Parametrised Functional Interpretations

TL;DR

This paper introduces a flexible framework for unifying various functional interpretations using parameter families, enabling the inclusion of recent bounded and Herbrandized interpretations.

Contribution

It generalizes previous unification approaches by incorporating a parametrized system that encompasses newer functional interpretations.

Findings

Unified framework for functional interpretations

Includes bounded and Herbrandized interpretations

Generalizes previous unification methods

Abstract

This paper presents a general framework for unifying functional interpretations. It is based on families of parameters allowing for different degrees of freedom on the design of the interpretation. In this way we are able to generalise previous work on unifying functional interpretations, by including in the unification the more recent bounded and Herbrandized functional interpretations.