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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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. https://doi.org/10.1007/978-3-540-74915-8_32
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DOI: https://doi.org/10.1007/978-3-540-74915-8_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74914-1
Online ISBN: 978-3-540-74915-8
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