Affiliation:
1. University of Groningen, Netherlands
2. MPI-SWS, Germany
Abstract
The emergence of propositions-as-sessions, a Curry-Howard correspondence between propositions of Linear Logic and session types for concurrent processes, has settled the logical foundations of message-passing concurrency. Central to this approach is the resource consumption paradigm heralded by Linear Logic. In this paper, we investigate a new point in the design space of session type systems for message-passing concurrent programs. We identify O’Hearn and Pym’s Logic of Bunched Implications (BI) as a fruitful basis for an interpretation of the logic as a concurrent programming language. This leads to a treatment of non-linear resources that is radically different from existing approaches based on Linear Logic. We introduce a new π-calculus with sessions, called πBI; its most salient feature is a construct called spawn, which expresses new forms of sharing that are induced by structural principles in BI. We illustrate the expressiveness of πBI and lay out its fundamental theory: type preservation, deadlock-freedom, and weak normalization results for well-typed processes; an operationally sound and complete typed encoding of an affine λ-calculus; and a non-interference result for access of resources.
Funder
NWO
European Research Council
Publisher
Association for Computing Machinery (ACM)
Subject
Safety, Risk, Reliability and Quality,Software
Reference46 articles.
1. A calculus and logic of bunched resources and processes
2. LBI Cut Elimination Proof with BI-MultiCut
3. A λ-Calculus for Resource Separation
4. Robert Atkey . 2006. Substructural Simple Type Theories for Separation and In-place Update. Ph. D. Dissertation . University of Edinburgh. Robert Atkey. 2006. Substructural Simple Type Theories for Separation and In-place Update. Ph. D. Dissertation. University of Edinburgh.
5. Observed Communication Semantics for Classical Processes