OpenAI reports weak-to-strong normalization for pure type systems

For any pure type system, if every legal expression in every valid context has a terminating β-reduction sequence, then every β-reduction sequence from every such expression terminates, including reductions inside type annotations.

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Understanding the problem

Read the background

For any pure type system, if every legal expression in every valid context has a terminating β-reduction sequence, then every β-reduction sequence from every such expression terminates, including reductions inside type annotations.

Why it matters

If correct, resolves the β instance of the Barendregt–Geuvers–Klop normalization conjecture for arbitrary pure type systems.

What counts as progress

Does system-wide weak β-normalization imply strong β-normalization for pure type systems?

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