Hardware devices were designed to assist vocalists in live performances over forty years ago. The problem arose because recording artists would often perform in a live venue and have trouble hearing themselves in the stage monitors and therefore were challenging to hold good pitch. In some cases artists could be coached in the studio to perform with good pitch, but could not sustain the same level of performance in public. The hardware devices were also used in recording studios to improve voice pitch and their function is at first glance fairly simple. The devices would take the incoming pitch and shift it to the nearest note.
Singing software can perform the same types of operations as hardware, only the programming logic can be much more complex. For example, vibrato is a vocal technique that raises and lowers pitch, and volume, above and below a target note. If the if the singing software or hardware were to correct this, the vibrato would be removed. Another problem is that frequency depends in cycles or frequency, which means it takes a certain amount of time to detect the current pitch. And, if the pitch is moving, which is always the case, then it is challenging for the software to determine the target pitch. Fortunately, the attack or onset of pitch correction can be delayed to accommodate for both concerns and software can be much more effective than hardware.