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Representing Guardedness in Call-By-Value Goncharov, Sergey Fine-grain call-by-value Abstract guardedness Freyd category Kleisli category Elgot iteration Like the notion of computation via (strong) monads serves to classify various flavours of impurity, including exceptions, non-determinism, probability, local and global store, the notion of guardedness classifies well-behavedness of cycles in various settings. In its most general form, the guardedness discipline applies to general symmetric monoidal categories and further specializes to Cartesian and co-Cartesian categories, where it governs guarded recursion and guarded iteration respectively. Here, even more specifically, we deal with the semantics of call-by-value guarded iteration. It was shown by Levy, Power and Thielecke that call-by-value languages can be generally interpreted in Freyd categories, but in order to represent effectful function spaces, such a category must canonically arise from a strong monad. We generalize this fact by showing that representing guarded effectful function spaces calls for certain parametrized monads (in the sense of Uustalu). This provides a description of guardedness as an intrinsic categorical property of programs, complementing the existing description of guardedness as a predicate on a category. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sergey Goncharov 2023 Is Part Of LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSCD.2023.34 urn:nbn:de:0030-drops-180181 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.34 eng https://creativecommons.org/licenses/by/4.0/legalcode