Extensional Collapse Situations I: non-termination and unrecoverable errors

We consider a simple model of higher order, functional computations 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 λ-calculi, and by exploiting the fundamental lemma of logical relations.