Isomorphism and Equational Equivalence of Continuous λ-Models

Abstract

We will present several results on two types of continuous models of λ-calculus, namely graph models and extensional models. By introducing a variant of Engeler's model construction, we are able to generalize the results of [7] and to give invariants that determine a large family of graph models up to applicative isomorphism. This covers all graph models considered in the litterature so far. We indicate briefly how these invariants may be modified in order to determine extensional models as well.

Furthermore, we use our construction to exhibit $2^{N_0 }$graph models that are not equationally equivalent. We indicate once again how the construction passes on to extensional models.