Experiments with Choice in Dependently-Typed Higher-Order Logic

10 pages•Published: May 26, 2024

Daniel Ranalter, Chad Brown and Cezary Kaliszyk

Abstract

Recently 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.

Links:	https://easychair.org/publications/paper/lRJ1
	https://doi.org/10.29007/2v8h

BibTeX entry

@inproceedings{LPAR2024:Experiments_with_Choice_Dependently,
  author    = {Daniel Ranalter and Chad Brown and Cezary Kaliszyk},
  title     = {Experiments with Choice in Dependently-Typed Higher-Order Logic},
  booktitle = {Proceedings of 25th Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Nikolaj Bjørner and Marijn Heule and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {100},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/lRJ1},
  doi       = {10.29007/2v8h},
  pages     = {311-320},
  year      = {2024}}

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