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

Abstract

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.