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Certifying Algorithms and Relevant Properties of Reversible Primitive Permutations with Lean

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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

Reversible Primitive Permutations (RPP) are recursively defined functions designed to model Reversible Computation. We illustrate a proof, fully developed with the proof-assistant Lean, certifying that: “RPP can encode every Primitive Recursive Function”. Our reworking of the original proof of that statement is conceptually simpler, fixes some bugs, suggests a new more primitive reversible iteration scheme for RPP, and, in order to keep formalization and semi-automatic proofs simple, led us to identify a single pattern that can generate some useful reversible algorithms in RPP: Cantor Pairing, Quotient/Reminder of integer division, truncated Square Root. Our Lean source code is available for experiments on Reversible Computation whose properties can be certified.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università Degli Studi di Torino, Turin, Italy

    Giacomo Maletto

  2. Dipartimento di Informatica, Università Degli Studi di Torino, Turin, Italy

    Luca Roversi

Authors
  1. Giacomo Maletto
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  2. Luca Roversi
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Corresponding author

Correspondence to Luca Roversi .

Editor information

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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Maletto, G., Roversi, L. (2022). Certifying Algorithms and Relevant Properties of Reversible Primitive Permutations with Lean. 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_8

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  • DOI: https://doi.org/10.1007/978-3-031-09005-9_8

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  • Print ISBN: 978-3-031-09004-2

  • Online ISBN: 978-3-031-09005-9

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