On the characterization of models of H* : The operational aspect

We give a characterization, with respect to a large class of models of untyped λcalculus, of those models that are fully abstract for head-normalization, i.e., whose equational theory is H. An extensional K-model D is fully abstract if and only if it is hyperimmune, i.e., non-well founded chains of elements of D cannot be captured by any recursive function. This article, together with its companion paper [5] form the long version of [6]. It is a standalone paper that present a purely syntactical proof of the result as opposed to its companion paper that present an independent and purely semantical proof of the exact same result.