## F.Honsell, M. Lenisa, and R. Redamalla.
Strict geometry of interaction graph models.
In *Proceedings of LPAR'03*, volume 2850 of *Lecture Notes in
Artificial Intelligence*, pages 403-417. Springer Verlag, 2003.

We study a class of ``wave-style'' Geometry of
Interaction (GoI) lambda-models based on the category
Rel of sets and relations. Wave GoI models 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
``countable power'' as the traced strong monoidal
functor bang. Abramsky hinted that the category Rel is
the basic setting for traditional denotational ``static
semantics''. However, Rel, together with the cartesian
product, apparently escapes Abramsky's original GoI
construction. Here we show that Rel can be axiomatized
as a strict GoI situation, i.e. a strict variant of
Abramsky's GoI situation, which gives rise to a rich
class of strict graph models. These are models of
restricted lambda-calculi in the sense of [HL99], such
as Church's lambda-I-calculus and the
lambda-beta-KN-calculus.

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