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Journal Articles Logical Methods in Computer Science Year : 2023

Stateful Realizers for Nonstandard Analysis

Abstract

In this paper we propose a new approach to realizability interpretations for nonstandard arithmetic. We deal with nonstandard analysis in the context of (semi) intuitionistic realizability, focusing on the Lightstone-Robinson construction of a model for nonstandard analysis through an ultrapower. In particular, we consider an extension of the λ-calculus with a memory cell, that contains an integer (the state), in order to indicate in which slice of the ultrapower M^N the computation is being done. We pay attention to the nonstandard principles (and their computational content) obtainable in this setting. In particular, we give non-trivial realizers to Idealization and a non-standard version of the LLPO principle. We then discuss how to quotient this product to mimic the Lightstone-Robinson construction.
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hal-04053612 , version 1 (31-03-2023)

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Bruno Dinis, Étienne Miquey. Stateful Realizers for Nonstandard Analysis. Logical Methods in Computer Science, 2023, Volume 19, Issue 2, ⟨10.46298/LMCS-19(2:7)2023⟩. ⟨hal-04053612⟩
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