Q: Can you mix old-style and new-style function syntax?
A: Doing so is legal (and can be useful for backwards compatibility), but requires a certain amount of care (see especially question 11.3). Modern practice, however, is to use the prototyped form in both declarations and definitions. (The old-style syntax is marked as obsolescent, so official support for it may be removed some day.)
ISO Sec. 6.7.1, Sec. 6.9.5
H&S Sec. 9.2.2 pp. 265-7, Sec. 9.2.5 pp. 269-70