A new criterion for safe program transformations

Previous studies on safety of program transformations with respect to performance considered two criteria: preserving performance within a constant factor and preserving complexity. However, as the requirement of program transformations used in compilers the former seems too restrictive and the latter seems too loose. We propose a new safety criterion: a program transformation preserves performance within a factor proportional to the size of a source program. This criterion seems natural since several compilation methods have effects on performance proportional to the size of a program. Based on this criterion we have shown that two semantics formalizing the size of stack space are equivalent. We also discuss the connection between this criterion and the properties of local program transformations rewriting parts of a program.