A recursive normalizing one-step reduction strategy for the distributive lambda calculus

Abstract

We positively answer the question A.1.6 in J. Klop's "Ustica Notes": "Is there a recursive normalizing one-step reduction strategy for micro $\lambda$-calculus?" Micro $\lambda$-calculus refers to an implementation of the $\lambda$-calculus due to Revesz, implementing $\beta$-reduction by means of "micro steps" recursively distributing a $\beta$-redex $(\lambda x.M)\ N$ over its body $M$.