Result: A Curry-Howard Correspondence for Linear, Reversible Computation
Title:
A Curry-Howard Correspondence for Linear, Reversible Computation
Authors:
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
Document Type:
Academic journal
Article<br />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:
Rights:
CC BY
Accession Number:
edsair.doi.dedup.....3da2a93a80c6a990d1a6db977a6586a3
Database:
OpenAIRE
Further Information
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.