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The \(\aleph \)-Calculus

A Declarative Model of Reversible Programming

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Reversible Computation (RC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13354))

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Abstract

A novel model of reversible computing, the \(\aleph \)-calculus, is introduced. It is declarative, reversible-Turing complete, and has a local term-rewriting semantics. Unlike previously demonstrated reversible term-rewriting systems, it does not require the accumulation of history data. Terms in the \(\aleph \)-calculus, in combination with the program definitions, encapsulate all program state. An interpreter was also written.

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Notes

  1. 1.

    No such constraint need be applied to invalid computational states [4].

  2. 2.

    The name of the calculus is inspired by the Greek meaning ‘not forgotten’,

  3. 3.

    In the examples in Sect. 2 the reader may notice this is violated. This is for programmer convenience, and must be resolved manually or by the compiler.

  4. 4.

    The requirement of halting, combined with computational inertia, ensures each sub-multiterm takes on a unique state at production and before consumption.

  5. 5.

    https://github.com/hannah-earley/alethe-repl.

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Acknowledgements

The author would like to acknowledge the invaluable help and support of her PhD supervisor, Gos Micklem. This work was supported by the Engineering and Physical Sciences Research Council, project reference 1781682.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Cambridge, Cambridge, UK

    Hannah Earley

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  1. Hannah Earley
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Correspondence to Hannah Earley .

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Editors and Affiliations

  1. University of Urbino, Urbino, Pesaro-Urbino, Italy

    Claudio Antares Mezzina

  2. University of Łódź, Lodz, Poland

    Krzysztof Podlaski

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Earley, H. (2022). The \(\aleph \)-Calculus. In: Mezzina, C.A., Podlaski, K. (eds) Reversible Computation. RC 2022. Lecture Notes in Computer Science, vol 13354. Springer, Cham. https://doi.org/10.1007/978-3-031-09005-9_11

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  • DOI: https://doi.org/10.1007/978-3-031-09005-9_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-09004-2

  • Online ISBN: 978-3-031-09005-9

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