Extensional Collapse Situations I: non-termination and unrecoverable errors

TL;DR

This paper explores a model of higher-order functional computation over booleans, extended to include non-termination and unrecoverable errors, and analyzes their relationships through a lattice structure based on extensional collapse.

Contribution

It introduces a lattice framework for comparing models of computation with non-termination and errors, using applied lambda-calculi and logical relations.

Findings

Models form a lattice under extensional collapse relation

The framework captures non-termination and unrecoverable errors

Logical relations are used to establish the results

Abstract

We consider a simple model of higher order, functional computation over the booleans. Then, we enrich the model in order to encompass non-termination and unrecoverable errors, taken separately or jointly. We show that the models so defined form a lattice when ordered by the extensional collapse situation relation, introduced in order to compare models with respect to the amount of "intensional information" that they provide on computation. The proofs are carried out by exhibiting suitable applied {\lambda}-calculi, and by exploiting the fundamental lemma of logical relations.