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A Curry-Howard Correspondence for Linear, Reversible Computation

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Τίτλος: A Curry-Howard Correspondence for Linear, Reversible Computation
Συγγραφείς: Chardonnet, Kostia, Saurin, Alexis, Valiron, Benoît
Συνεισφορές: Saurin, Alexis, Kostia Chardonnet and Alexis Saurin and Benoît Valiron
Πηγή: Logical Methods in Computer Science. 21
Publication Status: Preprint
Στοιχεία εκδότη: Centre pour la Communication Scientifique Directe (CCSD), 2025.
Έτος έκδοσης: 2025
Θεματικοί όροι: 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
Περιγραφή: 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.
Τύπος εγγράφου: Article
Conference object
Περιγραφή αρχείου: application/pdf
Γλώσσα: 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
Σύνδεσμος πρόσβασης: 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
Αριθμός Καταχώρησης: edsair.doi.dedup.....3da2a93a80c6a990d1a6db977a6586a3
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  Data: A Curry-Howard Correspondence for Linear, Reversible Computation
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  Data: Saurin, Alexis<br />Kostia Chardonnet and Alexis Saurin and Benoît Valiron
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  Data: 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.
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      – SubjectFull: FOS: Computer and information sciences
        Type: general
      – SubjectFull: Theory of computation → Linear logic
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