Program transformations in a denotational setting

TL;DR: It is shown how a denotational setting can be useful for validating language-to-same-language transformations, and consideration of a transformation-exploiting liveness of variables indicates that a more satisfactory approach may be possible.

Abstract: 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 transformations, it is shown how a denotational setting can be useful for validating such program transformations.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 transformation-exploiting liveness of variables indicates that a more satisfactory approach may be possible.