Linear Realizability

  • Naohiko Hoshino
Conference paper

DOI: 10.1007/978-3-540-74915-8_32

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4646)
Cite this paper as:
Hoshino N. (2007) Linear Realizability. In: Duparc J., Henzinger T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg

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.

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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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