Author:
JACOBS BART,HEUNEN CHRIS,HASUO ICHIRO
Abstract
AbstractArrows are an extension of the well-established notion of a monad in functional-programming languages. This paper presents several examples and constructions and develops denotational semantics of arrows as monoids in categories of bifunctorsCop×C→C. Observing similarities to monads – which are monoids in categories of endofunctorsC→C– it then considers Eilenberg–Moore and Kleisli constructions for arrows. The latter yields Freyd categories, mathematically formulating the folklore claim ‘Arrows are Freyd categories.’
Publisher
Cambridge University Press (CUP)
Cited by
31 articles.
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