Standard Template Library Programmer's Guide

Expression	Precondition	Semantics
Equality	x == y	x and y are in the domain of ==
Inequality	x != y	x and y are in the domain of ==	Equivalent to !(x == y)

Invariants

Identity	&x == &y implies x == y
Reflexivity	x == x
Symmetry	x == y implies y == x
Transitivity	x == y and y == z implies x == z

Models

• int
• vector<int>

See also

LessThanComparable.

LessThan Comparable

Category: utilities

Component type: concept

Description

A type is LessThanComparable if it is ordered: it must be possible to compare two objects of that type using operator<, and operator< must be a partial ordering.

Notation

X A type that is a model of LessThanComparable

x, y, z Object of type X

Definitions

Consider the relation !(x < y) && !(y < x). If this relation is transitive (that is, if !(x < y) && !(y < x) && !(y < z) && !(z < y) implies !(x < z) && !(z < x)), then it satisfies the mathematical definition of an equivalence relation. In this case, operator< is a strict weak ordering.

If operator< is a strict weak ordering, and if each equivalence class has only a single element, then operator< is a total ordering.

Valid expressions

Name	Expression	Return type
Less	x < y	Convertible to bool
Greater	x > y	Convertible to bool
Less or equal	x <= y	Convertible to bool
Greater or equal	x >= y	Convertible to bool

Expression semantics

Name