# Reversible monadic computing

arXiv: https://arxiv.org/abs/1505.04330 · HTML: https://mlsanity.com/paper/1505.04330/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2015.

## Built on by (most cited first, 1 of 1)

- [Categorical Semantics of Reversible Pattern-Matching](https://mlsanity.com/paper/2109.05837/) (2021)

## Abstract (arXiv)

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.