A Curry-Howard Correspondence for Linear, Reversible Computation
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| Title: | A Curry-Howard Correspondence for Linear, Reversible Computation |
|---|---|
| Authors: | Chardonnet, Kostia, Saurin, Alexis, Valiron, Benoît |
| Contributors: | Saurin, Alexis, Kostia Chardonnet and Alexis Saurin and Benoît Valiron |
| Source: | Logical Methods in Computer Science. 21 |
| Publication Status: | Preprint |
| Publisher Information: | Centre pour la Communication Scientifique Directe (CCSD), 2025. |
| Publication Year: | 2025 |
| Subject Terms: | FOS: Computer and information sciences, Theory of computation → Linear logic, [INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO], Logic in Computer Science, Curry-Howard, 0102 computer and information sciences, 02 engineering and technology, Linear Logic, 01 natural sciences, Logic in Computer Science (cs.LO), Reversible Computation, 0202 electrical engineering, electronic engineering, information engineering, Theory of computation → Equational logic and rewriting, ddc:004 |
| Description: | 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 $μ$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 $μ$MALL validity criterion and how the language simulates the cut-elimination procedure of $μ$MALL. |
| Document Type: | Article Conference object |
| File Description: | application/pdf |
| Language: | English |
| ISSN: | 1860-5974 |
| DOI: | 10.46298/lmcs-21(3:4)2025 |
| DOI: | 10.48550/arxiv.2302.11887 |
| DOI: | 10.4230/lipics.csl.2023.13 |
| Access URL: | http://arxiv.org/abs/2302.11887 https://hal.science/hal-04308283v1/document https://doi.org/10.4230/lipics.csl.2023.13 https://hal.science/hal-04308283v1 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2023.13 |
| Rights: | CC BY |
| Accession Number: | edsair.doi.dedup.....3da2a93a80c6a990d1a6db977a6586a3 |
| Database: | OpenAIRE |
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