# Symmetries in reversible programming: from symmetric rig groupoids to reversible programming languages

@article{Choudhury2021SymmetriesIR, title={Symmetries in reversible programming: from symmetric rig groupoids to reversible programming languages}, author={Vikraman Choudhury and Jacek Karwowski and Amr Sabry}, journal={Proceedings of the ACM on Programming Languages}, year={2021}, volume={6}, pages={1 - 32} }

The Pi family of reversible programming languages for boolean circuits is presented as a syntax of combinators witnessing type isomorphisms of algebraic data types. In this paper, we give a denotational semantics for this language, using weak groupoids à la Homotopy Type Theory, and show how to derive an equational theory for it, presented by 2-combinators witnessing equivalences of type isomorphisms. We establish a correspondence between the syntactic groupoid of the language and a formally…

## 2 Citations

### Free Commutative Monoids in Homotopy Type Theory

- MathematicsArXiv
- 2021

We develop a constructive theory of ﬁnite multisets in Homotopy Type Theory, deﬁning them as free commutative monoids. After recalling basic structural properties of the free commutative-monoid…

### Qunity: A Unified Language for Quantum and Classical Computing

- Computer ScienceProceedings of the ACM on Programming Languages
- 2023

Qunity is introduced, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing, and its syntax, type system, and denotational semantics are presented, showing how it can cleanly express several quantum algorithms.

### The Quantum Effect: A Recipe for QuantumPi

- Physics
- 2023

Free categorical constructions characterise quantum computing as the combination of two copies of a reversible classical model, glued by the complementarity equations of classical structures. This…

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