SGI Logo


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.

Refinement of

Associated types

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 Type requirements 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 Expression Precondition Semantics Postcondition
Less x < y x and y are in the domain of <    
Greater x > y x and y are in the domain of < Equivalent to y < x [1]  
Less or equal x <= y x and y are in the domain of < Equivalent to !(y < x) [1]  
Greater or equal x >= y x and y are in the domain of < Equivalent to !(x < y) [1]  

Complexity guarantees

Invariants

Irreflexivity x < x must be false.
Antisymmetry x < y implies !(y < x) [2]
Transitivity x < y and y < z implies x < z [3]

Models

Notes

[1] Only operator< is fundamental; the other inequality operators are essentially syntactic sugar.

[2] Antisymmetry is a theorem, not an axiom: it follows from irreflexivity and transitivity.

[3] Because of irreflexivity and transitivity, operator< always satisfies the definition of a partial ordering. The definition of a strict weak ordering is stricter, and the definition of a total ordering is stricter still.

See also

EqualityComparable, StrictWeakOrdering


STL Main Page

Contact Us | Site Map | Trademarks | Privacy | Using this site means you accept its Terms of Use
Copyright © 2009 - 2016 Silicon Graphics International. All rights reserved.