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type	http://eprints.org/ontology/ArticleEPrint http://eprints.org/ontology/EPrint Article Academic Article
seeAlso	HTML Summary of #84635 Unifying graded and parameterised monads
http://eprints.org/ontology/hasDocument	Unifying graded and parameterised monads (PDF) Unifying graded and parameterised monads (Other) Unifying graded and parameterised monads (Other) Unifying graded and parameterised monads (Other) Unifying graded and parameterised monads (Other) Unifying graded and parameterised monads (Other)
http://eprints.org/ontology/hasPublished	Unifying graded and parameterised monads (PDF)
dc:hasVersion	Unifying graded and parameterised monads (PDF)
Title	Unifying graded and parameterised monads
described by	https://demo.openlinksw.com/about/id/entity/https/www.cs.kent.ac.uk/people/staff/akj22/materials/CO644/export_kar_RDFN3.n3
Date	2020-05-01
Creator	Harley Eades Philip Wadler Dominic Orchard
status	peer reviewed published
abstract	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.
Is Part Of	Proceedings Eighth Workshop on Mathematically Structured Functiona Programming, MSFP@ETAPS 2020, Dublin, Ireland, 25th April 2020 https://kar.kent.ac.uk/id/repository
list of authors	https://kar.kent.ac.uk/id/eprint/84635#authors
presented at	Proceedings Eighth Workshop on Mathematically Structured Functional Programming, MSFP@ETAPS 2020
is topic of	https://www.cs.kent.ac.uk/people/staff/akj22/materials/CO644/export_kar_RDFN3.n3
is primary topic of	HTML Summary of #84635 Unifying graded and parameterised monads

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