Abstract
A lens is an optical device which refracts light. Properly adjusted, it can be used to project sharp images of objects onto a screen—a principle underlying photography as well as human vision. Striving for clarity, we shift our focus to lenses as abstractions for bidirectional programming. By means of standard mathematical terminology as well as intuitive properties of bidirectional programs, we observe different ways to characterize lenses and show exactly how their laws interact. Like proper adjustment of optical lenses is essential for taking clear pictures, proper organization of lens laws is essential for forming a clear picture of different lens classes. Incidentally, the process of understanding bidirectional lenses clearly is quite similar to the process of taking a good picture.
By showing that it is exactly the backward computation which defines lenses of a certain standard class, we provide an unusual perspective, as contemporary research tends to focus on the forward computation.
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References
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Acknowledgements
We appreciate the help of Janis Voigtländer, Jeremy Gibbons, Alcino Cunha, Nikita Danilenko, Insa Stucke, and José Nuno Oliveira who have looked at drafts of our picture.
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© 2015 Springer International Publishing Switzerland
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Fischer, S., Hu, Z., Pacheco, H. (2015). A Clear Picture of Lens Laws. In: Hinze, R., Voigtländer, J. (eds) Mathematics of Program Construction. MPC 2015. Lecture Notes in Computer Science(), vol 9129. Springer, Cham. https://doi.org/10.1007/978-3-319-19797-5_10
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DOI: https://doi.org/10.1007/978-3-319-19797-5_10
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