Publications

2025

1. arXiv

   All you need is controlled-V: universality of a standard two-qubit gate by catalytic embedding

   R. Kaarsgaard

   2025

   PDF

2024

1. POPL

   With a Few Square Roots, Quantum Computing is as Easy as Pi

   J. Carette, C. Heunen, R. Kaarsgaard, and A. Sabry

   Proceedings of the ACM on Programming Languages, 2024

   Bib HTML Code Slides

   @article{sqrts,
     title = {With a Few Square Roots, Quantum Computing is as Easy as Pi},
     author = {Carette, J. and Heunen, C. and Kaarsgaard, R. and Sabry, A.},
     journal = {Proceedings of the ACM on Programming Languages},
     volume = {8},
     number = {POPL},
     pages = {546–574},
     year = {2024},
   }

2. ICFP

   How to Bake a Quantum Pi

   J. Carette, C. Heunen, R. Kaarsgaard, and A. Sabry

   Proceedings of the ACM on Programming Languages, 2024

   Bib HTML Code

   @article{howtobake,
     title = {How to Bake a Quantum Pi},
     author = {Carette, J. and Heunen, C. and Kaarsgaard, R. and Sabry, A.},
     journal = {Proceedings of the ACM on Programming Languages},
     volume = {8},
     number = {ICFP},
     pages = {1-29},
     year = {2024},
   }

3. RC

   Jeopardy: An Invertible Functional Programming Language

   J. T. Kristensen, R. Kaarsgaard, and M. K. Thomsen

   In 16th International Conference on Reversible Computation (RC 2024), 2024

   Bib HTML PDF

   @inproceedings{jeopardy,
     title = {Jeopardy: An Invertible Functional Programming Language},
     author = {Kristensen, J. T. and Kaarsgaard, R. and Thomsen, M. K.},
     editor = {Mogensen, T. Æ. and Mikulski, L.},
     booktitle = {16th International Conference on Reversible Computation (RC
                       2024)},
     pages = {124-141},
     publisher = {Springer},
     year = {2024},
   }

4. RC

   Compositional Reversible Computation

   J. Carette, C. Heunen, R. Kaarsgaard, and A. Sabry

   In 16th International Conference on Reversible Computation (RC 2024), 2024

   Bib HTML PDF

   @inproceedings{comprc,
     title = {Compositional Reversible Computation},
     author = {Carette, J. and Heunen, C. and Kaarsgaard, R. and Sabry, A.},
     editor = {Mogensen, T. Æ. and Mikulski, L.},
     booktitle = {16th International Conference on Reversible Computation (RC
                       2024)},
     pages = {10-27},
     publisher = {Springer},
     year = {2024},
   }

2023

1. QPL

   Universal Properties of Partial Quantum Maps

   P. Andrés-Martinez, C. Heunen, and R. Kaarsgaard

   In 19th International Conference on Quantum Physics and Logic (QPL 2022), 2023

   Bib HTML PDF Slides

   @inproceedings{uniprop,
     title = {Universal Properties of Partial Quantum Maps},
     author = {Andrés-Martinez, P. and Heunen, C. and Kaarsgaard, R.},
     editor = {Gogioso, S. and Hoban, M.},
     booktitle = {19th International Conference on Quantum Physics and Logic
                       (QPL 2022)},
     pages = {192-207},
     publisher = {OPA},
     year = {2023},
   }

2. NIKT

   Branching execution symmetry in Jeopardy by available implicit arguments analysis

   J. T. Kristensen, R. Kaarsgaard, and M. K. Thomsen

   Norwegian ICT Conference for Research and Education, 2023

   Bib HTML

   @article{branchexec,
     title = {Branching execution symmetry in Jeopardy by available implicit arguments analysis},
     author = {Kristensen, J. T. and Kaarsgaard, R. and Thomsen, M. K.},
     journal = {Norwegian ICT Conference for Research and Education},
     volume = {1},
     year = {2023},
   }

3. RC

   Tail recursion transformation for invertible functions

   J. T. Kristensen, R. Kaarsgaard, and M. K. Thomsen

   In 15th International Conference on Reversible Computation (RC 2023), 2023

   Bib HTML PDF

   @inproceedings{tailrec,
     title = {Tail recursion transformation for invertible functions},
     author = {Kristensen, J. T. and Kaarsgaard, R. and Thomsen, M. K.},
     editor = {Kutrib, M. and Meyer, U.},
     booktitle = {15th International Conference on Reversible Computation (RC
                       2023)},
     pages = {73–88},
     publisher = {Springer},
     year = {2023},
   }

