2.11 Interval Function Domains

   

The requirement that an interval number be non-collapsing will be relaxed. The number system   is the number system with the restriction, that intervals be non-collapsing, removed:

These number systems are not used directly. They are used in the construction of other number systems. Some research has shown that such number systems may be used, to simplify interval arithmetic proofs, and to align interval arithmetic with more established mathematics [34].

The number system   extends the number system by allowing collapsing intervals. Each interval can be described by two intervals, and :  

Parameter value is in the domain of interval if the domain constraint is satisfied:

The value of is given by v while the domain is given by d and . At the interval is:

• not defined if ,
• defined if , and
• potentially defined if .

The number is contained in interval , , for parameter value if the interval is (potentially) defined at and x lies within :

Since it is common to use the same number system as the basis for both the value and domain, there is an abbreviated syntax:

Jeff Tupper

March 1996