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Semantics for a Turing-Complete Reversible Programming Language with Inductive Types

Authors Kostia Chardonnet, Louis Lemonnier , Benoît Valiron

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Author Details

Kostia Chardonnet
  • Department of Computer Science and Engineering, University of Bologna, Italy
Louis Lemonnier
  • Université Paris-Saclay, CNRS, ENS Paris-Saclay, Inria, Laboratoire Méthodes Formelles, Gif-sur-Yvette, France
Benoît Valiron
  • Université Paris-Saclay, CNRS, CentraleSupélec, ENS Paris-Saclay, Inria, Laboratoire Méthodes Formelles, Gif-sur-Yvette, France

Funding

This work has been partially funded by the French National Research Agency (ANR) by the projects ANR-21-CE48-0019, ANR-19-CE48-0014, ANR-22-CE47-0012, and within the framework of "Plan France 2030", under the project ANR-22-PETQ-0007, ANR-22-PNCQ-0001.
  • Chardonnet, Kostia: is partially supported by the MIUR FARE project CAFFEINE, "Compositional and Effectful Program Distances", R20LW7EJ7L.

Acknowledgements

The authors thank Vladimir Zamdzhiev for his expert insight on specific parts of the denotational semantics.

Cite AsGet BibTex

Kostia Chardonnet, Louis Lemonnier, and Benoît Valiron. Semantics for a Turing-Complete Reversible Programming Language with Inductive Types. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.FSCD.2024.19

Abstract

This paper is concerned with the expressivity and denotational semantics of a functional higher-order reversible programming language based on Theseus. In this language, pattern-matching is used to ensure the reversibility of functions. We show how one can encode any Reversible Turing Machine in said language. We then build a sound and adequate categorical semantics based on join inverse categories, with additional structures to capture pattern-matching and to interpret inductive types and recursion. We then derive a notion of completeness in the sense that any computable, partial, first-order injective function is the image of a term in the language.

Subject Classification

ACM Subject Classification
  • Theory of computation → Program semantics
Keywords
  • Reversible programming
  • functional programming
  • Computability
  • Denotational Semantics

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