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A Tangled Web of 12 Lens Laws

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Reversible Computation (RC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12805))

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Abstract

Bidirectional transformation has played important roles in broad areas, database management, programming language, and model-driven development after Foster et al. revisited view updating problems introduced by Bancilhon and Spyratos. They introduced the concept of (asymmetric) lens as a pair of a forward \( get \) and a backward \( put \) functions to synchronize a source data and its view consistently. For the \( get \) and \( put \) functions to be consistent, they should satisfy several lens laws such as the (StrongGetPut), (GetPut), (PutGet) and (PutPut) laws. By combining some of these lens laws, we can represent how consistent a lens satisfying the laws is. Fischer et al. has introduced nine meaningful weaker lens laws to give a “clear picture” of the laws where they show relations among lens laws, for example, that one law implies another and combination of two laws is equivalent to combination of the other three laws. This paper gives more precise relationship among 12 lens laws that have been presented in literature. The relationship makes an intertwined implication diagram like a tangled web. The results can be used for easily verifying the desirable lens laws.

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Notes

  1. 1.

    In [3], a lens is said to be undoable when not only (Undoability) but also (PutGet) hold in our terminology.

  2. 2.

    We prefer a shorter name though it might be called the StrongGetPut family.

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Acknowledgment

The author thanks Mirai Ikebuchi and anonymous referees for their helpful comments. This work was supported by JSPS KAKENHI Grant Numbers JP17H06099, JP18H04093, and JP21K11744.

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Authors and Affiliations

  1. Research Institute of Electrical Communication, Tohoku University, Sendai, Japan

    Keisuke Nakano

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  1. Keisuke Nakano
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Correspondence to Keisuke Nakano .

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Editors and Affiliations

  1. Ritsumeikan University, Kusatsu, Japan

    Shigeru Yamashita

  2. Nanzan University, Nagoya, Japan

    Tetsuo Yokoyama

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Nakano, K. (2021). A Tangled Web of 12 Lens Laws. In: Yamashita, S., Yokoyama, T. (eds) Reversible Computation. RC 2021. Lecture Notes in Computer Science(), vol 12805. Springer, Cham. https://doi.org/10.1007/978-3-030-79837-6_11

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  • DOI: https://doi.org/10.1007/978-3-030-79837-6_11

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