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Generic Point-free Lenses

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Mathematics of Program Construction (MPC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6120))

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Abstract

Lenses are one the most popular approaches to define bidirectional transformations between data models. A bidirectional transformation with view-update, denoted a lens, encompasses the definition of a forward transformation projecting concrete models into abstract views, together with a backward transformation instructing how to translate an abstract view to an update over concrete models. In this paper we show that most of the standard point-free combinators can be lifted to lenses with suitable backward semantics, allowing us to use the point-free style to define powerful bidirectional transformations by composition. We also demonstrate how to define generic lenses over arbitrary inductive data types by lifting standard recursion patterns, like folds or unfolds. To exemplify the power of this approach, we “lensify” some standard functions over naturals and lists, which are tricky to define directly “by-hand” using explicit recursion.

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Authors and Affiliations

  1. DI-CCTC, Universidade do Minho, Braga, Portugal

    Hugo Pacheco & Alcino Cunha

Authors
  1. Hugo Pacheco
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  2. Alcino Cunha
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Editors and Affiliations

  1. Département d’informatique et de génie logiciel, Pavillon Adrien-Pouliot, Université Laval, 1065 Avenue de la Médicine, G1V 0A6, Québec, Canada

    Claude Bolduc , Jules Desharnais  & Béchir Ktari ,  & 

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Pacheco, H., Cunha, A. (2010). Generic Point-free Lenses. In: Bolduc, C., Desharnais, J., Ktari, B. (eds) Mathematics of Program Construction. MPC 2010. Lecture Notes in Computer Science, vol 6120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13321-3_19

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  • DOI: https://doi.org/10.1007/978-3-642-13321-3_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13320-6

  • Online ISBN: 978-3-642-13321-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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