"Wave-style" Geometry of Interaction Models are Graph-like λ-models

We study the connections between graph models and "wavestyle " Geometry of Interaction (GoI) #-models. The latters arise when Abramsky's GoI construction, which generalizes Girard's original GoI, is applied to a traced monoidal category with the categorical product as tensor, using the countable power as traced strong monoidal functor !. Abramsky hinted that the category of sets and relations is the basic setting for traditional "static semantics". Here we support this view by showing that a large class of graph-like models can be viewed as arising from a suitable generalization of the GoI construction. Furthermore, we show that the class of untyped #-theories induced by wave-style GoI models is richer than that induced by game models