Program transformations in a denotational setting

Program transformations are frequently performed by optimizing compilers, and the correctness of applying them usually depends on data flow information. For language-to-same-language transfor-mations, it is shown how a denotational setting can be useful for validating such program transfor-mations. Strong equivalence is obtained for transformations that exploit information from a class of forward data flow analyses, whereas only weak equivalence is obtained for transformations that exploit information from a class of backward data flow analyses. To obtain strong equivalence, both the original and the transformed program must be data flow analysed, but consideration of a transfor-mation-exploiting liveness of variables indicates that a more satisfactory approach may be possible