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Communication Dans Un Congrès Année : 2023

Diller-Nahm Bar Recursion

Résumé

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.

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Dates et versions

hal-04144888 , version 1 (28-06-2023)

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Valentin Blot. Diller-Nahm Bar Recursion. FSCD 2023 - 8th International Conference on Formal Structures for Computation and Deduction, Jul 2023, Rome, Italy. pp.32:1-32:16, ⟨10.4230/LIPIcs.FSCD.2023.32⟩. ⟨hal-04144888⟩
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