2022

1. POPL

   Quantum Information Effects

   C. Heunen, and R. Kaarsgaard

   Proceedings of the ACM on Programming Languages, 2022

   Bib HTML PDF Video Code Slides

   @article{qinfeff,
     title = {Quantum Information Effects},
     author = {Heunen, C. and Kaarsgaard, R.},
     journal = {Proceedings of the ACM on Programming Languages},
     volume = {6},
     number = {POPL},
     pages = {1-27},
     year = {2022},
   }

2. MSFP

   The Programming of Algebra

   F. Henglein, R. Kaarsgaard, and M. K. Mathiesen

   In Proceedings Ninth Workshop on Mathematically Structured Functional Programming (MSFP 2022), 2022

   Bib HTML

   @inproceedings{progalg,
     title = {The Programming of Algebra},
     author = {Henglein, F. and Kaarsgaard, R. and Mathiesen, M. K.},
     editor = {Gibbons, J. and New, M.},
     booktitle = {Proceedings Ninth Workshop on Mathematically Structured
                       Functional Programming (MSFP 2022)},
     publisher = {OPA},
     pages = {71–92},
     year = {2022},
   }

3. MSFP

   Combinatory adjoints and differentiation

   M. Elsman, F. Henglein, R. Kaarsgaard, M. K. Mathiesen, and R. Schenck

   In Proceedings Ninth Workshop on Mathematically Structured Functional Programming (MSFP 2022), 2022

   Bib HTML

   @inproceedings{combadjdiff,
     title = {Combinatory adjoints and differentiation},
     author = {Elsman, M. and Henglein, F. and Kaarsgaard, R. and Mathiesen, M. K. and Schenck, R.},
     editor = {Gibbons, J. and New, M.},
     booktitle = {Proceedings Ninth Workshop on Mathematically Structured
                       Functional Programming (MSFP 2022)},
     publisher = {OPA},
     pages = {1-26},
     year = {2022},
   }

4. TCS

   From Reversible Programming Languages to Reversible Metalanguages

   R. Glück, R. Kaarsgaard, and T. Yokoyama

   Theoretical Computer Science, 2022

   Bib HTML PDF

   @article{revmeta,
     title = {From Reversible Programming Languages to Reversible Metalanguages},
     author = {Glück, R. and Kaarsgaard, R. and Yokoyama, T.},
     journal = {Theoretical Computer Science},
     volume = {920},
     pages = {46–63},
     year = {2022},
   }

5. RC

   Algeo: An Algebraic Approach to Reversibility

   F. Henglein, R. Kaarsgaard, and M. K. Mathiesen

   In Reversible Computation (RC 2022), 2022

   Bib HTML PDF

   @inproceedings{algeo,
     title = {Algeo: An Algebraic Approach to Reversibility},
     author = {Henglein, F. and Kaarsgaard, R. and Mathiesen, M. K.},
     editor = {Mezzina, C. A. and Podlaski, K.},
     booktitle = {Reversible Computation (RC 2022)},
     publisher = {Springer},
     pages = {128–145},
     year = {2022},
   }

2021

1. QPL

   Bennett and Stinespring, Together at Last

   C. Heunen, and R. Kaarsgaard

   In 18th International Conference on Quantum Physics and Logic (QPL 2021), 2021

   Bib HTML PDF Video Slides

   @inproceedings{bennettstinespring,
     title = {Bennett and Stinespring, Together at Last},
     author = {Heunen, C. and Kaarsgaard, R.},
     editor = {Backens, M. and Heunen, C.},
     booktitle = {18th International Conference on Quantum Physics and Logic
                       (QPL 2021)},
     pages = {102–118},
     publisher = {OPA},
     year = {2021},
   }

2. MFCS

   Graph Traversals as Universal Constructions

   S. Bhaskar, and R. Kaarsgaard

   In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021), 2021

   Bib HTML PDF

   @inproceedings{graphtrav,
     title = {Graph Traversals as Universal Constructions},
     author = {Bhaskar, S. and Kaarsgaard, R.},
     editor = {Bonchi, F. and Puglisi, S. J.},
     booktitle = {46th International Symposium on Mathematical Foundations of
                       Computer Science (MFCS 2021)},
     pages = {17:1-17:20},
     publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
     year = {2021},
   }

