Reversible Monadic Computing
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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2015-12-21
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en
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21
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Electronic Notes in Theoretical Computer Science, Volume 319, pp. 217-237
Abstract
We extend categorical semantics of monadic programming to reversible computing, by considering monoidal closed dagger categories: the dagger gives reversibility, whereas closure gives higher-order expressivity. We demonstrate that Frobenius monads model the appropriate notion of coherence between the dagger and closure by reinforcing Cayley's theorem; by proving that effectful computations (Kleisli morphisms) are reversible precisely when the monad is Frobenius; by characterizing the largest reversible subcategory of Eilenberg-Moore algebras; and by identifying the latter algebras as measurements in our leading example of quantum computing. Strong Frobenius monads are characterized internally by Frobenius monoids.Description
Keywords
dagger category, Frobenius monad, quantum measurement, reversible computing
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Citation
Heunen, C & Karvonen, M 2015, ' Reversible Monadic Computing ', Electronic Notes in Theoretical Computer Science, vol. 319, pp. 217-237 . https://doi.org/10.1016/j.entcs.2015.12.014