Operators

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An operator predicate is a predicate which is invoked by one of the C++ operators ==, !=, <, <=, >, or >=. We denote these predicates by the relations $=$ , $!=$ , $<$ , $<=$ , $>$ , and $>=$ , respectively.

Equalities

The $=$ and $!=$ stand for set-equality and set-unequality. If one is defined, then so is the other, and the predicates are related by $(a = b) <=> !(a != b)$ , for all $a$ and $b$ .

Inequalities

The $<$ and $>$ stand for strict weak orders, and $<=$ and $>=$ stand for total preorders. If one is defined, then so are the others, and the predicates are related by $(a < b) <=> (b > a) <=> !(b <= a) <=> !(a >= b)$ , for all $a$ and $b$ .

Equivalence

The inequalities induce an equivalence relation by $(a ~ b) <=> !(a < b) and !(b < a)$ . This equivalence should not be confused for the set-equality, unless the $<$ is a strict partial order, or equivalently, the $<=$ is a partial order (antisymmetric).

Operators

Equalities

Inequalities

Equivalence

Files

Operators as functions

Testing for operators