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Weak and strong βη-normalization in pure type systems with βη-conversion

Ankit Pradhan, Cole Vick, Ruijie Fang, Carl Kwan

Palomar Registrypalomar/PALOMAR-2026-10-27-000027Oct 27, 2026cs.LOscore 0

A Lean formalization of the Barendregt-Geuvers-Klop conjecture, "weak normalization implies strong normalization", for the pure type systems PTS_βη of Geuvers (Logics and Type Systems, 1993), whose conversion rule uses βη-conversion. For every PTS specification, with no functionality assumption, it proves two theorems about the legal terms of PTS_βη. If every legal term is weakly βη-normalizing, then every legal term is strongly βη-normalizing. If every legal term is weakly β-normalizing, then every legal term is strongly βη-normalizing. The proof adapts OpenAI's 2026 proof of the β case for…

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