Download PDFOpen PDF in browserExperiments with Choice in Dependently-Typed Higher-Order Logic10 pages•Published: May 26, 2024AbstractRecently an extension to higher-order logic — called DHOL — was introduced, enrich- ing the language with dependent types, and creating a powerful extensional type theory. In this paper we propose two ways how choice can be added to DHOL. We extend the DHOL term structure by Hilbert’s indefinite choice operator ε, define a translation of the choice terms to HOL choice that extends the existing translation from DHOL to HOL and show that the extension of the translation is complete and give an argument for soundness. We finally evaluate the extended translation on a set of dependent HOL problems that require choice.Keyphrases: choice, dependent hol, proof translation In: Nikolaj Bjørner, Marijn Heule and Andrei Voronkov (editors). Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 100, pages 311-320.
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