Optimization Under the Perspective of Soundness, Completeness, and Reusability

While soundness and completeness are unchallengedly the surveyor's rod for evaluating the worthiness of proof calculi in program verification, it is not common to refer to these terms for rating the worthiness of performance improving transformations in program optimization. In this article we reconsider optimization under the perspective of soundness, completeness, and, additionally, reusability. Soundness can here be interpreted as semantics preservation, completeness as optimality in a specific, well-defined sense, and reusability as paradigm-transcending robustness of the rationale guaranteeing soundness and completeness of an optimization for a specific setting. Using partial redundancy elimination (PRE) for illustration, we demonstrate that these rationales are usually quite sensitive to paradigm changes. Neither completeness nor soundness are generally preserved. Hence, the reuse of optimization strategies in new paradigms requires usually paradigm-specific adaptations in order to accommodate their specifics. We exemplify this for PRE, and demonstrate that it is generally worth the effort, and an effective means for mastering the complexity of compiler construction in the specific field of code optimization.