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}}</ref> This is typically achieved by ensuring that every primitive operation and composite statement within the language is locally invertible.<ref name="Glück-2022.06.010"/> Local invertibility means that each basic computational step has a well-defined inverse, and the inverse of a sequence of steps is the sequence of inverse steps performed in reverse order.
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}}</ref> Clean reversible languages aim to perform computations and their reversals using only the specified input and output variables.
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}}</ref> An important restriction is that the variable being updated (e.g., x in <code>x += e</code>) must not appear in the expression on the right-hand side (e) to ensure the operation is bijective.<ref name="Yokoyama-2010.02.007"/> The swap operation (<code>x <=> y</code>), which exchanges the values of two variables, is another fundamental reversible update.<ref name="Choudhury">{{cite web
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* '''Computational Power:''' A common benchmark for the power of a reversible language is [[Turing completeness|r-Turing completeness]], which means the language can simulate any Reversible Turing Machine cleanly (without garbage accumulation).<ref name="Choudhury"/>
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}}</ref> simulates a free-falling object. It includes a main section to call and "uncall" (reverse) a subroutine named Fall, which contains the core simulation logic.
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* '''ROOPL:''' The first reversible object-oriented programming language.<ref>{{cite conference
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}}</ref> It extends the imperative reversible paradigm with features like user-defined data types (classes), inheritance, and subtype polymorphism.<ref>{{cite arXiv
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}}</ref>, Pi/Pi^o,<ref name="Choudhury"/> Inv <ref>{{cite journal
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}}</ref>, Yarel <ref>{{cite arXiv
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}}</ref>, Hermes (focused on cryptography) <ref>{{cite web |url=https://reversible-computation-2020.github.io/slides/day-1-session-2-torben-mogensen.pdf |title=Hermes: A Language for Lightweight Encryption |website=Reversible Computation (RC) Lecture |access-date=April 9, 2025}}</ref>, and Revs (compiling F# subset to circuits).<ref>{{cite book
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