The categorical abstract machine
Science of Computer Programming
Theoretical Computer Science - International Joint Conference on Theory and Practice of Software Development, P
Categorical abstract machines for higher-order typed &lgr;-calculi
MFPS '92 Selected papers of the meeting on Mathematical foundations of programming semantics. Part II : lambda calculus and domain theory: lambda calculus and domain theory
A Term Calculus for Intuitionistic Linear Logic
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
On Explicit Substitution and Names (Extended Abstract)
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
A Mixed Linear and Non-Linear Logic: Proofs, Terms and Models (Extended Abstract)
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Categorical Models for Intuitionistic and Linear Type Theory
FOSSACS '00 Proceedings of the Third International Conference on Foundations of Software Science and Computation Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software,ETAPS 2000
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Indexed categories provide models of cartesian calculi of explicit substitutions. However, these structures are inherently non-linear and hence cannot be used to model linear calculi of explicit substitution. This paper replaces indexed categories with pre-sheaves, thus providing a categorical semantics covering both the linear and cartesian cases. We further justify our models by proving soundness and completeness results.