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Up: 3.3 Linear Interval Arithmetic
Previous: 3.3.16 Partial Functions
We now consider an example partial function, the square root function:
The function g is defined for non-negative extended real numbers:
We let the domain description set include 
:
This allows a trivial implementation of 
:
Which, in turn, allows a trivial implementation of
:
if 
may return a member of 
,
as is the case when implementing 
models.
If must return a member of 
,
the result may simply be demoted:
The evaluation of 
;
proceeds as follows:
The following figures are presented to aid the reader in
understanding the preceding evaluation.
The evaluation of ;
proceeds as follows:
with
and
Perusal of the following figures may ease the comprehension
of the preceding evaluation.
Since the evaluation is of a 
model, the domain constraint must be folded into a single constraint.
An evaluation of a 
model
may finish earlier, with the domain described by
rather than 
.
Note that a better bound is possible by taking 
into account when determining v':
With such an approach, the bound appears as follows.
Next: 3.3.18 Discontinuous Functions
Up: 3.3 Linear Interval Arithmetic
Previous: 3.3.16 Partial Functions
