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

We positively answer the question A.1.6 in [2]: “Is there a recursive normalizing one-step reduction strategy for micro λ-calculus?” Micro λ-calculus refers to an implementation of the λ-calculus due to [1], implementing β-reduction by means of “micro steps” recursively distributing a β-redex (λx.M)N over its body M . 1 Inner spine strategy First, we provide “micro λ-calculus” with a more systematic name. Definition 1. Distributive reduction is defined as βd = β i d ∪ β c d ∪ β l d ∪ β a d , where β d = {