DEFINITION 2.5
Two computations are equivalent if, on the same inputs, they produce identical values for output variables at the time output statements are executed and the output statements are executed in the same order.
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It is clear that a compiler transformation should never introduce an error that would not have occurred in the original program. However, should transformation that eliminate error exceptions while maintaining the equivalence of outputs be permitted? The conventional answer for Fortran is "yes," but in languages like Java with stricter semantics and explicit exceptions, this may be unacceptable. Since this book focuses on Fortran and similar languages, we will permit transformations that eliminate exceptions or adjust the time at which those exceptions occur, so long as no transformation introduces an exception for a given input that would not have occurred on the original program with the same input.引自 2.2.3 Dependence and Transformations
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