Abstract. The problem of locally transforming or translating programs without altering their semantics is central to the construction of correct compilers. For concurrent shared-memory programs this task is challenging because (1) concurrent threads can observe transformations that would be undetectable in a sequential program, and (2) contemporary multiprocessors commonly use relaxed memory models that complicate the reasoning. In this paper, we present a novel proof methodology for verifying that a local program transformation is sound with respect to a specific hardware memory model, in the sense that it is not observable in any context. The methodology is based on a structural induction and relies on a novel compositional denotational semantics for relaxed memory models that formalizes (1) the behaviors of program fragments as a set of traces, and (2) the effect of memory model relaxations as local trace rewrite operations. To apply this methodology in practice, we implemented a semi-automated tool called Traver and used it to verify/falsify several compiler transformations for a number of different hardware memory models.