A bunch of sessions: a propositions-as-sessions interpretation of bunched implications in channel-based concurrency

The emergence of propositions-as-sessions, a Curry-Howard correspondence between propositions Linear Logic and session types for concurrent processes, has settled the logical foundations message-passing concurrency. Central to this approach is resource consumption paradigm heralded by Logic. In paper, we investigate new point in design space type systems programs. We identify O’Hearn Pym’s Bunched Implications (BI) as fruitful basis an interpretation logic programming language. This leads treatment non-linear resources that radically different from existing approaches based on introduce π-calculus with sessions, called πBI; its most salient feature construct spawn, which expresses forms sharing are induced structural principles BI. illustrate expressiveness πBI lay out fundamental theory: preservation, deadlock-freedom, weak normalization results well-typed processes; operationally sound complete typed encoding affine λ-calculus; non-interference result access resources.