2.7.3 Inclusion Property

  There are guidelines to follow when implementing interval operators. It is crucial that the implementations follow the spirit of interval arithmetic: the intervals represent any fixed real number in their range, and that the operator's result represents every possible real result. The inclusion property formally states this.

Unary function has the inclusion property if

A binary function has the inclusion property if

A function which has the inclusion property can also be said to satisfy the inclusion property. Since intervals are essentially a computational tool, a function will often be identified with, or described by, an algorithm. The function is said to model the underlying function .

In general, an n-ary function satisfies the inclusion property if

The inclusion property codifies validity. The implementation of real function is a valid implementation if has the inclusion property.

Jeff Tupper

March 1996