From Herbrand schemes to functional interpretation

Sebastian Enqvist-Pyk

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arXiv · 2603.14933

From Herbrand schemes to functional interpretation

Sebastian Enqvist-Pyk

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Abstract

Herbrand schemes are a method to extract Herband disjunctions directly from sequent calculus proofs, without appealing to cut elimination, using a formal grammar known as a higher-order recursion scheme. In this note, we show that the core ideas of Herbrand schemes can be reformulated as a functional interpretation of classical sequent calculus, similar to the functional interpretation of classical logic due to Gerhardy and Kohlenbach. We argue that this provides a natural computational interpretation of classical sequent calculus, in the same spirit as the game-theoretic approach due to Alcolei et al. that has previously been used to analyze Herbrand's theorem in terms of concurrency.

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Sebastian Enqvist-Pyk. 2026-03-16. From Herbrand schemes to functional interpretation. https://arxiv.org/abs/2603.14933

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