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The classical concepts of partial and total correctness identify all types of runtime errors and divergence. We argue that the associated notions of translation correctness cannot cope adequately with practical questions like optimizations and finiteness of machines. As a step towards a solution we propose more fine-grained correctness notions, which are parameterized in sets of acceptable failure outcomes, and study a corresponding family of predicate transformers that generalize the well-known wp and wlp transformers. We also discuss the utility of the resulting setup for answering compiler correctness questions.

On excusable and inexcusable failures towards an adequate notion of translation correctness