Arrows, like monads, are monoids

Arrows, like monads, are monoids (2006)

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by Chris Heunen , Bart Jacobs

Venue:	Proc. of 22nd Ann. Conf. on Mathematical Foundations of Programming Semantics, MFPS XXII, v. 158 of Electron. Notes in Theoret. Comput. Sci
Citations:	10 - 1 self

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Datum	Value	Source
TITLE	Arrows, like monads, are monoids	INFERENCE
AUTHOR NAME	Chris Heunen	SVM HeaderParse 0.2
AUTHOR AFFIL	Institute for Computing and Information Sciences; Radboud University, Nijmegen, the Netherlands,	SVM HeaderParse 0.2
AUTHOR NAME	Bart Jacobs	SVM HeaderParse 0.2
AUTHOR AFFIL	Institute for Computing and Information Sciences; Radboud University, Nijmegen, the Netherlands,	SVM HeaderParse 0.2
ABSTRACT	Monads are by now well-established as programming construct in functional languages. Recently, the notion of “Arrow ” was introduced by Hughes as an extension, not with one, but with two type parameters. At first, these Arrows may look somewhat arbitrary. Here we show that they are categorically fairly civilised, by showing that they correspond to monoids in suitable subcategories of bifunctors C op ×C → C. This shows that, at a suitable level of abstraction, arrows are like monads — which are monoids in categories of functors C → C. Freyd categories have been introduced by Power and Robinson to model computational effects, well before Hughes ’ Arrows appeared. It is often claimed (informally) that Arrows are simply Freyd categories. We shall make this claim precise by showing how monoids in categories of bifunctors exactly correspond to Freyd categories.	SVM HeaderParse 0.2
YEAR	2006	INFERENCE
VENUE	Proc. of 22nd Ann. Conf. on Mathematical Foundations of Programming Semantics, MFPS XXII, v. 158 of Electron. Notes in Theoret. Comput. Sci	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	219--236	INFERENCE
CITATIONS	28 found	ParsCit 1.0