Unifying Functional Interpretations: Past and Future

TL;DR

This survey reviews recent advances in unifying various functional interpretations in logic, highlighting lessons learned and proposing future research directions in the field.

Contribution

It provides a comprehensive overview of the unification efforts of multiple functional interpretations and identifies key open questions for future exploration.

Findings

Identified common themes across different functional interpretations

Highlighted unresolved questions in the unification process

Outlined potential future research directions

Abstract

This article surveys work done in the last six years on the unification of various functional interpretations including G\"odel's dialectica interpretation, its Diller-Nahm variant, Kreisel modified realizability, Stein's family of functional interpretations, functional interpretations "with truth", and bounded functional interpretations. Our goal in the present paper is twofold: (1) to look back and single out the main lessons learnt so far, and (2) to look forward and list several open questions and possible directions for further research.