Categorical semantics for arrows

B.P.F. Jacobs; C. Heunen; I. Hasuo

doi:10.1017/S0956796809007308

Categorical semantics for arrows

B.P.F. Jacobs, C. Heunen, I. Hasuo

Mathematics and Computer Science

Research output: Contribution to journal › Article › Academic › peer-review

35 Citations (Scopus)

Abstract

Arrows 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 bifunctors Cop × C ¿ C. Observing similarities to monads – which are monoids in categories of endofunctors C ¿ 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.’

Original language	English
Pages (from-to)	403-438
Journal	Journal of Functional Programming
Volume	19
Issue number	3-4
DOIs	https://doi.org/10.1017/S0956796809007308
Publication status	Published - 2009

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title = "Categorical semantics for arrows",

abstract = "Arrows 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 bifunctors Cop × C ¿ C. Observing similarities to monads – which are monoids in categories of endofunctors C ¿ C – it then considers Eilenberg–Moore and Kleisli constructions for arrows. The latter yields Freyd categories, mathematically formulating the folklore claim {\textquoteleft}Arrows are Freyd categories.{\textquoteright}",

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AB - Arrows 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 bifunctors Cop × C ¿ C. Observing similarities to monads – which are monoids in categories of endofunctors C ¿ 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.’

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DO - 10.1017/S0956796809007308

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EP - 438

JO - Journal of Functional Programming

JF - Journal of Functional Programming

IS - 3-4

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Categorical semantics for arrows

Abstract

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