Realizability with stateful computations for nonstandard analysis

Bruno Dinis (1) , Étienne Miquey (2)

1 ULISBOA - Universidade de Lisboa = University of Lisbon
2 PLUME - Preuves et Langages

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.

Mots clés: ultrafilters; Łoś ' theorem; glueing; states; nonstandard analysis; realizability

Domaines: Logique en informatique [cs.LO]

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