LIPIcs.FSCD.2023.32.pdf
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Diller-Nahm Bar Recursion
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8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Formal Structures for Computation and Deduction (FSCD) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2023-06-28
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Valentin Blot. Diller-Nahm Bar Recursion. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.FSCD.2023.32
Abstract
We present a generalization of Spector’s bar recursion to the Diller-Nahm variant of Gödel’s Dialectica interpretation. This generalized bar recursion collects witnesses of universal formulas in sets of approximation sequences to provide an interpretation to the double-negation shift principle. The interpretation is presented in a fully computational way, implementing sets via lists. We also present a demand-driven version of this extended bar recursion manipulating partial sequences rather than initial segments. We explain why in a Diller-Nahm context there seems to be several versions of this demand-driven bar recursion, but no canonical one.
Subject Classification
ACM Subject Classification
- Theory of computation → Proof theory
Keywords
- Dialectica
- Bar recursion
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References
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