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A List of Successes That Can Change the World pp 132–151Cite as

Comprehending Ringads

For Phil Wadler, on the Occasion of his 60th Birthday

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9600))

Abstract

List comprehensions are a widely used programming construct, in languages such as Haskell and Python and in technologies such as Microsoft’s Language Integrated Query. They generalize from lists to arbitrary monads, yielding a lightweight idiom of imperative programming in a pure functional language. When the monad has the additional structure of a so-called ringad, corresponding to ‘empty’ and ‘union’ operations, then it can be seen as some kind of collection type, and the comprehension notation can also be extended to incorporate aggregations. Ringad comprehensions represent a convenient notation for expressing database queries. The ringad structure alone does not provide a good explanation or an efficient implementation of relational joins; but by allowing heterogeneous comprehensions, involving both bag and indexed table ringads, we show how to accommodate these too.

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Acknowledgements

I am very grateful to Ralf Hinze, Nicolas Wu, Fritz Henglein, Tarmo Uustalu, and Oleg Kiselyov for their helpful discussions, to Eerke Boiten for finding a copy of Wadler’s note (Wadler 1990), to Shin-ya Katsumata for sharing unpublished work (Fujii et al. 2016) on graded monads, and to the anonymous reviewers for constructive criticism. This work was partially supported by EPSRC grants Unifying Theories of Generic Programming (EP/J010995/1) and A Theory of Least Change for Bidirectional Transformations (EP/K020919/1).

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Authors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, UK

    Jeremy Gibbons

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  1. Jeremy Gibbons
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Editors and Affiliations

  1. Informatics Forum, University of Edinburgh Informatics Forum, Edinburgh, United Kingdom

    Sam Lindley

  2. University of Strathclyde , Glasgow, United Kingdom

    Conor McBride

  3. University of Glasgow , Glasgow, United Kingdom

    Phil Trinder

  4. Informatics Forum, University of Edinburgh Informatics Forum, Edinburgh, United Kingdom

    Don Sannella

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Gibbons, J. (2016). Comprehending Ringads. In: Lindley, S., McBride, C., Trinder, P., Sannella, D. (eds) A List of Successes That Can Change the World. Lecture Notes in Computer Science(), vol 9600. Springer, Cham. https://doi.org/10.1007/978-3-319-30936-1_7

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  • DOI: https://doi.org/10.1007/978-3-319-30936-1_7

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