Unifying graded and parameterised monads

Dominic Orchard, Philip Wadler, Harley Eades

Research output: Contribution to journalConference articlepeer-review

5 Scopus citations


Monads are a useful tool for structuring effectful features of computation such as state, non-determinism, and continuations. In the last decade, several generalisations of monads have been suggested which provide a more fine-grained model of effects by replacing the single type constructor of a monad with an indexed family of constructors. Most notably, graded monads (indexed by a monoid) model effect systems and parameterised monads (indexed by pairs of pre- and post-conditions) model program logics. This paper studies the relationship between these two generalisations of monads via a third generalisation. This third generalisation, which we call category-graded monads, arises by generalising a view of monads as a particular special case of lax functors. A category-graded monad provides a family of functors T f indexed by morphisms f of some other category. This allows certain compositions of effects to be ruled out (in the style of a program logic) as well as an abstract description of effects (in the style of an effect system). Using this as a basis, we show how graded and parameterised monads can be unified, studying their similarities and differences along the way.

Original languageEnglish (US)
Pages (from-to)18-38
Number of pages21
JournalElectronic Proceedings in Theoretical Computer Science, EPTCS
StatePublished - May 1 2020
Event8th Workshop on Mathematically Structured Functional Programming, MSFP 2020 - Dublin, Ireland
Duration: Apr 25 2020 → …

ASJC Scopus subject areas

  • Software


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