Let denote a constant interval arithmetic, such as or . We will not ensure that R represents directly; we will instead work with . The interval specification is computed by evaluating the specification S using the interval arithmetic . The interval inclusion property assures us that
As we only assume that may be computed, S may be partial: the domain of S must be taken into account. With interval arithmetics that track , such as , the domain of is bounded, and the domain of S may be accounted for. With interval arithmetics that do not track , such as , we have no information as to the domain of . Two approaches may be taken with such arithmetics. This lack of information may be accounted for when performing the interval comparisons which occur while evaluating , or after the evaluation of has completed. We call the former approach ``early accounting'', and the latter approach ``deferred accounting''. The latter approach is preferable, as it allows for better renderings. The two approaches are compared in section .
Jeff Tupper | March 1996 |