By Edward Sang

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Subject to the shared time domain T, the schedule S of a run is required to be “compatible” with the failure pattern F and detector history H: (1) a process cannot take a step after it has crashed (according to F ); (2) when a process takes a step and queries its failure detector module, it gets the current value output by its local failure detector module (according to H). A process is correct in a given run, if it does not crash in this run. It may, though, crash in other runs. Let crashed(R) := crashed(F ) := t∈T F (t) denote the processes that have crashed in run R according to its failure pattern F .

Myers and B. Liskov. A decentralized model for information flow control. In Proceedings of the 16th ACM Symposium on Operating Systems Principles (SOSP), pages 129–142, 1997. 16. F. Pottier and S. Conchon. Information flow inference for free. In ICFP ’00, 5th ACM Conference on Functional Programming, pages 46–57, September 2000. 17. F. Pottier and V. Simonet. Information flow inference for ML. ACM SIGPLAN Notices, 31(1):319–330, January 2002. 18. A. Sabelfeld and A. Myers. Language-based information-flow security.

Now that we have determined the labels to propagate we have to choose the type constraints to decorate them with. Let L be a list [ 1 2 . . n ] of labels, t a type, and e an expression, we use the notation (L)t :e to denote the expression t1 : t2 : . . tn : e obtained by prefixing e by the t-indexed labels in L. e v1 v2 ❀ e[v1 / f ; v2 /x] ( t : v1 )v2 ❀ t•s : (v1 v2 ) match v with p1 ➔e1 |p2 ➔e2 ❀ (v//// p1 )t : e1 [v/p1 ] if ∅ v2 : s and t • s is defined if v/p1 = Ω and ∅ match v with p1 ➔e1 |p2 ➔e2 ❀ (v //// p1 )t : (v //// p2 )t : e2 [v/p2 ] e1 [v/p1 ] : t if v/p1 =Ω, v/p2 =Ω and ∅ e2 [v/p2 ] : t The rule for “unlabeled” applications does not change, while the one for applications of a labeled function changes as we explained early in this section.

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A new table of seven-place logarithms by Edward Sang


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