3. MFPS

   Join inverse rig categories for reversible functional programming, and beyond

   R. Kaarsgaard, and M. Rennela

   In Proceedings 37th Conference on Mathematical Foundations of Programming Semantics (MFPS XXXVII), 2021

   Bib HTML PDF Slides

   @inproceedings{jinvrigcats,
     title = {Join inverse rig categories for reversible functional
                       programming, and beyond},
     author = {Kaarsgaard, R. and Rennela, M.},
     editor = {Sokolova, A.},
     booktitle = {Proceedings 37th Conference on Mathematical Foundations of
                       Programming Semantics (MFPS XXXVII)},
     pages = {152-167},
     publisher = {OPA},
     year = {2021},
   }

2020

1. RPLA

   Reversible Programs Have Reversible Semantics

   R. Glück, R. Kaarsgaard, and T. Yokoyama

   In FM 2019 Workshops, 2020

   Bib HTML PDF Slides

   @inproceedings{rprs,
     title = {Reversible Programs Have Reversible Semantics},
     author = {Glück, R. and Kaarsgaard, R. and Yokoyama, T.},
     editor = {Sekerinski, E. and others},
     booktitle = {FM 2019 Workshops},
     pages = {413–427},
     publisher = {Springer},
     year = {2020},
   }

2. Book Chapter

   Foundations of Reversible Computation

   B. Aman, G. Ciobanu, R. Glück, R. Kaarsgaard, J. Kari, M. Kutrib, and 9 more authors

   In Reversible Computation: Extending Horizons of Computing (Selected Results of the COST Action IC1405), 2020

   HTML

2019

1. RC

   Inversion, Iteration, and the Art of Dual Wielding

   R. Kaarsgaard

   In Reversible Computation (RC 2019), 2019

   Bib HTML PDF

   @inproceedings{dualwielding,
     title = {Inversion, Iteration, and the Art of Dual Wielding},
     author = {Kaarsgaard, R.},
     editor = {Thomsen, M. K. and Soeken, M.},
     booktitle = {Reversible Computation (RC 2019)},
     pages = {34-50},
     publisher = {Springer},
     year = {2019},
   }

2. MFPS

   Condition/Decision Duality and the Internal Logic of Extensive Restriction Categories

   R. Kaarsgaard

   In Proceedings of the Thirty-Fifth Conference on the Mathematical Foundations of Programming Semantics (MFPS XXXV), 2019

   Bib HTML PDF

   @inproceedings{conddecduality,
     title = {Condition/Decision Duality and the Internal Logic of Extensive
                       Restriction Categories},
     author = {Kaarsgaard, R.},
     editor = {König, B.},
     booktitle = {Proceedings of the Thirty-Fifth Conference on the
                       Mathematical Foundations of Programming Semantics
                       (MFPS XXXV)},
     pages = {179–202},
     publisher = {Elsevier},
     year = {2019},
   }

3. MPC

   En garde! Unguarded iteration for reversible computation in the Delay monad

   R. Kaarsgaard, and N. Veltri

   In 13th International Conference on Mathematics of Program Construction (MPC 2019), 2019

   Bib HTML PDF

   @inproceedings{engarde,
     title = {En garde! Unguarded iteration for reversible computation in the
                       Delay monad},
     author = {Kaarsgaard, R. and Veltri, N.},
     editor = {Hutton, G.},
     booktitle = {13th International Conference on Mathematics of Program
                       Construction (MPC 2019)},
     pages = {366-384},
     publisher = {Springer},
     year = {2019},
   }

2018

1. MFPS

   Reversible effects as inverse arrows

   C. Heunen, R. Kaarsgaard, and M. Karvonen

   In Proceedings of the Thirty-Fourth Conference on the Mathematical Foundations of Programming Semantics (MFPS XXXIV), 2018

   Bib HTML PDF

   @inproceedings{reff,
     title = {Reversible effects as inverse arrows},
     author = {Heunen, C. and Kaarsgaard, R. and Karvonen, M.},
     editor = {Staton, S.},
     booktitle = {Proceedings of the Thirty-Fourth Conference on the
                       Mathematical Foundations of Programming Semantics
                       (MFPS XXXIV)},
     pages = {179–199},
     publisher = {Elsevier},
     year = {2018},
   }

