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. © Springer-Verlag Berlin Heidelberg 2007.
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CITATION STYLE
Hoshino, N. (2007). Linear realizability. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4646 LNCS, pp. 420–434). Springer Verlag. https://doi.org/10.1007/978-3-540-74915-8_32
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