Certifying expressive power and algorithms of reversible primitive permutations with Lean
Reversible primitive permutations (RPP) is a class of recursive functions that models reversible computation. We present a proof, which has been verified using the proof-assistant Lean, that demonstrates RPP can encode every primitive recursive function (PRF-completeness) and that each RPP can be en...
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| Published in | Journal of logical and algebraic methods in programming Vol. 136; p. 100923 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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01.01.2024
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| Abstract | Reversible primitive permutations (RPP) is a class of recursive functions that models reversible computation. We present a proof, which has been verified using the proof-assistant Lean, that demonstrates RPP can encode every primitive recursive function (PRF-completeness) and that each RPP can be encoded as a primitive recursive function (PRF-soundness). Our proof of PRF-completeness is simpler and fixes some errors in the original proof, while also introducing a new reversible iteration scheme for RPP. By keeping the formalization and semi-automatic proofs simple, we are able to identify a single programming pattern that can generate a set of reversible algorithms within RPP: Cantor pairing, integer division quotient/remainder, and truncated square root. Finally, Lean source code is available for experiments on reversible computation whose properties can be certified. |
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| AbstractList | Reversible primitive permutations (RPP) is a class of recursive functions that models reversible computation. We present a proof, which has been verified using the proof-assistant Lean, that demonstrates RPP can encode every primitive recursive function (PRF-completeness) and that each RPP can be encoded as a primitive recursive function (PRF-soundness). Our proof of PRF-completeness is simpler and fixes some errors in the original proof, while also introducing a new reversible iteration scheme for RPP. By keeping the formalization and semi-automatic proofs simple, we are able to identify a single programming pattern that can generate a set of reversible algorithms within RPP: Cantor pairing, integer division quotient/remainder, and truncated square root. Finally, Lean source code is available for experiments on reversible computation whose properties can be certified. |
| ArticleNumber | 100923 |
| Author | Maletto, Giacomo Roversi, Luca |
| Author_xml | – sequence: 1 givenname: Giacomo surname: Maletto fullname: Maletto, Giacomo email: giacomo.maletto@edu.unito.it organization: Università degli Studi di Torino, Dipartimento di Matematica, Italy – sequence: 2 givenname: Luca orcidid: 0000-0002-1871-6109 surname: Roversi fullname: Roversi, Luca email: luca.roversi@unito.it organization: Università degli Studi di Torino, Dipartimento di Informatica, Italy |
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| Cites_doi | 10.1063/1.881299 10.1007/BF01341281 10.1016/0304-3975(89)90155-2 10.1016/S0304-3975(02)00486-3 10.1147/rd.53.0183 10.1007/s00354-018-0039-1 10.1016/j.tcs.2019.11.029 10.1007/s10817-007-9070-5 10.1016/j.tcs.2019.10.005 |
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| Keywords | Lean Primitive recursion Reversible computation |
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| Snippet | Reversible primitive permutations (RPP) is a class of recursive functions that models reversible computation. We present a proof, which has been verified using... |
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| Title | Certifying expressive power and algorithms of reversible primitive permutations with Lean |
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