierarchy
Summary: We show that an upper bound function for the Church-Rosser theorem of type-free \(\lambda\)-calculus with \(\beta\)-reduction must be in the fourth level of the Grzegorczyk hierarchy, i.e., the smallest Grzegorczyk class properly extending the class of elementary functions. At this level we also find common reducts for the confluence property. The proof method here can be applied not only to type-free \(\lambda\)-calculus with \(\beta\eta\)-reduction but also to typed \(\lambda\)-calculi such as Pure Type Systems.