期刊
ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
卷 319, 期 -, 页码 217-237出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.entcs.2015.12.014
关键词
Frobenius monad; dagger category; reversible computing; quantum measurement
资金
- Engineering and Physical Sciences Research Council [EP/L002388/1]
- EPSRC [EP/L002388/2, EP/L002388/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/L002388/2, EP/L002388/1] Funding Source: researchfish
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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