LessThanComparable<T> Concept

A type whose objects can be compared with operators <, >, <= and >=.

Examples

int , String , List .

Definition

Line 77 of System.Base/Concept.cm

Type Parameters

Constraints

bool operator<(T, T)

Axioms

axiom irreflexive(T a)
{
    !(a < a)
}

axiom antisymmetric(T a, T b)
{
    a < b=>!(b < a)
}

axiom transitive(T a, T b, T c)
{
    a < b && b < c=>a < c
}

axiom total(T a, T b)
{
    a < b || a == b || a > b
}

axiom greaterThan(T a, T b)
{
    a > b<=>b < a
}

axiom greaterThanOrEqualTo(T a, T b)
{
    a >= b<=>!(a < b)
}

axiom lessThanOrEqualTo(T a, T b)
{
    a <= b<=>!(b < a)
}