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Conference Papers Year : 2023

A Curry-Howard Correspondence for Linear, Reversible Computation

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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hal-04308283 , version 1 (28-11-2023)

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Kostia Chardonnet, Alexis Saurin, Benoît Valiron. A Curry-Howard Correspondence for Linear, Reversible Computation. CSL 2023 - 31st EACSL Annual Conference on Computer Science Logic, Bartek Klin and Elaine Pimentel, Feb 2023, Varsovie (Warsaw), Poland. ⟨10.4230/LIPIcs.CSL.2023.13⟩. ⟨hal-04308283⟩
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