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arXiv · 2507.10181

A simple formalization of alpha-equivalence

Kalmer Apinis·Danel Ahman
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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.

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Kalmer Apinis, Danel Ahman. 2025-07-14. A simple formalization of alpha-equivalence. https://arxiv.org/abs/2507.10181

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