Par means parallel: multiplicative linear logic proofs as concurrent functional programs

F Aschieri, FA Genco - Proceedings of the ACM on Programming …, 2019 - dl.acm.org
Proceedings of the ACM on Programming Languages, 2019dl.acm.org
Along the lines of Abramsky's “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 λ-calculus with parallelism and
communication primitives, called λpar. We shall prove that λpar satisfies all the desirable
properties for a typed programming language: subject reduction, progress, strong …
Along the lines of Abramsky’s “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 λ-calculus with parallelism and communication primitives, called λpar. We shall prove that λpar satisfies all the desirable properties for a typed programming language: subject reduction, progress, strong normalization and confluence.
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