A Curry-Howard Correspondence for Linear, Reversible Computation

Authors Kostia Chardonnet, Alexis Saurin, Benoît Valiron

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Author Details

Kostia Chardonnet
  • Université Paris-Saclay, Inria, CNRS, ENS Paris-Saclay, LMF, 91190, Gif-sur-Yvette, France
  • Équipe Quacs, Inria, Palaiseau, France
  • Université Paris Cité, CNRS, IRIF, 75013, Paris, France
Alexis Saurin
  • Université Paris Cité, CNRS, IRIF, 75013, Paris, France
  • Inria $π r^2$, Paris, France
Benoît Valiron
  • Université Paris-Saclay, Inria, CentraleSupélec, CNRS, ENS Paris-Saclay, LMF, 91190, Gif-sur-Yvette, France

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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)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Linear logic
  • Theory of computation → Equational logic and rewriting
  • Reversible Computation
  • Linear Logic
  • Curry-Howard


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