Note in particular this fragment from near the end of the docs for sort:

The comparison function is required to behave. If it returns inconsistent results (sometimes saying $x[1] is less than $x[2] and sometimes saying the opposite, for example) the results are not well-defined.

"Consistent" means, for example, that if your comparison function says A > B, then it should also say B < A if called with the arguments the other way round. A comparator that specifies something different for $a than for $b will almost certainly not be consistent, and should be avoided.

As others have noted, the apparent redundancy stems from having the most general possible form of comparator - a piece of code that does the comparison. Some of the standard special forms such as the Schwartzian Transform (ST) and the Guttman-Rosler Transform (GRT) also have the side effect of reducing the redundancy. For more information on those see the excellent set of links at 11135952 provided by eyepopslikeamosquito.

In reply to Re: Notation of sort function by hv
in thread Notation of sort function by Alphaphi

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