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Our concern is the mechanical certification of transformations of sequential program executions into parallel executions with equivalent semantics. The objective of such transformations is to accelerate the execution of programs. The result reported here is a mechanically certified theorem of optimality. We present a transformation which applies to every program in a particular programming language, the language of sorting networks. This transformation transforms the sequential execution of any sorting network into an execution which is as fast or faster than any other transformation which applies to every sorting network. The theorem is stated formally in a mechanized logic.

A mechanically certified theorem about optimal concurrency of sorting networks