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...

Full description

Saved in:
Bibliographic Details
Published inJournal of logical and algebraic methods in programming Vol. 136; p. 100923
Main Authors Maletto, Giacomo, Roversi, Luca
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2024
Subjects
Lean
Primitive recursion
Reversible computation
Lean
Primitive recursion
Reversible computation
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:2352-2208
DOI:10.1016/j.jlamp.2023.100923