Linear Realizability

  • Naohiko Hoshino
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4646)


We define a notion of relational linear combinatory algebra (rLCA) which is a generalization of a linear combinatory algebra defined by Abramsky, Haghverdi and Scott. We also define a category of assemblies as well as a category of modest sets which are realized by rLCA. This is a linear style of realizability in a way that duplicating and discarding of realizers is allowed in a controlled way. Both categories form linear-non-linear models and their coKleisli categories have a natural number object. We construct some examples of rLCA’s which have some relations to well known PCA’s.


Natural Transformation Full Subcategory Monoidal Category Left Adjoint Monoidal Functor 
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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Naohiko Hoshino
    • 1
  1. 1.RIMS, Kyoto University 

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