Comparing Type Systems for Deadlock-Freedom
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Communication-centric software systems exhibit non trivial forms of concurrency and distribution, they are expected to respect intended protocols among interacting services, but also to never "get stuck". This intuitive requirement has been expressed by liveness properties such as progress or (dead)lock freedom, various type systems ensure these properties for concurrent processes. Unfortunately, very little is known about the precise relationship between these type systems and the typed processes they induce. This paper puts forward the first comparative study of different type systems for enforcing deadlock-freedom in message-passing concurrent processes. We compare two representative classes of deadlock-free typed processes, here denoted L and K. The class L stands out for its canonicity: it results naturally from Curry-Howard interpretations of linear logic propositions as session types. The class K, obtained by encoding session types into Kobayashi's usage types, includes processes not typable in other type systems. We show that L is strictly included in K. We also identify the precise condition under which L and K coincide. One key observation is that the degree of sharing between parallel processes determines a new expressiveness hierarchy for typed concurrent processes. Furthermore, we provide two type-preserving procedures for rewriting processes in K into processes in L. Our two procedures suggest that, while effective, the degree of sharing is a rather subtle criterion for distinguishing typed concurrent processes
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