Realizability with stateful computations for nonstandard analysis - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2021

Realizability with stateful computations for nonstandard analysis

Bruno Dinis
  • Function : Author
  • PersonId : 1081463
Étienne Miquey

Abstract

In this paper we propose a new approach to realizability interpretations for nonstandard arithmetic. We deal with nonstandard analysis in the context of 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 the computation is being done. We shall pay attention to the nonstandard principles (and their computational content) obtainable in this setting. We then discuss how this product could be quotiented to mimic the Lightstone-Robinson construction.
Fichier principal
Vignette du fichier
main.pdf (424.81 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-03002239 , version 1 (12-11-2020)

Identifiers

  • HAL Id : hal-03002239 , version 1

Cite

Bruno Dinis, Étienne Miquey. Realizability with stateful computations for nonstandard analysis. CSL 2021 - Computer Science Logic, Jan 2021, Ljubljana, Slovenia. ⟨hal-03002239⟩
90 View
113 Download

Share

Gmail Facebook X LinkedIn More