(\unicode{8523}\) means Parallel: Multiplicative Linear Logic Proofs as Concurrent Functional Programs

• Published in: arXiv.org
• Main Authors: Aschieri, Federico, Genco, Francesco A
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 08.07.2019
• Subjects: Deduction; Functional programming; Programming languages
• ISSN: 2331-8422

Along the lines of the Abramsky ``Proofs-as-Processes'' program, we present an interpretation of multiplicative linear logic as typing system for concurrent functional programming. In particular, we study a linear multiple-conclusion natural deduction system and show it is isomorphic to a simple and natural extension of \(\lambda\)-calculus with parallelism and communication primitives, called \(\lambda_{\unicode{8523}}\). We shall prove that \(\lambda_{\unicode{8523}}\) satisfies all the desirable properties for a typed programming language: subject reduction, progress, strong normalization and confluence.