Abstract
We study the connections between graph models and “wave-style” Geometry of Interaction (GoI) λ-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 !. 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 λ-theories induced by wave-style GoI models is richer than that induced by game models.
Research supported by the MIUR Projects COFIN 2001013518 Cometa and 20022018192_002 Protocollo, and by the UE Project IST-2000-29001 Types.
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Honsell, F., Lenisa, M. (2004). “Wave-Style” Geometry of Interaction Models in Rel Are Graph-Like Lambda-Models. In: Berardi, S., Coppo, M., Damiani, F. (eds) Types for Proofs and Programs. TYPES 2003. Lecture Notes in Computer Science, vol 3085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24849-1_16
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DOI: https://doi.org/10.1007/978-3-540-24849-1_16
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