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What is a categorical model of arrows?

Atkey, Robert (2011) What is a categorical model of arrows? Electronic Notes in Theoretical Computer Science, 229 (5). pp. 19-37. ISSN 1571-0661

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We investigate what the correct categorical formulation of Hughes’ Arrows should be. It has long been folklore that Arrows, a functional programming construct, and Freyd categories, a categorical notion due to Power, Robinson and Thielecke, are somehow equivalent. In this paper, we show that the situation is more subtle. By considering Arrows wholly within the base category we derive two alternative formulations of Freyd category that are equivalent to Arrows—enriched Freyd categories and indexed Freyd categories. By imposing a further condition, we characterise those indexed Freyd categories that are isomorphic to Freyd categories. The key differentiating point is the number of inputs available to a computation and the structure available on them, where structured input is modelled using comonads.

Item type: Article
ID code: 34344
Keywords: arrows, categorical model, functional programming , Hughes arrows, Freyd categories, Electronic computers. Computer science, Computational Theory and Mathematics
Subjects: Science > Mathematics > Electronic computers. Computer science
Department: Faculty of Science > Computer and Information Sciences
Depositing user: Pure Administrator
Date Deposited: 12 Nov 2011 10:06
Last modified: 24 Jul 2015 11:24
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