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arXiv · 2302.11887

A Curry-Howard Correspondence for Linear, Reversible Computation

Kostia Chardonnet·Alexis Saurin·Benoît Valiron
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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 $\mu$MALL: 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 $\mu$MALL validity criterion and how the language simulates the cut-elimination procedure of $\mu$MALL.

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Kostia Chardonnet, Alexis Saurin, Benoît Valiron. 2023-02-23. A Curry-Howard Correspondence for Linear, Reversible Computation. https://doi.org/10.46298/lmcs-21(3%3A4)2025

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