Why can void pointers be subtracted but not added?

Question

Why does

printf("%ld\n", (void *)0 - (void *)0);

compile, but

printf("%ld\n", (void *)0 + (void *)0);

does not?

Answer 1

It is useful to find the difference between two pointers. This gives an integer (a ptrdiff_t).^[1]

It is useful to add a difference to a pointer, so we can add an integer to a pointer (and vice-versa). The inverse operation of ptrdiff = p2 - p1 is p2 = p1 + ptrdiff.^[1]

However, there's no sensible meaning to adding two pointers together. So that's not allowed.

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1. Note that this is undefined behaviour for void * pointers, and for pointers that aren't to parts of the same object.