Is it undefined behavior to redefine a standard name?

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At least one reason why it’s UB is that string.h can introduce macros. For internal implementation reasons, those macros might have been written on the assumption that strcmp is the “real” strcmp function. If you define strcmp to be something else and then use those macros, strcmp will expand to my_strcmp in the macros, with unexpected consequences.

Rather than try to work out exactly what code would be OK in the ... and what would not, the standard puts an early stop to your shenanigans.

Also note that aside from the fact that the standard flat-out forbids it, your #define strcmp my_strcmp might be a macro re-definition, because string.h is permitted to do #define strcmp __strcmp or whatever. So on some conforming implementations your code is ill-formed.

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