Linear Realizability

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.

• Type: Conference
• Year: 2007
• Where: CSL
• Authors: Naohiko Hoshino
• Keywords: CSL 2007, Linear Combinatory Algebra, Modest Sets, Relational Linear