2. RC

   CoreFun: A Typed Functional Reversible Core Language

   P. A. H. Jacobsen, R. Kaarsgaard, and M. K. Thomsen

   In Reversible Computation (RC 2018), 2018

   Bib HTML PDF

   @inproceedings{corefun,
     title = {CoreFun: A Typed Functional Reversible Core Language},
     author = {Jacobsen, P. A. H. and Kaarsgaard, R. and Thomsen, M. K.},
     editor = {Kari, J. and Ulidowski, I.},
     booktitle = {Reversible Computation (RC 2018)},
     pages = {304–321},
     publisher = {Springer},
     year = {2018},
   }

3. LMCS

   A categorical foundation for structured reversible flowchart languages: Soundness and adequacy

   R. Kaarsgaard, and R. Glück

   Logical Methods in Computer Science, 2018

   Bib HTML PDF

   @article{catsrfllmcs,
     title = {A categorical foundation for structured reversible flowchart
                       languages: Soundness and adequacy},
     author = {Kaarsgaard, R. and Glück, R.},
     journal = {Logical Methods in Computer Science},
     volume = {14},
     number = {3},
     pages = {1-38},
     year = {2018},
   }

4. The Logic of Reversible Computing - Theory and Practice

   R. Kaarsgaard

   Department of Computer Science, University of Copenhagen, 2018

   PDF Slides

2017

1. JLAMP

   Join Inverse Categories and Reversible Recursion

   R. Kaarsgaard, H. B. Axelsen, and R. Glück

   Journal of Logical and Algebraic Methods in Programming, 2017

   Bib HTML PDF

   @article{jinvrrjlamp,
     title = {Join Inverse Categories and Reversible Recursion},
     author = {Kaarsgaard, R. and Axelsen, H. B. and Glück, R.},
     journal = {Journal of Logical and Algebraic Methods in Programming},
     volume = {87},
     pages = {33–50},
     year = {2017},
   }

2. MFPS

   A Categorical Foundation for Structured Reversible Flowchart Languages

   R. Glück, and R. Kaarsgaard

   In Proceedings of the Thirty-Third Conference on the Mathematical Foundations of Programming Semantics (MFPS XXXIII), 2017

   Bib HTML PDF

   @inproceedings{catsrfl,
     title = {A Categorical Foundation for Structured Reversible Flowchart Languages},
     author = {Glück, R. and Kaarsgaard, R.},
     editor = {Silva, A.},
     booktitle = {Proceedings of the Thirty-Third Conference on the
                       Mathematical Foundations of Programming Semantics
                       (MFPS XXXIII)},
     pages = {155–171},
     publisher = {Elsevier},
     year = {2017},
   }

2016

1. FOSSACS

   Join inverse categories as models of reversible recursion

   H. B. Axelsen, and R. Kaarsgaard

   In Foundations of Software Science and Computation Structures (FOSSACS 2016), 2016

   Bib HTML PDF

   @inproceedings{jinvrr,
     title = {Join inverse categories as models of reversible recursion},
     author = {Axelsen, H. B. and Kaarsgaard, R.},
     editor = {Jacobs, B. and Löding, C.},
     booktitle = {Foundations of Software Science and Computation Structures
                       (FOSSACS 2016)},
     pages = {73–90},
     publisher = {Springer},
     year = {2016},
   }

2. WOLLIC

   A Classical Propositional Logic for Reasoning about Reversible Logic

   H. B. Axelsen, R. Glück, and R. Kaarsgaard

   In Logic, Language, Information, and Computation (WoLLIC 2016), 2016

   Bib HTML PDF

   @inproceedings{cpl,
     title = {A Classical Propositional Logic for Reasoning about Reversible Logic},
     author = {Axelsen, H. B. and Glück, R. and Kaarsgaard, R.},
     editor = {Väänänen, J. and Hirvonen, Å. and de Queiroz, R.},
     booktitle = {Logic, Language, Information, and Computation (WoLLIC 2016)},
     pages = {52–67},
     publisher = {Springer},
     year = {2016},
   }

2015

1. RC

   Ricercar: A Language for Describing and Rewriting Reversible Circuits with Ancillae and its Permutation Semantics

   M. K. Thomsen, R. Kaarsgaard, and M. Soeken

   In Reversible Computation (RC 2015), 2015

   Bib HTML PDF

   @inproceedings{ricercar,
     title = {Ricercar: A Language for Describing and Rewriting Reversible
                       Circuits with Ancillae and its Permutation
                       Semantics},
     author = {Thomsen, M. K. and Kaarsgaard, R. and Soeken, M.},
     editor = {Krivine, J. and Stefani, J.-B.},
     booktitle = {Reversible Computation (RC 2015)},
     pages = {200–215},
     publisher = {Springer},
     year = {2015},
   }