Reversible Monadic Computing

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2015-12-21

Department

Department of Mathematics and Systems Analysis

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Language

en

Pages

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.

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Keywords

dagger category, Frobenius monad, quantum measurement, reversible computing

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DOI

10.1016/j.entcs.2015.12.014

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

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https://urn.fi/URN:NBN:fi:aalto-201705114350

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[article-cris] Perustieteiden korkeakoulu / SCI