Parameterised notions of computation

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Moggi’s Computational Monads and Power et al’s equivalent notion of Freyd category have captured a large range of computational effects present in programming languages such as exceptions, side-effects, input/output and continuations. We present generalisations of both constructs, which we call parameterised monads and parameterised Freyd categories, that also capture computational effects with parameters. Examples of such are composable continuations, side-effects where the type of the state varies and input/output where the range of inputs and outputs varies. By also considering monoidal parameterisation, we extend the range of effects to cover separated side-effects and multiple independent streams of I/O. We also present two typed λ-calculi that soundly and completely model our categorical definitions — with and without monoidal parameterisation — and act as prototypical languages with parameterised effects.
Original languageEnglish
Title of host publicationWorkshop on Mathematically Structured Functional Programming (MSFP 2006) (MSFP)
Place of PublicationLondon
PublisherBritish Computer Society
Publication statusPublished - 2006

Publication series

NameElectronic Workshops in Computing
PublisherBritish Computer Society


  • computational effects
  • computational monads
  • Freyd categories


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