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DOI: 10.4230/LIPIcs.FSCD.2026.11

Approximation Theory for Distant Bang Calculus

Authors: Kostia Chardonnet, Jules Chouquet, and Axel Kerinec

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract

Approximation semantics capture the observable behaviour of λ-terms. Böhm Trees and Taylor Expansion are its two central paradigms, related by the Commutation Theorem. While these notions are well understood in Call-by-Name (CbN), they have only recently been developed for Call-by-Value (CbV), which motivate the search for a unified approximation framework. The Bang-calculus provides such a framework: it subsumes both CbN and CbV through linear-logic translations and enjoys robust rewriting properties. We develop the approximation semantics of dBang (the Bang-calculus with explicit substitutions and distant reductions) by introducing approximation trees in the Böhm tradition together with Taylor expansion. We establish their fundamental properties, including a commutation theorem. Via translations, our results recover the CbN and CbV cases within a single unifying framework capturing infinitary and resource-sensitive semantics.

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Kostia Chardonnet, Jules Chouquet, and Axel Kerinec. Approximation Theory for Distant Bang Calculus. In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chardonnet_et_al:LIPIcs.FSCD.2026.11,
  author =	{Chardonnet, Kostia and Chouquet, Jules and Kerinec, Axel},
  title =	{{Approximation Theory for Distant Bang Calculus}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.11},
  URN =		{urn:nbn:de:0030-drops-263612},
  doi =		{10.4230/LIPIcs.FSCD.2026.11},
  annote =	{Keywords: Lambda-calculus, B\"{o}hm Trees, Taylor expansion of lambda-terms}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2026.12

Resource-Aware Quantum Programming with General Recursion and Quantum Control

Authors: Kostia Chardonnet, Emmanuel Hainry, Romain Péchoux, and Thomas Vinet

Published in: LIPIcs, Volume 378, 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)

Abstract

This paper introduces the hybrid quantum language with general recursion {{Hyrql}}, driven towards resource-analysis. By design, {{Hyrql}} does not require the specification of an initial set of quantum gates. Hence, it is well amenable towards a generic cost analysis, unlike languages that use different sets of quantum gates, which yield quantum circuits of distinct complexity. Regarding resource-analysis, we show how to relate the runtime of an expressive fragment of {{Hyrql}} programs with the size of the corresponding quantum circuits. We also manage to capture the class of functions computable in quantum polynomial time, which, by Yao’s Theorem, corresponds to families of circuits of polynomial size. Consequently, this result paves the way for the use of termination and runtime-analysis techniques designed for classical programs to guarantee bounds on the size of quantum circuits.

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Kostia Chardonnet, Emmanuel Hainry, Romain Péchoux, and Thomas Vinet. Resource-Aware Quantum Programming with General Recursion and Quantum Control. In 11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 378, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chardonnet_et_al:LIPIcs.FSCD.2026.12,
  author =	{Chardonnet, Kostia and Hainry, Emmanuel and P\'{e}choux, Romain and Vinet, Thomas},
  title =	{{Resource-Aware Quantum Programming with General Recursion and Quantum Control}},
  booktitle =	{11th International Conference on Formal Structures for Computation and Deduction (FSCD 2026)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-433-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{378},
  editor =	{Pfenning, Frank},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2026.12},
  URN =		{urn:nbn:de:0030-drops-263626},
  doi =		{10.4230/LIPIcs.FSCD.2026.12},
  annote =	{Keywords: Hybrid Quantum Programs, Resource Analysis}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2024.19

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

Authors: Kostia Chardonnet, Louis Lemonnier, and Benoît Valiron

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

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.

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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)

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@InProceedings{chardonnet_et_al:LIPIcs.FSCD.2024.19,
  author =	{Chardonnet, Kostia and Lemonnier, Louis and Valiron, Beno\^{i}t},
  title =	{{Semantics for a Turing-Complete Reversible Programming Language with Inductive Types}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.19},
  URN =		{urn:nbn:de:0030-drops-203487},
  doi =		{10.4230/LIPIcs.FSCD.2024.19},
  annote =	{Keywords: Reversible programming, functional programming, Computability, Denotational Semantics}
}

Document

DOI: 10.4230/LIPIcs.CSL.2023.13

A Curry-Howard Correspondence for Linear, Reversible Computation

Authors: Kostia Chardonnet, Alexis Saurin, and Benoît Valiron

Published in: LIPIcs, Volume 252, 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)

Abstract

In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of clauses is enough to ensure reversibility. The language allows to represent any Primitive Recursive Function. We then give a Curry-Howard correspondence with the logic μMALL: linear logic extended with least fixed points allowing inductive statements. The critical part of our work is to show how primitive recursion yields circular proofs that satisfy μMALL validity criterion and how the language simulates the cut-elimination procedure of μMALL.

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Kostia Chardonnet, Alexis Saurin, and Benoît Valiron. A Curry-Howard Correspondence for Linear, Reversible Computation. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chardonnet_et_al:LIPIcs.CSL.2023.13,
  author =	{Chardonnet, Kostia and Saurin, Alexis and Valiron, Beno\^{i}t},
  title =	{{A Curry-Howard Correspondence for Linear, Reversible Computation}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.13},
  URN =		{urn:nbn:de:0030-drops-174747},
  doi =		{10.4230/LIPIcs.CSL.2023.13},
  annote =	{Keywords: Reversible Computation, Linear Logic, Curry-Howard}
}

Document

DOI: 10.4230/LIPIcs.MFCS.2021.30

Geometry of Interaction for ZX-Diagrams

Authors: Kostia Chardonnet, Benoît Valiron, and Renaud Vilmart

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract

ZX-Calculus is a versatile graphical language for quantum computation equipped with an equational theory. Getting inspiration from Geometry of Interaction, in this paper we propose a token-machine-based asynchronous model of both pure ZX-Calculus and its extension to mixed processes. We also show how to connect this new semantics to the usual standard interpretation of ZX-diagrams. This model allows us to have a new look at what ZX-diagrams compute, and give a more local, operational view of the semantics of ZX-diagrams.

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Kostia Chardonnet, Benoît Valiron, and Renaud Vilmart. Geometry of Interaction for ZX-Diagrams. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 30:1-30:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{chardonnet_et_al:LIPIcs.MFCS.2021.30,
  author =	{Chardonnet, Kostia and Valiron, Beno\^{i}t and Vilmart, Renaud},
  title =	{{Geometry of Interaction for ZX-Diagrams}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{30:1--30:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.30},
  URN =		{urn:nbn:de:0030-drops-144701},
  doi =		{10.4230/LIPIcs.MFCS.2021.30},
  annote =	{Keywords: Quantum Computation, Linear Logic, ZX-Calculus, Geometry of Interaction}
}

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Documents authored by Chardonnet, Kostia

Approximation Theory for Distant Bang Calculus

Abstract

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Resource-Aware Quantum Programming with General Recursion and Quantum Control

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

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A Curry-Howard Correspondence for Linear, Reversible Computation

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Geometry of Interaction for ZX-Diagrams

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