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Linear Realizability

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

Abstract

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.

Keywords

Natural Transformation Full Subcategory Monoidal Category Left Adjoint Monoidal Functor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

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

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