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Constructing Applicative Functors

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Mathematics of Program Construction (MPC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7342))

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Abstract

Applicative functors define an interface to computation that is more general, and correspondingly weaker, than that of monads. First used in parser libraries, they are now seeing a wide range of applications. This paper sets out to explore the space of non-monadic applicative functors useful in programming. We work with a generalization, lax monoidal functors, and consider several methods of constructing useful functors of this type, just as transformers are used to construct computational monads. For example, coends, familiar to functional programmers as existential types, yield a range of useful applicative functors, including left Kan extensions. Other constructions are final fixed points, a limited sum construction, and a generalization of the semi-direct product of monoids. Implementations in Haskell are included where possible.

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Author information

Authors and Affiliations

  1. City University London, UK

    Ross Paterson

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  1. Ross Paterson
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Oxford University, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Jeremy Gibbons

  2. Facultad de Informática, Universidad Politécnica de Madrid, Campus de Montegancedo s/n, 28660, Boadilla del Monte, Madrid, Spain

    Pablo Nogueira

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Paterson, R. (2012). Constructing Applicative Functors. In: Gibbons, J., Nogueira, P. (eds) Mathematics of Program Construction. MPC 2012. Lecture Notes in Computer Science, vol 7342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31113-0_15

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  • DOI: https://doi.org/10.1007/978-3-642-31113-0_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31112-3

  • Online ISBN: 978-3-642-31113-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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