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 parameterized 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.

@article{paperbot4027,
  title = {Representing Guardedness in Call-by-Value and Guarded Parametrized Monads},
  author = {Sergey Goncharov},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 22, Issue 1},
  year = {2026},
  doi = {10.46298/lmcs-22(1:9)2026}
}