A simple formalization of alpha-equivalence

Abstract

While teaching untyped $\lambda$-calculus to undergraduate students, we were wondering why $\alpha$-equivalence is not directly inductively defined. In this paper, we demonstrate that this is indeed feasible. Specifically, we provide a grounded, inductive definition for $\alpha$-equivalence and show that it conforms to the specification provided in the literature. The work presented in this paper is fully formalized in the Rocq Prover.

added links to definitions and proofs on GitHub