Stateful Realizers for Nonstandard Analysis

• Autor(a) principal: Dinis, Bruno
• Data de Publicação: 2023
• Outros Autores: Miquey, Étienne
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10174/35335; https://doi.org/Bruno Dinis ; Étienne Miquey - Stateful Realizers for Nonstandard Analysis lmcs:10137 - Logical Methods in Computer Science, April 25, 2023, Volume 19, Issue 2 - https://doi.org/10.46298/lmcs-19(2:7)2023; https://doi.org/10.46298/lmcs-19(2:7)2023
• topic: realizabiliy; nonstandard arithmetic; stateful computations; ultrafilters; glueing

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 lambda-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.