In previous work we have developed a transition trace semantic framework, suitable for shared-memory parallel programs and asynchronously communicating processes, and abstract enough to support compositional reasoning about safety and liveness properties. We now use this framework to formalize and generalize some techniques used in the literature to facilitate such reasoning. We identify a sequential-to-parallel transfer theorem which, when applicable, allows us to replace a piece of a parallel program with another code fragment which is sequentially equivalent, with the guarantee that the safety and liveness properties of the overall program are unaffected. Two code fragments are said to be sequentially equivalent if they satisfy the same partial and total correctness properties. We also specify both coarse-grained and fine-grained version of trace semantics, assuming different degrees of atomicity, and we provide a coarse-to-fine-grained transfer theorem which, when applicable, allows replacement of a code fragment by another fragment which is coarsely equivalent, with the guarantee that the safety and liveness properties of the overall program are unaffected even if we assume fine-grained atomicity. Both of these results permit the use of a simpler, more abstract semantics, together with a notion of semantic equivalence which is easier to establish, to facilitate reasoning about the behavior of a parallel system which would normally require the use of a more sophisticated semantic model.
This research is sponsored in part by the National Science Foundation (NSF) under Grant No. CCR-9988551. The views and conclusions contained in this document are those of the author, and should not be interpreted as representing the official policies, either expressed or implied, of the NSF or the U.S. government.
