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
describe 
, using an
element of 
:
by considering
.
The remaining sections detail how
may be determined.
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 |