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My code works with the < or > comparator, but will crash with <= or >=. [After] some debugging I doubt the std::sort behaves unexpectedly, so i found the strict weak ordering description in its comp. It seems that only less or greater qualifies. After some reading i still didn't get it... Can anyone explain this? Why <= or >= won't work?

Because internally, these algorithms implement "is equal to" as !(a < b) && !(b < a). If you used <= as the ordering operator, then this will return false when a == b. A broken equality check will screw up nearly any algorithm.

Similarly, they implement "is not equal to" as (a < b) || (b < a), and once again, if you provided <= as the ordering operator, then this will return false when a != b. So the equality check is broken in both directions.

The whole point of limiting the library to a less-than operator is that all of the logical operators can be implemented in terms of it:

• <(a, b): (a < b)
• <=(a, b): !(b < a)
• ==(a, b): !(a < b) && !(b < a)
• !=(a, b): (a < b) || (b < a)
• >(a, b): (b < a)
• >=(a, b): !(a < b)

This works as long as your provided operator meets the conditions of a strict weak ordering. The standard <= and >= operators do not.