## F.Honsell and M. Lenisa.
Wave-style geometry of interaction models in rel are graph-like
lambda models.
In *Proceedings of TYPES'03*, Lecture Notes in Computer Science.
Springer Verlag, 2003.

We study the connections between graph models and
``wave-style'' Geometry of Interaction (GoI)
lambda-models. The latters arise when Abramsky's GoI
axiomatization, which generalizes Girard's original
GoI, is applied to a traced monoidal category with the
categorical product as tensor, using a countable power
as the traced strong monoidal functor bang. Abramsky
hinted that the category Rel of sets and relations is
the basic setting for traditional denotational ``static
semantics''. However, the category Rel together with
the cartesian product apparently escapes original
Abramsky's axiomatization. Here we show that, by moving
to the category Rel* of pointed sets and relations
preserving the distinguished point, and by sligthly
relaxing Abramsky's GoI axiomatization, we can recover
a large class of graph-like models as wave models.
Furthermore, we show that the class of untyped
lambda-theories induced by wave-style GoI models is
richer than that induced by game models.

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